Mystery of the Missing Cap Question Answer Class 12 Invitation English Non-Detailed Chapter 3 CHSE Odisha

Odisha State Board CHSE Odisha Class 12 Invitation to English 2 Solutions Non-Detailed Chapter 3 Mystery of the Missing Cap Textbook Exercise Questions and Answers.

Class 12th Invitation English Non-Detailed Chapter 3 Mystery of the Missing Cap Question Answers CHSE Odisha

Mystery of the Missing Cap Class 12 Questions and Answers

Unit- I

Gist:
The writer takes us back to the early days of independent India. He acquaints the readers with Shri Moharana who was rich and an ideal host. He was known for his sense of duty and generosity. With the attainment of independence, a caste of patriots became a dominant force in India. Every village witnessed not only different castes, but some lovers of country as well. Moharana’s hospitality was reflected in the service of fish, especially to the emerging breed of patriots. He nurtured the ambition to become an MLA. Those who supported him in his aspiration thought that his maiden entry into politics should enjoy the blessing of Virkishore, the Minister of Fisheries and Fine Arts. Those were the days when a minister’s daily routine was mainly to deliver speeches at public receptions. The writer recounts for the minister’s reception led by Sri Moharana. Hectic preparation was on in for a fortnight. The children of the village lower primary school practised welcome song for Virkishore.

ସାରମର୍ମ :
ସ୍ଵାଧୀନ ଭାରତର ପରବର୍ତ୍ତୀ ସାମାଜିକ ରାଜନୀତିକ ଅବସ୍ଥାକୁ ନେଇ ଏହି ଗଳ୍ପଟି ରଚିତ ହୋଇଛି । ଶ୍ରୀ ମହାରଣା ଥିଲେ ଖୁବ୍ ସମ୍ଭ୍ରାନ୍ତ ଓ ଆଦର୍ଶ ଅତିଥ୍ୟସତ୍କାରକାରୀ । କର୍ତ୍ତବ୍ୟପରାୟଣ ବ୍ୟକ୍ତି ଭାବରେ ସେ ଖ୍ୟାତି ଅର୍ଜନ କରିଥିଲେ । ଦେଶ ସ୍ଵାଧୀନତା ପାଇବା ସହିତ ଦେଶରେ ସୃଷ୍ଟି ହୋଇଥିଲେ ଦଳେ ତଥାକଥିତ ଦେଶପ୍ରେମୀ । ପ୍ରତ୍ୟେକ ଗାଁରେ ବିଭିନ୍ନ ଜାତି ସହ କେତେକ ଦେଶପ୍ରେମୀ ରହିଥିଲେ । ଏହି ଦେଶପ୍ରୀତି ଥ‌ିବା ବ୍ୟକ୍ତିମାନଙ୍କ ନିମନ୍ତେ ମହାରଣାଙ୍କର ଆତିଥ୍ୟ ପ୍ରକାଶ ପାଇଥିଲା । ସେ ଜଣେ ବିଧାୟକ ହେବାପାଇଁ ଆଶା ପୋଷଣ କରିଥିଲେ । ସେ ଭାବିଥିଲେ ତାଙ୍କର ପ୍ରଥମ ବିଜୟ ମତ୍ସ୍ୟ ଓ କଳା ବିଭାଗର ମନ୍ତ୍ରୀ ବୀରକିଶୋରଙ୍କର ଆଶୀର୍ବାଦରୁ ହେବ । ସେହି ସମୟରେ ଜଣେ ପ୍ରଥମ ବିଜୟ ମତ୍ସ୍ୟ ଓ କଳା ବିଭାଗର ମନ୍ତ୍ରୀ ବୀରକିଶୋରଙ୍କର ଆଶୀର୍ବାଦରୁ ହେବ । ସେହି ସମୟରେ ଜଣେ
ଆସିବାର ପନ୍ଦର ଦିନ ପୂର୍ବରୁ ମହାରଣାଙ୍କଦ୍ୱାରା ପ୍ରସ୍ତୁତି କାର୍ଯ୍ୟ ଚାଲିଥିଲା । ବୀରକିଶୋରଙ୍କୁ ସ୍ଵାଗତ କରିବାପାଇଁ ନିମ୍ନ ପ୍ରାଥମିକ ବିଦ୍ୟାଳୟର ପିଲାମାନେ ସ୍ବାଗତ ସଙ୍ଗୀତ ଗାଇବା ଅଭ୍ୟାସ କରିଥିଲେ ।

Glossary :
recounting: narrating (ବର୍ଣ୍ଣନା କରି )
episode: event (ଘଟଣା)
raise a laugh: ହସ ସୃଷ୍ଟି କରିଥିଲା
on the contrary : ଅପରପକ୍ଷେ
sympathy: ସହାନୁଭୂତି
well-to-do: rich (ସ୍ଵଚ୍ଛଳ)
on the eve of : ଠିକ୍ ପୂର୍ବରୁ/ଆରମ୍ଭରୁ
attraction: ଆକର୍ଷଣ
folks: people (ଲୋକ)
nearby: ନିକଟସ୍ଥ
carried out: executed (ସମ୍ପାଦନ କରାଗଲା )
host: ଅତିଥ୍
time immemorial: ଆବହମାନ କାଳରୁ
emerging: ଆବିର୍ଭାବ ହେବା
boost: to increase (ବଦ୍ଧିତ କରିବା)
honour: respect (ସମ୍ମାନ)
nursed: nurtured (ପୋଷଣ କଲେ)
ambition: ଆକାଂକ୍ଷା/ଇଚ୍ଛା
incident: event (ଘଟଣା)
outset: beginning (ଆରମ୍ଭ)
endeavour: effort (ପ୍ରଚେଷ୍ଟା)
matured: grew (ପାକଳ ହୋଇଥିଲା|
full-fledged: ସମ୍ପୁର୍ଣ୍ଣ
portfolios: ବିଭାଗମାନ
sponsors : a person who first puts forward a proposal (ପ୍ରସ୍ତାବ ଆଗତକାରୀ)
debut: first appearance (an ପଦାର୍ପଣ )
reception: ସ୍ୱାଗତ
huge: ପ୍ରଚୁର
ancestral: ପୂର୍ବପୁରୁଷ ସମ୍ପର୍କିତ
symbolism: The white-washed house stood as a symbol of new, independent India
century: a hundred years (ଶତାବ୍ଦୀ)
considerable: substantial
reputation: fame
conscientious: a person who is guided by a sense of duty
generous: a person who is ready to give freely (ଦୟାଳୁ)
exemplary : serving as a model
laced: ଖଣ୍ଡିତ
devoted: spent (ଅତିବାହିତ କରିଥିଲେ)
strange: ଅଦ୍ଭୁତ
phenomena: facts (ଘଟଣାବଳୀ)
seamstress: a woman who can sew(ସ୍ତ୍ରୀ-ଦରଜି)
wrought by: brought by (ଅଣାଯାଇଥିଲା )
poetic: କାବ୍ୟକ
refrain of the song : ଗୀତରୁ ଦୂରେଇ ରୁହନ୍ତୁ
echoes: ପ୍ରତିଧ୍ୱନି
literal: ସାହିତ୍ୟିକ
mighty: powerful (ଶକ୍ତିଶାଳୀ )
catalogued: made a list of things (ତାଲିକା ପ୍ରସ୍ତୁତ କରାଗଲା )
blushed: ଲଜ୍ଜା ଅନୁଭବ କରିଥିଲେ
recited: ଆବୃତ୍ତି କଲେ
raga: ରାଗ
wrangled: argued (ଯୁକ୍ତି କରିଥିଲେ )
throbbing: ଛାତି ଥରିବା
stopped: arrived (ପହଞ୍ଚିଲେ)
hectically: ଅବିଶ୍ୱସନୀୟ ଭାବରେ
excited: ଉତ୍ତେଜିତ ହୋଇଗଲେ
gave up: ତ୍ୟାଗ କଲେ
prior: ପୂର୍ବବର୍ତ୍ତୀ

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 3 Mystery of the Missing Cap

Think it out

Question 1.
What impression of Sri Moharana do you get from the text?
Answer:
Sri Moharana, the pivot of the extract, is a rich man. He is the only person to own a beautiful building in an area of twenty villages. He is considerably known for his conscientiousness and generosity. He is a benevolent host. He is a happy villager. The early days of post-independent India witnessed Moharana in a new light. He emerges as a patriot ahead of others. He is ambitious of becoming a Member of the Legislative Assembly. He is a die-hard sycophant and an able organizer.

Question 2.
Who is Babu Virkishore? How does the narrator describe him?
Answer:
Babu Virkishore, the Minister of Fisheries and Fine Arts, belongs to the narrator’s district. He carves out a name for himself in politics. Against this backdrop, Moharana’s first appearance as a politician needs his blessing. His daily routine comprises speech making at public receptions. Sri Moharana and his supporters look forward to honouring Babu Virkishore for his stature in politics.

Question 3.
What idea of the narrator do you get from this unit of the text?
Answer:
At first, we get the impression of the narrator as a keen observer of human nature. The way he has portrayed Sri Moharana and Babu Virkishore is a case in point. He is an adept in the art of portraying Sri Moharana with the radiance of delightful manner. The extract reveals that his language is simple, natural and vivid. The writer is a superb first-person narrator.

Question 4.
How does the narrator recount the preparation for the Minister’s reception?
Answer:
The narrator vividly recounts the preparation for the minister’s reception. He remembers how Sri Moharana gave a beautiful touch to his ancestral cane chair. For fifteen days, the children of the village lower primary school spent time in practicing the welcome song. The narrator says that the song still lingers in his memory. Moharana’s excitement knew no bounds. He took minute care of all the arrangements. Nervousness and uncertainty stared him in the face.

Unit – II

Gist:
The moment Shri Moharana and others had waited for came at last. Soon after his arrival, the former lavishly garlanded the minister who instead of getting into the jeep preferred to walk. Moharana and his friends responded to his gesture with great delight. Shouts of ‘Babu Virkishore ki jai’ rent the air. The procession continued with all the people alternatively shouting and looking at the minister with their mouths wide open. At last Sri Moharana profusely entertained the minister and his followers. At first they were offered fine coconut juice. Then they were treated to the most fabulous lunch the narrator had ever seen. Now it was time for the minister to take rest. The narrator refers to his eagerness to be as physically close to him as possible.

ସାରମର୍ମ :
ଶେଷରେ ସେହି ମୁହୂର୍ଭ ଉପସ୍ଥିତ ହେଲା, ଯେଉଁ ମୁହୂର୍ଭଟିକୁ ଶ୍ରୀ ମହାରଣା ଓ ଅନ୍ୟମାନେ ଅପେକ୍ଷା କରିଥିଲେ । ମନ୍ତ୍ରୀ ମହୋଦୟଙ୍କର ଆଗମନ ପରେ ଗାଁର ବାହାର ଫାଟକଠାରୁ ତାଙ୍କୁ ଫୁଲତୋଡ଼ା ଦେଇ ପାଛୋଟି ଅଣାଗଲା । ସେ ଜିପ୍‌ରେ ଆସିବା ପରିବର୍ତ୍ତେ ଚାଲିଚାଲି ଆସିବାପାଇଁ ପସନ୍ଦ କଲେ । ମନ୍ତ୍ରୀ ମହୋଦୟଙ୍କର ଏହି ଭଙ୍ଗୀକୁ ମହାରଣା ଓ ତାଙ୍କ ବନ୍ଧୁମାନେ ଆନନ୍ଦରେ ଉପଭୋଗ କରୁଥିଲେ । ‘ବାବୁ ବୀରକିଶୋର କି ଜୟ’’ ଧ୍ଵନି ବାୟୁମଣ୍ଡଳକୁ ପ୍ରକମ୍ପିତ କରୁଥିଲା । ସମସ୍ତ ଲୋକମାନଙ୍କ ମଧ୍ୟରେ ମନ୍ତ୍ରୀ ମହୋଦୟ ଚାଲୁଥିଲେ । ଶେଷରେ ଶୋଭାଯାତ୍ରା ମହାରଣାଙ୍କ ଘରେ ପହଞ୍ଚିଲା । ମହାରଣା ମନ୍ତ୍ରୀ ମହୋଦୟ ଓ ତାଙ୍କର ସହକାରୀମାନଙ୍କୁ ପଇଡ଼ ପାଣି ପିଇବା ପାଇଁ ଦେଇ ଆପ୍ୟାୟିତ କରିଥିଲେ । ତା’ପରେ ଉତ୍ତମ ଭୋଜନର ବ୍ୟବସ୍ଥା କରାଯାଇଥିଲା । ଭୋଜନ କରିସାରିଲା ପରେ ମନ୍ତ୍ରୀ ମହୋଦୟ ବିଶ୍ରାମ ନେଲେ ।

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 3 Mystery of the Missing Cap

Glossary:
the big day: the day the minister arrived (ମହନୀୟ ଦିବସ)
welcome arch : ସ୍ୱାଗତ ତୋରଣ
outskirts of village: ଗାଁ ଦାଣ୍ଡରେ ବାହାରେ
profusely: lavishly,sufficiently(ପ୍ରଚୁର ପରିମାଣରେ )
garlanded: ଫୁଲମାଳ ଦିଆଗଲା
destination: ଗନ୍ତବ୍ୟସ୍ଥଳ
furlong away: ଅଳ୍ପ ଦୂରରେ
destiny: ଭାଗ୍ୟ ପରୀକ୍ଷା
statement: ମନ୍ତବ୍ୟ
applauded: expressed praise by clapping(ପ୍ରଶଂସାସୂଚକତାଳି ମାରିଲେ)
elephantine: ଗୋଦରଗୋଡ଼ିଆ
plodded:walked slowly with heavy steps (ଚାଲିଲେ)
embarrassment: shy, ashamed
shrunken neck: କଣ୍ଟକିତ ଗ୍ରୀବା
Contented : pleased (ଖୁସି ହେଲା )
invalids: ଅକାର୍ୟ୍ୟ
alternatively : ବିକଳ୍ପ ଭାବରେ
gaping: ନିରେଖି ଚାହିଁବା
half-naked : ଅର୍ଦ୍ଧନଗ୍ନ
pot-bellied : ବଡ଼ ପେଟିଆ
guilty: ଦୋଷୀ
entourage: people who follow anImportant person(ପ୍ରଶଂସକ)
set apart: arranged separately(କରାଯାଇଥିଲା )
tender coconut juice : ପଇଡ଼ପାଣି
giant: ବିରାଟକାୟ
repose: rest (ବିଶ୍ରାମ)
mustering: gathering (ଏକତ୍ରିତ କରି)
self-confidence : ଆତ୍ମବିଶ୍ଵାସ
grove: ଅଙ୍କୁଶ

Think it out

Question 1.
How does the narrator describe the procession of the Minister in the village?
Answer:
The writer gives a beautiful description of the procession of the minister in the village. The minister walked slowly with the heavy steps through the village street amidst the thunderous applause and slogans in priase of the minister. Everyone in the village including the invalids took part in it, shouting slogans by turn and opening their mouths wide open.

Question 2.
How did Sri Moharana entertain his guests?
Answer:
When the procession reached Moharana’s house, Moharana lavishly entertained his guests. They were given tender coconut juice and treated to the most fabulous lunch the narrator had ever seen. The lunch Moharana had hosted comprised twenty dishes that were arranged around the sweetened, ghee-backed rice. After his lunch, the minister took rest in a cabin.

Unit – III

Gist:
The sight of the minister snoring heavily made the narrator not only ‘speechless’ but ‘witless’ as well. He witnessed Jhandoo, all on a sudden, advanced fast towards the window, picked up the minister’s cap and vanished into the grove. The writer was at a loss. He did not know which to give more importance – the minister’s cap or his snoring. He got back home in a sad mood. But soon the narrator became a mute spectator to the reactions of the minister’s officials and of Sri Moharana to the disappearance of the cap. The narrator saw Sri Moharana virtually trembling. Sri Moharana’s miserable condition broke his silence. The narrator’s narration of the cause of the missing cap left Sri Moharana speechless for a moment. His nervousness eventually abated. The incident deprived the occasion of its lustre. At that moment, the minister was inside the cabin, coughing at times. His missing cap was on everybody’s lip.

ସାରମର୍ମ :
ମନ୍ତ୍ରୀ ମହୋଦୟ ଜଣେ ସାଧାରଣ ବ୍ୟକ୍ତି ଭଳି ଘୁଙ୍ଗୁଡ଼ି ମାରୁଥ‌ିବାର ଦେଖୁ ଲେଖକ ଆଶ୍ଚର୍ଯ୍ୟ ହୋଇଗଲେ । ହଠାତ୍ ଝାଣ୍ଡୁ ଝରକା ପାଖକୁ ଆସି ମନ୍ତ୍ରୀଙ୍କର ଟୋପିଟିକୁ ଉଠାଇ ନେଇ ଆମ୍ବତୋଟା ମଧ୍ୟରେ ଅନ୍ତର୍ଦ୍ଧାନ ହୋଇଯିବାର ଲେଖକ ଦେଖିଲେ । ଲେଖକ କ’ଣ କରିବେ ଜାଣିପାରିଲେ ନାହିଁ । ସେ ଜାଣିପାରିଲେ ନାହିଁ କାହାକୁ ଗୁରୁତ୍ଵ ଦେବେ ମନ୍ତ୍ରୀଙ୍କର ହଜିଯାଇଥ‌ିବା ଟୋପିକୁ ନା ତାଙ୍କର ଘୁଙ୍ଗୁଡ଼ିକୁ । ସେ ଘରକୁ ଦୁଃଖରେ ଫେରିଲେ । ମନ୍ତ୍ରୀଙ୍କର ଅଧିକାରୀମାନଙ୍କର ପ୍ରତିକ୍ରିୟା ଦେଖି ଲେଖକ ଆଶ୍ଚର୍ଯ୍ୟ ହୋଇଗଲେ । ମହାରଣା ମଧ୍ୟ ଖୁବ୍ ପ୍ରତିକ୍ରିୟା ପ୍ରକାଶ କଲେ ।ଶ୍ରୀ ମହାରଣା ଡରରେ ଥରୁଥିବାର ଲେଖକ ଦେଖ‌ିଲେ । ମହାରଣାଙ୍କର ଅସହାୟ ଅବସ୍ଥା ଲେଖକଙ୍କର ନୀରବତାକୁ ଭଙ୍ଗ କରିଥିଲା । ଲେଖକଙ୍କଠାରୁ ଟୋପି ହଜିଯିବାର ରହସ୍ୟ ବିଷୟରେ ଜାଣି ଶ୍ରୀ ମହାରଣା ମୁହୂର୍ରେ ବାକ୍‌ଶୂନ୍ୟ ହୋଇଯାଇଥିଲେ । ତାଙ୍କ ଦୁର୍ବଳତାକ୍ରମେ ଉଭେଇଯାଇଥିଲା । ଏହି ଘଟଣା ଯୋଗୁଁ ଉତ୍ସବମୁଖର ପରିବେଶ ଶ୍ରୀହୀନ ହୋଇପଡ଼ିଥିଲା । ସେହି ସମୟରେ ମନ୍ତ୍ରୀ ମହୋଦୟ ପ୍ରକୋଷ୍ଠରେ ରହି ସମୟେ ସମୟେ କାଶୁଥିଲେ । ସମସ୍ତଙ୍କର ଓଠରେ କେବଳ ତାଙ୍କର ହଜିଯାଇଥିବା ଟୋପି କଥା ଚର୍ଚ୍ଚା ହୋଇଥିଲା ।

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 3 Mystery of the Missing Cap

Glossary :
disillusionment: ନିରାଶା
snoring: ଘୁଙ୍ଗୁଡ଼ି ମାରିବା
extraordinary : ଅସାଧାରଣ|ଅଦ୍ବିତୀୟ
bounce: ମାଡ଼ି ଆସିବା
stupefaction: astonishment (ବିସ୍ମୟ)
consequences : results (ଫଳାଫଳ)
fatal: deadly (ମାରାତ୍ମକ)
cease: stop (ବନ୍ଦ ହୋଇଯିବା)
dilemma: any difficult situation (ଦ୍ବନ୍ଦାତ୍ମକ ପରିସ୍ଥିତି)
value: ଗୁରୁତ୍ଵ ଦେବା
pensive: thoughtful (ଚିନ୍ତାଶୀଳ)
suppressed : ଚାପି ରଖୁଲେ
mumbling : ଗୁଣୁଗୁଣୁ ହେବା
dared: ସାହସ କଲେ
thunderstruck : stunned(ସ୍ତମ୍ଭୀଭୂତ ହୋଇଗଲେ)
disappeared: vanished( ଅଦୃଶ୍ୟ ହୋଇଗଲା)
deep-rooted: ଗଭୀର ମୂଳ
conspiracy: plot (ଷଡ଼ଯନ୍ତ୍ର)
gravity: seriousness (ଗୁରୁତ୍ବ)
exaggerated : ଅତିରଞ୍ଜିତ
devastating: terrible (ଭୟଙ୍କର)
shaking: trembling (ଥରୁଥା’ନ୍ତି)
sweating: ଝାଳ ବୋହିବା
like a bolt from the blue: an unexpected event(ଅପ୍ରତ୍ୟାଶିତ ଘଟଣା)
glance:ଚାହାଣି
profusely: ପ୍ରଚୁର ମାତ୍ରାରେ
conflict: ଦ୍ୱନ୍ଦ୍ୱ
mystery: ରହସ୍ୟମୟ
disclose: ଜଣେଇଦେବା
resolved: settled (ସ୍ଥିର କଲେ)
signalled: ସଙ୍କେତ ଦେଲେ
A ……straw: ବୁଡ଼ିଲା ଲୋକ କୁଟାଖିଅକୁ
dumb: speechless (ମୂକ)
wiping sweat: ଝାଳ ପୋଛିଦେଇ
diagnosed: ନିରୂପଣ କରାଗଲା
incurable: not able to be cured( ଦୁରାରୋଗ୍ୟ)
patted: ଥାପୁଡ଼େଇଲେ
reward: ପୁରସ୍କାର
throw a wet blanket : spoil the fun (ଆନନ୍ଦ ଭଙ୍ଗ କରିବା)
sepulchral: sad and rather frightening
intermittent: periodic (ମଝିରେ ମଝିରେ)
hang: ଫାଶୀ ଦେବା

Think it out

Question 1.
How did the minister’s cap disappear?
Answer:
The minister was taking rest in the cabin with his egg-bald head rested on a gigantic pillow. He had put his cap on a table near his bed. The writer noticed Jhandoo, all on a sudden, moved fast towards the window, picked the cap and vanished into the grove.

Question 2.
How did the minister’s officials react to the disappearance of the cap?
Answer:
The minister’s officials plunged into hush, when the cap disappeared. Nevertheless, they woke up to reality with a great deal of excitement. Like a butterfly, his Personal Assistant mumbled “Mysterious !” “Mysterious !”, repeatedly. He simply couldn’t believe it while the minister was inside the cabin. The Public Relations Officer linked the episode with a long-drawn conspiracy. He felt that the minister would not mind the loss of the cap, but the manner of its disappearance. He was afraid the missing cap might devastatingly affect the politics of India.

Question 3.
How did Sri Moharana feel about the loss of the cap?
Answer:
Sri Moharana felt stunned about the loss of the cap. He was virtually trembling. Tom by nervousness, he was sweating like an ice-cream.

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 3 Mystery of the Missing Cap

Question 4.
How did he feel when he came to know the cause of the missing of the cap?
Answer:
When he came to know the cause of the missing of the cap, Sri Moharana stood speechless for a moment, with his eyes shut. Then he came back to reality. He wiped sweat from his forehead. He gave an enigmatic smile. He admired the narrator. At last Sri Moharana advised him to keep the secret strictly to himself and promised to reward him.

Question 5.
What was the effect of disappearance of the cap on the ceremony?
Answer:
Disappearance of the cap threw a cold water on the ceremony. A pall of gloomy silence descended on the minister’s room. He was coughing periodically. When the minister coughed, anxiety dampened the spirit of the people.

Question 6. How did the narrator’s pals react to the situation?
Answer:
The narrator’s pals reacted to the situation in a state of anxiety. One of them visualised the culprit’s imprisonment, provided he was detected. Another person was apprehensive of the whole village suffering imprisonment bar. Even some credulous persons believed that the cap was a kind of Aladdin’s lamp- its owner would be a minister.

Unit – IV

Gist:
This unit begins with the narrator’s graphic presentation of the opening ceremony. Five thousand people had already been present before the minister climbed the specially built stage. His remarkable smile still adored his face. Sri Moharana’s niece garlanded him to the prolonged roaring applause of the people. It was a maiden sight for the villagers. Then Sri Moharana delivered a welcome speech. Initially he looked nervous, but his successful willpower made him rise to the occasion. His speech focussed on Babu Virkishore’s feats. The narrator was satisfied with his first speech.

But everybody had awaited Sri Moharana’s last observation. With a mysterious smile, he explained the reason behind the missing of the cap. He said that a gentleman of this area had taken it away secretly to preserve it as a remembrance of the past. The reverential Sri Moharana presented the humble amount of the hundred and one rupees, given by the gentleman, to the minister who gracefully accepted admist the thunderous praise and words of profuse appreciation. The minister responded to the reception in his characteristic ministerial manner. He wound up his speech, expressing his decision to remain without a cap on his head for that whole night, though many caps were tried for his bare head. Then the honourable people of the area went to the dinner. The minister’s head was the focus of all. They threw glances of fear and respect at it. The narrator marked a sense of guilt of telling lie about the missing of the cap haunt Sri Moharana but the minister looked extremely happy.

ସାରମର୍ମ :
ସ୍ୱତନ୍ତ୍ରଭାବେ ନିର୍ମିତ ସଭାମଞ୍ଚକୁ ମନ୍ତ୍ରୀ ଯିବା ପୂର୍ବରୁ ପାଞ୍ଚ ହଜାର ଲୋକ ଉପସ୍ଥିତ ଥିଲେ । ତାଙ୍କର ମୁଖମଣ୍ଡଳରେ ସ୍ମିତ ହାସ୍ୟ ଶୋଭା ପାଉଥିଲା । ଉପସ୍ଥିତ ଜନତାଙ୍କ କରତାଳି ଓ ଜୟଜୟକାର ଧ୍ଵନି ମଧ୍ୟରେ ଶ୍ରୀ ମହାରଣାଙ୍କର ଝିଆରୀ ତାଙ୍କର ବେକରେ ଫୁଲହାର ପିନ୍ଧାଇଦେଲେ । ମନ୍ତ୍ରୀ ମହୋଦୟଙ୍କୁ ସ୍ବାଗତ କରିବା ଥିଲା ସେହି ଗାଁର ବ୍ୟକ୍ତିମାନଙ୍କର ପ୍ରଥମ ଅନୁଭୂତି । ତା’ପରେ ମହାରଣା ସ୍ବାଗତ ଭାଷଣ ଦେଲେ । ପ୍ରଥମେ ସେ ଡରି ଯାଇଥିଲେ ପରେ କିନ୍ତୁ ସେ ନିଜକୁ ସମ୍ଭାଳିନେଲେ । ବାବୁ ବୀରକିଶୋରଙ୍କର ସଫଳତାକୁ ନେଇ ସେ ଭାଷଣ ଦେଲେ । ଲେଖକ ତାଙ୍କର ପ୍ରଥମ ଭାଷଣରେ ସନ୍ତୋଷ ଲାଭ କଲେ । ସ୍ମିତ ହସ ହସି ମହାରଣାବାବୁ ଟୋପି ହଜିଯିବାର ରହସ୍ୟ ଉନ୍ମୋଚନ କଲେ । ସେ କହିଲେ ସେହି ଅଞ୍ଚଳର ଜଣେ ଭଦ୍ରବ୍ୟକ୍ତି ସେହି ଟୋପିଟିକୁ ନେଇ ଯାଇଛନ୍ତି । ମହାରଣାବାବୁ ସେହି ଭଦ୍ରବ୍ୟକ୍ତି ଦେଇଥ‌ିବା୧୦୧ ଟଙ୍କା ମନ୍ତ୍ରୀ ମହୋଦୟଙ୍କୁ ପ୍ରଦାନ କରିଛନ୍ତି । ସେ ଏହାକୁ ନିଜର ସ୍ଵଭାବସୁଲଭ ଢଙ୍ଗରେ କରତାଳି ମଧ୍ୟରେ ଗ୍ରହଣ କରିଛନ୍ତି । ଯଦିଓ ଅନେକ ଟୋପିକୁ ତାଙ୍କ ଚନ୍ଦା ମୁଣ୍ଡରେ ମାପ କରାଗଲା, ସେ କିନ୍ତୁ ଦୃଢ଼ତାର ସହିତ କହିଲେ ସେହି ରାତିଟା ସେ ବିନା ଟୋପିରେ ରହିବେ । ତା’ପରେ ସେହି ଅଞ୍ଚଳର ମାନ୍ୟଗଣ୍ୟ ବ୍ୟକ୍ତିମାନେ ମନ୍ତ୍ରୀଙ୍କ ସହ ରାତ୍ରିଭୋଜନ କଲେ । ସବୁ ବ୍ୟକ୍ତିମାନେ ଭୟ ଓ ସମ୍ମାନର ସହିତ ମନ୍ତ୍ରୀଙ୍କ ଚନ୍ଦାମୁଣ୍ଡକୁ ଚାହୁଁଥିଲେ । ମନ୍ତ୍ରୀଙ୍କର ହଜିଯାଇଥବା ଟୋପି ବିଷୟରେ ମିଛ କହିଥିବାରୁ ଶ୍ରୀ ମହାରଣା ନିଜକୁ ଦୋଷୀ ମନେ କରୁଥିଲେ ।

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 3 Mystery of the Missing Cap

Glossary:
remarkable : ଉଲ୍ଲେଖନୀୟ
hitherto: till now (ଅଦ୍ୟାବଧୂ)
displayed: shown (କରାଯାଉଥିଲା )
prolonged: ଦୀର୍ଘାୟିତ
thunderous: ଗର୍ଜନକାରୀ
applause: praise publicly by clapping (ସମ୍ବର୍ଦ୍ଧନା ଜଣାଇବା)
greeted: welcomed (କରାଗଲା )
tales: stories (ଗଳ୍ପ)
chorus: ମିଳିତ ଗାନ
accompaniment : help (ସାହାଯ୍ୟ/ସହାୟତା)
awakward fashion : uggmo
grabbed : ଜାବୁଡ଼ି ଧରିଥିଲେ
glittering: shining (ଉଜ୍ଜ୍ବଳ).
chronological account:containing an account of events in the order of time
achievement: କୃତିତ୍ଵ
conveying: ବ୍ୟକ୍ତ କରିବା
departed soul: ବିଗତ ଆତ୍ମା
maiden: first (ପ୍ରଥମ)
uttered the lie :ମିଛ କହିଲେ
crescendo: a gradual increase in loudness
bare: ଖୋଲା
ascended: climbed (ଆରୋହଣ କଲେ)
clinging: (here) continuing
Mysteriously: ରହସ୍ୟମୟ ଭାବେ
glowed: ଆଲୋକିତ କଲା
dying: (here) anxious (ବ୍ୟଗ୍ର)
Preserve: ସାଇତି ରଖୁବା
sacred momento: sacred remnant of the past (ପବିତ୍ର ସ୍ମାରକୀ)
burning example : ଜ୍ଵଳନ୍ତ ଉଦାହରଣ
mission : ଯାତ୍ରା
bowed: ନତମସ୍ତକ ହେଲେ
handed over: ହସ୍ତାନ୍ତରିତ
hurricane: a violent storm (ଘୂର୍ଣ୍ଣିବାତ୍ଯା)
lack: want (ଚାହିଦା|ଅଭାବ )
surge: a number of (ଅନେକ)
undaunted: fearless
gave way: changed to (ପରିବର୍ତ୍ତିତ ହେଲା )
respectable: ସମ୍ମାନନୀୟ
awe:fear
esteem:respect (ସମ୍ମାନ)
guilt: ଦୋଷ
delighted: pleased (ଆନନ୍ଦିତ ହେଲେ)
constraint: control (ନିୟନ୍ତ୍ରଣ)

Think it out

Question 1.
How does the narrator describe the opening ceremony?
Answer:
The opening ceremony started with a bang. Soon after taking the stage, Moharana’s niece garlanded the minister to the prolonged defeaning applause of the villagers. Then the school-children sang the chorus ‘O mighty minister’ in the midst of fine music. This was followed by Moharana’s speech that was punctuated with the lavish praise of Sri Virkishore’s numerous feats. He finished his address expressing his gratitude to the minister on behalf of the nation.

