Class 12

Odisha State Board CHSE Odisha Class 12 Math Solutions Chapter 8 Application of Derivatives Ex 8(b) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 8 Application of Derivatives Exercise 8(b)

Question 1.
Find the equations to the tangents and normals to the following curves at the indicated points.
(i) y = 2x² + 3 at x = -1
Solution:
y = 2x² + 3 at x = -1
⇒ \(\frac{d y}{d x}\) = 4        ∴\(\left.\frac{d y}{d x}\right]_{-1}\) = -4
Thus slope of the tangent at x = -1 is -4.
Angin for x = -1 , y = 2 + 3 = 5
The point of contact is (-1, 5).
Equation of the tangent is y – 5 = -4 (x + 1)
⇒ 4x + y – 1 = 0
Slope of the normal = \(\frac{1}{4}\)
Eqn. of the normal is y – 5 = \(\frac{1}{4}\) (x + 1)
⇒ 4y – 20 = x + 1
⇒ x – 4y + 21 = 0

(ii) y = x³ – x at x = 2
Solution:
y = x³ – x at x = 2
When x = 2, y = 2³ – 2 = 6
The point is (2, 6).
Again \(\frac{d y}{d x}\) = 3x² – 1
\(\left.\frac{d y}{d x}\right]_{x=2}\) = 12 – 1 = 11
Slope of the tangent = 11.
Slope of the normal = –\(\frac{1}{11}\)
Equation of the tangent is
y – 6 = 11 (x – 2)
⇒ 11x – y – 16 = 0
Equation of the normal is
y – 6 = –\(\frac{1}{11}\)
⇒ 11y – 66 = – x + 2
⇒ x + 11y – 68 = 0

(iii) y = √x + 2x + 6 at x = 4
Solution:
y = √x + 2x + 6 at x = 4
For x = 4, y = 2 + 8 + 6 = 16
The point is (4, 16)
Again \(\frac{d y}{d x}\) = \(\frac{1}{2 \sqrt{x}}\) + 2
\(\left.\frac{d y}{d x}\right]_{x=4}\) = \(\frac{1}{4}\) + 2 = \(\frac{9}{4}\)
Slope of the tangent = \(\frac{9}{4}\)
Slope of the normal = –\(\frac{4}{9}\)
Equation of the tangent is
y – 16 = \(\frac{9}{4}\)(x – 4)
⇒ 9x – 4y + 28 = 0
Equation of the normal is
y – 16 = – \(\frac{4}{9}\)(x – 4)
⇒ 9y – 144 = -4x + 16
⇒ 4x + 9y – 160 = 0

(iv) y = √3 sin x + cos x at x = \(\frac{\pi}{3}\)
Solution:

(v) y = (log x)² at x = \(\frac{1}{e}\)
Solution:

(vi) y = \(\frac{1}{\log x}\) at x = 2
Solution:

(vii) y = xe^-x at x = 0
Solution:
y = xe^-x at x = 0
For x = 0, y = 0
The point is (0, 0).
\(\frac{d y}{d x}\) = e^-x + x . (-e^-x)
\(\left.\frac{d y}{d x}\right]_{x=0}\) = 1
Slope of the tangent = 1
Slope of the normal = -1
Equation of the tangent is y = x and equation of the normal is y = -x

(viii) y = a (θ – sin θ), y = a (1 – cos θ) at θ = \(\frac{\pi}{2}\)
Solution:
y = a (θ – sin θ), y = a (1 – cos θ) at θ = \(\frac{\pi}{2}\)

(ix) \(\left(\frac{x}{a}\right)^{2 / 3}\) + \(\left(\frac{y}{b}\right)^{2 / 3}\) = 1 at (a cos³ θ, b sin³ θ)
Solution:
\(\left(\frac{x}{a}\right)^{2 / 3}\) + \(\left(\frac{y}{b}\right)^{2 / 3}\) = 1 at (a cos³ θ, b sin³ θ)

Question 2.
Find the point on the curve y² – x² + 2x – 1 = 0 where the tangent is parallel to the x – axis.
Solution:
Given curve is y² – x² + 2x – 1 = 0 … (1)

Putting x = 1 in (1) we get
y² – 1 + 2 – 1 = 0 ⇒ y = 0
∴ The point is (1, 0).