Question 2.
How did Sri Moharana explain the reason behind the missing of the cap?
Answer:
Sri Moharana said that a certain gentleman of their area had taken away the minister’s cap to preserve it as a sacred memory. He took it secretly, because, a glittering epitome of modesty as he was, the minister, if he had known it, would have definitely deprive the gentleman of seeing the cap as a sacred thing.

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 3 Mystery of the Missing Cap

Question 3.
What impression of Sri Moharana do you get from this unit of the text?
Answer:
This extract throws light on Sri Moharana’s colourful and appetising lie. He cloaks the simple fact of the missing of the cap. He is a first rate sycophant. He plays the role of a typical politician. His mysterious smile and reverential attitude towards the minister beautifully exemplify this fact. He is remarkable for his presence of mind. That he has spent one hundred and one rupees to cover the monkey’s mischief of taking the minister’s cap is a burning example. Despite everything, Sri Moharana wears a guilt look for uttering a lie. He feels nervous inside.

Unit – V

Gist:
The time for the minister’s departure came at last. In the meantime the monkey Jhandoo appeared on the scene. In his infancy, his mother left him in Moharana’s house in order to save him from the anger of the latter’s father. Unfortunately, in his absence, Moharana’s servants put an end to the life of the mother monkey. Kindhearted as he was, Moharana affectionately brought up the baby monkey. He was named Jhandoo. The monkey, sitting down between the minister and Sri Moharana, put the cap on his head and then offered it to the minister most genially. The minister in a flash of anger and surprise, wanted Moharana to confirm whether the monkey was not the same gentleman that had taken away the cap. Moharana quite helplessly admitted that it was verily the same gentleman. Hearing this, the minister flared up and his eyes bulged and burnt like fire. The missing cap brought a great change in their lives. Both were not only disillusioned but also reduced to ridiculous position.

ସାରମର୍ମ :
ଶେଷରେ ମନ୍ତ୍ରୀ ମହୋଦୟଙ୍କର ବିଦାୟବେଳା ଉପସ୍ଥିତ ହେଲା । ଏହି ସମୟରେ ମାଙ୍କଡ଼ ଝାଣ୍ଡୁ ଆସି ଉପସ୍ଥିତ ହେଲା । ଛୋଟ ବୟସରେ ଝାଣ୍ଡୁର ମା’ ଝାଣ୍ଡୁକୁ ତା’ ବାପାର ରାଗରୁ ରକ୍ଷା କରିବାପାଇଁ ମହାରଣାଙ୍କ ଘରେ ଛାଡ଼ି ଦେଇଥିଲା । ଦୁର୍ଭାଗ୍ୟବଶତଃ, ମହାରଣାଙ୍କର ଅନୁପସ୍ଥିତିରେ ତାଙ୍କର ଚାକରମାନେ ମା’ ମାଙ୍କଡ଼କୁ ମାରିଦେଲେ । ମହାରଣା ଥିଲେ ସହୃଦୟ ବ୍ୟକ୍ତି । ସେ ଏହି ମାଙ୍କଡ଼ଟିକୁ ଶିଶୁ ଅବସ୍ଥାରୁ ସ୍ନେହ ଦେଇ ପାଳନ କରିଥିଲେ । ଝାଣ୍ଡୁ ବର୍ତ୍ତମାନ ମନ୍ତ୍ରୀ ଓ ମହାରଣାବାବୁଙ୍କ ମଝିରେ ବସିଥିଲା । ସେ ଖୁବ୍ ଭଦ୍ରଭାବେ ପିନ୍ଧିଥିବା ଟୋପିଟିକୁ ମନ୍ତ୍ରୀଙ୍କୁ ଦେଲା । ରାଗରେ ମନ୍ତ୍ରୀ ପଚାରିଲେ ଯେଉଁ ଭଦ୍ରବ୍ୟକ୍ତିଜଣଙ୍କ ତାଙ୍କର ଟୋପି ନେଇ ଯାଇଥିଲେ, ଇଏ ସେହି ଭଦ୍ରବ୍ୟକ୍ତି ନୁହଁନ୍ତି ତ। ମହାରଣା ନିରୁପାୟ ହୋଇ ସ୍ଵୀକାର କଲେ, ଏ ହେଉଛନ୍ତି ସେହି ଭଦ୍ରବ୍ୟକ୍ତି ଯେ କି ଟୋପି ନେଇ ଯାଇଥିଲେ ।
ଏହା ଶୁଣି ମନ୍ତ୍ରୀଙ୍କ ଆଖ୍ ରାଗରେ ଫୁଲିଗଲା ଓ ଜଳିଗଲା ପରି ଲାଗିଲା । ହଜିଯାଇଥିବା ଟୋପି ସେମାନଙ୍କ ଜୀବନରେ ବଡ଼ ପରିବର୍ତ୍ତନ ଆଣିଲା । ମାଙ୍କଡ଼ର ଟୋପି ଚୋରି ମାଧ୍ୟମରେ ଉଭୟଙ୍କ ଭ୍ରାନ୍ତି ଦୂର ହୋଇଛି ଏବଂ ସେମାନଙ୍କ ବ୍ୟକ୍ତିତ୍ଵ ବ୍ୟଙ୍ଗାତ୍ମକଭାବେ ହ୍ରାସ ପାଇଛି ।

Glossary:
moment of departure: ବିଦାୟର ମୁହୂର୍ତ୍ତ
sweetened curd : ମିଠା ଦହି
sipping: ଅଳ୍ପ ଅଳ୍ପ ଖାଇବା
choked: ରୁଦ୍ଧ ହେଲା
snatching: ଘୋଷାଡ଼ି ନେବା
accidental: ଅକସ୍ମାତ୍
rascal: ଅସଭ୍ୟ
ardently: deeply (ଆନ୍ତରିକ ଭାବରେ)
figurative sense : (here) sense of human being (ମନୁଷ୍ୟର ଜ୍ଞାନ)
real: ବାସ୍ତବ
shelter: ଆଶ୍ରୟ
wrath: anger (କ୍ରୋଧ)
compensate:to pay for the loss
nurtured: brought up (କରିଥିଲେ )
christened: named କରିଥିଲେ )
half-domesticated : ଅର୍ଥ-ଗୃହପାଳିତ
tolerated: ସହୁଥିଲେ
in vain : ନିଷ୍ଫଳ
got in: ପହଞ୍ଚ୍
in ….. eye: ଆଶ୍ଵିପିଛୁଳାକେ
taking it off: ଏହାକୁ କାଢ଼ିଦେଇ
genial: friendly (ବନ୍ଧୁତ୍ଵପୂର୍ଣ୍ଣ ଭାବେ )
heartbeat: ଛାତିର ସ୍ପନ୍ଦନ|ହୃତ୍‌ ନ୍ଦନ
trebled: ତ୍ରିଗୁଣିତ
pitable: ଶୋଚନୀୟ
fantastic: strange (ଅଦ୍ଭୁତ)
lip: ଓଠ
on the verge of : ଆସନ୍ନ
collapsing: fainting
bulging out: ବାହାରି ଆସିବା
broke in to tears : କାନ୍ଦି ପକାଇଲେ
P.A.: Personal Assistant (ବ୍ୟକ୍ତିଗତ ସହାୟକ)
gulped: ଢକ୍‌ଢକ୍ କରି ପିଇଗଲେ
redened eye: look of anger (ଚାହାଣି )
course of lives: ଜୀବନର ଗତିପଥ

Think it out

Question 1.
How did the minister find out the mystery of the missing cap?
Answer:
Both Moharana and the minister were in the veranda. In the meantime Jhandoo advanced towards them and reached in a flash. Sitting between Sri Moharana and the minister, wore the cap on his head and offered it to the minister most genially. In this way, the minister found out the mystery of the missing cap.

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 3 Mystery of the Missing Cap

Question 2.
What role did Jhandoo play in the story? Did he bring an anticlimax to the story? Give your reasons.
Answer:
Jhandoo plays a meaningful role in the story. It is instrumental in exposing the politicians and the sycophants. Sri Moharana told a colourful and appetising lie that a certain noble man had taken the cap secretly to preserve it as a sacred memento. But this fabrication was too tenuous to last long because the noble man in question appeared in the form of a monkey and presented the cap to the minister. Driven by anger and surprise, the minister asked Sri Moharana if the monkey was not the same gentleman that had taken away the cap. Moharana quite helplessly admitted that it was verily the same gentleman. His reply drove the minister to a rage. This marked a climax in the story. The monkey’s conduct was justified, because he proved that these two leaders could not cope with the new politics. Besides, as a result of the anti-climax brought by the monkey, the writer has achieved a unique assimilation between satire and sympathy.

CHSE Odisha Class 12 English Mystery of the Missing Cap Important Questions and Answers

Multiple-Choice Questions (MCQs) with Answers

Question 1.
__________ is the protagonist of the extract.
(A) Babu Virkishore
(B) The narrator
(C) Sri Moharana
(D) all of the above
Answer:
(C) Sri Moharana

Question 2.
Sri Moharana comes of a _________ family.
(A) cultured
(B) humble
(C) rich
(D) none of these
Answer:
(C) rich

Question 3.
Sri Moharana is known for his __________.
(A) generosity
(B) conscience
(C) patriotism
(D) remarkable hospitality
Answer:
(D) remarkable hospitality

Question 4.
India’s independence gave rise to ___________.
(A) four major castes
(B) some patriots
(C) politicians
(D) both (A) and (B)
Answer:
(B) some patriots

Question 5.
Sri Moharana’s ambition is to be an __________.
(A) M.A.
(B) M.P.
(C) M.L.A.
(D) Honourable Minister
Answer:
(C) M.L.A.

Question 6.
The word ‘debut’ means ___________.
(A) debt
(B) fast
(C) maiden
(D) contribution
Answer:
(C) maiden

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 3 Mystery of the Missing Cap

Question 7.
In an early Independent India, a minister’s daily life was mainly confined to _________.
(A) travelling
(B) delivering lectures at public functions
(C) meeting people
(D) none of these
Answer:
(B) delivering lectures at public functions

Question 8.
A _________ preparation was going on for the minister’s visit.
(A) hectic
(B) meticulous
(C) typical
(D) both (A) and (B)
Answer:
(D) both (A) and (B)

Question 9.
At last the big day came. The underlined words means _________________.
(A) the arrival of the minister
(B) fulfilment of Sri Moharana’s dream
(C) the memorable day for the villagers
(D) the narrator’s delight
Answer:
(A) the arrival of the minister

Question 10.
“………….he loved to keep his feet on the ground !” The underlined phrase means ___________.
(A) to maintain normalcy
(B) to keep up one’s prestige
(C) to keep a sensible and practical attitude in lip
(D) to keep in tact
Answer:
(C) to keep a sensible and practical attitude in lip

Question 11.
The elephantine minister’ indicates a/an ______________.
(A) elephant-like
(B) elegant
(C) majestic
(D) hyperbole
Answer:
(D) hyperbole

Question 12.
“My, my !” This implies _________.
(A) Sri Moharana’s dream came true
(B) the villager’s focuss on the minister
(C) Sri Moharana’s pleasure
(D) none of these
Answer:
(A) Sri Moharana’s dream came true

Question 13.
“…..the minister and his entourage were treated to tender-coconut juice.” The underlined words mean –
(A) the minister and his sycophants
(B) the minister and his cooks
(C) the minister and his relatives
(D) The minister and his assistants
Answer:
(D) The minister and his assistants

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 3 Mystery of the Missing Cap

Question 14.
Mustering all my self-confidence, I slowly approached the window facing the pond. The underlined word means _____________.
(A) rolling
(B) gathering
(C) brimming
(D) none of these
Answer:
(B) gathering

Question 15.
The most extra-ordinary event the narrator witnessed was –
(A) Jhandoo’s arrival
(B) the minister’s snoring
(C) Jhandoo’s exit with the minister’s cap
(D) the monkey’s glance
Answer:
(C) Jhandoo’s exit with the minister’s cap

Question 16.
The expression ‘like a bolt from the blue’ means-
(A) thunderous sound
(B) rumbling of the thunder
(C) unexpected surprise to happen
(D) stunned in disbelief
Answer:
(D) stunned in disbelief

Question 17.
Which of these words expresses the narrator’s sadness?
(A) ecstasy
(B) excitement
(C) frustration
(D) pensive
Answer:
(D) pensive

Question 18.
The narrator found himself ____________.
(A) at home
(B) at sea
(C) in a fix
(D) in a state ofexcitement
Answer:
(C) in a fix

Question 19.
Sri Moharana stood thunderstruck. The underlined word means _____________.
(A) terribly disapproval
(B) shocked or surprised
(C) nervous
(D) in a state of shouting
Answer:
(B) shocked or surprised

Question 20.
‘It may have devastating effects on the politics of the country’. ‘It’ refers to ____________.
(A) unravelling of the mysterious missing cap
(B) Sri Moharana’s strange behaviour
(C) the monkey
(D) none of these
Answer:
(A) unravelling of the mysterious missing cap

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 3 Mystery of the Missing Cap

Question 21.
The first one to apprise Moharana of the incident was _____________.
(A) P.A. to the minister
(B) the narrator
(C) a villager
(D) the entire staffof the minister
Answer:
(B) the narrator

Question 22.
The incident had thrown a wet blanket on the occasion. The underlined phrase means-
(A) coloured
(B) dampened
(C) defiled
(D) defaced
Answer:
(B) dampened

Question 23.
Sri Moharana excels on the art of –
(A) acting
(B) coaxing
(C) attracting the public attention
(D) all of these
Answer:
(C) attracting the public attention

Question 24.
The mystery of missing cap raised ____________.
(A) an excitement
(B) a fear
(C) a hue and cry
(D) numbness
Answer:
(C) a hue and cry

Question 25.
The word ‘ascended’ means ____________.
(A) climbed
(B) reacted
(C) departed
(D) none of these
Answer:
(A) climbed

Question 26.
Which one of the following statements is true?
(A) The minister’s presence was boring.
(B) Sri Moharana’s niece was one of the High-School-educated girls of the area.
(C) Sri Moharana lacked will-power.
(D) The narrator appreciates Sri Moharana’s first speech.
Answer:
(B) Sri Moharana’s niece was one of the High-School-educated girls of the area.

Question 27.
Which one of the following statements is false?
(A) Sri Moharana’s voice increased in gradual loudness.
(B) A nobleman has taken the minister’s cap purposefully.
(C) The minister gracefully accepted the money.
(D) The minister delivered a very short speech.
Answer:
(D) The minister delivered a very short speech.

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 3 Mystery of the Missing Cap

Question 28.
The word ‘esteem’ means –
(A) estimate
(B) respect
(C) fear
(D) tribute
Answer:
(B) respect

Question 29.
Which of these statements is true?
(A) The minister was very open.
(B) His excitement knew no limit.
(C) Sri Moharana was a liar.
(D) none of these
Answer:
(B) His excitement knew no limit.

Question 30.
The repetition of ‘ha! ha!’ indicates the ____________tone of the minister.
(A) comical
(B) ironic
(C) satirical
(D) tragic
Answer:
(C) satirical

Question 31.
What did the author want the readers to share?
(A) Laughter
(B) Sympathy
(C) The story
(D) Kindness
Answer:
(B) Sympathy

Question 32.
Who was the then Minister of Fisheries and Fine Arts?
(A) Sri Moharana
(B) Jhandoo
(C) Babu Virkishore
(D) Manoj Das
Answer:
(C) Babu Virkishore

Question 33.
Sri Moharana had the only pukka house in an area of ___________.
(A) ten villages
(B) twenty villages
(C) his constituency
(D) Babu Virkishore’s constituency
Answer:
(B) twenty villages

Question 34.
Why had Sri Moharana a considerable reputation?
(A) He was a kind man
(B) He was a wealthy man
(C) He was a conscientious and generous man
(D) He was a wealthy man and a good host
Answer:
(C) He was a conscientious and generous man

Question 35.
What did Sri Moharana have?
(A) Two ponds full of choice fish
(B) A number of well cared cows
(C) A big pukka house
(D) All of the above
Answer:
(D) All of the above

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 3 Mystery of the Missing Cap

Question 36.
What was the new caste that emerged post independence?
(A) Leaders
(B) Freedom fighters
(C) Patriots
(D) Industrialists
Answer:
(C) Patriots

Question 37.
What ambition had Sri Moharana nurtured?
(A) Becoming a patriot
(B) Being called an exemplary host
(C) Becoming a member of the state Legislature
(D) Becoming the Fisheries Minister
Answer:
(C) Becoming a member of the state Legislature

Question 38.
Where was the author’s maternal house?
(A) In Sri Moharana’s village
(B) Near Babu Virkishore’s house
(C) Near Sri Moharana’s house
(D) In Babu Virkishore’s village
Answer:
(C) Near Sri Moharana’s house

Question 39.
Who were not there in the early days of Swadeshi ministers?
(A) Deputy or sub-deputy ministers
(B) Sub-ministers
(C) Members of state Legislature
(D) Chief ministers
Answer:
(A) Deputy or sub-deputy ministers

Question 40.
Where was Babu Virkishore from?
(A) The author’s village
(B) The author’s district
(C) Sri Moharana’s village
(D) The author’s maternal village
Answer:
(B) The author’s district

Question 41.
Who thought that Sri Moharana’s debut in politics should have the blessings of Babu Virkishore?
(A) Sri Moharana’s sponsors
(B) Bbu Virkishore’s sponsors
(C) The author and his friends
(D) Sri Moharana’s villagers
Answer:
(A) Sri Moharana’s sponsors

Question 42.
What was a minister’s daily life largely made up of in those days?
(A) Arranging meetings
(B) Speech-making at public receptions
(C) Attending feasts and meeting people
(D) Performing administrative tasks
Answer:
(B) Speech-making at public receptions

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 3 Mystery of the Missing Cap

Question 43.
Who was the chairman of the reception committee?
(A) Babu Virkishore
(B) Sri Moharana
(C) The author
(D) The author’s maternal uncle
Answer:
(B) Sri Moharana

Question 44.
What did the children of the village lower primary school do for a fortnight?
(A) Practised the welcome song
(B) Decorated Sri Moharana’s house
(C) Prepared for the minister’s arrival
(D) Learnt English words to impress the minister
Answer:
(A) Practised the welcome song

Question 45.
Who had composed the welcome song?
(A) Sri Moharana
(B) Babu Virkishore
(C) The head-pundit of the village school
(D) The author
Answer:
(C) The head-pundit of the village school

Question 46.
How old was the head-pundit?
(A) Sixty
(B) Sixty-seven
(C) Seventy
(D) Seventy- two
Answer:
(B) Sixty-seven

Question 47.
What questions were asked by the children?
(A) Does a minister sleep?
(B) What does a minister eat and drink?
(C) Does a minister ever have colic or colds?
(D) All of the above
Answer:
(D) All of the above

Question 48.
Why did Sri Moharana give up his habit of sleeping in the afternoon?
(A) To make the arrangements
(B) To examine the details of the arrangements
(C) To make the children practice the welcome song
(D) All of the above
Answer:
(B) To examine the details of the arrangements

Introducing the Author :
Manoj Das is one of the foremost writers of the generation of Indian writers. It goes without saying that he is the Indian Chekhov in his awareness of human misery and ironies of life, in the art of exposing all that is vulgar, shameful and pitiable. The basic material of his stories is obtained from his observation of human experience. Like Maupassant-and Chekhov, he possesses a ‘sublime curiosity’ about human affairs in abundance but with great skill and psychological subtlety he succeeds in recreating that experience and revealing its underlying significance. His stories are refreshingly free from the elements of horror, sex and violence, the crudities which make most of the modern writings morbidly distasteful and keep the reader’s mind sullenly down. His themes are essentially Indian, evoking the Indian scene and atmosphere. Manoj Das is traditional in form and technique, but modem in idea and sensibility. He is original in devising plot, invention and the subtle interpretation of things. His language is lucid and clear, tales, candid and fresh sparkling with humour and human essence.

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 3 Mystery of the Missing Cap

About the Story :
“Mystery of the Missing Cap” is a brilliant comical, historical and realistic story which deals with a minister’s visit to a village in Odisha. Here the writer has thrown light on the rise of the new class of patriots, the ministerial demigod like stance and style, the sponsors like Moharana, the benevolent host and an aspirant for a seat in the legislature, the sycophants like PRO, and the complacent and facetious Minister of Fisheries and Fine Arts. The whole state of affairs has been mocked at end travestied by the monkey. A distinct and unmistakable Odia flavour permeates the whole story. The rural scence is vividly portrayed with a plethora of details. Set in the backdrop of the early days of independent India, the story gives a glimpse of the socio-political picture and atmosphere of the then India. “Mystery of the Missing Cap”, right from beginning to the end, glows with the radiance of a delightful humour. Here the humour is at its peak almost in the manner of a gala day celebration, observation of ritual. It is genuine, broad, farcical, rustic, pawky and satirical.

ବିଷୟ ସୂଚନା :
“Mystery of the Missing Cap” ଗଳ୍ପଟି ଏକ ଚମତ୍କାର ହାସ୍ୟାଦ୍ଦୀପକ ଐତିହାସିକ ଏବଂ ବାସ୍ତବ ଗଳ୍ପ ଯାହାକି ଜଣେ ମନ୍ତ୍ରୀଙ୍କର ଓଡ଼ିଶାର ଗୋଟିଏ ଗାଁକୁ ପରିଦର୍ଶନ କରିଆସିବା ଘଟଣା ଉପରେ ଆଲୋକପାତ କରେ। ସେ ଏହି ଗଳ୍ପରେ ଶ୍ରୀ ମହାରଣାଙ୍କ ଭଳି ସଦୟ ଅତିଥ୍ୟସତ୍କାରକାରୀ ଯିଏକି ବିଧାନସଭା ଆସନଟିଏ ପାଇବାପାଇଁ ଇଚ୍ଛୁକ, ଲୋକସମ୍ପର୍କ ଅଧିକାରୀଙ୍କ ପରି ତୋଷାମଦକାରୀ ଏବଂ ଆତ୍ମଗର୍ବୀ ମତ୍ସ୍ୟ ଓ କଳା ବିଭାଗର ମନ୍ତ୍ରୀଙ୍କ ବିଷୟରେ ବର୍ଣ୍ଣନା କରିଛନ୍ତି । ସମ୍ପୂର୍ଣ ଘଟଣାକୁ ମାଙ୍କଡ଼ର ହାସ୍ୟାଦ୍ଦୀପକ କାର୍ଯ୍ୟ ମାଧ୍ୟମରେ ବ୍ୟଙ୍ଗ, ବିଦ୍ରୁପ କରାଯାଇଛି । ଏକ ସ୍ପଷ୍ଟ ଓ ଅଭ୍ରାନ୍ତ ଓଡ଼ିଆ ରୁଚିସମ୍ପନ୍ନ ଭାବଧାରାକୁ ଗଳ୍ପରେ ପ୍ରକାଶ କରିଯାଇଛି । ଗ୍ରାମ୍ୟ ପରିବେଶକୁ ମଧ୍ୟ ଗଳ୍ପରେ ସ୍ପଷ୍ଟ ଭାବରେ ବର୍ଣ୍ଣନା କରାଯାଇଛି । ଏହି ଗଳ୍ପଟି ଭାରତ ସ୍ଵାଧୀନତା ପାଇବାର ପରବର୍ତ୍ତୀ ସମୟର ଘଟଣାବଳୀକୁ ନେଇ ରଚିତ । ଏଥରେ ଭାରତର ସାମାଜିକ ଓ ରାଜନୈତିକ ଅବସ୍ଥାକୁ ବର୍ଣ୍ଣନା କରାଯାଇଛି । ଏହି ଗଳ୍ପରେ ସେହି ସମୟର ଭାରତର ପରିସ୍ଥିତି ଓ ପରିବେଶ ଉପରେ ଆଲୋକପାତ କରାଯାଇଛି । ଆମର ପାରମ୍ପରିକ ଚଳଣି ଓ ନୀତିକୁ ବ୍ୟଙ୍ଗାତ୍ମକ ଢଙ୍ଗରେ ଗଳ୍ପଟିରେ ବର୍ଣ୍ଣନା କରାଯାଇଛି । ଏହି ବର୍ଣ୍ଣନା ସ୍ପଷ୍ଟ, ପରିବ୍ୟାପ୍ତ, ଲୋକଦେଖାଣିଆ, ଗ୍ରାମ୍ୟଭିତ୍ତିକ ଏବଂ ବ୍ୟଙ୍ଗାତ୍ମକ ହୋଇପାରିଛି ।

Summary :
The writer takes us back to the early days of post-independent India, when there was the rise of the hew class of patriots. Sri Moharana was a burning example. He was not only rich, but also a benevolent host. The village-patriot was ambitious of becoming a member of the Legislative Assembly. The writer refers to another politician – Babu Virkishore, Minister of Fisheries and Fine Arts. His daily life comprised speech-making at public receptions. Shri Moharana decided to accord a grand reception to the minister in his village, The writer vividly recounts the preparation for the minister’s reception. He remembers how Sri Moharana gave a beautiful touch to his ancestral cane chair. For fifteen days, the children of the village lower primary school spent time in practising the welcome song. The narrator says that the song still lingers in his memory. Moharana’s excitement knew no bounds. He took minute care of all the arrangements. Nervousness
and uncertainty stared him in the face.

The day Moharana and his sycophants waited for had come at last. Alighting from his jeep the minister entered the very first welcome gate on the outskirts of the village. Moharana garlanded in profusion. Instead of getting into the jeep, the minister preferred to walk.
The writer gives a beautiful description of the procession of the minister in the village. The minister walked slowly with the heavy steps through the village street amidst the thunderous applause and slogans in priase of the minister. Everyone in the village including the invalids took part in it, shouting slogans by turn and opening their mouths wide open.

The procession reached Moharana’s house. Moharana lavishly entertained his guests. They were given tender coconut juice and treated to the most fabulous lunch the narrator had ever seen. The lunch Moharana had hosted comprised twenty dishes that were arranged around the sweetened, ghee-backed rice. Then the minister took rest in a cabin. The minister’s staff was given a separate accommodation for rest. The narrator got the first shock of disillusionment when he discovered that the minister was snoring like an ordinary person. He was speechless. Meanwhile, the narrator saw Jhandoo bounce suddenly. The monkey picked up the cap and vanished into grove. The incident made the narrator speechless and clueless.

He was confused for sometime. The narrator found himself in a fix to which he should give importance the minister’s cap or his snoring – disturbed him. The incident of missing cap came to light very fast. The minister’s personal assistant flitting about like a butter-fly and the public relation officer responded to the matter in a diplomatic way number of times. In their view, the Honourable Minister would give much importance to the way in which the cap had disappeared. Sri Moharana was stunned concerning the loss of the cap. He sensed a well-planned plot behind the sudden disappearance of the cap.

He was afraid the incident was likely to produce very serious effects on the political lives of India. The narrator noticed Moharana virtually trembling in nervousness. He was sweating profusedly. His condition led him into a conflicting situation if he would hide the episode of the mystery of the missing cap or disclose it. At last the narrator apprised Moharana of the matter; the latter stood speechless for the moment The disappearance of the cap threw a cold water to the occasion. In other words, the missing cap robbed the occasion of its glit and glitter. A pall of gloomy silence descended on the minister’s room. The narrator heard the minister’s periodic coughing. His anxiety dampened the spirit of the people. The narrator’s pals reacted to the situation in great anxiety.

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 3 Mystery of the Missing Cap

One of them visualised the culprit’s imprisonment, provided he was detected. Another person was apprehensive of the whole village suffering imprisonment bar. Even some credulous persons believed that the cap was a kind of Aladdin’s lampits owner would be a minister. Sri Moharana was aware of the mystery behind the missing cap. He acted smartly. The minister accompanying Moharana was seen in a smiling mood. He climbed the specially constructed stage. His remarkable smile still adored his face. The ceremony started with a bang. Moharana delivered the welcome speech that highlighted the minister’s achievements and his immense gratitude to the latter. Moharana’s first speech was excellent. In his speech, he told a lie in connection with the mysterious disappearance of the minister’s cap. He said that a certain noble man in their area had done this mischief.

Then he offered one hundred one rupees to the minister to fulfil the latter’s wish to serve the people. The minister gracefully accepted the gift and delivered his speech. At last, all the important people of the area attended the dinner that was arranged in honour of the minister. The time for the minister’s departure arrived. Meanwhile the monkey named Jhandoo appeared on the scene. The writer narrates its arrival in Moharana’s house; the monkey’s mother had left him in latter’s house in its infancy in order to get rid of his father’s anger. Unfortunately, in his absence Moharana’s servants killed its mother. Kind-hearted as he was, Moharana brought up the baby monkey with deep affection. Now here was the grown-up Jhandhoo.

The anti-climax of the story came when Jhandoo sitting between the minister and Sri Moharana, wore the cap on his head and then offered it to the minister most genially. Driven by a flush of anger and surprise the minister wanted to confirm whether the monkey was not the same gentleman that had taken away the cap. Moharana’s colourful and appetising lie in connection with the mysterious dissapearance of the cap could not last long. He quite helplessly admitted that it was verily the same gentleman. In response to his reply, the minister flared up and his eyes bulged and burnt like fire. Ironically, the missing cap brought a great change in their lives. They were not disillusioned but also reduced to ridiculous position.

ସାରାଂଶ :
ଲେଖକ ଭାରତର ସ୍ଵାଧୀନତା ପରବର୍ତ୍ତୀ ସମୟର ସାମାଜିକ ଓ ରାଜନୈତିକ ଜୀବନ ଉପରେ ଆଲୋକପାତ କରିଛନ୍ତି । ସେତେବେଳେ ନୂତନକରି ସୃଷ୍ଟି ହୋଇଛନ୍ତି ଏକ ଦେଶପ୍ରେମୀ ଗୋଷ୍ଠୀ । ଶ୍ରୀ ମହାରଣା ହେଉଛନ୍ତି ଏହାର ଏକ ଜ୍ଵଳନ୍ତ ଉଦାହରଣ । ସେ କେବଳ ଜଣେ ଧନୀ ବ୍ୟକ୍ତି ନ ଥିଲେ ସେ ମଧ୍ୟ ଜଣେ ଦୟାଳୁ ବ୍ୟକ୍ତି ଥିଲେ । ଗାଁର ଏହି ଦେଶପ୍ରେମୀ ବ୍ୟକ୍ତିଜଣଙ୍କ ବିଧାନସଭାର ସଭ୍ୟ ହେବାପାଇଁ ଅଭିଳାଷ ପୋଷଣ କରିଥିଲେ । ଲେଖକ ବାବୁ ବୀରକିଶୋର ନାମକ ଅନ୍ୟ ଜଣେ ରାଜନେତାଙ୍କ ନାମକୁ ଏଠାରେ ଉଲ୍ଲେଖ କରିଛନ୍ତି ଯିଏ ମତ୍ସ୍ୟ ଓ କଳା ବିଭାଗର ମନ୍ତ୍ରୀ ଥିଲେ । ସର୍ବସାଧାରଣ ଅଭ୍ୟର୍ଥନା ସଭାଗୁଡ଼ିକରେ ଭାଷଣ ଦେବା ତାଙ୍କର ନିତିଦିନିଆ କାର୍ଯ୍ୟ ଥିଲା । ଶ୍ରୀ ମହାରଣା ତାଙ୍କ ଗାଁରେ ମନ୍ତ୍ରୀ ମହୋଦୟଙ୍କୁ ଉଚ୍ଚ ମାନର ସମ୍ବୋଧନ କରି ସ୍ଵାଗତ କରିବାକୁ ସ୍ଥିର କଲେ ।

ମନ୍ତ୍ରୀ ମହୋଦୟଙ୍କୁ ସ୍ଵାଗତ କରିବାପାଇଁ ଯେଉଁଭଳି ଭାବେ ପ୍ରସ୍ତୁତି ଚାଲିଥିଲା, ଏଠାରେ ତାହାର ବର୍ଣ୍ଣନା ଦିଆଯାଇଛି । ଶ୍ରୀ ମହାରଣା ତାଙ୍କର ପୂର୍ବପୁରୁଷରୁ ଥିବା ଏକ ପୁରୁଣା ବେତଚୌକିକୁ ସୁନ୍ଦର ଭାବେ ସଜାଇଲେ । ପନ୍ଦର ଦିନ ପର୍ଯ୍ୟନ୍ତ ଗାଁର ପ୍ରାଥମିକ ବିଦ୍ୟାଳୟର ଛାତ୍ରଛାତ୍ରୀମାନେ ସ୍ଵାଗତ ସଙ୍ଗୀତ ଅଭ୍ୟାସ କରିଥିଲେ । ଲେଖକ କହନ୍ତି ଯେ ସେହି ଗୀତର ସ୍ମୃ ତି ଏବେ ବି ତାଙ୍କର ସ୍ମୃତିପଟ୍ଟରେ ବାଜି ଉଠେ । ମହାରଣା ଖୁବ୍ ଉତ୍ସାହିତ ହୋଇ ପଡ଼ିଥିଲେ । ତାଙ୍କର ମୁଖମଣ୍ଡଳରେ ହତାଶା ଓ ଅନିଶ୍ଚିତତାର ଚିହ୍ନ ବାରି ହୋଇ ପଡ଼ୁଥିଲା । ସେ ସବୁ ବ୍ୟବସ୍ଥାର ଟିକିନିଖ୍ ତଦାରଖ କରୁଥିଲେ ।

ଶେଷରେ ମହାରଣା ଏବଂ ତାଙ୍କର ଅନ୍ୟ ନିର୍ମିତ ପ୍ରଥମ ସ୍ଵାଗତ ଫାଟକ ଅତିକ୍ରମ କରିବା ବଡ଼ ଫୁଲହାର ଝୁଲାଇଦେଲେ । ଜିପ୍‌ରେ ଆସିବା ପ୍ରଶଂସକମାନେ ଅପେକ୍ଷା କରିଥିବା ଦିନଟି ଆସିଗଲା । ଗାଁର ବାହାରେ ସମୟରେ ମନ୍ତ୍ରୀ ଜିପ୍‌ ଓହ୍ଲାଇଲେ । ମହାରଣା ତାଙ୍କର ବେକରେ ଏକ ପରିବର୍ତ୍ତେ ମନ୍ତ୍ରୀ ମହୋଦୟ ସେଠାରୁ ଚାଲିଚାଲି ଆସିବାପାଇଁ ପସନ୍ଦ କଲେ ।

ଲେଖକ ଗାଁରେ ମନ୍ତ୍ରୀ ମହୋଦୟଙ୍କର ଶୋଭାଯାତ୍ରାର ଏକ ସୁନ୍ଦର ବର୍ଣ୍ଣନା ଦେଇଛନ୍ତି । ମନ୍ତ୍ରୀଙ୍କର ପ୍ରଶଂସାରେ ଗ୍ରାମ୍ୟ ପରିବେଶ ପ୍ରକମ୍ପିତ ହେଉଥିଲା । ସେହି ଜନଗହଳି ମଧ୍ୟରେ ମନ୍ତ୍ରୀ ମହୋଦୟ ଗାମ୍ଭୀର୍ଯ୍ୟପୂର୍ଣ୍ଣ ପଦଚାରଣ କରି ଆସ୍ତେ ଆସ୍ତେ ଚାଲୁଥିଲେ । ଗାଁର ସମସ୍ତେ ଏହି ସ୍ଵାଗତ ଉତ୍ସବରେ ଅଂଶଗ୍ରହଣ କରିଥିଲେ । ଏପରିକି ଶାରୀରିକ ବିକଳାଙ୍ଗମାନେ ମଧ୍ୟ ଅଂଶଗ୍ରହଣ କରିଥିଲେ । ସେମାନେ ମଧ୍ୟ ବଡ଼ପାଟିରେ ସ୍ଲୋଗାନ୍ ଦେଉଥଲେ । ଶେଷରେ ମନ୍ତ୍ରୀ ମହୋଦୟ ମହାରଣାଙ୍କ ଘରେ ପହଞ୍ଚିଥିଲେ ମହାରଣା ପଇଡ଼ପାଣି ରସ ପିଆଇ ଅତିଥିମାନଙ୍କର ସତ୍କାର କରିଥିଲେ ଏବଂ ମଧ୍ୟାହ୍ନ ପାଇଁ ସୁଖାଦ୍ୟ ଭୋଜନର ବ୍ୟବସ୍ଥା କରାଯାଇଥିଲା । କୋଡ଼ିଏ ପ୍ରକାରର ଖାଦ୍ୟ ସହ କର୍ମଚାରୀମାନେ ମଧ୍ୟ ଅନ୍ୟ ଏକ ପ୍ରକେଷ୍ଠରେ ବିଶ୍ରାମ ନେଇଥିଲେ ।

ଲେଖକ ଆଶ୍ଚର୍ଯ୍ୟ ହୋଇଗଲେ ଯେତେବେଳେ ସେ ଦେଖିଲେ ମନ୍ତ୍ରୀ ମହୋଦୟ ଜଣେ ସାଧାରଣ ବ୍ୟକ୍ତିଙ୍କ ଭଳି ଘୁଙ୍ଗୁଡ଼ି ମାରୁଛନ୍ତି । ସେ ଏହା ଦେଖି ବାକ୍‌ଶୂନ୍ୟ ହୋଇଗଲେ । ହଠାତ୍ ମାଙ୍କଡ଼ ଝାଣ୍ଡୁ ଡେଇଁ ଡେଇଁ ଆସି ପହଞ୍ଚିଗଲା । ସେ ମନ୍ତ୍ରୀଙ୍କର ଟୋପିଟିକୁ ନେଇ ଚାଲିଗଲା । କିଛି ସମୟ ପାଇଁ ଲେଖକ ଦ୍ବନ୍ଦ୍ବରେ ପଡ଼ିଗଲେ ଓ ସେ କାହାକୁ ଗୁରୁତ୍ଵ ମନ୍ତ୍ରୀ ମହୋଦୟଙ୍କର ହଜିଯାଇଥିବା ଟୋପିକୁ ନା ତାଙ୍କ ଘୁଙ୍ଗୁଡ଼ିକୁ ।

ଖୁବ୍ ଶୀଘ୍ର ମନ୍ତ୍ରୀଙ୍କର ଟୋପି ହଜିଯାଇଥିବା କଥା ସମସ୍ତେ ଜାଣି ଯାଇଥିଲେ । ପ୍ରଜାପତି ଭଳି ଫଡ୍‌ଫଡ୍‌ ହେଉଥ‌ିବା ମନ୍ତ୍ରୀଙ୍କର ବ୍ୟକ୍ତିଗତ ସହକାରୀ ଓ ସାଧାରଣ ଲୋକ ସମ୍ପର୍କ ଅଧିକାରୀ ଏହି ବିଷୟରେ ଭିନ୍ନ ଭିନ୍ନ କଥା କହିଥିଲେ । ସେମାନଙ୍କ ମତରେ ସମ୍ମାନନୀୟ ମନ୍ତ୍ରୀ ମହୋଦୟଙ୍କ ଟୋପିଟି ଯେଉଁଭଳି ଭାବରେ ହଜିଯାଇଛି ତା’ ଉପରେ ଗୁରୁତ୍ଵ ଦେବା ଆବଶ୍ୟକ । ଟୋପି ହଜିଯିବା ଘଟଣାରେ ମହାରଣା ଆଶ୍ଚର୍ଯ୍ୟ ହୋଇଗଲେ । ଏହି ଟୋପି ହଜିବା ଘଟଣା ଭାରତୀୟ ରାଜନୈତିକ ଜୀବନରେ ଗୁରୁତ୍ଵପୂର୍ଣ୍ଣ ପ୍ରଭାବ ପକାଇବ ଭାବି ମହାରଣା ଡରିଯାଇଥିଲେ । ଏହା ପଛରେ ନିର୍ଦ୍ଦିଷ୍ଟ ଭାବରେ କିଛି ଯୋଜନା ଥିବା କଥା ସେ ଚିନ୍ତା କଲେ ।

ମହାରଣା ଭୟରେ ଥରୁଥିବାର ଲେଖକ ଦେଖୁଥିଲେ । ତାଙ୍କ ଦେହରୁ ଝାଳ ବୋହି ଯାଉଥିଲା । ମହାରଣାଙ୍କର ସେହି ସମୟର ଅବସ୍ଥା ଲେଖକଙ୍କୁ ଦ୍ବନ୍ଦ୍ବରେ ପକାଇଲା । ପ୍ରକୃତ ଘଟଣାକୁ ଲେଖକ ଲୁଚାଇବେ କି ପ୍ରକାଶ କରିବେ ଚିନ୍ତା କରିପାରିଲେ ନାହିଁ । ଶେଷରେ ସେ ସତ ଘଟଣାଟି ପ୍ରକାଶ କଲେ । ଏହା ଶୁଣି ମହାରଣା ସେହି ସମୟରେ ଆଶ୍ଚର୍ଯ୍ୟ ହୋଇ ବାକ୍‌ଶୂନ୍ୟ ହୋଇଗଲେ ।

ମନ୍ତ୍ରୀ ମହୋଦୟଙ୍କ ଟୋପିଟି ହଜିଯିବାରୁ ଉତ୍ସବମୁଖର ହୋଇ ଉଠୁଥ‌ିବା ସଭାସ୍ଥଳଟି ଶ୍ରୀହୀନ ହୋଇପଡ଼ିଥିଲା । ସମସ୍ତଙ୍କର ଉତ୍ସାହ କମିଯାଇଥଲା । ମନ୍ତ୍ରୀଙ୍କ ପ୍ରକୋଷ୍ଠରେ ନୀରବତାର ଦୁଃଖ ଖେଳି ଯାଇଥିଲା। ସମୟେ ସମୟେ ମନ୍ତ୍ରୀଙ୍କର କାଶ ଲେଖକ ଶୁଣିପାରୁଥିଲେ । ତାଙ୍କ ମନରେ ଅବସାଦ ଆସିଯାଇଥିଲା । ଲୋକମାନଙ୍କର ମନୋବଳ ଭାଙ୍ଗି ଯାଇଥିଲା । ଲେଖକଙ୍କର ବନ୍ଧୁମାନେ ମଧ୍ୟ ପ୍ରତିକ୍ରିୟା ପ୍ରକାଶ କଲେ । ସେମାନଙ୍କ ମଧ୍ୟରୁ ଜଣେ କହିଲା, ‘‘ଦୋଷୀଙ୍କୁ ବନ୍ଦୀ କରି କରାଗାରକୁ ପଠାଇ ଦିଆଯାଉ । ଯାହାବି ହେଉ ତାଙ୍କୁ ଧରିବାର ଅଛି ।’’ ଆଉ ଜଣେ ସନ୍ଦେହ କଲା ଯେ ଗାଁର ସମସ୍ତ ଲୋକଙ୍କୁ କାରାଗାରକୁ ପଠାଇ ଦିଆଯାଇପାରେ । ଆଉ କେତେକ ଚତୁର ବ୍ୟକ୍ତି କହିଲେ ମନ୍ତ୍ରୀ ମହୋଦୟଙ୍କର ଟୋପି ଥିଲା ଆଲ୍ମାଦ୍ଦିନ୍‌ଙ୍କ ଲ୍ୟାମ୍ପ ଭଳି ଏହାର ମାଲିକ ବି ମନ୍ତ୍ରୀ ହେବେ ।

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 3 Mystery of the Missing Cap

ଶ୍ରୀ ମହାରଣା ହଜିଯାଇଥିବା ଟୋପିର ରହସ୍ୟ ବିଷୟରେ ସଚେତନ ଥିଲେ । ସେ ଚତୁରତାର ସହ କାର୍ଯ୍ୟ କଲେ । ମନ୍ତ୍ରୀ ମହୋଦୟ ସ୍ଵତନ୍ତ୍ର ଭାବେ ନିର୍ମିତ ସଭାସ୍ଥଳ ଉପରକୁ ଯାଇଥିଲେ । ତାଙ୍କର ସେହି ସ୍ଵତନ୍ତ୍ର ପ୍ରକାରର ହସ ତାଙ୍କ ମୁଖମଣ୍ଡଳରେ ଶୋଭା ପାଉଥିଲା । ଉତ୍ସବ ଆରମ୍ଭ ହେଲା । ମହାରଣା ସ୍ବାଗତ ଭାଷଣ ଦେଲେ ଏବଂ ମନ୍ତ୍ରୀଙ୍କର ସଫଳତା ବିଷୟରେ ଆଲୋକପାତ କରି ତାଙ୍କ ପ୍ରତି କୃତଜ୍ଞତା ପ୍ରକାଶ କଲେ ।

ଅଦୃଶ୍ୟ ହୋଇଗଲା, ସେ ସମୟରେ ସେ ଏକ ମିଛ କହିଲେ । ସେ କହିଲେ ଯେ ତାଙ୍କ ଅଞ୍ଚଳର ଜଣେ ଭଦ୍ରବ୍ୟକ୍ତି ଏହି ଅପରାଧ କରିଛନ୍ତି । ତା’ପରେ ସେ ମନ୍ତ୍ରୀଙ୍କୁ ସେହି ଭଦ୍ରବ୍ୟକ୍ତିଙ୍କ ତରଫରୁ ସେବା କାର୍ଯ୍ୟରେ ବିନିଯୋଗ କରିବାପାଇଁ ଶହେ ଏକ ଟଙ୍କା ଉପହାର ଦେଇଥିଲେ । ମନ୍ତ୍ରୀ ଖୁସିରେ ସେହି ଉପହାରକୁ ଗ୍ରହଣ କଲେ ଏବଂ ଭାଷଣ ଦେଲେ । ଶେଷରେ ସେହି ଅଞ୍ଚଳର ଗୁରୁତ୍ଵପୂର୍ଣ୍ଣ ବ୍ୟକ୍ତିମାନେ ମନ୍ତ୍ରୀ ମହୋଦୟଙ୍କ ସହ ମିଶି ରାତ୍ରଭୋଜନ କଲେ ।

ମନ୍ତ୍ରୀଙ୍କର ବିଦାୟ ନେବାର ସମୟ ଆସିଗଲା । ଏହି ସମୟରେ ମାଙ୍କଡ଼ ଝାଣ୍ଡୁ ଉପସ୍ଥିତ ହେଲା । ମାଙ୍କଡ଼ଟି କିପରି ମହାରଣାଙ୍କ ଘରକୁ ଆସିଥିଲା ତାହା ଲେଖକ ବର୍ଣ୍ଣନା କରିଛନ୍ତି । ଏହି ମାଙ୍କଡ଼ର ମା’ ତାକୁ ଶିଶୁ ଅବସ୍ଥାରେ ତା’ ବାପାର କ୍ରୋଧରୁ ତାକୁ ରକ୍ଷା କରିବା ନିମନ୍ତେ ମହାରଣାଙ୍କ ଘରେ ଛାଡ଼ି ଚାଲିଯାଇଥିଲା । ଦୁର୍ଭାଗ୍ୟବଶତଃ, ତାଙ୍କର ଅନୁପସ୍ଥିତିରେ ମହାରଣାଙ୍କର ଚାକରମାନେ ଏହି ମାଙ୍କଡ଼ର ମା’କୁ ମାରିଦେଇଥିଲେ । ଦୟାଳୁ ମହାରଣା ଏହି ମାଙ୍କଡ଼ଟିକୁ ଗଭୀର ସ୍ନେହ ଓ ଶ୍ରଦ୍ଧାର ସହିତ ପାଳନ କରିଥିଲେ । ସେ ଏବେ ବଡ଼ ହୋଇଯାଇଥିବା ‘ଝାଣ୍ଡୁ’ ଥିଲା ।

ଗଳ୍ପର ଶେଷ ପର୍ଯ୍ୟାୟରେ ଝାଣ୍ଡୁ ଆସି ମନ୍ତ୍ରୀ ମହୋଦୟ ଏବଂ ଶ୍ରୀ ମହାରଣାଙ୍କ ମଝିରେ ଟୋପି ପିନ୍ଧି ବସିପଡ଼ିଲା ତା’ପରେ ଭଦ୍ରଲୋକଙ୍କ ଭଳି ମନ୍ତ୍ରୀ ମହୋଦୟଙ୍କୁ ଟୋପିଟି ଦେଇଦେଲା । ରାଗରେ ମନ୍ତ୍ରୀ ମହାରଣାଙ୍କୁ ପଚାରିଲେ ଯେ ଟୋପି ନେଇଥ‌ିବା ଭଦ୍ରବ୍ୟକ୍ତିଜଣକ ଏହି ମାଙ୍କଡ଼ ନୁହେଁ ତ ? ମହାରଣା ଚତୁରତାର ସହ ଟୋପି ହଜିଯିବା ବିଷୟରେ ଯେଉଁ ରଙ୍ଗିନ୍ ମିଛ କଥା କହିଥିଲେ ତାହା ଧରାପଡ଼ିଗଲା । ସେ ଅସହାୟ ଭାବେ ସ୍ଵୀକାର କଲେ ଯେ ଏହି ମାଙ୍କଡ଼ ହିଁ ସେହି ଭଦ୍ରବ୍ୟକ୍ତି । ଏହା ଶୁଣି ମନ୍ତ୍ରୀ ମହୋଦୟଙ୍କର ଆଖ୍ ରାଗରେ ଜଳି ଉଠିଲା ଓ ଫୁଲିଗଲା । ହଜିଯାଇଥିବା ଟୋପିଟି ସେମାନଙ୍କ ଜୀବନରେ ବହୁତ ପରିବର୍ତ୍ତନ ଆଣିଥିଲା । ସେମାନଙ୍କ ଆତ୍ମମର୍ଯ୍ୟାଦା ଭୂଲୁଣ୍ଠିତ ହୋଇ ଯାଇଥିଲା ।

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My Mother Question Answer Class 12 Invitation English Non-Detailed Chapter 5 CHSE Odisha

Odisha State Board CHSE Odisha Class 12 Invitation to English 2 Solutions Non-Detailed Chapter 5 My Mother Textbook Exercise Questions and Answers.

Class 12th Invitation English Non-Detailed Chapter 5 My Mother Question Answers CHSE Odisha

My Mother Class 12 Questions and Answers

Unit – 1

Gist:
This unit begins with Chaplin’s description of his father; the latter liked to live in a state of isolation. He was not only an entertainer, but also a silent, thoughtful man with dark eyes. In his mother’s view, his father possessed a Napoleonic appearance. He was endowed with a grave and deep voice. Above all, he was a very good artist. In those days, he earned forty pounds a week. His addiction to drinking led to hic parent’s divorce. The writer refers to the entertainers of those times. They easily drank in those days, because all theatres sold alcohol. Some theatres earned greater profit in the bar than from the box office.

A number of stars earned handsomely because of their talent as well as their lavish spending on drinks. This destroyed many artists. The writer’s mother said that her husband was a die-hard drunkard, and therefore, died an early death at the age of thirty-seven. The mother’s attitude towards Chaplin’s father was blend of sympathy and sadness. He burst into a devastating temper at the time of drinking. When Chaplin was only one-year-old, his parents were divorced. A star as she was, she did not seek a maintenance. She looked after herself and her children without any difficulty. However, misfortune also could make her ask for relief. At last her theatrical engagement collapsed, when she suffered from prolonged inflammation of larynx as a result of slight cold.

ସାରମର୍ମ :
ଏହି ଭାଗର ଆରମ୍ଭରେ ଚାପ୍‌ଲିନ୍ ତାଙ୍କ ପିତାଙ୍କ କଥା ବର୍ଣ୍ଣନା କରିଛନ୍ତି । ତାଙ୍କ ବାପା ଏକୁଟିଆ ରହିବାକୁ ଭଲ ପାଉଥିଲେ । ସେ କେବଳ ଜଣେ ଅଭିନେତା ନ ଥିଲେ, ବରଂ ଜଣେ ନୀରବ ଓ ଚିନ୍ତାଶୀଳ ବ୍ୟକ୍ତି ଥିଲେ । ମା’ଙ୍କର ଦୃଷ୍ଟିରେ ତାଙ୍କ ବାପା ନୋପୋଲିୟନ୍‌ଙ୍କ ଭଳି ଦେଖା ଯାଉଥିଲେ । ତାଙ୍କର ସ୍ଵର ଥିଲା ଗୁରୁଗମ୍ଭୀର । ସେ ଜଣେ ସୁନ୍ଦର କଳାକାର ଥିଲେ । ସେତେବେଳେ ସେ ସପ୍ତାହକୁ ଚାଳିଶ ପାଉଣ୍ଡ ଆୟ କରୁଥିଲେ । ତାଙ୍କର ମଦନିଶା ତାଙ୍କ ପିତାମାତାଙ୍କର ବିବାହ ବିଚ୍ଛେଦର କାରଣ ହୋଇଥିଲା । ଲେଖକ ତତ୍କାଳୀନ ମନୋରଞ୍ଜନକାରୀଙ୍କ ଚରିତ୍ର ଚିତ୍ରଣ କରିଛନ୍ତି । ସେମା ନେ ପ୍ରାୟତଃ ମଦ୍ୟପାନ କରୁଥିଲେ । କାରଣ ସବୁ ଥୁଟର ମଦ ବିକ୍ରୟ କରୁଥିଲେ।

ନାଟକ ପ୍ରଦର୍ଶନ ଅପେକ୍ଷା ଥୁଟରଗୁଡ଼ିକ ମଦବିକ୍ରିରୁ ବେଶୀ ଟଙ୍କା ଉପାର୍ଜନ କରୁଥିଲେ । ପ୍ରତିଭା ଯୋଗୁଁ ଏବଂ ଥୁଟରର ମଦଶାଳାରେ ବେଶୀ ଟଙ୍କା ‘ଖର୍ଚ୍ଚ କରୁଥିବାରୁ ଅନେକ କଳାକାର ବହୁଳ ପରିମାଣରେ ଟଙ୍କା ପାଉଥିଲେ । ଏହା ଅନେକ କଳାକାରଙ୍କର ନଷ୍ଟର କାରଣ ଥିଲା । ମା’ ଚାପ୍‌ଲିନ୍‌ଙ୍କୁ କୁହିଛନ୍ତି ଯେ ତାଙ୍କ ବାପା ଭୟଙ୍କର ମଦ୍ୟପ ଥିଲେ ଏବଂ ସେଥ‌ିପାଇଁ ସେ ମାତ୍ର ୩୭ ବର୍ଷରେ ଅକାଳରେ ମରିଗଲେ । ଚାପ୍‌ଲିନ୍‌ଙ୍କର ବାପାଙ୍କ ପ୍ରତି ମା’ଙ୍କର ଦୃଷ୍ଟିଭଙ୍ଗୀ ଥିଲା ଦୁଃଖ ଓ ସହାନୁଭୂତିର ଏକ ମିଶ୍ରିତ ଭାବନା । ମଦ ପିଇବା ସମୟରେ ସେ ଭୟଙ୍କର କ୍ରୋଧୀ ହୋଇଯାଉଥିଲେ । ଯେତେବେଳ ଚାପଲିନ୍‌ଙ୍କୁ ମାତ୍ର ଏକ ବର୍ଷ, ସେତେବେଳେ ତାଙ୍କ ପିତାମାତାଙ୍କର ବିବାହ ବିଚ୍ଛେଦ ହୋଇଯାଇଥିଲା । ଯେହେତୁ ସେ ଏକ ତାରକା ଥିଲେ, ସେ ତାଙ୍କ ବାପାଙ୍କଠାରୁ ଭରଣପୋଷଣ ଖର୍ଚ୍ଚ ଦାବି କରି ନ ଥିଲେ । କେବଳ ବିପତ୍ତି ସମୟରେ ସେ ସାହାଯ୍ୟ ଲୋଡୁଥିଲେ । ସର୍ବଶେଷରେ ତାଙ୍କୁ ଥିଏଟରରେ କାମ ମିଳିବା କମିଗଲା, କାରଣ ସାମାନ୍ୟ ଥଣ୍ଡା ଯୋଗୁଁ ତାଙ୍କର କଣ୍ଠସ୍ଵର ବହୁ ସମୟ ଧରି ଖରାପ ହୋଇ ଯାଉଥିଲା ।

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 5 My Mother

Glossary :
hardly : କ୍ବଚିତ୍
aware of : know (ଜାଣିବା)
vaudevillian: an entertainer who performs a dramatic or musical work for an audience ଅଭିନୟ କରନ୍ତି କିମ୍ବା ବାଦ୍ୟ
quiet: ଶାନ୍ତ
brooding: thoughtful (ଚିନ୍ତାଶୀଳ)
light : ହାଲୁକା
baritone: grave and deep (male voice) (ଗମ୍ଭୀର ସ୍ଵର)
artist: କଳାକାର
considerable: substantial (ପର୍ଯ୍ୟାପ୍ତ)
large: ପ୍ରଚୁର
Laryngitis: inflammation of the larynx (କଣ୍ଠରେ ସଂକ୍ରମଣ)
progressively worse : ଦ୍ରୁତ ଗତିରେ ଖରାପ
crack: ଫାଟ
ruined: ବରବାଦ
violent: ହିଂସାତ୍ମକ
tantrums: childish outburst of temper (ପିଲାଳିଆ ରାଗ)
frantic: ରୋମାଞ୍ଚକର
bitterness: ତିକ୍ତତା
drunkenness : ମଦ୍ୟାସକ୍ତ ଅବସ୍ଥା
ruefully: sadly (ଦୁଃଖରେ)
“You gutter’: କ୍ରୋଧରେ ମା’ Chaplin ଙ୍କୁ କୁହିଛି, ‘ତୁ ଦିନେ ତୋ ବାପାଙ୍କ ଭଳି ଦୁଃଖ ଭୋଗିବୁ ।’’
alimony: means of living (ଭରଣପୋଷଣ)
ill fortune: ଦୁର୍ଭାଗ୍ୟ
booing: a sound uttered to show dislike, scorn, or disappointment (ଘୃଣାବ୍ୟଞ୍ଜକ ସ୍ଵର)
impaired: weakened
fell off : କମିଗଲା

Think it out

Question 1.
What does Chaplin speak about his father?
Answer:
Chaplin states that his father liked to live in a state of isolation. He was an entertainer, a silent, thoughtful man with dark eyes. He learnt from his mother that his father looking like Napoleon, was endowed with a deep voice. He was a beautiful artist. He was addicted to drinking which eventually led to his death at the age of thirty-seven. He flew into a devastating temper at the time of drinking. He was legally seprated from his mother.

Question 2.
What account of the vaudevillians do you get from the text?
Answer:
From the text we learn that vandevillians were die-hard drunkards. They earned handsomely not only for their talent, but because of they spent most part of their earnings at the theatre bar. As a result, many artists were ruined by drinking.

Question 3.
What is the mother’s attitude towards Charlie’s father?
Answer:
The mother’s attitude towards Charlie’s father is a blend of sympathy and sadness. She never showed bitterness towards him.

Question 4.
Why did his mother’s theatrical engagements fall off?
Answer:
His mother’s voice lost her strength. A little cold caused an inflammation of her larynx. Her suffering continued for weeks. Nevertheless, she was compelled to go on working and therefore, her voice went from bad to worse. In the middle of singing the cracking in her voice or its sudden disappearance into a low sound drew laughter and shouting from the audience. Her health deteriorated. She grew nervous. As a result, mother’s theatrical engagements fell off.