Question 3.
Find the point (s) on the curve x = \(\frac{3 a t}{1+t^2}\), y = \(\frac{3 a t^2}{1+t^2}\) where the tangent is perpendicular to the line 4x + 3y + 5 = 0.
Solution:

Question 4.
Find the point on the curve x² + y² – 4xy + 2 = 0 where the normal is parallel to the x axis.
Solution:
x² + y² – 4xy + 2 = 0

Question 5.
Show that the line y = mx + c touches the parabola y² = 4ax if c = \(\frac{a}{m}\).
Solution:
Given line is y = mx + c … (1)
Given parabola is y² = 4ax

Question 6.
Show that the line y = mx + c touches the ellipse
\(\frac{x^2}{a^2}\) + \(\frac{y^2}{b^2}\) = 1 if c² = a²m² + b²
[Hints: Find equation to tangent at a point (x’, y’) of the curve and compare it with
y = mx + c].
Solution:

Question 7.
Show that the sum of the intercepts on the coordinate axes of any tangent to the curve
√x + √y = √a is constant.
Solution:

Question 8.
Show that the curves y = 2^x and y = 5^x intersect at an angle
tan^-1 \(\left|\frac{\ln \left(\frac{5}{2}\right)}{1+\ln 2 \ln 5}\right|\)
(Note: Angle between two curves is the angle between their tangents at the point of intersection)
Solution:
Given curves are
y = 2^x … (1)
and y = 5^x … (2)
Differentiating (1) we get \(\frac{d y}{d x}\) = 2^x . In 2
Differentiating (2) we get \(\frac{d y}{d x}\) = 5^x . In 2
Slope of the tangent to the first curve at (x, y) = 2^x . In 2
Slope of the tangent to the second curve at (x, y) = 5^x . In 2
Solving (1) and (2) we get 2^x = 5^x ⇒ x = 0
For x = 0, y = 1
∴ The point of intersection is (0, 1).
At (0, 1) slope of the 1st tangent = In 2
Slope of the second tangent = In 5
If θ is the angle between two tangents
then \(\frac{\ln 5-\ln 2}{1+\ln 5 \cdot \ln 2}\) = \(\frac{\ln \frac{5}{2}}{1+\ln 5 \cdot \ln 2}\)
= tan^-1 \(\left(\frac{\ln \frac{5}{2}}{1+\ln 5 \cdot \ln 2}\right)\)
We know that angle between two curves is the angle between their tangents at the point of intersection.
Hence the two curves intersect at an angle.
\(\left(\tan ^{-1} \cdot \frac{\ln \frac{5}{2}}{1+\ln 5 \cdot \ln 2}\right)\)

Question 9.
Show that the curves ax² + by² =1 and a’x² + b’y² = 1. Intersect at right angles if
\(\frac{1}{a}\) – \(\frac{1}{a}\) = \(\frac{1}{a^{\prime}}\) – \(\frac{1}{b^{\prime}}\).
Solution:
Given curves are
ax²+ by²= 1 … (1)
and a’x² + b’y² = 1 … (2)
Differentiating (1) we get

Question 10.
Find the equation of the tangents drawn from the point (1, 2) to the curve.
y² – 2x³ – 4y + 8 = 0
Solution:
Given curve is
y² – 2x³ – 4y + 8 = 0 … (1)

⇒ -(k – 2)² = 3h² – 3h³
⇒ (k – 2)² = 3h³ – 3h²
Putting it in (2) we get
k² – 2h³ – 4k + 8 = 0
⇒ k² – 4k + 4 – 2h³ + 4 = 0
⇒ (k – 2)² – 2h³ + 4 = 0
⇒ 3h³ – 3h² – 2h³ + 4 = 0
⇒ h³ – 3h² + 4 = 0
⇒ h³ + h² – 4h² + 4 = 0
⇒ h² (h + 1) – 4 (h² – 1) = 0
⇒ h² (h + 1) – 4 (h + 1) (h – 1) = 0
⇒ (h + 1) (h² – 4h + 4) = 0
⇒ (h + 1) (h – 2)² = 0
⇒ h = -1, 2.
For h = -1, k is imaginary.
For h = 2, k = 2 + 2√3
The point at which the tangent is drawn is (2, 2 + 2√3).
Slope of the tangents
= \(\frac{3 h^2}{k-2}\) = \(\frac{12}{\pm 2 \sqrt{3}}\) = ± 2√3
Equations of the tangental
y – (2 ± 2√3) = ± 2√3(x – 2)