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 5 My Mother

Unit – II

The mother’s miserable vocal condition made Chaplin go to the stage at the age of five. She did not like him to live alone in rented rooms at night. Therefore, she brought him to the theatre. His mother entertained mostly soldiers who were indecent to the core. They made his mother and other performers objects of derision and laughter. Chaplin walks down the memory lane. While standing in the wings, he saw her voice crack and became almost inaudible. The audience laughed at her miserable condition. They sang and whistled aloud. The noise did not stop.

Then his mother was compelled to walk off the stage. When she left it, she was quite worried. Chaplin still remembers the stage manager grabbing him by the hand followed by a rational appeal to the audience and leaving him on the stage alone. He rose to the occasion. In the midst of the glare of footlights and smoking audience, he began to sing a famous song called Jack Jones. His song, though unfinished, evoked a tremendous positive response from the typical audience. They threw money to the stage in abundance. In short, the audience responded quite enthusiastically to his debut on the stage. Chaplin wanted to stop, pick the money and sing again and his words drew peals of laughter from the audience.

They learnt that he was ready to sing again. The stage manager handed over the money to his mother. Then Chaplin interacted with the audience, danced and sang many songs imitating one of his mother’s on Irish march. He repeated the chorus. He keenly imitated his mother’s cracking voice amidst the tumultuous cheer and laughter and money-throwing of the audience. When mother appeared on the stage to take him, her presence was greeted with roaring applause. That night marked Chaplin’s first performance on the stage. Mother never performed again. Mother’s voice never came to its former condition. When her career on the stage ended, his mother made her living by spending a little money she had saved and this had disappeared soon. And then she mortgaged jewellery and other small belongings. Nevertheless, she was hopeful about regaining her voice.

ସାରମର୍ମ :
ମା’ଙ୍କର ଦୟନୀୟ କଣ୍ଠସ୍ଵର ଅବସ୍ଥା ପାଞ୍ଚବର୍ଷ ବୟସର ଚାପ୍‌ଲିନ୍‌ଙ୍କୁ ମଞ୍ଚ ଉପରକୁ ଟାଣି ନେଇଥିଲା । ରାତିରେ ମା’ ତାଙ୍କୁ ଭଡ଼ାଘର କୋଠରି ଭିତରେ ଏକୁଟିଆ ଛାଡ଼ିବାକୁ ଚାହୁଁ ନ ଥିଲେ । ସେଥ‌ିପାଇଁ ଚାପ୍‌ଲିନ୍‌ଙ୍କୁ ତାଙ୍କ ସାଙ୍ଗରେ ଥ୍ଟରକୁ ଆଣୁଥିଲେ । ତାଙ୍କ ମା’ ପ୍ରାୟ ସୈନିକମାନଙ୍କର ମନୋରଞ୍ଜନ କରୁଥିଲେ । ଏହି ସୈନିକମାନେ ବହୁମାତ୍ରାରେ ଅସଭ୍ୟ ଥିଲେ । ଏକଦା ମଞ୍ଚର ଏକ କୋଣରେ ଛିଡ଼ା ହୋଇଥିବାବେଳେ ଚାପ୍‌ଲିନ୍ ଦେଖ‌ିଲେ ମା’ ଗୀତ ଗାଇବାବେଳେ ତାଙ୍କ ସ୍ଵର ଭାଙ୍ଗିପଡ଼ିଲା ଏବଂ ଅସ୍ପଷ୍ଟ ହୋଇଗଲା । ଶ୍ରୋତାମାନେ ତାଙ୍କ ମା’ଙ୍କର ଅସହାୟତାରେ ଥଟ୍ଟା କଲେ । ସେମାନେ ଗୀତ ଗାଇଲେ ଏବଂ ଉଚ୍ଚସ୍ୱରରେ ସିସିକାରୀ ମାରିଲେ ।

କୋଳାହଳ ବନ୍ଦ ହେଲା ନାହିଁ । ବାଧ୍ୟହୋଇ ମା’ ମଞ୍ଚ ଛାଡ଼ି ଚାଲିଆସିଲେ । ସେ ବ୍ୟସ୍ତ ବିବ୍ରତ ହୋଇପଡ଼ିଲେ । ପରିଚାଳକ ତାଙ୍କୁ ଜବରଦସ୍ତ ଟାଣି ଆଣି ମଞ୍ଚ ଉପରେ ଏକୁଟିଆ ଛାଡ଼ିଯିବାର ଦୃଶ୍ୟ ଏବେବି ଚାପ୍‌ଲିନ୍‌ଙ୍କର ସ୍ମୃତିରେ ରହିଛି । ସେ ଚମତ୍କାର ପ୍ରଦର୍ଶନ କଲେ । ଝଲସୁଥିବା ଆଲୋକ ଏବଂ ଧୂମ୍ରପାନ କରୁଥିବା ଶ୍ରୋତାମାନଙ୍କ ଉପସ୍ଥିତିରେ ସେ ଲୋକପ୍ରିୟ Jack Jones ଗୀତ ଗାଇଲେ । ଚାପ୍‌ଲିନ୍‌ଙ୍କର ମଞ୍ଚ ଉପରେ ଏହି ପ୍ରଥମ ପଦାର୍ପଣ ଶ୍ରୋତାମାନଙ୍କ ଉପରେ ଗଭୀର ପ୍ରଭାବ ପକାଇଲା । ସେମାନେ ମଞ୍ଚ ଉପରକୁ ଟଙ୍କା ଫୋପାଡ଼ିବାକୁ ଲାଗିଲେ ।

ପ୍ରଥମେ ଟଙ୍କା ଗୋଟାଇବେ ଏବଂ ପରେ ଗୀତ ଗାଇବେ ବୋଲି ଚାପ୍‌ଲିନ୍ ଘୋଷଣା କଲେ । ଏଥିରେ ଶ୍ରୋତୃମଣ୍ଡଳୀ ଖୁସି ହୋଇଗଲେ । ମଞ୍ଚ ପରିଚାଳକ ସବୁ ଟଙ୍କା ଚାପ୍‌ଲିନ୍‌ଙ୍କ ମା’ଙ୍କୁ ଦେଇଦେଲେ । ଏହାପରେ ଚାପ୍‌ଲିନ୍ ଶ୍ରୋତାମାନଙ୍କ ସହିତ ବାକ୍ୟାଳାପ କଲେ, ନାଚିଲେ ଏବଂ ଅନେକ ଗୀତ ଅନୁକରଣ କରି ଗାଇଲେ । ଏହା ମଧ୍ୟରେ ତାଙ୍କ ମା’ଙ୍କର Irish march ତାଙ୍କର ଭଗ୍ନ କଣ୍ଠସ୍ଟର ଅନୁକରଣ କରି ଗାଇବା ସମସ୍ତଙ୍କୁ ପ୍ରଭାବିତ କରିଥିଲା । ଶ୍ରୋତାମାନଙ୍କ ଉପରେ ଏହାର ପ୍ରଭାବ ତାଙ୍କୁ ଆଶ୍ଚର୍ଯ୍ୟାନ୍ବିତ କରିଥିଲା । ସେ ସେମାନଙ୍କର ହସ, ପ୍ରଫୁଲ୍ଲତା ଏବଂ ଟଙ୍କା ଫୋପଡ଼ା ଦେଖ‌ିଲେ । ଚାପ୍‌ଲିନ୍‌ଙ୍କୁ ନେବାପାଇଁ ମା’ ମଞ୍ଚକୁ ଆସିବାବେଳେ ଶ୍ରୋତାମାନେ ତାକୁ ଉଚ୍ଛସିତ ପ୍ରଶଂସାରେ ପୋତି ପକାଇଥିଲେ । ସେଇ ରାତି ଥିଲା ଚାପ୍‌ଲିନ୍‌ଙ୍କର ପ୍ରଥମ ମଞ୍ଚ ଅଭିନୟ । ମା’ଙ୍କର ତାହା ଶେଷ ଅଭିନୟ ଥିଲା । ମା’ ତାଙ୍କ ପୂର୍ବ ସ୍ବର ଫେରି ପାଇଲେ ନାହିଁ । ଆର୍ଥିକ ଅବସ୍ଥାରେ ଅବନତି ଘଟିଲା । କିଛି ଟଙ୍କା ସଞ୍ଚୟ କରିଥିବାରୁ ସେ ଜୀବନ ଧାରଣ କରିନେଲେ । କିନ୍ତୁ ଏହା ସରିଗଲା । ତା’ ପରେ ସେ ଗହଣା ଏବଂ ଅନ୍ୟ ଜିନିଷଗୁଡ଼ିକୁ ବନ୍ଧକ ରଖିଲେ । ଆଶା କରିଥିଲେ ତାଙ୍କ ପୂର୍ବ ସ୍ଵର ଫେରିଆସିବ ।

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 5 My Mother

Glossary :
Owing to: because of
vocal condition : କଣ୍ଠସ୍ଵର ଅବସ୍ଥା
Aldershot : a town in south central England
grubby: dirty (ଅପରିଷ୍କାର)
mean: small
Catering : satisfying
rowdy: noisy causing trouble
excuse: plea
deride: treat with scorn
ridicule: make fun of, laugh at (ଥଟ୍ଟା କରିବା)
terror: ଭୟ
falsetto: a false voice (କୃତ୍ରିମ ସ୍ୱର)
valueless: meaningless (ÅDIA)
quite : totally (ସମ୍ପୂର୍ଣ୍ଣ ଭାବରେ )
walk off: left (ପରିତ୍ୟାଗ କରିବା|ଛାଡ଼ି
upset: disappointed
letting : allowing (ଅନୁମତି ଦେବା)
turmoil : noise (କୋଳାହଳ)
glare : ତୀବ୍ର ଆଲୋକ
half way through : ଅଧା ଗୀତ ଗାଉଥ‌ିବା ସମୟରେ
a shower of money : ଟଙ୍କା ବୃଷ୍ଟି
poured: ଗଦା ହେଲା
pick up: collect (ଗୋଟାଇ ନେବା)
gather : ଏକାଠି କରିବା
Conveyed: ଜଣେଇ ଦିଆଗଲା
at home : comfortable (ସ୍ଵଚ୍ଛନ୍ଦ)
chorus: ମିଳିତ ସଙ୍ଗୀତ
impact: ପ୍ରଭାବ
evoked: generated (ଉତ୍ପନ୍ନ କଲା)
tremendous : ବହୁତ
applause: କରତାଳି
fate: ଭାଗ୍ୟ
destiny : fate (ଭାଗ୍ୟ)
heed: notice (ଧ୍ୟାନ ଦେବା )
pity: ଦୟା
justice: ନ୍ୟାୟ
dealt with: behaved ଦେଖାଇଲେ )
regained: ଫେରି ପାଇଲେ
vanished: ଅଦୃଶ୍ୟ ହୋଇଗଲା
pawned: mortgaged (ବନ୍ଧା ପକାଇଲେ)

Think it out

Question 1.
How and why did Charlie first go to the theatre?
Answer:
Mother usually went to the theatre at night. Therefore, she did not want Charlie to stay alone in rented rooms. Besides, her vocal condition was not in a good shape. These factors made Charlie first go to the theatre at the age of five.

Question 2.
Why did his mother walk off the stage?
Answer:
The writer remembers standing on the side of the stage when mother’s voice crecked and relapsed into a state of slow sound. To his utter confusion, she; evoked a ridiculous response from the audience. They started laughing, singing and whistling loudly. As a result, his mother walked off the stage.

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 5 My Mother

Question 3.
How did Charlie make his debut on the stage?
Answer:
Her cracking voice and the audience’s contemptuous treatment to her made Charlie’s mother walk off the stage. Then she came into the wings and argued with the stage manager. But the stage manager, being influenced by the Charlie’s performance before his ‘mother’s friends begged her permission to let Charlie go on to the stage. Then amidst of loud uproar led Charlie by the hand. After appealing to the audience, she left Charlie on the stage alone. Then Charlie rose to the occasion.

Question 4.
How did the audience respond to his frist performance on the stage?
Answer:
At first Charlie sang a popular song called Jack Jones. It enthralled the audience. Money flowed to the stage. Chaplin’s announcement to gather the money first and then sing drew laughter from the audience. The stage manager gave the money to Chaplin’s mother; then Chaplin interacted with the audience, danced and imitated many songs including his mother’s Irish march. His perfect imitation of mother’s cracking voice profoundly impressed the audience. His first appearance on the stage evoked their laughter, lusty cheers and at last more money-throwing.

Question 5.
How did his mother make her living when her career on the stage ended?
Answer:
When her career on the stage ended, his mother made her living by spending a little money she had saved and mortgaging her jewellery and other small belongings.

Unit – III

Gist:
Chaplin and his mother had to undergo a lot of suffering when she gave up stage performance. All their belongings went down. Charlie’s mother turned to religion with a hope that she would get back her voice again. Her regular visit to Christ Church in the Westminister Bridge Road was a case in point. Every Sunday, Chaplin was an avid listener to Bach’s organic music. He, with painful impatience, lent his ears to Reverend EB. Meyer’s enthusiastic and dramatic voice that reverbrated the long central part of the church. His scintillating oration moved mother to tears.

Charlie remembers the Holy Communion on the hot summer’s day. The gathering in the church was treated to cool tasty grape-juice in silvery cups. Mother gently restrained him drink it excessively. The Reverend’s act of closing the Bible filled him with great relief. As a result, there would be no sermons but prayers and the final religious songs. Mother’s theatrical world became a thing of the past. They lived in a state of oppressive misery. Mother’s suffering knew no bounds.

She fell a victim to the social condition of the Victorian age where fabulous wealth and abject poverty were rolled into society and where poorclass women could not but do small works. Small, gracious, sensitive as she was, mother endured the hardships without any protest. Her employment as a nurse was of short duration. She made theatrical costumes. She was able to earn a little for her skilful needle-work and dress making for the members of the church.. In spite of her struggle, their life of hardship did not change.

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 5 My Mother

ସାରମର୍ମ :
ଯେତେବେଳେ ଚାପ୍‌ଲିନ୍‌ଙ୍କ ମା’ ମଞ୍ଚ ଅଭିନୟ ଛାଡ଼ିଦେଲେ ତାଙ୍କ ମା’ ଓ ସେ ବହୁ କଷ୍ଟ ଭୋଗ କରିଥିଲେ । ତାଙ୍କ କଣ୍ଠକୁ ପୁନଶ୍ଚ ଫେରି ପାଇବା ଆଶାରେ ତାଙ୍କ ମା’ ଧର୍ମକୁ ଆଦରି ନେଲେ । ପ୍ରତିଦିନ ସେ ଗୀର୍ଜାକୁ ଯାଉଥିଲେ । ସମ୍ମାନନୀୟ ଧର୍ମଯାଜକଙ୍କର ଜୀବନ୍ତ ସ୍ବରରେ ଗୀର୍ଜାର ଲମ୍ବା ମଧ୍ୟଭାଗ ପ୍ରତିଧ୍ଵନିତ ହେଉଥିଲା

ବେଳେବେଳେ ତାଙ୍କର ଭାଷଣ ମା’ଙ୍କ ଆସ୍‌ରେ ଲୁହ ଭରି ଦେଇଥିଲା । ଗ୍ରୀଷ୍ମଦିନର ଏକ ପବିତ୍ର ସମାବେଶକୁ ଚାପ୍‌ଲିନ୍ ମନେ ପକାଇଛନ୍ତି ।ସମସ୍ତଙ୍କୁ ଥଣ୍ଡା ରୁପା କପ୍‌ରେ ସୁସ୍ଵାଦୁ ଅଙ୍ଗୁର ରସ ଦିଆଯାଇଥିଲା । ଯେତେବେଳେ ଧର୍ମଯାଜକ ବାଇବେଲ ବନ୍ଦ କରୁଥିଲେ ତାହା ଧର୍ମଶିକ୍ଷାର ଅନ୍ତକୁ ସୂଚାଇ ଦେଉଥିଲା । ଦିନ ଗଡ଼ି ଚାଲିଲା । ମା’ଙ୍କର ଥ୍ଟର ସମ୍ବନ୍ଧୀୟ ଦୁନିଆ ଅତୀତ ହୋଇଗଲା । ଅନ୍ୟ କ୍ଷେତ୍ରରେ ତାଙ୍କ ଅଭିଜ୍ଞତାର ଅଭାବ ନୂଆ କାମ ପାଇଁ ଏକ ପ୍ରତିବନ୍ଧକ ଥିଲା ।

ଅକୁହା କଷ୍ଟ ସତ୍ତ୍ବେ ସେ ସଂଗ୍ରାମ ଜାରି ରଖୁଥିଲେ । ଭିକ୍ଟେରିୟାନ ଯୁଗର ଦାରିଦ୍ର୍ୟ ପ୍ରପୀଡ଼ିତା ସ୍ତ୍ରୀ ଲୋକମାନଙ୍କୁ ଛୋଟ କାମ କରିବାକୁ ପଡୁଥିଲା । ବେଳେବେଳେ ସେ ଧାଈର ଭୂମିକା ଗ୍ରହଣ କରୁଥିଲେ । କିନ୍ତୁ ଏହା କ୍ଷଣସ୍ଥାୟୀ ଥିଲା । ଏଇସବୁ ଦୟନୀୟ ଅବସ୍ଥା ସତ୍ତ୍ବେ ମା’ ହତୋତ୍ସାହ ହୋଇଯାଇ ନଥିଲେ । ସେ ଛୁଞ୍ଚ୍ କାମରେ ନିପୁଣା ଥିଲେ । ଗୀର୍ଜାର ସଦସ୍ୟମାନଙ୍କ ପାଇଁ ସେ ପୋଷାକ ତିଆରି କରୁଥିଲେ । ସଂଗ୍ରାମ ସତ୍ତ୍ବେ ସେମାନଙ୍କର ଦୁର୍ଦ୍ଦଶାର ପରିବର୍ତ୍ତନ ହେଲା ନାହିଁ ।

Glossary:
dwindling: going down
drabber: more miserable
turned to: looked to
shuffling: walking slowly and noisily without lifting one’s feet (ଘୋଷାରି ଚାଲିବା)
orations: speeches (ବକ୍ତୃତା)
appealing: touching the feelings (ଭାବନା ଉଦ୍ରେକକାରୀ )
occasionally : at times (ବେଳେବେଳେ)
delicious: ସ୍ୱାଦିଷ୍ଟ
congragation : gathering (ସମ୍ମଳନ)
relieved: ଆଶ୍ଵସ୍ତ ହେଲେ
sermon: a speech made by a priest (ପୂଜକଙ୍କ ଧର୍ମବାଣୀ)
hymn: religious song (ଧର୍ମସଂକ୍ରାନ୍ତୀୟ ସଙ୍ଗୀତ)
wretched: in a miserable state
interim: gap (ବ୍ୟବଧାନ)
travail: painful work
cheerless: dull
fervent: enthusiastic (ଉତ୍ସାହଜନକ)
echoing: ଇକୋ
nave: long central part of the church (ଚର୍ଚ୍ଚର ଦୀର୍ଘ)
twilight: ଗୋଧୂଳି ସମୟ
untutored: did not learn (ଶିଖ୍ ନ)
handicapped: (here) faced problem (ବାଧା ପାଇଲା)
Dainty: small and attractive in a delicate way
sensitive: likely to be upset easily (ସଚେତନ)
odds: obstacles (ପ୍ରତିବନ୍ଧକ)
Victorian era: ଭିକ୍ଟୋରିଆନ୍ ଯୁଗ
menial work : work considered of low status (ମର୍ଯ୍ୟାଦାହୀନ କାମ)
drudges: menial work like the job of an attendant
nevertheless: but still
resourceful: good at finding with effective ways to deal problems
costumes: ପୋଷାକ
But…..us: Chaplin says that mother’s income was not sufficient for their existence.

Think it out

Question 1.
Why did Charlie’s mother turn to religion?
Answer:
Chaplin and his mother had to undergo a lot of suffering when she gave up stage performance. All their belongings went down. Charlie’s mother turned to religion with a hope that she would get back her voice again.

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 5 My Mother

Question 2.
How does Charlie remember the Holy Communion on one hot summer’s day?
Answer:
Charlie’s mind goes back to the Holy Communion on one hot summer’s day. The gathering was treated to tasty grape-juice contained in the cool silver cup. The Reverend’s act of closing the Bible marked the end of preaching religious teaching and the beginning of prayers and the final religious song.

Question 3.
Give an account of his mother’s suffering.
Answer:
With the disappearance of her theatrical world, mother along with Charlie lived amidst miserable conditions. Her lack of experience in any other field was an obstacle to find a job. Small, graceful and sensitive as she was, his mother struggled against unbelievably hostile conditions in a Victorian age when poor-class women were bound to resort to do low work. At times, mother joined the nursing work. She earned a little by making dresses for the members of the church. But it was not enough for their existence.

CHSE Odisha Class 12 English My Mother Important Questions and Answers

Multiple-Choice Questions (MCQs) with Answers

Question 1.
Chaplin’s father was ____________.
(A) thoughtful
(B) silent
(C) a brilliant artist
(D) all of these
Answer:
(C) a brilliant artist

Question 2.
He was endowed with a __________ voice.
(A)soft
(B) harsh
(C) magical
(D) grave and deep
Answer:
(D) grave and deep

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 5 My Mother

Question 3.
The vaudevillians during Chaplin’s time were –
(A) refined
(B) exceptionally brilliant artists
(C) quite sensitive
(D) addicted to drinking
Answer:
(D) addicted to drinking

Question 4.
A majority of stars were paid _____________ because they spent their money lavishly at the theatre bar.
(A) miserably
(B) weekly
(C) handsomely
(D) all of these
Answer:
(C) handsomely

Question 5.
Chaplin’s father died because of his –
(A) alcoholic habit
(B) addiction to drinking
(C) utter carelessness
(D) isolation from his family
Answer:
(A) alcoholic habit

Question 6.
When drinking, Chaplin’s father was in a ________mood.
(A) defensive
(B) frustrating
(C) violent
(D) sober
Answer:
(C) violent

Question 7.
Chaplin’s parents __________ in his infancy.
(A) divorced
(B) were fine
(C) were typical
(D) none of these
Answer:
(A) divorced

Question 8.
His mother was a ___________singer.
(A) non-descript
(B) moderate
(C) celebrated
(D) gifted
Answer:
(C) celebrated

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 5 My Mother

Question 9.
The word ‘laryngitis’ means –
(A) weak
(B) inflammation of the larynx
(C) incurably weak
(D) long breaths
Answer:
(B) inflammation of the larynx

Question 10.
The cracking voice of Chaplin’s mother was met with ____________ responses from the audience.
(A) ridiculous
(B) sorrowful
(C) delirious
(D) gloomy
Answer:
(A) ridiculous

Question 11.
Chaplin made his ___________appearance on the stage, when he was five.
(A) brilliant
(B) first and last
(C) maiden
(D) none of these
Answer:
(C) maiden

Question 12.
The cracking voice of Chaplin’s mother met with the audeience’s _______.
(A) shock
(B) wrath
(C) derision
(D) all of these
Answer:
(C) derision

Question 13.
Mother led Chaplin to the stage amidst great _________.
(A) noise
(B) excitement
(C) pleasure
(D) uncertainty
Answer:
(A) noise

Question 14.
Jack Jones was a great ___________.
(A) comedy
(B) lyric
(C) elegy
(D) song
Answer:
(D) song

Question 15.
Chaplin’s first appearance on the stage was quite _________.
(A) encouraging
(B) hopeless
(C) contemptuous
(D) none of these
Answer:
(A) encouraging

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 5 My Mother

Question 16.
Presence of Chaplin’s mother on the stage was __________.
(A) painful
(B) sorrowful
(C) electrifying
(D) all of these
Answer:
(C) electrifying

Question 17.
At last, fate ________on her.
(A) sailed
(B) showered
(C) frowned
(D) both (A) and (B)
Answer:
(C) frowned

Question 18.
In her moment of crisis, Chaplin’s mother resorted to –
(A) saying prayers
(B) religion
(C) the priest’s help
(D)none of these
Answer:
(B) religion

Question 19.
The sight of mother’s tear _________ Chaplin a little.
(A) shocked
(B) saddened
(C) vexed
(D) none of these
Answer:
(C) vexed

Question 20.
After going to church, mother’s relationship with her friends almost –
(A) snapped
(B) completely abated
(C) turned strange
(D) soured
Answer:
(A) snapped

Question 21.
The word ’travail’ means ___________.
(A) wandering
(B) tiredness
(C) tordy
(D) painful work
Answer:
(D) painful work

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 5 My Mother

Question 22.
The Victorian age is marked by ___________and poverty.
(A) comfort
(B) sloth
(C) affluence
(D) none of these
Answer:
(C) affluence

Question 23.
Chaplin’s mother was short, __________and sensitive.
(A) fat
(B) weak
(C) pretty
(D) dainty
Answer:
(D) dainty

Question 24.
During Chaplin’s time, job such as, nursing was quite ______.
(A) popular
(B) infrequent
(C) prestigeous
(D) none of these
Answer:
(B) infrequent

Question 25.
Despite all odds, Chaplin’s mother was _________.
(A) fine
(B) tolerant
(C) happy
(D) all of these
Answer:
(B) tolerant

Introducing the Author :
Sir Charles Spencer Chaplin (1889-1977) is one of the greatest comedians of the silent movies. It is an record that Chaplin made his first stage appearance when he was five as a replacement for his mother. Till twenty he could hardly find an anchor and drifted until he came to the United States, after having made a name as a child actor. The rapidly growing film industry and the daring experiments of producers opened new vistas for Chaplin. He was soon recognised as ‘an original and indisputable laughgetter’, his fantastic apparel becoming a symbol of great comedy. Almost every picture in which he featured became famous. Among these are ‘The Floor Walker’, ‘The Count’, ‘The Immigrant’, ‘Easy Street’, ‘The Gold Rush’, ‘City Lights’, ‘Monsieur Verdoux’ and then ‘Lime Light’, his great hit. Bernard Shaw called Chaplin ‘the only genius developed by the motion pictures’, Chaplin produced ‘Lime Light’ at the age of sixty three, when it looked as if he had retired. But the film was hailed as ‘a kind of cinematic poem about humanity’, and Chaplin as one of the supreme geniuses of the film world and comedy.

About the Story :
‘‘My Mother”, an extract from Chaplin’s ‘My Autobiography’ deals with the nature of his father and mother. This article also presents Charlie’s first appearance on the stage and the sufferings he and his mother had experienced when the latter relinquished the stage. A superb touch of clarity characterised ‘‘My Mother”.

ବିଷୟ ସୂଚନା :
ଚାପ୍‌ଲିନ୍‌ଙ୍କର ‘My Autobiography’ରୁ ଉଦ୍ଧୃତ ହୋଇଥିବା “My Mother” ତାଙ୍କ ପିତାମାତାଙ୍କ ବିଷୟରେ ଆଲୋଚନା କରିଛି । ଏହି ବିଷୟଟି ମଞ୍ଚ ଉପରେ ଚାପ୍‌ଲିନ୍‌ଙ୍କର ପ୍ରଥମ ଅବିର୍ଭାବ ଏବଂ ତାଙ୍କ ମା’ଙ୍କର ମଞ୍ଚ କାର୍ଯ୍ୟ ତ୍ୟାଗ କରିବା ପରେ ସେମାନେ ସମ୍ମୁଖୀନ ହୋଇଥ‌ିବା ଦୁର୍ଦ୍ଦଶା ଉପରେ ଆଲୋକପାତ କରିଛି । ସ୍ପଷ୍ଟ ଅଭିବ୍ୟକ୍ତି ହେଉଛି “My Mother” ଗଳ୍ପଟିର ବୈଶିଷ୍ଟ୍ୟ |

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 5 My Mother

Summary :
Walking down the memory lane, Chaplin reminisces his father, who was an entertainer, a silent, a thoughtful man with dark eyes. He learnt from his mother that his father, looking like Napoleon, was endowed with a deep voice. He was a beautiful artist. Even in those days when jobs were scarce, he earned the substantial income of forty pounds a week. Mother also said that his father’s addiction to drinking was the; cause of their divorce. Chaplin throws light on the entertainers of the time. They were die-hard drunkards, because all theatres dealt in alcohol. Handsome salaries made a number of stars spend a lot at the theatre bar. As a result, many artists including Chaplin’s father invited ruin.

His father fell a prey to excessive alcohol at the age of thirty-seven. In a state of drunkenness, he showed a devastating temper. Chaplin’s mother’s attitude towards his father lacked objectivity. At times, it was a blend of sympathy and sadness. Chaplin states that his mother did not demand any means of living, despite his parents’ divorce. A star as she was, she did not face any problem in maintaining herself and her children. Only in times of crisis, she sought relief. She never resorted to legal steps. Chaplin refers to his mother’s voice growing worse. Just a little cold caused a prolonged inflammation of her larynx, but circumstances compelled her to go on singing. Her voice cracked and suddenly became inaudible in the middle of singing. She met with the scorn and laughter of the audience. It led to the deterioration of her health. She grew nervous.

As a result his mother’s theatrical engagements fell off and eventually came to a close. The writer states that his mother’s pathetic vocal condition paved the way for his debut on the stage, when he was five. She was entertaining mostly Soldiers at Aldershot. They were indecent. They did not mind making the performers objects of scorn and laughter. The writer remembers standing on the side of the stage when mother’s voice cracked and relapsed into a state of slow sound.

To his utter confusion, she evoked a ridiculous response from the audience. They started laughing, singing and whistling loudly. As a result, his mother left the stage. Instead of being cowed down by their sarcasm, the stage manager left him on the stage alone. Chaplin splendidly rose to the occasion. He sang a popular song called Jack Jones. The audience responded to his first performance on the stage in a manner that was incredible. Money flodded the stage. Chaplin’s announcement to gather the money first and then sing drew laughter from the audience.

The stage manager gave the money to Chaplin’s mother; the latter interacted with the audience, danced and imitated many songs including his mother’s Irish march one. His perfect imitation of mother’s cracking voice, vastly impressed the audience. Chaplin found himself in the midst of their cheerful response. They threw money to the stage. The spectacle of mother’s presence on the stage was electrifying. She drew lavish praise from the audience. That night marked his debut on the stage and mother’s last performance. , Fate, Chaplin states, governs human destiny. It knows no pity, no justice.

His mother fell a victim to cruel fate. She never got back her voice again. His mother made her living out of a little money, that she had saved and mortgaging the jewellery and other small possessions she had mortgaged. Everything was exhausted soon. She always hoped that she would regain her voice. But it was a futile hope. Chaplin and his mother had to undergo a lot of hardships when she gave up stage performance. She looked to religion, hoping that it would bring back her voice again. She became a frequent visitor to the church. The Reverend’s lively and dramatic voice reverberated the long central part of the church. At times his speeches moved her to tears.

The writer’s mind goes back to the holy gathering on one hot summer’s day. Each of them was treated to tasty grape-juice contained in the cool silver cup. The Reverend’s act of closing the Bible marked the end of preaching religious teaching and the beginning of prayers and the final religious song. Days rolled by. Mother’s theatrical world became a thing of the past. Her lack of experience in other field was an obstacle to find a new job. Small, graceful and sensitive woman as she was, Chaplin’s mother kept on struggling against untold hardships. She lived in a Victorian age, where poverty-stricken women resorted to low jobs. At times, she played the role of a nurse, but such employment was not always available. Besides, the work of nursing lasted for a short time. In spite of these adverse conditions, mother was capable of finding alternative sources for existence. She excelled in the art of needle-work. Dress-making for the members of the church was a case in point. But it was not enough for their livelihood.

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 5 My Mother

ସାରାଂଶ :

ସ୍ମୃତିଚାରଣ କରି ଚାପ୍‌ଲିନ୍ ତାଙ୍କ ବାପାଙ୍କ କଥା ମନେ ପକାଇଛନ୍ତି । ତାଙ୍କ ବାପା ଥିଲେ ଜଣେ ମନୋରଞ୍ଜନକାରୀ, ନୀରବ ଏବଂ ଚିନ୍ତାଶୀଳ ବ୍ୟକ୍ତି । ତାଙ୍କ ମା’ଙ୍କଠାରୁ ଚାପ୍‌ଲିନ୍ ଜାଣିଥିଲେ ଯେ ତାଙ୍କ ବାପା ନେପୋଲିୟନ୍ ଭଳି ଦେଖାଯାଉଥିଲେ ଓ ତାଙ୍କର ସ୍ଵର ଥିଲା ଗମ୍ଭୀର । ସେ ଜଣେ ସୁନ୍ଦର କଳାକାର ଥିଲେ । ସେଇ ସମୟର ଚାକିରିର ଘୋର ଅଭାବ ଥିଲା, ତଥାପି ତାଙ୍କ ବାପା ସପ୍ତାହରେ ଚାଳିଶ ପାଉଣ୍ଡ ଅର୍ଜନ କରୁଥିଲେ ।‘ତାଙ୍କ ବାପା ଥିଲେ ମଦ୍ୟପ ଏବଂ ତାହା ତାଙ୍କ ପିତାମାତାଙ୍କ ବିବାହ ବିଚ୍ଛେଦର କାରଣ ହୋଇଥିଲା ।

ଚାପ୍‌ଲିନ୍ ତତ୍କାଳୀନ ମନୋରଞ୍ଜନକାରୀମାନଙ୍କ ଉପରେ ଆଲୋକପାତ କରିଛନ୍ତି । ସେମାନେ ମଦ୍ୟପ ଥିଲେ କାରଣ ସବୁ ଥୁଟରଗୁଡ଼ିକ ମଦ ବ୍ୟବସାୟ କରୁଥିଲେ । ମୋଟା ଦରମା ପାଉଥିବା ଯୋଗୁଁ ଅନେକ ତାରକା ଥୁଟର ମଦଶାଳାରେ ବହୁତ ସମୟ କଟାଉଥିଲେ । ଫଳରେ ଚାପୁଲିନ୍‌ଙ୍କର ବାପା କିଭଳି ଅନେକ କଳାକାର ଧ୍ଵଂସକୁ ଡାକି ଆଣିଥିଲେ । ସଇଁତିରିଶ ବର୍ଷ ବୟସରେ ତାଙ୍କର ବାପା ଅତ୍ୟଧ୍ଵ ମଦ୍ୟପାନର ଶିକାର ହୋଇ ମୃତ୍ୟୁବରଣ କରିଥିଲେ । ମଦ୍ୟପାନ ଅବସ୍ଥାରେ ସେ ଭୟଙ୍କର କୋପ ଦେଖାଉଥିଲେ । ତାଙ୍କ ବାପାଙ୍କ ପ୍ରତି ମା’ଙ୍କର ଦୃଷ୍ଟିଭଙ୍ଗୀରେ ବିରୋଧଭାବ ନ ଥିଲା । ବେଳେବେଳେ ଏହା ଥିଲା ଦୁଃଖ ଓ ସହାନୁଭୂତିର ମିଶ୍ରଣ ଥିଲା ।

ବିବାହ ବିଚ୍ଛେଦ ସତ୍ତ୍ବେ ମା’ ତାଙ୍କ ବାପାଙ୍କଠାରୁ ଭରଣପୋଷଣ ଦାବି କରି ନ ଥିଲେ ବୋଲି ଚାପଲିନ୍ କହିଛନ୍ତି । ଜଣେ ତାରକା ହିସାବରେ ନିଜ ପିଲାମାନଙ୍କୁ ଚଳାଇବାରେ ସେ କୌଣସି ଅସୁବିଧାର ସମ୍ମୁଖୀନ ହୋଇ ନ ଥିଲେ । କେବଳ ଘଡ଼ିସନ୍ଧି ମୁହୂର୍ତ୍ତରେ ସେ ସାହାଯ୍ୟ ଚାହୁଁଥିଲେ । ତାଙ୍କ ମା’ଙ୍କର କଣ୍ଠସ୍ଵର ଧୀରେ ଧୀରେ ଖରାପ ହୋଇଯାଉଥିବା କଥା ଚାପ୍‌ଲିନ୍ କହିଛନ୍ତି । ସାମାନ୍ୟ ଥଣ୍ଡା ତାଙ୍କର କଣ୍ଠକୁ ବହୁଦିନ ଧରି ଆକ୍ରାନ୍ତ କରୁଥିଲା; କିନ୍ତୁ ପରିସ୍ଥିତିର ତାଡ଼ନାରେ ତାଙ୍କୁ ଗୀତ ଗାଇବାକୁ ପଡ଼ୁଥିଲା । ଗୀତ ଗାଇଲାବେଳେ ତାଙ୍କ ସ୍ଵର ଭାଙ୍ଗି ପଡୁଥିଲା ଏବଂ ଗୀତ ଗାଇବା ମଝିରେ ଅସ୍ପଷ୍ଟ ହୋଇଯାଉଥିଲା । ଯାହାଫଳରେ ସେ ଶ୍ରୋତାମାନଙ୍କର ଅଟ୍ଟହାସ୍ୟର ଶିକାର ହେଉଥିଲେ । ଫଳରେ ତାଙ୍କ ସ୍ଵାସ୍ଥ୍ୟର ଅବନତି ଘଟିଲା । ସେ ଭୀତତ୍ରସ୍ତା ହୋଇଗଲେ । ଫଳସ୍ବରୂପ ତାଙ୍କୁ ଥୁଟରରେ କାମ ମିଳିବା କମିଯିବାକୁ ଲାଗିଲା । ମା’ଙ୍କ କଣ୍ଠସ୍ୱରର ଅବସ୍ଥା ଚାପ୍‌ଲିନ୍‌ଙ୍କୁ ପ୍ରଥମ ଥର ପାଇଁ ମଞ୍ଚ ଉପରକୁ ଆସିବାକୁ ବାଧ୍ୟ କରିଥିଲା ।

ସେତେବେଳକୁ ତାଙ୍କ ବୟସ ଥିଲା ପାଞ୍ଚ ବର୍ଷ । ସେତେବେଳେ ତାଙ୍କ ମା’ ଆଲଡର୍‌ସଟ୍‌ରେ ଥିବା ସୈନ୍ୟମାନଙ୍କର ମନୋରଞ୍ଜନ କରାଉଥିଲେ । ଏଇ ସୈନିକମାନେ ଅଭଦ୍ର ଥିଲେ । ସେମାନେ ମନୋରଞ୍ଜନକାରୀମାନଙ୍କୁ ଅପମାନ ଏବଂ ଥଟ୍ଟା କରିବାକୁ ଭୁଲୁ ନଥିଲେ । ଏକଦା ଚାପ୍‌ଲିନ୍ ମଞ୍ଚର ଏକ କୋଣରେ ଛିଡ଼ା ହୋଇଥିଲେ । ଏହି ସମୟରେ ତାଙ୍କ ମା’ଙ୍କର କଣ୍ଠସ୍ଵର ଭାଙ୍ଗିପଡ଼ିଲା ଓ ସ୍ଵର ଅସ୍ପଷ୍ଟ ହୋଇଗଲା। ଶ୍ରୋତାମାନେ ତାଙ୍କୁ ଥଟ୍ଟା କରିଥିଲେ । ସେମାନେ ହସିବା, ଗୀତ ଗାଇବା ଏବଂ ସିଟି ବଜାଇବାରେ ଲାଗିପଡ଼ିଲେ । ତା’ପରେ ତାଙ୍କ ମା’ ମଞ୍ଚ ଛାଡ଼ି ଚାଲିଯାଇଥିଲେ । ସେମାନଙ୍କର ବିଦ୍ରୁପ ସାମ୍‌ନାରେ ମୁଣ୍ଡ ନ ଝୁଙ୍କାଇ ପରିଚାଳକ ଚାପ୍‌ଲିନ୍‌ଙ୍କୁ ଏକୁଟିଆ ମଞ୍ଚ ଉପରେ ଛାଡ଼ିଦେଲେ । ଚାପ୍‌ଲିନ୍ କିଛି କମ୍ ନ ଥିଲେ । ସେ ଲୋକପ୍ରିୟ ଗୀତ Jack Jones ଗାଇଥିଲେ ।

ତାଙ୍କର ପ୍ରଥମ ଅଭିନୟକୁ ଶ୍ରୋତାମାନେ ଅବିଶ୍ବସନୀୟ ଭାବେ ପସନ୍ଦ କଲେ । ସେମାନେ ମଞ୍ଚ ଉପରକୁ ଟଙ୍କା ଫୋପାଡ଼ିବାକୁ ଲାଗିଲେ । ପ୍ରଥମେ ଟଙ୍କା ଗୋଟାଇବେ ଏବଂ ପରେ ଗୀତ ଗାଇବେ ବୋଲି ଚାପ୍‌ଲିନ୍ ଘୋଷଣା କଲେ । ଏଥିରେ ଶ୍ରୋତୃମଣ୍ଡଳୀ ଖୁସି ହୋଇଗଲେ । ମଞ୍ଚ ପରିଚାଳକ ସବୁ ଟଙ୍କା ଚାପ୍ଲିନ୍ ମା’ଙ୍କୁ ଦେଇଦେଲେ । ଏହାପରେ ଚାପ୍‌ଲିନ୍ ଶ୍ରୋତାମାନଙ୍କ ସହିତ ବାକ୍ୟାଳାପ କଲେ, ନାଚିଲେ ଏବଂ ଅନେକ ଗୀତ ଅନୁକରଣ କରି ଗାଇଲେ । ଏହା ମଧ୍ୟରେ ତାଙ୍କ ମା’ଙ୍କର Irish march ଗୀତକୁ ତାଙ୍କର ଭଗ୍ନ କଣ୍ଠସ୍ଵର ଅନୁକରଣ କରି ଗାଇବା ସମସ୍ତଙ୍କୁ ପ୍ରଭାବିତ କରିଥିଲା । ସେମାନେ ମଞ୍ଚ ଉପରକୁ ଟଙ୍କା ଫୋପାଡ଼ିବାକୁ ଲାଗିଲେ । ମଞ୍ଚ ଉପରେ ତାଙ୍କ ମା’ଙ୍କର ଉପସ୍ଥିତିର ଦୃଶ୍ୟ ଚମତ୍କାର ଥିଲା । ଶ୍ରୋତାମାନେ ତାଙ୍କର ଭୂୟସୀ ପ୍ରଶଂସା କଲେ । ସେଇ ରାତି ପରଦା ଉପରେ ଚାପ୍‌ଲିନ୍‌ଙ୍କର ପ୍ରଥମ ଏବଂ ମା’ଙ୍କର ଶେଷ ଉପସ୍ଥିତିର ସାକ୍ଷୀ ଥିଲା ।

ଚାପ୍‌ଲିନ୍ କହିଛନ୍ତି ଯେ ଭାଗ୍ୟ ମଣିଷର ଗତିପଥ ନିର୍ଦ୍ଧାରଣ କରେ । ଏହା ପାଖରେ ଦୟା ବା ନ୍ୟାୟର ସ୍ଥାନ ନ ଥାଏ । ତାଙ୍କର ମା’ ନିଷ୍ଠୁର ଭାଗ୍ୟର ଶିକାର ହୋଇଗଲେ । ସେ ତାଙ୍କର ସ୍ଵର ଆଉ ଫେରିପାଇଲେ ନାହିଁ । ତାଙ୍କ ମା’ ସଞ୍ଚୟ କରିଥିବା ସ୍ଵଚ୍ଛ ଟଙ୍କା, ଗହଣା ଏବଂ ଅନ୍ୟ ଜିନିଷଗୁଡ଼ାକର ବନ୍ଧକ ରଖି ଜୀବିକା ନିର୍ବାହ କଲେ । ସବୁକିଛି ଅଳ୍ପଦିନ ମଧ୍ୟରେ ସରିଗଲା । ସେ ସବୁବେଳେ ଆଶା କରୁଥିଲେ ତାଙ୍କର କଣ୍ଠସ୍ଵର ଫେରିଆସିବ, କିନ୍ତୁ ଏହା ଥିଲା ଦୀ ଆଶା । ତାଙ୍କ ମା’ ମଞ୍ଚ ଛାଡ଼ିଲା ପରେ ଚାପ୍‌ଲିନ୍ ଏବଂ ସେ ବହୁତ ଅସୁବିଧାର ସମ୍ମୁଖୀନ ହୋଇଥିଲେ । ତାଙ୍କ କଣ୍ଠସ୍ବର ପୁନଶ୍ଚ ଫେରି ପାଇବା ଆଶାରେ ସେ ଧର୍ମର ଆଶ୍ରୟ ନେଇଥିଲେ । ସେ ପ୍ରତିଦିନ ଗୀର୍ଜାକୁ ଯାଉଥିଲେ । ସମ୍ମାନନୀୟ ଧର୍ମଯାଜକଙ୍କର ଜୀବନ୍ତ ଏବଂ ନାଟକୀୟ ସ୍ବରରେ ଗୀର୍ଜାର ଲମ୍ବା ମଧ୍ୟଭାଗ ପ୍ରତିଧ୍ଵନିତ ହେଉଥିଲା । ବେଳେବେଳେ ତାଙ୍କର ଭାଷଣ ମା’ଙ୍କ ଆସ୍‌ରେ ଲୁହ ଭରି ଦେଉଥିଲା । ଗ୍ରୀଷ୍ମଦିନର ଏକ ପବିତ୍ର ସମାବେଶକୁ ଲେଖକ ମନେ ପକାଇଛନ୍ତି । ସମସ୍ତଙ୍କୁ ଥଣ୍ଡା ରୁପ କମ୍‌ରେ ସୁସ୍ୱାଦୁ ଫାଙ୍ଗୁର ରସ ପିଇବାକୁ ଦିଆଯାଇଥିଲା । ଯେତେବେଳେ ଧର୍ମଯାଜକ ବାଇବେଲ ବନ୍ଦ କରୁଥିଲେ, ତାହା ଧର୍ମଶିକ୍ଷା ସମାପ୍ତି ଓ ଧର୍ମ ସଙ୍ଗୀତ ଆରମ୍ଭ ହେବାର ସୂଚନା ଦେଉଥିଲା ।

ଦିନ ଗଡ଼ି ଚାଲିଲା । ମା’ଙ୍କର ଥାଏଟର ସମ୍ବନ୍ଧୀୟ ଦୁନିଆ ଅତୀତ ହୋଇଗଲା । ଅନ୍ୟ କ୍ଷେତ୍ରରେ ତାଙ୍କ ଅଭିଜ୍ଞତାର ଅଭାବ ନୂଆ କାମ ମିଳିବାପାଇଁ ଏକ ପ୍ରତିବନ୍ଧକ ଥିଲା । ଅବ୍ୟକ୍ତ ବେଦନା ସତ୍ତ୍ଵେ ତାଙ୍କ ମା’ ସଂଗ୍ରାମ ଜାରି ରଖିଲେ । ଭିକ୍ଟୋରିଆ ଯୁଗର ଦାରିଦ୍ର୍ୟ ପ୍ରପୀଡ଼ିତା ସ୍ତ୍ରୀ ଲୋକମାନଙ୍କୁ ଛୋଟ କାମ କରିବାକୁ ପଡୁଥିଲା । ବେଳେବେଳେ ସେ ଧାଈର ଭୂମିକା ଗ୍ରହଣ କରୁଥିଲେ । କିନ୍ତୁ ଏହା କ୍ଷଣସ୍ଥାୟୀ ଥିଲା । ଏଇସବୁ ଦୟନୀୟ ଅବସ୍ଥା ସତ୍ତ୍ବେ ମା’ ହତୋତ୍ସାହ ହୋଇ ଯାଇନଥିଲେ । ସେ ଛୁଞ୍ଚ୍ କାମରେ ନିପୁଣା ଥିଲେ । ଗୀର୍ଜାର ସଦସ୍ୟମାନଙ୍କ ପାଇଁ ସେ ପୋଷାକ ତିଆରି କରୁଥିଲେ । କିନ୍ତୁ ସେମାନଙ୍କ ଭରଣପୋଷଣ ପାଇଁ ଏହା ଯଥେଷ୍ଟ ନଥିଲା ।

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CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h)

Odisha State Board Elements of Mathematics Class 12 Solutions CHSE Odisha Chapter 9 Integration Ex 9(h) Textbook Exercise questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Exercise 9(h)

Evaluate the following Integrals.
Question 1.
(i) ∫\(\frac{d x}{4+5 \cos x}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.1(1)

(ii) ∫\(\frac{d x}{3+\cos x}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.1(2)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h)

(iii) ∫\(\frac{d x}{3+\sin x}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.1(3)

(iv) ∫\(\frac{d x}{1+2 \sin x}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.1(4)

(v) ∫\(\frac{d x}{2 \sin x+3 \cos x}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.1(5)

BSE Odisha

(vi) ∫\(\frac{d x}{1+\cos x+\sin x}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.1(6)

Question 2.
(i) ∫\(\frac{3 \sin x+28 \cos x}{5 \sin x+6 \cos x}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.2(1)

(ii) ∫\(\frac{12 \sin x-2 \cos x+3}{\sin x+\cos x}\) dx
Solution:
Let 12 sin x – 2 cos x = A (sin x + cos x) + B ( cos x – sin x)
[Note that cos x – sin x is the derivative of sin x + cos x]
Then A – B = 12, A + B = -2
⇒ 2A = 10
⇒ A = 5, B = -7
Thus 12 sin x – 2 cos x = 5 (sin x + cos x) – 7 (cos x – sin x)
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.2(2)

(iii) ∫\(\frac{5 \sin x}{3-2 \sin x}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.2(3)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h)

(iv) ∫\(\frac{2 \cos x+7}{4-\sin x}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.2(4)
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.2(4.1)

Question 3.
(i) ∫\(\frac{d x}{2 \cos ^2 x+3 \cos x}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.3(1)

(ii) ∫\(\frac{d x}{4 \sin ^2 x-\sin x}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.3(2)
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.3(2.1)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h)

(iii) ∫\(\frac{\sin x \cos x}{x \sin ^2 x-2 \sin x+3}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.3(3)

(iv) ∫\(\frac{d x}{\cos x-\cos 3 x}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.3(4)

Question 4.
(i) ∫\(\frac{d \theta}{4+3 \sin ^2 \theta}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.4(1)

(ii) ∫\(\frac{d \theta}{2-3 \cos ^2 \theta}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.4(2)

(iii) ∫\(\frac{d \theta}{4 \cos ^2 \theta+9 \sin ^2 \theta}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.4(3)

(iv) ∫\(\frac{d \theta}{2+3 \cos ^2 \theta-4 \sin ^2 \theta}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.4(4)

Question 5.
(i) ∫\(\frac{\sin 3 x}{\cos 7 x \cos 4 x}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.5(1)

(ii) ∫\(\frac{\cos 2 x}{\sin 7 x \cos 5 x}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.5(2)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h)

Question 6.
(i) ∫\(\frac{d x}{\cos x(5+3 \cos x)}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.6(1)

(ii) ∫\(\frac{d x}{\cos x(1+2 \sin x)}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(h) Q.6(2)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g)

Odisha State Board Elements of Mathematics Class 12 Solutions CHSE Odisha Chapter 9 Integration Ex 9(g) Textbook Exercise questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Exercise 9(g)

Evaluate the following Integrals.
Question 1.
(i) ∫\(\frac{\sqrt{2 x+3}}{x}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.1(1)

(ii) ∫\(\frac{\sqrt{x^2-7}}{x}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.1(2)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g)

(iii) ∫\(\frac{\sqrt{x}}{x+2}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.1(3)

(iv) ∫x\((3 x+2)^{\frac{1}{3}}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.1(4)

(v) ∫\(\frac{x+2}{(2 x-1)^{\frac{1}{3}}}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.1(5)

(vi) ∫(x + 2)\((x+1)^{\frac{1}{4}}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.1(6)

(vii) ∫\(\frac{x-1}{(x+2)^{\frac{3}{4}}}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.1(7)

(viii) ∫\(\frac{d x}{\sqrt{x}-\sqrt[3]{x}}\) (x = t6)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.1(8)

Question 2.
(i) ∫\(\frac{3 x+4}{\sqrt{2 x-3}}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.2(1)

(ii) ∫(7x + 4)\(\sqrt{3 x+2}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.2(2)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g)

(iii) ∫(3x + 1)\((x-2)^{\frac{9}{2}}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.2(3)

(iv) ∫\(\frac{2 x+5}{(x+2)^{\frac{7}{2}}}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.2(4)

(v) ∫\(\frac{x^2+2 x+1}{\sqrt{x+4}}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.2(5)

(vi) ∫(x2 + 2x + 7)\(\sqrt{x+1}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.2(6)

Question 3.
(i) ∫\(\frac{d x}{\sqrt{4 x^2-4 x+5}}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.3(1)

(ii) ∫\(\sqrt{4 x^2-4 x+5}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.3(2)

(iii) ∫\(\frac{d x}{\sqrt{x^2-6 x+5}}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.3(3)

(iv) ∫\(\sqrt{x^2-6 x+5}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.3(4)

(v) ∫\(\frac{d x}{\sqrt{1+2 x-x^2}}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.3(5)

(vi) ∫\(\sqrt{1+2 x-x^2}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.3(6)

Question 4.
(i) ∫\(\frac{d x}{(1+x) \sqrt{1-x^2}}\) (1 + x = \(\frac{1}{t}\))
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.4(1)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g)

(ii) ∫\(\frac{d x}{(2-x) \sqrt{5-4 x+x^2}}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.4(2)

Question 5.
(i) ∫\(\frac{d x}{(2 x+5) \sqrt{x+2}}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.5(1)

(ii) ∫\(\frac{1+x^2}{x \sqrt{x^4+1}}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.5(2)

(iii) ∫\(\sqrt{\frac{x-1}{2 x+1}}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.5(3)

(iv) ∫\(\frac{x}{\left(a^2-x^2\right)\left(x^2-b^2\right)}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(g) Q.5(4)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f)

Odisha State Board Elements of Mathematics Class 12 Solutions CHSE Odisha Chapter 9 Integration Ex 9(f) Textbook Exercise questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Exercise 9(f)

Evaluate the following Integrals.
Question 1.
(i) ∫\(\frac{4 x-9}{x^2-5 x+6}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.1(1)

(ii) ∫\(\frac{3 x}{(x-4)(x+2)}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.1(2)

(iii) ∫\(\frac{5 x-12}{(2 x-3)(x-6)}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.1(3)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f)

(iv) ∫\(\frac{20 x+3}{6 x^2-x-2}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.1(4)

(v) ∫\(\frac{2 x^2}{(x-1)(x-2)(x-3)}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.1(5)

(vi) ∫\(\frac{12 x^4-2 x^3-4 x^2+x-3}{6 x^2-x-2}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.1(6)

Question 2.
(i) ∫\(\frac{2 x+9}{(x+3)^2}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.2(1)

(ii) ∫\(\frac{5 x^2+4 x+4}{(x+2)(x+2)^2}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.2(2)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f)

(iii) ∫\(\frac{x^2+7 x+4}{x^3+x^2-x-1}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.2(3)

(iv) ∫\(\frac{x^4+3 x^3+x^2-1}{x^3+x^2-x-1}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.2(4)

Question 3.
(i) ∫\(\frac{4 x^2-x+3}{\left(x^2+1\right)(x-1)}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.3(1)

(ii) ∫\(\frac{5 x}{\left(x^2-2 x+2\right)(x+1)}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.3(2)

(iii) ∫\(\frac{3}{x^3-1}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.3(3)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f)

(iv) ∫\(\frac{x^5+x^4+x^3+x^2+4 x+1}{x^3+1}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.3(4)
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.3(4.1)

Question 4.
(i) ∫\(\frac{d x}{x^2-5}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.4(1)

(ii) ∫\(\frac{d x}{2 x^2+8 x+7}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.4(2)

(iii) ∫\(\frac{x+3}{2 x^2+8 x+7}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.4(3)

(iv) ∫\(\frac{4 x^2+20 x+25}{2 x^2+8 x+7}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.4(4)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f)

(v) ∫\(\frac{e^x}{e^{2 x}+3 e^x+1}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.4(5)

(vi) ∫\(\frac{\tan ^2 \theta+1}{\tan ^2 \theta-1}\) dθ
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.4(6)

Question 5.
(i) ∫\(\frac{d x}{3-x^2}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.5(1)

(ii) ∫\(\frac{d x}{7-x^2+6 x}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.5(2)

(iii) ∫\(\frac{x-5}{7-x^2+6 x}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.5(3)

(iv) ∫\(\frac{\cos \theta}{3-\sin ^2 \theta}\) dθ
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.5(4)

(v) ∫\(\frac{x^2 d x}{\left(x^2+3\right)\left(x^2+2\right)}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.5(5)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f)

(vi) ∫\(\frac{x^3 d x}{x^4+3 x^2+2}\) (Put x2 = t)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.5(6)

(vii) ∫\(\frac{d x}{\sin x(3+2 \cos x)}\) (Put cos x = z)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(f) Q.5(7)

BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c)

Odisha State Board BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) Textbook Exercise Questions and Answers.

BSE Odisha Class 9 Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c)

Question 1.
ନିମ୍ନଲିଖ ଉକ୍ତିଗୁଡ଼ିକ ଠିକ୍ ବା ଭୁଲ ଲେଖ ।
(a) L1 || L2 L2 || L3 ହେଲେ L1 || L3
ସମାଧାନ:
ଠିକ୍

(b) L1 ⊥ ଓ L2 ⊥ L3 ହେଲେ L1 ⊥ L3
ସମାଧାନ:
ଭୁଲ

(c)  L1 = L2 ହେଲେ L1 || L2
ସୂଚନା : L1 = L2 ର ଅର୍ଥ ହେଉଛି L1 ଓ L2 ରେଖା ଏକ ଅଭିନ୍ନ ।
ସମାନ୍ତର ସରଳରେଖା ସଂଜ୍ଞା ବ୍ୟବହାର କର ।
ସମାଧାନ:
ଠିକ୍

(d) ଦୁଇଟି ସମାନ୍ତର ସରଳରେଖା ଏକ ସମତଳରେ ଅବସ୍ଥିତ ।
ସମାଧାନ:
ଭୁଲ

(e) ∠ABC ଓ ∠DEF ମଧ୍ୟରେ \(\overleftrightarrow{\mathbf{AB}}\) || \(\overleftrightarrow{\mathbf{ED}}\) ଓ \(\overleftrightarrow{\mathbf{BC}}\) || \(\overleftrightarrow{\mathbf{EF}}\) ହେଲେ m∠ABC = m∠DEF ହେବ ।
ସମାଧାନ:
ଠିକ୍

BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c)

Question 2.
ପାର୍ଶ୍ୱସ୍ଥ ଚିତ୍ରରେ L1 || L2 ଓ L3 ସେମାନଙ୍କର ଛେଦକ । ଛେଦବିନ୍ଦୁରେ ଉତ୍ପନ୍ନ କୋଣଗୁଡ଼ିକ 1, 2, 3 …. 8 ସଂଖ୍ୟା ଦ୍ଵାରା ଚିହ୍ନିତ । m∠3 = 65° ହେଲେ, ଅନ୍ୟ କୋଣଗୁଡ଼ିକର ପରିମାଣ ସ୍ଥିର କର ।
ସମାଧାନ:
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 1
ପାର୍ଶ୍ୱସ୍ଥ ଚିତ୍ରରେ L1 || L2 ଓ L3 ଛେଦକ ।
m∠3 = 65° (ଦତ୍ତ)
∴ m∠3 + m∠1 = 180° (ସନ୍ନିହିତ ପରିପୂରକ)
⇒ m∠1 = 180° – m∠3 = 180° – 65° = 115°
m∠1 = m∠4 (ପ୍ରତୀପ କୋଣ) ⇒ m∠4 = 115°
m∠3 = m∠2 (ପ୍ରତୀପ କୋଣ) ⇒ m∠2 = 65°
m∠4 = m∠5 (ଏକାନ୍ତର କୋଣ) ⇒ m∠5 = 115°
m∠5 = m∠8 (ପ୍ରତୀପ କୋଣ) ⇒ m∠8 = 115°
m∠4 = m∠7 (ଏକାନ୍ତର କୋଣ) ⇒ m∠7 = 1 15°
m∠7 = m∠6 (ପ୍ରତୀପ କୋଣ) ⇒ m∠6 = 65°
∴ m∠1 = m∠4 = m∠5 = m∠8 = 115° ଏବଂ m∠2 = m∠3 = m∠6 = m∠7 = 65°

Question 3.
ପାର୍ଶ୍ୱସ୍ଥ ଚିତ୍ରରେ L1 || L2 ଏବଂ L3 || L4 ଚିତ୍ରରୁ ନିମ୍ନଲିଖ କୋଣଗୁଡ଼ିକର ପରିମାଣ ସ୍ଥିର କରି ଶୂନ୍ୟସ୍ଥାନଗୁଡ଼ିକୁ ପୂରଣ କର ।
m∠x = ________, m∠z = ________
m∠p = ________, m∠q = ________
m∠r = ________, m∠s = ________
ସମାଧାନ:
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 2
ପାର୍ଶ୍ୱସ୍ଥ ଚିତ୍ରରେ L1 || L2 ଓ L3 || L4
m∠x = 60°, m∠z = 60° (ଅନୁପୂରକ)
m∠p = 60° = m∠z, m∠z = m∠q = 120° (ପରସ୍ପର ପରିପୂରକ)
m∠r = 120° (ପ୍ରତୀପ), m∠s = 120° ( ∠x ଓ ∠r ପରସ୍ପର ପରିପୂରକ)