Question 11.
Show that the equation to the normal to x^2/3 + y^2/3 = a^2/3 is y cos θ – x sin θ = a cos 2θ where θ is the inclination of the normal to x – axis.
Solution:

The point is (a² sin³ θ, a² cos³ θ).
Equation of the normal is
y – a² cos³ θ = tan θ (x – a² sin³ θ)
⇒ y cos θ – a² cos⁴ θ = x sin θ – a² sin⁴ θ
⇒ y cos θ – x sin θ = a² (cos⁴ θ – sin⁴ θ)
= a² (cos² θ + sin² θ) (cos² θ – sin² θ)
= a² cos 2θ.
∴ Equation of the normal is
y cos θ – x sin θ = a² cos 2θ.(Proved)

Question 12.
Show that the length of the portion of the tangent to x^2/3 + y^2/3 = a^2/3 intercepted between the axes is constant.
Solution:

Question 13.
Find the tangent to the curve y = cos (x + y), 0 < x ≤ 2π which is parallel to the line
x + 2y = 0.
Solution:
y = cos (x + y) … (1)

Question 14.
If tangents are drawn from the origin to the curve y = sin x then show that the locus of the points of contact is x²y² = x² – y²
Solution:
Given curve is
y = sin x … (1)
\(\frac{d y}{d x}\) = cos x
Slope of the tangent to the cure (1) at any point (x, y) is cos x.
Let (h, k) be the point of contact.
Then slope of the tangent at (h, k) = cos h.
Equation of the tangent to the curve (1) at (h, k) is
y – k = cos h (x – h) … (2)
If the tangent is drawn from the origin then -k = -h cos h
⇒ k = h cos h … (3)
As (h, k) is the poitn of contact then we have
k = sin h … (4)
From (3) we get,
k = h\(\sqrt{1-\sin ^2 h}\) = h\(\sqrt{1-k^2}\) by (4).
Squaring both sides we get
k² = h² (1 – k²)
⇒ k² = h² – h²k²
⇒ h²k² = h² – k²
The locus of (h, k) is x².y² = x² – y² (Proved)

Question 15.
Find the equation of the normal to the curve given by
x = 3 cos θ – cos³ θ
y = 3 sin θ – sin³ θ at θ = \(\frac{\pi}{4}\)
Solution:
x = 3 cos θ – cos³ θ
y = 3 sin θ – sin³ θ
Differentiating we get
\(\frac{d x}{d \theta}\) = -3 sin θ + 3 cos² θ . sin θ
\(\frac{d x}{d \theta}\) = 3 cos θ – 3 sin² θ . cos θ

Question 16.
If x cos α + y sin α = p is a tangent to the curve \(\left(\frac{x}{a}\right)^{\frac{n}{n-1}}\) + \(\left(\frac{y}{b}\right)^{\frac{n}{n-1}}\) = 1
then show that (a cos α)ⁿ + (b sin α)ⁿ = pⁿ
Solution:
Given straight line is x cos α + y sin α = p … (1)
Given curve is

Question 17.
Show that the tangent to the curve
x = a (t – sin t), y = at (1 + cos t) at t = \(\frac{\pi}{2}\) has slope. (1 – \(\frac{\pi}{2}\))
Solution:
Given curve is x = a (t – sin t)
y = at (1 + cos t)

Odisha State Board CHSE Odisha Class 12 Invitation to English 4 Solutions Grammar Tense Patterns Unit 6 The Past Simple and the Past Perfect Textbook Activity Questions and Answers.