Question 4.
ପାର୍ଶ୍ୱସ୍ଥ ଚିତ୍ରରେ L1 || L2 । ଚିତ୍ରକୁ ବ୍ୟବହାର କରି a, b, c, d ଦ୍ଵାରା ଚିହ୍ନିତ କୋଣଗୁଡ଼ିକର ପରିମାଣ ସ୍ଥିର କର ।
ସମାଧାନ:
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 3
ପାର୍ଶ୍ୱସ୍ଥ ଚିତ୍ରରେ L1 || L2
m∠a = 75° (ପ୍ରତୀପ କୋଣ)
m∠b = 130° (ପ୍ରତୀପ କୋଣ)
m∠b = m∠c = 130° (ଅନୁପୂରକ କୋଣ)
m∠a = m∠d = 75° (ଅନୁପୂରକ କୋଣ)

BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c)

Question 5.
ପାର୍ଶ୍ୱସ୍ଥ ଚିତ୍ରରେ AB || CD ଏବଂ AD || BC । ଚିତ୍ରରୁ x, y, z ର ମାନ ସ୍ଥିର କର ।
ସମାଧାନ:
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 4
ଦତ୍ତ ଚିତ୍ରରେ AB || CD, AD || BC ଏବଂ m∠B = 48° ।
mB + mC = 180° ( AB || CD)
⇒ 48° + mx – 180° ⇒ x = 180° – 48° = 132°
ସେ୍ହିପରି mC + mD = 180° ( AD || BC)
⇒ x + y = 1 80°
⇒ 132 + y = 180° ⇒ y = 180° – 132° = 48°
ପୁନଣ୍ଚ mD + mA = 180° ( AB || CD)
⇒ y + z = 180°
⇒ 48 + z = 180°
⇒ z = 180° – 48° = 132°
x = 132°, y = 48°, z = 132°

Question 6.
ପାର୍ଶ୍ୱସ୍ଥ ଚିତ୍ରରେ PQ || RS \(\overleftrightarrow{\mathbf{RS}}\) କୁ \(\overleftrightarrow{\mathbf{BN}}\) C ବିନ୍ଦୁରେ ଛେଦ କରେ । ଚିତ୍ରରୁ x ଓ y ର ମାନ ସ୍ଥିର କର ।
ସମାଧାନ:
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 5
ଦତ୍ତ ଚିତ୍ରରେ m∠ACN + m∠ACB = 180° (ସନ୍ନିହିତ ପରିପୂରକ କୋଣ) 
m∠PBC = m∠ACN = 130° (ଅନୁଗୁପ)
∴ mACB = 180° – 130° = 50°
\(\overleftrightarrow{\mathbf{PQ}}\) || \(\overleftrightarrow{\mathbf{RS}}\)
⇒ mACB = mCBQ = 50° = y (ଏକାନ୍ତର କୋଣ)
mABP = mPBC – mABC = 130° – 55° = 75°
∴ mCAB = mABP (ଏକାନ୍ତର)
∴ x = 75°
∴ x = 75° ଓ y = 50°

BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c)

Question 7.
ଚିତ୍ରରେ ପ୍ରତ୍ୟେକ ଚିତ୍ର ଦୁଇଯୋଡ଼ା ସମାନ୍ତର ରେଖାଦ୍ଵାରା ଗଠିତ ଏବଂ ପ୍ରତ୍ୟେକ ଚିତ୍ରରେ ଦୁଇଟି କୋଣର ପରିମାଣ ସଂକେତରେ ଦର୍ଶାଯାଇଛି ।
(i) ଚିତ୍ର (a) ରୁ x ଓ y ମଧ୍ଯରେ ସମ୍ବନ୍ଧ ସ୍ଥିର କର ।
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 6
ସମାଧାନ:
ଦତ୍ତ ଚିତ୍ରରେ \(\overleftrightarrow{\mathbf{AB}}\) || \(\overleftrightarrow{\mathbf{CD}}\) ଓ \(\overleftrightarrow{\mathbf{PQ}}\) || \(\overleftrightarrow{\mathbf{ST}}\)
ଚିତ୍ର (a) ରୁ m∠x + m∠CQP = 180° ( \(\overleftrightarrow{\mathbf{AB}}\) || \(\overleftrightarrow{\mathbf{CD}}\))
ସେ୍ହିପରି m∠CQP = m∠QRS (ଅନୁଗୁପ କୋଣ) ( \(\overleftrightarrow{\mathbf{PQ}}\) || \(\overleftrightarrow{\mathbf{ST}}\))
m∠APQ = m∠PQR (ଏକାନ୍ତର କୋଣ) = x
∴ m∠x + m∠QRS = 180° ( \(\overleftrightarrow{\mathbf{PQ}}\) || \(\overleftrightarrow{\mathbf{ST}}\))
ମାତ୍ର m∠y + m∠QRS = 180°
∴ m∠x + m∠QRS = m∠y + m∠QRS
⇒ m∠x – m∠y
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 8

(ii) ଚିତ୍ର (b) ରୁ a ଓ b ମଧ୍ୟରେ ସମ୍ବନ୍ଧ ସ୍ଥିର କର ।
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 7
ସମାଧାନ:
ଦତ୍ତ ଚିତ୍ରରେ \(\overleftrightarrow{\mathbf{AB}}\) || \(\overleftrightarrow{\mathbf{CD}}\) ଓ \(\overleftrightarrow{\mathbf{PT}}\) || \(\overleftrightarrow{\mathbf{RS}}\)
⇒ m∠QPB = m∠TQR = a° (ଅନୁଗୁପ କୋଣ)
ଏବଂ ∠TQR + m∠SRQ = 180° (ସନ୍ନିହିତ ପରିପୂରକ)
⇒ m∠a + m∠b = 180°
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 9

Question 8.
(i) ପାର୍ଶ୍ୱସ୍ଥ ଚିତ୍ରରେ m∠ABC = 74°, m∠EDC = 38° ଓ m∠BCD = 36° । ପ୍ରମାଣ କର ଯେ, \(\overrightarrow{\mathrm{DE}}\) || \(\overrightarrow{\mathrm{BA}}\) ।
ସମାଧାନ:
ଦତ୍ତ : ଦତ୍ତ ଚିତ୍ରରେ m∠ABC = 74°, m∠EDC = 38° ଓ m∠BCD = 36° ।
ପ୍ରାମାଣ୍ୟ : \(\overrightarrow{\mathrm{DE}}\) || \(\overrightarrow{\mathrm{BA}}\)
ପ୍ରମାଣ : ΔCDF ରେ ବତ୍ହିଃସ୍ଥ m∠EFC = m∠FDC + m∠FCD = 38° + 36° = 74°
m∠ABF = 74°
∴ m∠ABF = m∠EFC = 74°
ତେଣୁ ଏମାନେ ଅନୁରୂପ । ⇒ \(\overleftrightarrow{\mathbf{DE}}\) || \(\overleftrightarrow{\mathbf{BA}}\) (ପ୍ରମାଣିତ)
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 10

(ii) ପାର୍ଶ୍ୱସ୍ଥ ଚିତ୍ରରେ m∠ABC = 60°, m∠EDC = 38° ଏବଂ \(\overrightarrow{\mathrm{DE}}\) || \(\overrightarrow{\mathrm{BA}}\) । ହେଲେ ଦର୍ଶାଅ ଯେ m∠BCD = 22° ।
ସମାଧାନ:
ଦତ୍ତ : ଦତ୍ତ ଚିତ୍ରରେ m∠ABC = 60°, m∠EDC = 38° ଓ \(\overrightarrow{\mathrm{DE}}\) || \(\overrightarrow{\mathrm{BA}}\) ।
ପ୍ରାମାଣ୍ୟ : mBCD = 22°
ପ୍ରମାଣ : \(\overrightarrow{\mathrm{DE}}\) || \(\overrightarrow{\mathrm{BA}}\)
mABF = mEFC = 60° (ଅନୁଗୁପ କୋଣ)
ΔCDF ରେ ବତ୍ହିଃସ୍ଥ mEFC = 60°
mFCD = 60° – 38° = 22°
m∠BCD ର ପରିମାଣ 22° ।
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 11

Question 9.
(i) ପାର୍ଶ୍ୱସ୍ଥ ଚିତ୍ରରେ ∠ACD ର ସମଦ୍ବିଖଣ୍ଡକ \(\overrightarrow{\mathrm{CE}}\)
ଏବଂ AB ସହ ସମାନ୍ତର ହେଲେ, ପ୍ରମାଣ କର ଯେ, m∠A = m∠B ।
ସମାଧାନ:
ଦତ୍ତ : \(\overrightarrow{\mathrm{CE}}\) || AB ଓ \(\overrightarrow{\mathrm{CE}}\), ∠ACD ର ସମଦ୍ବିଖଣ୍ଡକ । 
ପ୍ରାମାଣ୍ୟ : m∠A = m∠B
ପ୍ରମାଣ : AB || \(\overrightarrow{\mathrm{CE}}\) ଏବଂ AC ଛେଦକ ।
⇒ m∠A = m∠ACE (ଏକାନ୍ତର କୋଣ)
ସେହିପରି AB || \(\overrightarrow{\mathrm{CE}}\) ଏବଂ BD ଛେଦକ ।
⇒ m∠ABC = m∠ECD (ଅନୁରୂପ କୋଣ)
ମାତ୍ର mACE = mECD (ଦତ୍ତ)
ସମୀକରଣ (i) ଓ ସମୀକରଣ (ii) ରୁ m∠A = m∠ABC
mA = mB
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 12 (ପ୍ରମାଣିତ)

(ii) ପାର୍ଶ୍ୱସ୍ଥ ଚିତ୍ରରେ \(\overrightarrow{\mathrm{CE}}\) || AB, m∠ECD = 70° ଏବଂ 
m∠A = 50° ହେଲେ ଦର୍ଶାଅ ଯେ, m∠ACB = 60° ।
ସମାଧାନ:
ଦତ୍ତ : ଦତ୍ତ ଚିତ୍ରରେ \(\overrightarrow{\mathrm{CE}}\) || AB, m∠ECD = 70° ଓ mZA = 50° ।
ପ୍ରାମାଣ୍ୟ : mACB = 60°
ପ୍ରମାଣ : \(\overrightarrow{\mathrm{CE}}\) || AB, BD ଛେଦକ ।
⇒ mECD = mABC = 70° (ଅନୁରୂପ କୋଣ)
ପୁନଶ୍ଚ mA = mACE = 50°
mACD = mACE + mECD = 50° + 70° = 120°
କିନ୍ତୁ ACB ACD ସନ୍ନିହିତ ପରିପୂରକ
∴ mACB = 180° – 120° = 60°
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 13 (ପ୍ରମାଣିତ)

BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c)

Question 10.
ପାର୍ଶ୍ୱସ୍ଥ ଚିତ୍ରରେ L1 || L2 ଓ L1, L2 ର ଛେଦକ L3
(i) m∠2 = 2m∠1 ହେଲେ, ∠1 ଓ ∠2 ର ପରିମାଣ ସ୍ଥିର କର । 
ସମାଧାନ:
ଦତ୍ତ : L1 || L2 L3 ଛେଦକ m2 = 2m∠1
ନିଶ୍ଚେୟ : ∠1 ଓ ∠2 ର ପରିମାଣ ।
m∠1 = m∠3 (ପ୍ରତୀପ)
m2 + m3 = 180° (ଛେଦକର ଏକ ପାର୍ଶ୍ଵସ୍ଥ ଅନ୍ତରସ୍ଥ କୋଣ)
⇒ 2m∠1 + m∠1 = 180° ( m2 = 2m∠1)
⇒ 3m∠1 = 180°
∠1 = \(\frac{180°}{3}\) = 60°
⇒ m2 = 2m∠1 = 2 × 60° = 120°
∴ m∠1 = 60° m2 = 120°
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 14

(ii) m∠2 = 3m∠1 ହେଲେ, ∠1 ଓ ∠2 ର ପରିମାଣ ସ୍ଥିର କର । 
ସମାଧାନ:
ଦତ୍ତ : ଦତ୍ତ ଚିତ୍ରରେ m∠2 = 3m∠1
ନିଶ୍ଚେୟ : ∠1 ଓ ∠2 ର ପରିମାଣ ।
m∠1 = m∠3 (ପ୍ରତୀପ)
m2 + m3 = 180° (ଛେଦକର ଏକ ପାର୍ଶ୍ଵସ୍ଥ ଅନ୍ତରସ୍ଥ କୋଣ)
31 + 1 = 180° ( m2 = 3m∠1)
41 = 180°
⇒ ∠1 = \(\frac{180°}{4}\) = 45°
⇒ ∠2 = 3m∠1 = 45° × 3 = 135°
∴ ∠1 = 45° 2 = 135°
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 15

(iii) m∠1 : m∠2 = 2 : 3 ହେଲେ, ∠1 ଓ ∠2 ର ପରିମାଣ ସ୍ଥିର କର ।
ସମାଧାନ:
ଦତ୍ତ : m∠1 : m∠2 = 2 : 3
ନିଶ୍ଚେୟ : ∠1 ଓ ∠2 ର ପରିମାଣ ।
ମକେତେ m1 = 2x° ଓ m∠2 = 3x°
m∠1 = m3 (ପ୍ରତୀପ)
m2 + m3 = 180° (ଛେଦକର ଏକ ପାର୍ଶ୍ଵସ୍ଥ ଅନ୍ତରସ୍ଥ କୋଣ)
⇒ 3x + 2x = 180°
⇒ 5x = 180°
⇒ x = \(\frac{180°}{5}\) = 36°
∴ m1 = 2x = 2 × 36° = 72°
m2 = 3x = 3 × 36° = 108°
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 16

Question 11.
ପାର୍ଶ୍ୱସ୍ଥ ଚିତ୍ରରେ L1 || L2 | L3 ଛେଦକ L1 ଓ L2 ସରଳ ରେ ଖାଦ୍ୟକୁ ଯଥାକ୍ରମେ A ଓ C ବିନ୍ଦୁରେ ଛେଦକରେ । ∠BACର ସମଦ୍ଵିଖଣ୍ଡକ ଓ ∠ACDର ସମଦ୍ବିଖଣ୍ଡକ ପରସ୍ପରକୁ O ବିନ୍ଦୁରେ ଛେଦକରନ୍ତି । ଦର୍ଶାଅ ଯେ, ∠AOC = 90° ।
ସମାଧାନ:
ଦତ୍ତ : L1 || L2 ଓ L3 ଛେଦକ । 
AO, ∠Aର ସମଦ୍ବିଖଣ୍ଡକ ଓ CO, ∠Cର ସମଦ୍ବିଖଣ୍ଡକ ।
ପ୍ରାମାଣ୍ୟ : m∠AOC = 90° 
ପ୍ରମାଣ : mA + mC = 180° (ଛେଦକର ଏକ ପାର୍ଶ୍ଵସ୍ଥ ଅନ୍ତରସ୍ଥ କୋଣର ସମଷ୍ଟି 180°)
⇒ mOAC + 2mOCA = 180° (AO, ∠BACର ସମଦ୍ବିଖଣ୍ଡକ ଓ CO, ∠ACD ର ସମଦ୍ବିଖଣ୍ଡକ)
⇒ mOAC + mOCA = \(\frac{180°}{2}\) = 90°
ΔAOC ରେ m∠OAC + m∠OCA + m∠AOC = 180°
⇒ 90° + mAOC = 180°
⇒ mAOC = 180° – 90° = 90°
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 17 (ପ୍ରମାଣିତ)

Question 12.
(i) ପାର୍ଶ୍ୱସ୍ଥ ଚିତ୍ରରେ \(\overleftrightarrow{\mathbf{AB}}\) || \(\overleftrightarrow{\mathbf{CD}}\), m∠OAB = 135°, m∠OCD = 145° ହେଲେ ∠AOCର ପରିମାଣ ସ୍ଥିର କର ।
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 18
ସମାଧାନ:
ଦତ୍ତ : \(\overleftrightarrow{\mathbf{AB}}\) || \(\overleftrightarrow{\mathbf{CD}}\), m∠OAB = 35° m∠OCD = 145°
ନିର୍ଦେୟ : ∠AOCର ପରିମାଣ ।
ଅଙ୍କନ : O ବିନ୍ଦୁରେ \(\overrightarrow{\mathrm{OE}}\) || \(\overrightarrow{\mathrm{AB}}\) ଅଙ୍କନ କର ।
ପ୍ରମାଣ : \(\overrightarrow{\mathrm{AB}}\) || \(\overrightarrow{\mathrm{OE}}\)
⇒ mBAO + mAOE = 180°
⇒ mAOE = 180° – mBAO
= 180° – 105° = 45° ( mBAO = 135°)
ସେହିପରି \(\overrightarrow{\mathrm{OE}}\) || \(\overrightarrow{\mathrm{CD}}\) (\(\overrightarrow{\mathrm{AB}}\)  || \(\overrightarrow{\mathrm{CD}}\))
⇒ mOCD + mEOC = 180°
⇒ mEOC = 180° – mOCD
⇒ mEOC = 180° – 145° = 35°
∴ mAOC = mAOE + mCOE = 45° + 35° = 80°
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 19

(ii) ପାର୍ଶ୍ୱ ସ୍ଥ ଚିତ୍ରରେ \(\overleftrightarrow{\mathbf{XB}}\) || \(\overleftrightarrow{\mathbf{YD}}\), mXAO = 60°, mYCO = 70° ହେଲେ ଦର୍ଶାଅ ଯେ mAOC = 130°
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 20
ସମାଧାନ:
ଦତ୍ତ : \(\overleftrightarrow{\mathbf{XB}}\) || \(\overleftrightarrow{\mathbf{YD}}\), mXAO = 60° mYCO = 70°
ପ୍ରାମାଣ୍ୟ : mAOC = 130°
ଅଙ୍କନ : \(\overrightarrow{\mathrm{AO}}\), YD କୁ E ବିନ୍ଦୁରେ ଛେଦ କରୁ ।
ପ୍ରମାଣ : \(\overleftrightarrow{\mathbf{XB}}\) || \(\overleftrightarrow{\mathbf{YD}}\) ଏବଂ AE ଛେଦକ ।
⇒ mXAE = mOEC = 60° (ଏକାନ୍ତର କୋଣ)
ΔOEC ରେ ବତ୍ହିଃସ୍ଥ mAOC = mOEC + mOCE = 60° + 70° = 130°
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 21

BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c)

Question 13.
ଗୋଟିଏ ସରଳରେଖା ଅନ୍ୟ ଦୁଇଟି ସମାନ୍ତର ସରଳରେଖାକୁ ଛେଦକଲେ ପ୍ରମାଣ କର ଯେ,
(i) ଯେକୌଣସି ଏକାନ୍ତର କୋଣ ଦୁଇଟିର ଅନ୍ତଃସମଦ୍ୱିଖଣ୍ଡକଦ୍ବୟ ପରସ୍ପର ସମାନ୍ତର ।
ସମାଧାନ:
ଦତ୍ତ : L1 || L2 ଏବଂ L3 ଛେଦକ । \(\overrightarrow{\mathrm{AF}}\), ∠Aର ସମଦ୍ୱିଖଣ୍ଡକ ଏବଂ \(\overrightarrow{\mathrm{BE}}\), ∠Bର ସମଦ୍ବିଖଣ୍ଡକୁ
ପ୍ରାମାଣ୍ୟ : \(\overrightarrow{\mathrm{AF}}\) || \(\overrightarrow{\mathrm{BE}}\)
ପ୍ରମାଣ : m∠GAB = m∠ABD (ଏକାନ୍ତର )
⇒ \(\frac{1}{2}\)mGAB = \(\frac{1}{2}\)mABD
⇒ mFAB = mABE
ମାତ୍ର ଏମାନେ ଏକାନ୍ତର ।
\(\overrightarrow{\mathrm{AF}}\) || \(\overrightarrow{\mathrm{BE}}\)
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 22 (ପ୍ରମାଣିତ)

(ii) ଯେକୌଣସି ଅନୁରୂପ କୋଣ ଦୁଇଟିର ଅନ୍ତଃସମଦ୍ବିଖଣ୍ଡକଦ୍ବୟ ପରସ୍ପର ସମାନ୍ତର ।
ସମାଧାନ:
ଦତ୍ତ : L1 || L2 ଏବଂ L3 ଛେଦକ l \(\overrightarrow{\mathrm{AE}}\), ∠Aର ସମଦ୍ୱିଖଣ୍ଡକ ଏବଂ \(\overrightarrow{\mathrm{BF}}\), ∠Bର ସମଦ୍ବିଖଣ୍ଡକ ।
ପ୍ରାମାଣ୍ୟ : \(\overrightarrow{\mathrm{AE}}\) || \(\overrightarrow{\mathrm{BF}}\)
ପ୍ରମାଣ : m∠GAC = m∠ABD (ଅନୁରୂପ)
⇒ \(\frac{1}{2}\)mGAC = \(\frac{1}{2}\)mABD
⇒ mGAE = mABF
(\(\overrightarrow{\mathrm{AE}}\) mGAC ଏବଂ \(\overrightarrow{\mathrm{BF}}\), mABD ର ସମଦ୍ବିଖଣ୍ଡକ)
 କିନ୍ତୁ ଏମାନେ ଅନୁରୂପ କୋଣ ।
⇒ \(\overrightarrow{\mathrm{AE}}\) || \(\overrightarrow{\mathrm{BF}}\)
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 23 (ପ୍ରମାଣିତ)

Question 14.
ΔABCର m∠B = m∠C, B͞C ସହ ସମାନ୍ତର କରି ଅଙ୍କିତ ସରଳରେଖା AB ଓ AC କୁ ଯଥାକ୍ରମେ P ଓ Q ବିନ୍ଦୁରେ ଛେଦକଲେ ଦର୍ଶାଅ ଯେ, m∠APQ = m∠AQP ।
ସମାଧାନ:
ଦତ୍ତ : ΔABC ରେ mB = mC BC || \(\overleftrightarrow{\mathbf{PQ}}\)
ପ୍ରାମାଣ୍ୟ : mAPQ = mAQP
ପ୍ରମାଣ : BC || \(\overleftrightarrow{\mathbf{PQ}}\)
⇒ mAPQ = mB ଏବଂ mAQP = mC (ଅନୁଗୁପ କୋଣ)
ମାତ୍ର B = C (ଦତ୍ତ)
⇒ mAPQ = mAQP
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 24 (ପ୍ରମାଣିତ)

Question 15.
ଗୋଟିଏ କୋଣର ଦୁଇବାହୁ ଅନ୍ୟ ଏକ କୋଣର ଦୁଇବାହୁ ସହ ସମାନ୍ତର ହେଲେ ପ୍ରମାଣ କର ଯେ, କୋଣଦ୍ଵୟ ସମପରିମାଣ ବିଶିଷ୍ଟ ବା ପରିପୂରକ ହେବେ ।
ସମାଧାନ:
ଦତ୍ତ : ଦତ୍ତ ଚିତ୍ରରେ \(\overrightarrow{\mathrm{BA}}\) || \(\overrightarrow{\mathrm{ED}}\) ଏବଂ \(\overrightarrow{\mathrm{BC}}\) || \(\overrightarrow{\mathrm{EF}}\)
ପ୍ରାମାଣ୍ୟ : (i) m∠B = m∠E
(ii) m∠B + m∠E = 180°
ପ୍ରମାଣ : \(\overrightarrow{\mathrm{AB}}\) || \(\overrightarrow{\mathrm{DP}}\) ଏବଂ \(\overrightarrow{\mathrm{BC}}\)  ଛେଦକ
⇒ m∠ABC = m∠DPC (ଅନୁଗୁପ କୋଣ)
ପୁନଶ୍ଚ \(\overrightarrow{\mathrm{BC}}\) || \(\overrightarrow{\mathrm{EF}}\) ଏବଂ \(\overrightarrow{\mathrm{PE}}\) ଛେଦକ
⇒ m∠DPC = m∠PEF (ଅନୁଗୁପ କୋଣ)
ସମୀକରଣ (i) ଓ (ii) ରୁ m∠ABC = m∠PEF
⇒ m∠B = m∠E
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 25 (ପ୍ରମାଣିତ)

(ii) \(\overrightarrow{\mathrm{AB}}\) || \(\overrightarrow{\mathrm{ED}}\) ଏବଂ \(\overrightarrow{\mathrm{BC}}\) ଛେଦକ
⇒ m∠B = m∠CPE (ଅନୁଗୁପ କୋଣ)
ପୁନଶ୍ଚ \(\overrightarrow{\mathrm{PC}}\) || \(\overrightarrow{\mathrm{EF}}\) ଏବଂ \(\overrightarrow{\mathrm{PE}}\) ଛେଦକ
⇒ m∠CPE + m∠PEF = 180°
⇒ m∠B + m∠PEF = 180° ( m∠B = m∠CPE)
⇒ m∠B + m∠E = 180°
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 26 (ପ୍ରମାଣିତ)

BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c)

Question 16.
ଗୋଟିଏ ସରଳରେଖା ଦୁଇଟି ସମାନ୍ତର ସରଳରେଖାକୁ ଛେଦକରି ସେଥୁମଧ୍ୟରୁ କୌଣସି ଗୋଟିଏ ପ୍ରତି ଲମ୍ବ ହେଲେ, ପ୍ରମାଣ କର ଯେ ତାହା ଅନ୍ୟଟି ପ୍ରତି ମଧ୍ୟ ଲମ୍ବ ହେବ ।
ସମାଧାନ:
ଦତ୍ତ : L1 || L2 ଏବଂ L3 ଛେଦକ । L3 ⊥ L1
ପ୍ରାମାଣ୍ୟ : L3 ⊥ L2
ପ୍ରମାଣ :  L1 || L2 ଏବଂ L3 ଛେଦକ ।
⇒ m∠PAC = m∠ABD (ଅନୁଗୁପ କୋଣ)
ମାତ୍ର m∠PAC = 90° (ଦତ୍ତ)
m∠ABD = 90° ⇒ L1 ⊥ L2
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(c) 27 (ପ୍ରମାଣିତ)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e)

Odisha State Board Elements of Mathematics Class 12 Solutions CHSE Odisha Chapter 9 Integration Ex 9(e) Textbook Exercise questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Exercise 9(e)

Evaluate the following:
Question 1.
(i) ∫(1 + x) ex dx
Solution:
∫(1 + x) ex dx
[Choolse 1 + x as first and ex as second function
= (1 + x) ex – ∫1 . ex dx
= ( 1 + x) ex – ex + C = xex + C

(ii) ∫x3 ex dx
Solution:
∫x3 ex dx = x3 ex – ∫3x2 ex dx
= x3 ex – 3{x2 ex – ∫2x ex dx}
= x3 ex – 3x2 ex + 6 ∫x ex dx
= x3 ex – 3x2 ex +6 {x . ex – ∫1 . ex dx}
= x3 ex – 3x2 ex + 6x ex – 6ex + C

(iii) ∫x2 eax dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.1(3)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e)

(iv) ∫(3x + 2)2 e2x dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.1(4)

Question 2.
(i) ∫x sin x dx
Solution:
∫x sin x dx
[x = first function
sin x = 2nd function]
= x (-cosx) – ∫\(\frac{d}{d x}\)(x) . (-cos x) dx
= -x cos x + ∫cos x dx
= -x cos x + sin x + C

(ii) ∫x2 cos x dx
Solution:
∫x2 cos x dx
[x2 = 1st
cos x = 2nd]
= x2 . sin x – ∫\(\frac{d}{d x}\)(x2) sin x dx
= x2 sin x – ∫2x . sin x dx
[x = 1st
sin x = 2nd]
= x2 sin x – 2 {x . (-cos x) – ∫1 . (-cos x) dx}
= x2 sin x + 2x cos x – 2∫cos x dx
= x2 sin x + 2x cos x – 2 sin x + C

(iii) ∫x2 sin ax dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.2(3)

(iv) ∫x cos2 x dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.2(4)

(v) ∫x sin3 x dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.2(5)

(vi) ∫2x sin 2x cos x dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.2(6)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e)

(vii) ∫2x cos 3x cos 2x dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.2(7)

(viii)∫2x3 cos x2 dx
Solution:
∫2x3 cos x2 dx
[Put x2 =t
Then 2x dx = dt]
= ∫x2 . cos x2 . 2x dx
= ∫t . cos t dt
= t . sin t – ∫1 . sin t dt
= t sin t + cos t + C
= x2 sin x2 + cos x2 + C

(ix) ∫x cosec2 x dx
Solution:
∫x cosec2 x dx
[x = 1st
cosec2 x = 2nd]
= x ∫cosec2 x dx – ∫[\(\frac{d}{d x}\)(x) × ∫cosec2 x dx] dx
= -x cot x + ∫cot x dx
= -x cot x + ln |sin x| + C

(x) ∫x tan2 x dx
Solution:
∫x tan2 x dx = ∫x (sec2 x – 1) dx
= ∫x sec2 x dx – ∫x dx
= x tan x – ∫1 . tan x dx – \(\frac{1}{2}\)x2
[x = 1st
sec2 x = 2nd]
= x tan x + ln |cos x| – \(\frac{x^2}{2}\) + C

Question 3.
(i) ∫x ln (1 + x) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.3(1)

(ii) ∫x7 ln x dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.3(2)

(iii) ∫(ln x)3 dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.3(3)

(iv) ∫ln(x2 + 1) dx
Solution:
∫ln (x2 + 1) dx
= ∫ln (x2 + 1) . 1 dx
[Put ln (x2 + 1 ) as first function and 1 as the second function.]
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.3(4)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e)

(v) ∫\(\frac{\ln x}{x^5}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.3(5)

(vi) ∫ln (x2 + x + 2) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.3(6)

(vii) ∫ln (x + \(\sqrt{x^2+a^2}\)) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.3(7)

(viii) ∫ln (x + \(\sqrt{x^2-a^2}\)) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.3(8)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e)

Question 4.
(i) ∫sin-1 x dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.4(1)

(ii) ∫x sin-1 dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.4(2)

(iii) ∫cos-1 x dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.4(3)

(iv) ∫x tan-1 dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.4(4)

(v) ∫x2 tan-1 x dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.4(5)

(vi) ∫sec-1 x dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.4(6)

(vii) ∫x cosec-1 x dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.4(7)

Question 5.
(i) ∫e3x cos 2x dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.5(1)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e)

(ii) ∫ex sin x dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.5(2)

(iii) ∫ex cos2 x dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.5(3)

(iv) ∫x \(e^{x^2}\) sin x2 dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.5(4)

(v) ∫eax sin (bx + c) dx
Solution:
Let I = ∫eax sin (bx + c) dx
Integrating by parts we get
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.5(5)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e)

(vi) ∫(2x2 + 1)\(e^{x^2}\) dx
Solution:
I = ∫(2x2 + 1)\(e^{x^2}\) dx
= ∫2x2 \(e^{x^2}\) dx + ∫\(e^{x^2}\) . 1 dx
= ∫2x2 \(e^{x^2}\) dx + x2 \(e^{x^2}\) ∫2x\(e^{x^2}\) .x dx
= x\(e^{x^2}\) + C

Question 6.
(i) ∫\(\sqrt{9-x^2}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.6(1)

(ii) ∫\(\sqrt{5-4 x^2}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.6(2)

(iii) ∫\(\sqrt{1-x^2-2 x}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.6(3)

(iv) ∫ez \(\sqrt{4-e^{2 z}}\) dz
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.6(4)

(v) ∫cos θ \(\sqrt{5-\sin ^2 \theta}\) dθ
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.6(5)

Question 7.
(i) ∫\(\sqrt{x^2+4}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.7(1)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e)

(ii) ∫\(\sqrt{7 x^2+2}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.7(2)

(iii) ∫\(\sqrt{4 x^2+12 x+13}\) dx (2x + 3 = z)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.7(3)

(iv) ∫e2z \(\sqrt{e^{4 z}+6}\) dz
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.7(4)

(v) ∫sec2 θ \(\sqrt{\sec ^2 \theta+3}\) dθ
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.7(5)

(vi) ∫(2x2 +1) \(e^{x^2}\) dx
Solution:
Same as No. 5 (vi).

Question 8.
(i) ∫\(\sqrt{x^2-8}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.8(1)

(ii) ∫\(\sqrt{3 x^2-2}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.8(2)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e)

(iii) ∫\(\sqrt{x^2-4 x+2}\) dx (x – 2 = z)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.8(3)

(iv) ∫az \(\sqrt{a^{2 z}-4}\) dz
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.8(4)

(v) ∫sec θ tan θ \(\sqrt{\tan ^2 \theta-3}\) dθ
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.8(5)

Question 9.
(i)∫ex (tan x + ln sec x) dx
Solution:
∫ex (tan x + ln sec x) dx
= ∫ex tan x dx + ∫ex ln sec x dx
(Integrating by parts)
= ∫ex tan x dx + ex ln sec x – ∫ex tan x dx
= ex ln(sec x) + C

(ii) ∫ex (cot x + ln sin x) dx
Solution:
∫ex (cot x + ln sin x) dx
[Integrating by parts taking ex as first function and cot x as second function.]
= ∫ex ln sin x – ∫ex ln sin x dx + ∫ex ln sin x dx + C
= ex ln sin x + C

(iii) ∫\(\frac{e^x}{x}\) (1 + x ln x) dx
Solution:
∫\(\frac{e^x}{x}\) (1 + x ln x) dx
= ∫\(\frac{e^x}{x}\) dx + ∫\(\frac{e^x}{x}\) ex ln x dx + C
= ex ln x + C

(iv) ∫\(\frac{x e^x}{(1+x)^2}\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.9(4)

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e)

Question 10.
(i) ∫\(\left[\frac{1}{\ln x}-\frac{1}{(\ln x)^2}\right]\) dx
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.10(1)

(ii) ∫sin (ln x) dx
Solution:
Let I = ∫sin (ln x) dx
[Integrating by parts taking sin (ln x) as first and 1 as second function.]
CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(e) Q.10(2)

(iii) ∫sin x ln (cosec x – cot x) dx
Solution:
∫sin x ln (cosec x – cot x) dx
[Integrating by parts taking In (cosec x cot x) as first function and sin x as second function.]
= ln (cosec x – cot x) . – cos x – ∫\(\frac{1}{{cosec} x-\cot x}\)× – cosec x . cot x + cosec2 x × – cos x dx
= -cos x . ln (cosec x – cot x) + ∫\(\frac{{cosec} x({cosec} x-\cot x)}{{cosec} x-\cot x}\) . cos x dx
= -cos x . ln (cosec x – cot x) + ∫cot x dx
= -cos x . ln (cosec x – cot x) + ln sin x + C

BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b)

Odisha State Board BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b) Textbook Exercise Questions and Answers.

BSE Odisha Class 9 Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b)

Question 1.
ନିମ୍ନଲିଖତ ପଦଗୁଡ଼ିକର ସଂଜ୍ଞା ଲେଖ ।
କୋଣର ଅନ୍ତର୍ଦେଶ, ସନ୍ନିହିତ କୋଣ, ପ୍ରତୀପ କୋଣ, ପରିପୂରକ କୋଣ, ଅନୁପୂରକ କୋଣ ।
ସମାଧାନ:
କୋଣର ଅନ୍ତର୍ଦେଶ:
ABC ର \(\overleftrightarrow{\mathrm{BC}}\) ର A – ପାର୍ଶ୍ବ \(\overleftrightarrow{\mathrm{AB}}\) ର C – ପାର୍ଶ୍ଵର ଛେଦକୁ ∠ABC ର ଅନ୍ତର୍ଦେଶ କୁହାଯାଏ । ∠ABC ର ଅନ୍ତର୍ଦେଶରେ ଥ‌ିବା ପ୍ରତ୍ୟେକ ବିନ୍ଦୁକୁ ∠ABC ର ଅନ୍ତଃସ୍ଥ ବିନ୍ଦୁ କୁହାଯାଏ । ଦତ୍ତ ଚିତ୍ରରେ P, ∠ABC ର ଗୋଟିଏ ଅନ୍ତସ୍ଥ  ବିନ୍ଦୁ ଅଟେ । ଏହିପରି ଅସଂଖ୍ୟ ବିନ୍ଦୁକୁ ନେଇ କୋଣର ଅନ୍ତର୍ଦେଶ ଗଠିତ ।
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b) 1

ସନ୍ନିହିତ କୋଣ: 
ଦୁଇଟି କୋଣର ଗୋଟିଏ ସାଧାରଣ ବାହୁ ଓ କୋଣଦ୍ୱୟର ଅନ୍ୟ ବାହୁ ଦୁଇଟି ସାଧାରଣ ବାହୁର ବିପରୀତ ପାର୍ଶ୍ବରେ ବିସ୍ତୃତ ହେଲେ, ସେମାନଙ୍କୁ ସନ୍ନିହିତ କୋଣ (Adjacent angles) କୁହାଯାଏ ।
ଦତ୍ତ ଚିତ୍ରରେ ∠PSQ ଓ ∠QSR ସନ୍ନିହିତ ଅଟନ୍ତି ।
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b) 2

ପ୍ରତୀପ କୋଣ:
ଗୋଟିଏ କୋଣର ବାହୁଦ୍ୱୟର ବିପରୀତ ରଶ୍ମିମାନଙ୍କ ଦ୍ବାରା ଗଠିତ କୋଣକୁ ଉକ୍ତ  କୋଣର ପ୍ରତୀପ କୋଣ (Vertically OppositeAngle) କୁହାଯାଏ । ଦତ୍ତ ଚିତ୍ରରେ ∠BOC ଓ ∠AOD ପରସ୍ପର ପ୍ରତୀପ ଏବଂ ∠AOC ଓ ∠BOD  ପରସ୍ପର ପ୍ରତୀପ ଅଟନ୍ତି ।
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b) 3

ପରିପୂରକ କୋଣ:
ଗୋଟିଏ ରଶ୍ମିର ଶୀର୍ଷବିନ୍ଦୁ ଅନ୍ୟ ଏକ ରେଖାରେ ଅବସ୍ଥିତ ହେଲେ ଯେଉଁ ଦୁଇଟି ସନ୍ନିହିତ କୋଣ ଉତ୍ପନ୍ନ ହୁଅନ୍ତି, ସେମାନେ ପରସ୍ପର ପରି ପୂରକ (Supplementary angle); ଅର୍ଥାତ୍ ସେମାନଙ୍କର ପରିମାଣର ସମଷ୍ଟି 180° ଅଟେ ।
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b) 4
ଦତ୍ତ ଚିତ୍ରରେ m∠ACD + m∠BCD = 180° ଅର୍ଥାତ୍ ∠ACD ଓ ∠BCD ପରସ୍ପର ପରିପୂରକ ଅଟନ୍ତି ।

ଅନୁପୂରକ କୋଣ:
 ଦୁଇଟି କୋଣର ପରିମାଣର ସମଷ୍ଟି 90° ହେଲେ ସେମାନଙ୍କୁ ପରସ୍ପର ଅନୁପୂରକ କୋଣ (Complementary angles) କୁହାଯାଏ ।

BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b)

Question 2.
ନିମ୍ନ ପ୍ରଶ୍ନଗୁଡ଼ିକର ଉତ୍ତର ଦିଅ ।
(i) ଗୋଟିଏ କୋଣର କେତୋଟି ବାହୁ ଥାଏ ?
ସମାଧାନ:
ଦୁଇଟି

(ii) ଗୋଟିଏ କୋଣର କେତୋଟି ଶୀର୍ଷବିନ୍ଦୁ ଥାଏ ?
ସମାଧାନ:
ଗୋଟିଏ

(ii) କୋଣର ଅନ୍ତର୍ଦେଶରେ କେତୋଟି ବିନ୍ଦୁ ଥାଏ ?
ସମାଧାନ:
ଅସଂଖ୍ୟ

(iv) କୋଣ ଓ ଏହାର ଅନ୍ତର୍ଦେଶର ଛେଦରେ କେତୋଟି ବିନ୍ଦୁ ଥାଏ ?
ସମାଧାନ:
କୌଣସି ବିନ୍ଦୁ ନଥାଏ

Question 3.
ନିମ୍ନରେ ଦିଆଯାଇଥ‌ିବା ତାଲିକାରୁ କେଉଁଗୁଡ଼ିକ ଉତ୍ତଳ ସେଟ୍ ଦର୍ଶାଅ ।
(i) ରେଖାଖଣ୍ଡ 
(ii) ରଶ୍ମି
(iii) ରେଖା
(iv) କୋଣ
(v) କୋଣର ଅନ୍ତର୍ଦ୍ଦେଶ 
(vi) ସମତଳ
(vii) କୋଣର ବହିର୍ଦେଶ
ସମାଧାନ:
(i) ରେଖାଖଣ୍ଡ 
(ii) ରଶ୍ମି 
(iii) ରେଖା 
(v) କୋଣର ଅନ୍ତଦ୍ଦେଶ ଓ 
(vi) ସମତଳ

Question 4.
ତିନୋଟି ସରଳରେଖା ପରସ୍ପରକୁ ଛେଦକରୁଥିବାର ଏକ ଚିତ୍ର ଅଙ୍କନ କର । ତତ୍ପରେ ଚିତ୍ରକୁ ଦେଖ୍ ପ୍ରତୀପ କୋଣ ।
ସମାଧାନ:
ପ୍ରତୀପ କୋଣ ଯୋଡ଼ା:
(i) ∠EAD ଓ ∠BAC
(ii) ∠EAB ଓ ∠CAD
(iii) ∠FBG ଓ ∠ABC
(iv) ∠FBA ଓ ∠GBC
(v) ∠ICH ଓ ∠ACB
(vi) ∠ACI ଓ ∠BCH
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b) 5

Question 5.
ଦୁଇଟି ସରଳରେଖା ପରସ୍ପରକୁ ଗୋଟିଏ ବିନ୍ଦୁରେ ଛେଦ କରୁଥ‌ିବାର ଚିତ୍ରଟିଏ ଅଙ୍କନ କର । ତତ୍ପରେ ଚିତ୍ରରୁ ସନ୍ନିହିତ ପରିପୂରକ କୋଣଯୋଡ଼ାଗୁଡ଼ିକୁ ଲେଖ ।
ସମାଧାନ:
(i) ∠AOBର ସନ୍ନିହିତ ପରିପୂରକ ∠AOD
(ii) ∠AOBର ସନ୍ନିହିତ ପରିପୂରକ ∠BOC
(ii) ∠BOCର ସନ୍ନିହିତ ପରିପୂରକ ∠COD
(iv) ∠CODର ସନ୍ନିହିତ ପରିପୂରକ ∠AOD
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b) 6

BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b)

Question 6.
XY ସରଳରେଖାର ବିପରୀତ ପାର୍ଶ୍ବରେ M ଓ N ବିନ୍ଦୁକୁ ଚିହ୍ନଟ କର । ଅଙ୍କିତ ସରଳରେଖାର N-ପାର୍ଶ୍ଵରେ C ବିନ୍ଦୁ ଏବଂ M-ପାର୍ଶ୍ବରେ B ବିନ୍ଦୁ ଚିହ୍ନଟ କର । ଚିତ୍ର ମାଧ୍ୟମରେ ଦର୍ଶାଅ ଯେ, BM ଓ NC ରେଖାଖଣ୍ଡଦ୍ଵୟ ସରଳରେଖାର ବିପରୀତ ପାର୍ଶ୍ବରେ ରହିବେ ?
ସମାଧାନ:
 (i) \(\overleftrightarrow{\mathrm{XY}}\) (ସରଳରେଖା)ର ବିପରୀତ ପାର୍ଶ୍ବରେ M ଓ N ବିନ୍ଦୁ ଚିହ୍ନଟ ହୋଇଛି ।
(ii) ଅଙ୍କିତ ସରଳରେଖାର N ପାର୍ଶ୍ଵରେ C ବିନ୍ଦୁ ଓ M ପାର୍ଶ୍ବରେ B ବିନ୍ଦୁ ଚିହ୍ନଟ ହୋଇଛି ।
(iii) ଚିତ୍ରରୁ ସୁସ୍ପଷ୍ଟ ଯେ, \(\overline{\mathrm{BM}}\) ଓ \(\overline{\mathrm{NC}}\) ରେଖାଖଣ୍ଡଦ୍ଵୟ \(\overleftrightarrow{\mathrm{XY}}\) ସରଳରେଖାର ବିପରୀତ ପାର୍ଶ୍ଵରେ ଅଛନ୍ତି ।
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b) 7

Question 7.
ନିମ୍ନ ପ୍ରଶ୍ନଗୁଡ଼ିକର ଉତ୍ତର ଦିଅ । ଆବଶ୍ୟକସ୍ଥଳେ ଚିତ୍ର ଅଙ୍କନ କର ।
(i) X ବିନ୍ଦୁ \(\overleftrightarrow{\mathrm{AB}}\) ଉପରେ ଅବସ୍ଥିତ ନ ହେଲେ ଓ A – O – B ହେଲେ,
m∠XOA + m∠XOB କେତେ ?
ସମାଧାନ:
m∠XOA + m∠XOB = 180°
( ∠XOA ଏବଂ ∠XOB ସନ୍ନିହିତ ପରିପୂରକ)
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b) 8

(ii) \(\overleftrightarrow{\mathrm{AB}}\) ଓ \(\overleftrightarrow{\mathrm{CD}}\) ର ଛେଦବିନ୍ଦୁ O ହେଲେ, ∠AOC ର ପ୍ରତୀପ କୋଣ
କେଉଁଟି ?
ସମାଧାନ:
\(\overleftrightarrow{\mathrm{AB}}\) ଓ \(\overleftrightarrow{\mathrm{CD}}\) ଦ୍ଵୟର ଛେଦବିନ୍ଦୁ O ।
∠AOC ର ପ୍ରତୀପ କୋଣ ∠BOD ।
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b) 9

(iii) mAOB ର ଅନ୍ତଃସ୍ଥ ବିନ୍ଦୁ mAOC = x ଓ mAOB = y ହେଲେ, mBOC କେତେ ?
ସମାଧାନ:
m∠AOB ର ଏକ ଅନ୍ତଃସ୍ଥ ବିନ୍ଦୁ C NC
m∠AOC = x ଏବଂ m∠AOB = y
∴ m∠BOC = m∠AOB – m∠AOC = y – x
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b) 10

(iv) ଦୁଇଟି ସରଳରେଖା ପରସ୍ପରକୁ ଛେଦକଲେ ଉତ୍ପନ୍ନ ହେଉଥ‌ିବା କୋଣଗୁଡ଼ିକ ମଧ୍ୟରୁ ଯଦି ଗୋଟିଏ କୋଣର ପରିମାଣ 30° ହୁଏ, ତେବେ ଏହାର ପ୍ରତୀପ କୋଣର ପରିପୂରକ କୋଣର ପରିମାଣ କେତେ ହେବ ?
ସମାଧାନ:
\(\overleftrightarrow{\mathrm{AB}}\) ଓ \(\overleftrightarrow{\mathrm{CD}}\) ଦ୍ଵୟ ପରସ୍ପରକୁ O ବିନ୍ଦୁରେ ଛେଦ କରନ୍ତି ।
ମନେକର m∠BOC = 30°
m∠BOC = m∠AOD (ପ୍ରତୀପ କୋଣ)
m∠AOD ର ପରିପୂରକ କୋଣର ପରିମାଣ = 180° – 30° = 150° ( ପରିପୂରକ କୋଣଦ୍ଵୟର ସମଷ୍ଟି 180° ।)
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b) 11

BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b)

Question 8.
(i) m∠AOB = x ଓ∠AOB ର ଅନୁପୂରକ କୋଣର ପରିମାଣ 2x° ହେଲେ xର ମାନ ଡିଗ୍ରୀରେ ପ୍ରକାଶ କର ।
ସମାଧାନ:
m∠AOB = x
m∠AOB କୋଣର ଅନୁପୂରକ କୋଣର ପରିମାଣ = 2x
⇒ ପ୍ରଶ୍ନନୁସାରେ, 90°- x = 2x
⇒ 2x + x = 90°
⇒ 3x = 90°
⇒ x = \(\frac{90^{\circ}}{3}\) = 30°

(ii) ଗୋଟିଏ କୋଣର ପରିମାଣ, ଏହାର ପରିପୂରକ କୋଣର ପରିମାଣର ଦୁଇଗୁଣରୁ 18° ଅଧିକ ହେଲେ, କୋଣଟିର ପରିମାଣ କେତେ ନିର୍ଣ୍ଣୟ କର ।
ସମାଧାନ:
ମନେକର କୋଣ ଦ୍ଵୟର ପରିମାଣ ଯଥାକ୍ରମେ θ ଏବଂ 2θ + 18°
ପ୍ରଶ୍ନନୁସାରେ କୌଣଦ୍ଵୟ ପରସ୍ପର ପରିପୂରକ । ଅର୍ଥାତ୍ θ + 2θ + 18° = 180°
⇒ 3θ = 180° – 18° = 162°
⇒ θ = \(\frac{162}{3}\) = 54°
ନିଶ୍ଚେୟ କୋଣର ପରିମାଣ = 2θ + 18° = 2 × 54 + 18 = 108 + 18 = 126°
ବିକଳ୍ପ ପ୍ରଣାଳୀ:
ମନେକର କୋଣଟିର ପରିମାଣ θ । ଏହାର ପରିପୂରକ କୋଣର ପରିମାଣ (180 – θ°) ।
ପ୍ରଶ୍ନନୁସାରେ θ = 2(180°- θ) + 18°
⇒ θ = 360° – 2θ + 18°
⇒ 3θ = 378°
⇒ θ = \(\frac{378}{3}\) = 126°

(iii) ଗୋଟିଏ କୋଣର ପରିମାଣ ତାହାର ପରିପୂରକ କୋଣର ପରିମାଣର ଏକପଞ୍ଚମାଂଶ ହେଲେ କୋଣଟିର ପରିମାଣ ସ୍ଥିର କର ।
ସମାଧାନ:
ମନେକର କୋଣଦ୍ଵୟର ପରିମାଣ θ ଏବଂ \(\frac{θ}{5}\)
ପ୍ରଶାନୁସାରେ, କୋଣଦ୍ଵୟ ପରସ୍ପର ପରିପୂରକ ।
θ + \(\frac{θ}{5}\) = 180° 
⇒ \(\frac{5 \theta+\theta}{5}\) = 180°
⇒ 6θ = 180° × 5
⇒ \(\frac{180^{\circ} \times 5}{6}\) = 150°
∴ ନିଶ୍ଚେୟ କୋଣର ପରିମାଣ = \(\frac{θ}{5}\) = \(\frac{150^{\circ}}{5}\) = 30°
ବିକଳ୍ପ ପ୍ରଣାଳୀ:
ମନେକର କୋଣଟିର ପରିମାଣ θ । ଏହାର ପରିପୂରକ କୋଣର ପରିମାଣ (180 – θ°)
ପ୍ରଶ୍ନନୁସାରେ θ = \(\frac{180^{\circ}-\theta}{5}\) 
⇒ 5θ = 180° – θ
⇒ 6θ = 180°
⇒ θ = 30°

(iv) ଦୁଇଟି ସନ୍ନିହିତ ପରିପୂରକ କୋଣର ପରିମାଣର ଅନୁପାତ 4 : 5 ହେଲେ, କୋଣଦ୍ୱୟର ପରିମାଣ ନିର୍ଣ୍ଣୟ କର ।
ସମାଧାନ:
ମନେକର ସନ୍ନିହିତ ପରିପୂରକ କୋଣଦ୍ୱୟର ପରିମାଣ ଯଥାକ୍ରମେ 4θ ଓ 5θ ।
ପ୍ରଶ୍ନନୁସାରେ, 4θ + 5θ = 180° 
9θ = 180° 
θ = \(\frac{180}{9}\) = 20°
∴ 4θ = 4 × 20° = 80° 5θ = 5 × 20° = 100°
∴ ନିର୍ଦେୟ କୋଣଦ୍ଵୟର ପରିମାଣ ଯଥାକ୍ରମେ 80° ଓ 100° ।

(v) ଗୋଟିଏ କୋଣର ପରିମାଣ, ତାହାର ପରିପୂରକ କୋଣର ପରିମାଣଠାରୁ 20° କମ୍ ହେଲେ, କୋଣଟିର ପରିମାଣ ନିର୍ଣ୍ଣୟ କର ।
ସମାଧାନ:
ମନେକର କୋଣଦ୍ଵୟର ପରିମାଣ ଯଥାକ୍ରମେ θθ – 20° ।
ପ୍ରଶ୍ନନୁସାରେ, କୋଣଦ୍ୱୟ ପରସ୍ପର ପରିପୂରକ ।
⇒ θ + θ – 20° = 180°
⇒ 20 = 180° + 20°
⇒ θ = \(\frac{200}{2}\) = 100°
∴ ନିଶ୍ଚେୟ କୋଣର ପରିମାଣ = θ – 20° = 100° – 20° = 80°

(vi) ଦୁଇଟି ସନ୍ନିହିତ ପରିପୂରକ କୋଣର ପରିମାଣର ଅନ୍ତର 30° ହେଲେ କୋଣଦ୍ୱୟର ପରିମାଣ ସ୍ଥିର କର ।
ସମାଧାନ:
ମନେକର କୋଣଦ୍ବୟର ପରିମାଣ ଯଥାକ୍ରମେ θ ଓ θ + 30° ।
θ + θ + 30° = 180°
⇒  2θ + 30° = 180°
⇒ 2θ = 180° – 30°
⇒ θ = \(\frac{150}{2}\) = 75°
∴ ବୃହତ୍ତର ପରିମାଣ ବିଶିଷ୍ଟ କୋଣର ପରିମାଣ = θ + 30° = 75° + 30° = 105°

(vii) ଗୋଟିଏ କୋଣର ପରିମାଣ ତାହାର ଅନୁପୂରକ କୋଣ ପରିମାଣର ଏକ-ପଞ୍ଚମାଂଶ ହେଲେ, କୋଣଟିର ପରିମାଣ ନିର୍ଣ୍ଣୟ କର ।
ସମାଧାନ: 
ମନେକର କୋଣଟିର ପରିମାଣ x° ।
ଏହାର ଅନୁପୂରକ କୋଣର ପରିମାଣ (90 – x°) ।
ପ୍ରଶ୍ନନୁସାରେ, x = \(\frac{90-x}{5}\)
 5x = 90 − x
6x = 90
⇒ x = \(\frac{90}{6}\) = 15°
∴ କୋଣଟିର ପରିମାଣ 15° ।

BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b)

Question 9.
ନିମ୍ନସ୍ଥ ଚିତ୍ରଗୁଡ଼ିକ ଅନୁସାରେ x ର ମାନ କେତେ ହେବ ସ୍ଥିର କର ।
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b) 12
ସମାଧାନ:
(i) ଚିତ୍ର (କ) ରେ ∠AOC ଓ ∠BOC ଦ୍ବୟ ସନ୍ନିହିତ ପରିପୂରକ ହେତୁ m∠AOC + m∠BOC = 180°
⇒ 3x + 2x = 180
⇒ 5x = 180
⇒ x = \(\frac{180}{5}\) = 36
∴ x = 36°

(ii) ଚିତ୍ର (ଖ) ରେ ∠PRS ଓ ∠ORS ଦ୍ବୟ ସନ୍ନିହିତ ପରିପୂରକ ହେତୁ m∠PRS + m∠QRS = 180°
(x – 4) + (3x + 8) = 180
⇒ 4x + 4 = 180
⇒ 4x = 180 – 4
⇒ x = \(\frac{176}{4}\) = 44
∴ x = 44°

(iii) ଚିତ୍ର (ଗ) ରେ mMOP + mPOQ + mQON = 180°
⇒ (x + 20) + (2x – 30) + (x + 10) = 180°
⇒ 4x = 180°
⇒ x = \(\frac{180}{4}\) = 45°
∴ x = 45°

Question 10.
ଦତ୍ତ ଚିତ୍ରରେ \(\overleftrightarrow{\mathrm{AB}}\) ଓ \(\overleftrightarrow{\mathrm{CD}}\) ସରଳରେଖାଦ୍ଵୟ ପରସ୍ପରକୁ O ବିନ୍ଦୁରେ ଛେଦ କରନ୍ତି ।
m∠COE = 90° ହେଲେ x, Y ଓ z ର ମାନ ନିର୍ଣ୍ଣୟ କର ।
ସମାଧାନ:
m∠AOC = m∠BOD (ପ୍ରତୀପ) ⇒ 2x = y
ସେହିପରି m∠AOD = m∠BOC (ପ୍ରତୀପ)
⇒ z = 90° + x (∴ m∠COE = 90°)
m∠AOC + m∠AOD = 180°
⇒ 2x + 90° + x = 180°
⇒ 3x = 90°
⇒ x = 30° ( m∠AOD = 90° + x)
y = 2x = 2 × 30° = 60°,
z = 90° + x = 90° + 30° = 120°
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b) 13

Question 11.
ଦତ୍ତ ଚିତ୍ରରେ \(\overleftrightarrow{\mathrm{PQ}}\) ଓ \(\overleftrightarrow{\mathrm{RS}}\) ଦ୍ବୟର ଛେଦବିନ୍ଦୁ O ଓ m∠POC = 75° ହେଲେ, a, b ଏବଂ c ର ମାନ ନିର୍ଣ୍ଣୟ କର ।
ସମାଧାନ:
∠ROP ଓ ∠POS ସନ୍ନିହିତ ପରିପୂରକ ହେତୁ,
mROP + mPOS = 180°
⇒ mROP + mPOC + mCOS = 180°
⇒ 4b + 75° + b = 180°
⇒ 5b + 75° = 180°
⇒ 5b = 180° – 75° = 105°
⇒ b = \(\frac{105}{5}\) = 21°
m∠QOS = m∠ROP (ପ୍ରତୀପ କୋଣ) 
a = 4b = b × 21 = 84°
ROQ QOS  mROQ + mQOS = 180°
⇒ 2c + a = 180°
⇒ 2c + 84° = 180°
⇒ 2c = 180° – 84° = 96°
∴ c = \(\frac{96°}{2}\) =48°
∴ a = 84°, b = 21°, c = 48°
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b) 14

BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b)

Question 12.
ପ୍ରମାଣ କର ଯେ, ଦୁଇଟି ପ୍ରତୀପ କୋଣର ସମଦ୍ବିଖଣ୍ଡକ ଏକ ସରଳରେଖା ଉପରିସ୍ଥ ଦୁଇଟି ବିପରୀତ ରଶ୍ମି ହେବେ । 
ସମାଧାନ:
 ଦତ୍ତ : \(\overleftrightarrow{\mathrm{AB}}\) ଓ \(\overleftrightarrow{\mathrm{CD}}\) ରେଖାଦ୍ବୟର ଛେଦବିନ୍ଦୁ O ।
\(\overrightarrow{\mathrm{OM}}\) ଏବଂ \(\overrightarrow{\mathrm{ON}}\) ଯଥାକ୍ରମେ ∠AOC ଓ ∠BOD ର ସମଦ୍ବିଖଣ୍ଡକ ।
ପ୍ରାମାଣ୍ୟ : \(\overrightarrow{\mathrm{OM}}\) ଏବଂ \(\overrightarrow{\mathrm{ON}}\) ବିପରୀତ ରଶ୍ମି ଅଟନ୍ତି ।
ପ୍ରାମାଣ୍ :  m∠AOC + m∠AOD = 180°
⇒ \(\frac{1}{2}\)m∠AOC + \(\frac{1}{2}\)m∠AOC + m∠AOD = 180°
(m∠AOC = \(\frac{1}{2}\)m∠AOC + \(\frac{1}{2}\)m∠AOC)
\(\frac{1}{2}\)m∠AOC + \(\frac{1}{2}\)m∠BOD + m∠AOD = 180°
m∠AOM + m∠DON + m∠AOD = 180°
m∠AOM + m∠AON = 180°
\(\overrightarrow{\mathrm{OM}}\) ଓ \(\overrightarrow{\mathrm{ON}}\) ବିପରୀତ ରଶ୍ମି ଅଟନ୍ତି । 
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b) 15 (ପ୍ରମାଣିତ)

Question 13.
ପ୍ରମାଣ କର ଯେ, ଦୁଇଟି ସନ୍ନିହିତ ପରିପୂରକ କୋଣର ସମଦ୍ବିଖଣ୍ଡକ ରଶ୍ମିଦ୍ବୟ ପରସ୍ପର ପ୍ରତି ଲମ୍ବ ।
ସମାଧାନ:
ଦତ୍ତ : ∠AOC ଓ ∠BOC ସନ୍ନିହିତ ପରିପୂରକ ।
OM ଓ ON ଯଥାକ୍ରମେ ∠BOC ଏବଂ ∠AOC ର ସମଦ୍ବିଖଣ୍ଡକ ।
ପ୍ରାମାଣ୍ୟ : \(\overrightarrow{\mathrm{OM}} \perp \overrightarrow{\mathrm{ON}}\) ଅର୍ଥାତ୍ m∠MON = 90°
ପ୍ରମାଣ : ∠AOC ଓ ∠BOC ସନ୍ନିହିତ ପରିପୂରକ ।
⇒ m∠AOC +m∠BOC = 180°
⇒ \(\frac{1}{2}\)m∠AOC + \(\frac{1}{2}\)m∠BOC = \(\frac{1}{2}\) × 180°
⇒ mCON + mCOM = 90° ( \(\overrightarrow{\mathrm{OM}}\), ∠BOC ର ଏବଂ \(\overrightarrow{\mathrm{ON}}\), ∠AOC ର ସମଦ୍ବିଖଣ୍ଡକ)
⇒ m∠MON = 90°
\(\overrightarrow{\mathrm{OM}} \perp \overrightarrow{\mathrm{ON}}\)
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b) 16 (ପ୍ରମାଣିତ)

Question 14.
ପାର୍ଶ୍ୱସ୍ଥ ଚିତ୍ରରେ ∠AOE ଏବଂ ∠EOB ଦୁଇଟି ସନ୍ନିହିତ ପରିପୂରକ କୋଣ ଓ \(\overrightarrow{\mathrm{OC}}\), ∠AOC କୁ ସମଦ୍ବିଖଣ୍ଡ କରେ ।
m∠COD = 90° ହେଲେ ଦର୍ଶାଅ ଯେ, \(\overrightarrow{\mathrm{OD}}\), ∠EOB ର ସମଦ୍ବିଖଣ୍ଡକ ହେବ ।
ସମାଧାନ:
ଦତ୍ତ : ∠AOE ଏବଂ ∠EOB ସନ୍ନିହିତ ପରିପୂରକ ।
\(\overrightarrow{\mathrm{OC}}\), ∠AOE କୁ ସମର୍ଦ୍ଦିଖଣ୍ଡ କରେ ଏବଂ m∠COD = 90°
ପ୍ରାମାଣ୍ୟ : \(\overrightarrow{\mathrm{OD}}\), ∠EOB ର ସମଦ୍ବିଖଣ୍ଡକ ।
ପ୍ରମାଣ : ∠AOE ଏବଂ ∠EOB ସନ୍ନିହିତ ପରିପୂରକ ।
⇒ m∠AOE + m∠EOB = 180°
⇒ \(\frac{1}{2}\)m∠AOE + \(\frac{1}{2}\)∠EOB = 90°
⇒ m∠COE + \(\frac{1}{2}\)m∠EOB = 90° … (i)
କିନ୍ତୁ mZCOD = 90° (ଦତ୍ତ)
∴ m∠COE + m∠EOD = 90° … (ii)
⇒ (i) ଓ (ii) ରୁ m∠COE + \(\frac{1}{2}\)m∠EOB = m∠COE + m∠EOD
⇒ \(\frac{1}{2}\)m∠EOB = m∠EOD
⇒ \(\overrightarrow{\mathrm{OD}}\), ∠EOB ର ସମଦ୍ବିଖଣ୍ଡକ । 
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b) 17 (ପ୍ରମାଣିତ)

BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b)

Question 15.
\(\overleftrightarrow{AB}\) ଓ \(\overleftrightarrow{CD}\) ପରସ୍ପରକୁ O ବିନ୍ଦୁରେ ଛେଦ କରନ୍ତି । m∠AOC ର ସମଦ୍ବିଖଣ୍ଡକ \(\overrightarrow{OX}\) । ପ୍ରମାଣ କର ଯେ, \(\overleftrightarrow{XO}\) କୋଣ BOD କୁ ସମର୍ଦ୍ଦିଖଣ୍ଡ କରେ ।
ସମାଧାନ:
ଦତ୍ତ : \(\overleftrightarrow{AB}\) ଓ \(\overleftrightarrow{CD}\) ପରସ୍ପରକୁ ଠ ବିନ୍ଦୁରେ ଛେଦ କରନ୍ତି ।
\(\overrightarrow{OX}\), ∠AOC ର ସମଦ୍ବିଖଣ୍ଡକ ।
\(\overrightarrow{OX}\) ର ବିପରୀତ ରଶ୍ମି \(\overrightarrow{OY}\) ।
ପ୍ରାମାଣ୍ୟ : \(\overrightarrow{OY}\), ZBOD ର ସମଦ୍ବିଖଣ୍ଡକ ।
ପ୍ରମାଣ : \(\overrightarrow{OX}\) ର ବିପରୀତ ରଶ୍ମି OY ହେତୁ ଏକ ସରଳରେଖା \(\overleftrightarrow{XY}\)
ଏବଂ \(\overleftrightarrow{AB}\) ପରସ୍ପରକୁ ଠ ବିନ୍ଦୁରେ ଛେଦ କରନ୍ତି । 
⇒ m∠AOX = m∠BOY (ପ୍ରତୀପ କୋଣ)
ପୁନଶ୍ଚ, \(\overleftrightarrow{XY}\) ଏବଂ \(\overleftrightarrow{CD}\) ପରସ୍ପରକୁ ଠ ବିନ୍ଦୁରେ ଛେଦ କରନ୍ତି । 
⇒ m∠XOC = m∠YOD (ପ୍ରତୀପ କୋଣ)
\(\overrightarrow{OX}\), ∠AOC ର ସମଦ୍ବିଖଣ୍ଡକ।
⇒ m∠A0X = m∠XOC
⇒ mBOY = mYOD ( AOX = BOY ଏବଂ XOC = YOD)
\(\overrightarrow{OY}\), ∠BOD ର ସମଦ୍ବିଖଣ୍ଡକ ।
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b) 18 (ପ୍ରମାଣିତ)

Question 16.
\(\overrightarrow{\mathrm{OA}}\), \(\overrightarrow{\mathrm{OB}}\), \(\overrightarrow{\mathrm{OC}}\) ଏକ ସମତଳରେ ଅବସ୍ଥିତ ରଶି । କୌଣସି ରଶି ଅନ୍ୟ ରଶି ଦଇଟି ଦାରା ଗଠିତ କୋଣର ଅନ୍ତର୍ଦେଶରେ ବିସ୍ତୃତ ନୁହେଁ । ପ୍ରମାଣ କର ଯେ, m∠AOB + m∠BOC + m∠COA =360°
ସମାଧାନ:
ଦତ୍ତ : \(\overrightarrow{\mathrm{OA}}\), \(\overrightarrow{\mathrm{OB}}\) \(\overrightarrow{\mathrm{OC}}\) , O ବିନ୍ଦୁଗାମୀ ତିନୋଟି ଭିନ୍ନ ଭିନ୍ନ ରଶ୍ମି ।
ପ୍ରାମାଣ୍ୟ : m∠AOB + m∠BOC + m∠AOC = 360°
ଅଙ୍କନ : \(\overrightarrow{\mathrm{OA}}\) ର ବିପରୀତ ରଶ୍ମି \(\overrightarrow{\mathrm{OD}}\) ଏବଂ \(\overrightarrow{\mathrm{OB}}\) ର ବିପରୀତ ରଶ୍ମି \(\overrightarrow{\mathrm{OE}}\) ଅଙ୍କନ କର ।
ପ୍ରମାଣ : m∠AOE +m∠EOD = 180° (ସନ୍ନିହିତ ପରିପୂରକ କୋଣ)
m∠AOE + m∠EOC + m∠COD = 180° … (i)
[ m∠EOD = m∠EOC + m∠COD]
ସେହିପରି m∠AOB + m∠BOD = 180° (ସନ୍ନିହିତ ପରିପୂରକ କୋଣ) … (ii) 
ସମୀକରଣ (i) ଓ (ii)କୁ ଯୋଗକଲେ,
mAOE + mEOC + mCOD + mAOB + mBOD = 180° + 180°
⇒ mAOB + (mBOD + mDOC) + (mAOE + mEOC) = 360°
⇒ mAOB + mBOC + mCOA = 360°
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b) 19  (ପ୍ରମାଣିତ)

Question 17.
ପାର୍ଶ୍ୱସ୍ଥ ଚିତ୍ରରେ \(\overrightarrow{\mathrm{OE}}\), ∠AOB ର ସମଦ୍ବିଖଣ୍ଡକ ରଶ୍ମି । \(\overrightarrow{\mathrm{OF}}\), \(\overrightarrow{\mathrm{OE}}\) ର ବିପରୀତ ରଶ୍ମି ହେଲେ, ଦର୍ଶାଅ ଯେ,
m∠BOF = m∠AOF l
ସମାଧାନ:
ଦତ୍ତ : \(\overrightarrow{\mathrm{OE}}\), ∠AOB ର ସମର୍ଦ୍ଦିଖଣ୍ଡକ । \(\overrightarrow{\mathrm{OF}}\) ର ବିପରୀତ ରଶ୍ମି \(\overrightarrow{\mathrm{OE}}\) l
ପ୍ରାମାଣ୍ୟ : m∠BOF=m∠AOF
ପ୍ରମାଣ : ∠BOF ଏବଂ ∠BOE ସନ୍ନିହିତ ପରିପୂରକ ।
⇒ m∠BOF + m∠BOE = 180° … (i)
ପୁନଶ୍ଚ, ∠AOF ଏବଂ ∠AOE ସନ୍ନିହିତ ପରିପୂରକ ।
⇒ m∠AOF + m∠AOE = 180° … (ii)
⇒ (i) ଓ (ii) ରୁ mBOF + mBOE = mAOF + mAOE
⇒ m∠BOF = m∠AOF (\(\overrightarrow{\mathrm{OE}}\), ∠AOB ର ସମଦ୍ବିଖଣ୍ଡକ)
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(b) 20  (ପ୍ରମାଣିତ)

CHSE Odisha Class 12 Math Notes Chapter 12 Vectors

Odisha State Board CHSE Odisha Class 12 Math Notes Chapter 12 Vectors will enable students to study smartly.

CHSE Odisha 12th Class Math Notes Chapter 12 Vectors

Important formulae:
1. If P = (x1, y1, z1) and Q = (x2, y2, z2) then
P͞Q = (x2 – x1) î + (y2 – y1 ) ĵ + (z2 – z1) k̂
where î, ĵ, k̂ are the unit vectors along x-axis, y-axis and z-axis.

2. Magnitude of a vector:
CHSE Odisha Class 12 Math Notes Chapter 12 Vectors 1
CHSE Odisha Class 12 Math Notes Chapter 12 Vectors 2

CHSE Odisha Class 12 Math Notes Chapter 12 Vectors

8. Properties of vector product:
(i) Area of a parallelogram whose adjacent sides are represented by the
CHSE Odisha Class 12 Math Notes Chapter 12 Vectors 3
CHSE Odisha Class 12 Math Notes Chapter 12 Vectors 4
12. The vector equation of a straight line:
(i) The vector equation of a straight line passing through a point with position vector \(\vec{a}\) and parallel to a vector \(\vec{b}\) is \(\vec{r}=\vec{a}+t \vec{b}\) where t is a parameter.
(ii) The equation ofa striaght line through two points with position vectors \(\vec{a}\) and \(\vec{b}\) is \(\vec{r}=\vec{a}+t(\vec{b}-\vec{a})\).
(iii) Equation of a straight line through a point with position vector \(\vec{a}\) and perpendicualr to two non-parallel \(\vec{b}\) and \(\vec{c}\) is \(\vec{r}=\vec{a}+t(\vec{b} \times \vec{a})\).

CHSE Odisha Class 12 Math Notes Chapter 12 Vectors

13. The vector equation of a plane:
(i) The vector equation of plane through a point \(\vec{a}\) and perpendicular to n̂ is \((\vec{r}-\vec{a}) \cdot \hat{n}\) = 0
(ii) The equation of a plane through a point \(\vec{a}\) and parallel to non-parallel vectors \(\vec{b}\) and \(\vec{c}\) is \(\vec{r}=\vec{a}+t \vec{b}+s \vec{c}\), where t and s are parameters.
(iii) Equation of the plane passing through the points \(\vec{a}, \vec{b}\) and parallel to \(\vec{c}\) is \(\vec{r}=(1-t) \vec{a}+t \vec{b}+s \vec{c}\).
(iv) Equation of the plane through three non collinear points \(\vec{a}, \vec{b}, \vec{c}\) is \(\vec{r}=(1-s-t) \vec{a}+t \vec{b}+s \vec{c}\).

BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(a)

Odisha State Board BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(a) Textbook Exercise Questions and Answers.

BSE Odisha Class 9 Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(a)

Question 1.
ନିମ୍ନଲିଖ ପଦଗୁଡ଼ିକରୁ ସଂଜ୍ଞାବିହୀନ ଓ ସଂଜ୍ଞାବିଶିଷ୍ଟ (ଯାହାର ସଂଜ୍ଞା ଅଛି) ପଦଗୁଡ଼ିକୁ ଚିହ୍ନାଅ ।
ରେଖାଖଣ୍ଡର ମଧ୍ୟବିନ୍ଦୁ, ସ୍ଥାନାଙ୍କ, ଦୂରତା, ସରଳରେଖା, ରଶ୍ମି, ରେଖାଖଣ୍ଡ, ସମତଳ, ବିନ୍ଦୁ ।
ସମାଧାନ:
ସଂଜ୍ଞାବିହୀନ ପଦ – ସରଳରେଖା, ସମତଳ, ବିନ୍ଦୁ, ।
ସଂଜ୍ଞାବିଶିଷ୍ଟ ପଦ – ରେଖାଖଣ୍ଡର ମଧ୍ୟବିନ୍ଦୁ, ସ୍ଥାନାଙ୍କ, ଦୂରତା, ରଶ୍ମି, ରେଖାଖଣ୍ଡ ।

Question 2.
ନିମ୍ନଲିଖତ ପ୍ରଶ୍ନଗୁଡ଼ିକର ସଂକ୍ଷିପ୍ତ ଉତ୍ତର ପ୍ରଦାନ କର ।
(କ) ଗୋଟିଏ ସରଳରେଖାରେ କେତୋଟି ବିନ୍ଦୁ ଥାଏ ?
ସମାଧାନ:
ଅସଂଖ୍ୟ

(ଖ) ଗୋଟିଏ ରେଖାଖଣ୍ଡରେ କେତୋଟି ବିନ୍ଦୁ ଥାଏ ?
ସମାଧାନ:
ଅସଂଖ୍ୟ

(ଗ) ଗୋଟିଏ ରେଖାଖଣ୍ଡରେ କେତୋଟି ପ୍ରାନ୍ତ ବିନ୍ଦୁ ଓ କେତୋଟି ମଧ୍ୟବିନ୍ଦୁ ଥାଏ ?
ସମାଧାନ:
ଦୁଇଟି ଓ ଗୋଟିଏ

(ଘ) ଗୋଟିଏ ରଶ୍ମି ଓ ତାହାର ବିପରୀତ ରଶ୍ମିର ସଂଯୋଗରେ କ’ଣ ଗଠିତ ହୁଏ ?
ସମାଧାନ:
ସରଳରେଖା

(ଙ) ଗୋଟିଏ ରଶ୍ମି ଓ ତାହାର ବିପରୀତ ରଶ୍ମିର ଛେଦରେ କେତୋଟି ବିନ୍ଦୁ ଥାଏ ?
ସମାଧାନ:
ଗୋଟିଏ

(ଚ) ତିନୋଟି ପୃଥକ୍ ସରଳରେଖା ପରସ୍ପରକୁ ଅତିବେଶିରେ କେତୋଟି ବିନ୍ଦୁରେ ଛେଦ କରିବେ ?
ସମାଧାନ:
ତିନୋଟି

(ଛ) ଚାରୋଟି ପୃଥକ୍ ସରଳରେଖା ପରସ୍ପରକୁ ଅତିବେଶିରେ କେତୋଟି ବିନ୍ଦୁରେ ଛେଦ କରିବେ ?
ସମାଧାନ:
ଛଅଗୋଟି

(ଜ) ଚାରୋଟି ପୃଥକ୍ ମଧ୍ୟବିନ୍ଦୁ ମଧ୍ୟରୁ କୌଣସି ତିନୋଟି ଏକରେଖୀ ହୋଇ ନଥିଲେ, ସେମାନଙ୍କ ଦ୍ବାରା କେତୋଟି ସରଳରେଖା ନିର୍ଦ୍ଧାରିତ ହୋଇ ପାରିବ ?
ସମାଧାନ:
ଛଅଗୋଟି

BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(a)

Question 3.
ଶୂନ୍ୟସ୍ଥାନ ପୂରଣ କର । ଦତ୍ତ ଅଛି A – B – C
(i) A͞B ∪ \(\overrightarrow{AC}\) = ________
ସମାଧାନ:
\(\overrightarrow{AC}\)

(ii) \(\overrightarrow{BA}\) ∪ \(\overrightarrow{BC}\) = ________
ସମାଧାନ:
\(\overleftrightarrow{AC}\)

(iii) A͞B ∪ B͞C = ________
ସମାଧାନ:
AC

(iv) \(\overrightarrow{AB}\) ∪ \(\overrightarrow{AC}\) = ________
ସମାଧାନ:
\(\overrightarrow{AB}\) ବା \(\overrightarrow{AC}\)

(v) \(\overrightarrow{AB}\) ∩ \(\overrightarrow{BA}\) = ________
ସମାଧାନ:
AB

(vi) A͞C ∩ B͞C = ________
ସମାଧାନ:
BC

(vii) \(\overrightarrow{BA}\) ∩ \(\overrightarrow{BC}\) = ________
ସମାଧାନ:
{B}

(viii) AC – BC = ________
ସମାଧାନ:
AB

(ix) AC – AB = ________
ସମାଧାନ:
BC

Question 4.
L ସରଳରେଖା ଉପରିସ୍ଥ À ଓ B ବିନ୍ଦୁଦ୍ଵୟର ସ୍ଥାନାଙ୍କ ଯଥାକ୍ରମେ – 3 ଓ 5 ହେଲେ AB କେତେ ?
ସମାଧାନ:
L ସରଳରେଖା ଉପରିସ୍ଥ A ଓ B ର ସ୍ଥାନାଙ୍କ ଯଥାକ୍ରମେ – 3 ଓ 5 ହେଲେ,
A͞B ର ଦୈର୍ଘ୍ୟ = AB = |-3 – 5| = |-8| = 8
ଅଥବା AB = |5 – (-3)| = |8| = 8

Question 5.
\(\overleftrightarrow{AB}\) ଉପରିସ୍ଥ A ଓ B ର ସ୍ଥାନାଙ୍କ ଯଥାକ୍ରମେ – 16 ଓ 20 ହେଲେ AB ର ମଧ୍ୟବିନ୍ଦୁର ସ୍ଥାନାଙ୍କ କେତେ ? 
ସମାଧାନ:
 A ଓ B ର ସ୍ଥାନାଙ୍କ ଯଥାକ୍ରମେ – 16 ଓ 20 ।
∴ AB ର ମଧ୍ୟବିନ୍ଦୁର ସ୍ଥାନାଙ୍କ = \(\frac{-16+20}{2}=\frac{4}{2}\) = 2

BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(a)

Question 6.
ନିମ୍ନସ୍ଥ ପ୍ରଶ୍ନଗୁଡ଼ିକରେ ସଂପୃକ୍ତ ସମସ୍ତ ବିନ୍ଦୁ ଏକରେଖୀ ଅଟନ୍ତି ।
(କ) A, B ଓ C ର ସ୍ଥାନାଙ୍କ ଯଥାକ୍ରମେ – 11, 4 ଓ 2 ହେଲେ, କେଉଁ ବିନ୍ଦୁଟି ଅନ୍ୟ ଦୁଇଟିର ମଧ୍ୟବର୍ତ୍ତୀ ?
ସମାଧାନ:
A, B, C ର ସ୍ଥାନାଙ୍କ ଯଥାକ୍ରମେ – 11, 4 ଓ 2 । ଏଠାରେ – 11 < 2 < 4 ଯୋଗୁଁ A – C – B
ଅର୍ଥାତ୍ C ବିନ୍ଦୁ A ଓ B ର ମଧ୍ୟବର୍ତ୍ତୀ ବିନ୍ଦୁ ହେବ ।
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(a) 1

(ଖ) PQ = 8, QR = 5 ଓ RP = 3 ହେଲେ P, Q, R ମଧ୍ଯରେ କେଉଁ ବିନ୍ଦୁଟି ଅନ୍ୟ ଦ୍ଵୟର ମଧ୍ୟବର୍ତ୍ତୀ ?
ସମାଧାନ:
PQ = 8, QR = 5, RP = 3 10166 PQ = QR + RP
ଅର୍ଥାତ୍ R ବିନ୍ଦୁ Q ଓ P ର ମଧ୍ୟବର୍ତ୍ତୀ ବିନ୍ଦୁ ହେବ ।
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(a)

(ଗ) A ର ସ୍ଥାନାଙ୍କ – 3, A – C – B, BC = 2 ଓ C ର ସ୍ଥାନାଙ୍କ – 4 ହେଲେ, B ର ସ୍ଥାନାଙ୍କ ଓ AB କେତେ ? 
ସମାଧାନ:
A ର ସ୍ଥାନାଙ୍କ – 3, BC = 2, C ର ସ୍ଥାନାଙ୍କ – 4 ଏବଂ A – C – B ।
∴ B ର ସ୍ଥାନାଙ୍କ = – 4 – 2 = -6
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(a) 2

BC = 2 ଯୋଗୁଁ, AB = |-6 -3| = |-9|  = 9

(ଘ) ଓ B ର ସ୍ଥାନାଙ୍କ ଯଥାକ୍ରମେ – 11 ଓ 21 ହେଲେ, A͞B ର ମଧ୍ୟବିନ୍ଦୁର ସ୍ଥାନାଙ୍କ କେତେ ଓ A ଠାରୁ ଏହାର ଦୂରତା କେତେ ?
ସମାଧାନ:
A ଓ B ର ସ୍ଥାନାଙ୍କ ଯଥାକ୍ରମେ – 11 ଓ 21 । A ଓ B ର ମଧ୍ୟବିନ୍ଦୁ C ହେଲେ
∴ A͞B ର ମଧ୍ୟବିନ୍ଦୁ ‘C’ ର ସ୍ଥାନାଙ୍କ = \(\frac{-11+21}{2}=\frac{10}{2}\) = 5
∴ A ଠାରୁ ମଧ୍ୟବିନ୍ଦୁ ‘C’ ର ଦୂରତା = |-11 – 5| = |-6| = 6
∴ AC = 16

(ଙ) A ର ସ୍ଥାନାଙ୍କ – 5 ଓ ĀB ର ମଧ୍ୟବିନ୍ଦୁର ସ୍ଥାନାଙ୍କ 0 ହେଲେ, B ର ସ୍ଥାନାଙ୍କ କେତେ ?
ସମାଧାନ:
A ର ସ୍ଥାନାଙ୍କ – 5 | AB ର ମଧ୍ୟବିନ୍ଦୁ (M) ର ସ୍ଥାନାଙ୍କ 0 |
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(a) 3
ମନେକର B ର ସ୍ଥାନାଙ୍କ ‘x’
∴ 0 = \(\frac{-5+x}{2}\) ⇒ x = 5
∴ B ବିନ୍ଦୁର ସ୍ଥାନାଙ୍କ = 5

BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(a)

Question 7.
A, L ସରଳରେଖା ଉପରିସ୍ଥ ଏକ ବିନ୍ଦୁ ଏବଂ A ର ସ୍ଥାନାଙ୍କ 5 ଅଟେ । A ଠାରୁ 2 ଏକକ ଦୂରତା ବିଶିଷ୍ଟ କେତୋଟି ବିନ୍ଦୁ L ଉପରେ ଅବସ୍ଥିତ ହେବ ଓ ସେମାନଙ୍କର ସ୍ଥାନାଙ୍କ କେତେ ହେବ ?
ସମାଧାନ:
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(a) 4
L ସରଳରେଖା ଉପରିସ୍ଥ A ବିନ୍ଦୁର ସ୍ଥାନାଙ୍କ 5 । A ଠାରୁ 2 ଏକକ ଦୂରତା ବିଶିଷ୍ଟ ଦୁଇଟି ବିନ୍ଦୁ L ଉପରେ ଅବସ୍ଥାନ କରିବ ।
ଆମେ ଜାଣୁ L ସରଳରେଖା ଉପରେ P ଏକ ବିନ୍ଦୁ ଏବଂ à ଏକ ଧନାତ୍ମକ ବାସ୍ତବ ସଂଖ୍ୟା ହେଲେ L 
ଉପରେ କେବଳ ଦୁଇଟି ବିନ୍ଦୁ ରହିବ; ଯାହାର ସ୍ଥାନାଙ୍କ P + a ଓ P – a ।
∴ L ଉପରେ ଦୁଇଟି ବିନ୍ଦୁ ରହିବ ଯଥା B ଓ C ଏବଂ ସେମାନଙ୍କର ସ୍ଥାନାଙ୍କ ଯଥାକ୍ରମେ 5 + 2 = 7 ଓ 5 – 2 = 3 

Question 8.
ନିମ୍ନଲିଖ ପଦଗୁଡ଼ିକୁ ଉଦାହରଣ ମାଧ୍ୟମରେ ବୁଝାଅ ।
ରେଖାଖଣ୍ଡର ମଧ୍ୟବିନ୍ଦୁ, ବିପରୀତ ରଶ୍ମି, ବିନ୍ଦୁମାନଙ୍କ ମଧ୍ୟସ୍ଥ ଦୂରତା, ମଧ୍ୟବର୍ତ୍ତିତା ।
ସମାଧାନ:
ରେଖାଖଣ୍ଡର ମଧ୍ୟବିନ୍ଦୁ : ଏକ ରେଖାଖଣ୍ଡର ଗୋଟିଏ ମାତ୍ର ମଧ୍ୟବିନ୍ଦୁ ଥାଏ । ମନେକର A ଓ B ର ସ୍ଥାନାଙ୍କ
ଯଥାକ୍ରମେ x ଓ y ଏବଂ AB ର ମଧ୍ୟବିନ୍ଦୁ ‘C’ ହେଲେ C ବିନ୍ଦୁର ସ୍ଥାନାଙ୍କ = \(\frac{x+y}{2}\) ହେବ ।
AC = CB = \(\frac{1}{2}\)AB 
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(a)
‘C’ ବିନ୍ଦୁଟି AB ର ମଧ୍ୟବିନ୍ଦୁ ହେବ ।

ବିପରୀତ ରଶ୍ମି : L ରେଖା ଉପରିସ୍ଥ A, O ଓ B ବିନ୍ଦୁ ଯେପରିକି A – O – B
ଏଠାରେ \(\overrightarrow{\mathrm{OA}}\) ଓ \(\overrightarrow{\mathrm{OB}}\) କୁ ବିପରୀତ ରଶ୍ମି କୁହାଯାଏ ।
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(a)
\(\overrightarrow{\mathrm{OA}}\) ଏବଂ \(\overrightarrow{\mathrm{OB}}\) ପରସ୍ପରର ବିପରୀତ ରଶ୍ମି ହେଲେ \(\overrightarrow{\mathrm{OA}}\) ∪ \(\overrightarrow{\mathrm{OB}}\) = \(\overleftrightarrow{\mathrm{AB}}\) = L
ଅର୍ଥାତ୍ ଦୁଇଟି ବିପରୀତ ରଶ୍ମି \(\overrightarrow{\mathrm{OA}}\) ଏବଂ \(\overrightarrow{\mathrm{OB}}\) ର ସଂଯୋଗ \(\overleftrightarrow{\mathrm{AB}}\) (AB ସରଳରେଖା) ଅଟେ ।

ବିନ୍ଦୁମାନଙ୍କ ମଧ୍ୟସ୍ଥ ଦୂରତା : A ଓ B ବିନ୍ଦୁଦ୍ଵୟର ସ୍ଥାନାଙ୍କ x ଓ y ହେଲେ,
A ଓ B ମଧ୍ୟସ୍ଥ ଦୂରତା = AB = |x – y| (∴ A ଓ B ର ସ୍ଥାନାଙ୍କ ଦ୍ଵୟର ଅଣଋଣାତ୍ମକ ଅନ୍ତର = AB) 
ଏ କ୍ଷେତ୍ରରେ AB ଗୋଟିଏ ଧନାତ୍ମକ ବାସ୍ତବ ସଂଖ୍ୟା ହେବ । ଯାହା ହେଉଛି A ଓ B ବିନ୍ଦୁ ମଧ୍ୟସ୍ଥ ଦୂରତା ।

ମଧ୍ୟବର୍ତ୍ତିତା : ତିନୋଟି ପୃଥକ୍ ବିନ୍ଦୁ A, B ଓ C ଯଦି ଏକ ସରଳରେଖା ଉପରେ ଅବସ୍ଥାନ
BSE Odisha 9th Class Maths Solutions Geometry Chapter 1 ରେଖା ଓ କୋଣ Ex 1(a) 5
କରନ୍ତି ଓ AB + BC = AC ହୁଏ; ତେବେ B କୁ A ଓ C
(କିମ୍ବା C ଓ A )ର ମଧ୍ୟବର୍ତ୍ତୀ ବିନ୍ଦୁ କୁହାଯାଏ ।
ବିନ୍ଦୁ ତ୍ରୟର ଏ ପ୍ରକାର ଅବସ୍ଥାକୁ ସାଙ୍କେତିକ ଭାଷାରେ A – B – C କିମ୍ବା C – B – A ଭାବରେ ଲେଖାଯାଏ ।

CHSE Odisha Class 12 Math Notes Chapter 5 Determinants

Odisha State Board CHSE Odisha Class 12 Math Notes Chapter 5 Determinants will enable students to study smartly.

CHSE Odisha 12th Class Math Notes Chapter 5 Determinants

Evaluation of determinants:
CHSE Odisha Class 12 Math Notes Chapter 5 Determinants 1
Note: We can evaluate a determinant along any row or column.

Minors and cofactors:
Minor of an element aij is the determinant obtained by deleting ith row and jth column denoted by Mij.
Example.
CHSE Odisha Class 12 Math Notes Chapter 5 Determinants 2

CHSE Odisha Class 12 Math Notes Chapter 5 Determinants

Properties of determinant:
(a) The value of a determinant remains unchanged by changing rows to columns and columns to rows.
(b) The interchange of two adjacent rows or columns of determinant changes the sign of a determinant without changing its numerical value
CHSE Odisha Class 12 Math Notes Chapter 5 Determinants 3
(c) If two rows or columns of a determinant are identical then the value of determinant is zero.
(d) If every element of any row or column is multiplied by a factor, then the determinant is multiplied by that factor.
(e) If every element of any row (or column) of a determinant is expressed as sum of two or more numbers, then the determinant can be expressed as the sum of two or more determinants.
CHSE Odisha Class 12 Math Notes Chapter 5 Determinants 4
(f) A determinant remains unchanged by adding k times the elements of any row (or column) to corresponding elements of any other row (or column) where k is any number or function.

Cramer’s rule to solve a system of linear equations:
Let
a1x + b1y + c1z = d1
a2x + b2y + c2z = d2
a3x + b3y + c3z = d3
is system of linear equations
CHSE Odisha Class 12 Math Notes Chapter 5 Determinants 5
Note:
(i) If D1 = D2 = D3 = D = 0 then the system has infinitely many solutions.
(ii) If D = 0 and atleast one of D1, D2 or D3 is not zero then the system has no solution.