CHSE Odisha 12th Class English Grammar Tense Patterns Unit 6 The Past Simple and the Past Perfect

SECTION – 1

Look at the sentences below.
(a) I reached the hostel in the morning and found that somebody had broken into my room during the night.
(b) She said that her friend had published a book.
(c) He had lived in this town for ten years; then he migrated to Japan.
Can you find the Past Perfect Tense in each sentence? Note that the sentence in which it occurs refers to two actions — the action expressed by the Past Perfect and another action expressed by the Past Simple. Of the two actions, which takes place earlier and which takes place later? List them below.

(a) (1) I reached the hotel in the morning and found. (later).
(2) that somebody had broken (earlier action) into my room during the night.
(b) (1) She said _________(later action).
(2) that her friend had published a book _________(earlier action).
(c) (1) _________then he migrated to Japan _________(later action).
(2) He had lived in this town for ten years, (earlier action).
Can you answer now? Which action does the Past Perfect refer to — the earlier one or the later one? Which action does the Past Simple refer to?
Answer:
The earlier action refers to Past Perfect and the later one refers to Past Simple Tense.

Activity – 23
Combine each pair of sentences below into a single sentence, using the Past Perfect to show which action took place earlier. (You may have to use words like after; when etc.
(a) (i) I finished my homework.
(ii) Then I went to buy a pen.
_____________________________________.
(b) (i) Then the doctor gave some medicine to the patient,
(ii) Then the patient regained his senses.
_____________________________________.
(c) (i) I read a few pages from the book.
(ii) After that I returned it to the librarian.
_____________________________________.
(d) (i) I worked in the garden for some time.
(ii) After that I had my breakfast.
____________________________
(e) (i) He left the place in a hurry.
(ii) After that his friend arrived.
____________________________
(f) (i) The young girl finished shopping.
(ii) Then she met with an accident.
____________________________
(g) (i) The thief ran away with the gold.
(ii) After that the police arrived.
____________________________
Answer:
(a) After I had finished my homework, I went to buy a pen.
(b) After the doctor had given some medicine to the patient, the patient regained his senses.
(c) After I had read a few pages from the book, I returned to the librarian.
(d) I had worked in the garden for some time before I had my breakfast.
(e) When he had left the place in a hurry. his friend arrived.
(f) After the young girl had finished shopping. she met with an accident.
(g) The thief had run away with the gold before the police arrived.

Activity — 24
Jatin arrived late at different places yesterday. What did he find when he arrived
at each place?
Example — When he arrived at the cricket stadium, the game had ended.
(a) the hank it / already I close.
____________________________
(b) his uncle’s house his uncle I go the sleep.
____________________________
(c) the bus stops the bus I already / leave.
____________________________
(d) book shop the book he wanted/sold out already.
_________________________________
(e) the club his friends/leave.
_________________________________
(f) the hostel everyone / go to bed.
_________________________________
Answer:
(a) When he arrived at the bank, it had already closed.
(b) When he got to his uncle’s house, his uncle had gone to sleep.
(c) When he reached the bus stop, the bus had already left.
(d) When he came to the bookshop, the book he wanted had been sold out already.
(e) When he arrived at the club, his friends had left.
(f) When he came to the hostel, everyone had gone to bed.

Activity – 25
Use the verb supplied in brackets in the appropriate form.
(a) We went to Anil’s house and _____________(knock) on the door but there _____________ (be) no answer. Either he _____________ (go) out or he _____________ (not want) to see anyone.
(b) Sadhan _____________(go) for a walk yesterday because the doctor _____________(tell) him last week that he _____________(need) exercise.
(c) A : _____________(Seema / arrive) at the party in time last night ?
B: No, she was late. By the time, we got there, everyone _____________(leave).
Answer:
(a) We went to Anil’s house and knocked on the door but there was no answer. Either he had gone out or he did not want to see anyone.
(b) Sadhan went for a walk yesterday because the doctor told him last week that he needed exercise.
(c) A: Did Seema arrive at the party in time last night?
B: No, she was late. By the time, we got there, everyone had left.

Odisha State Board CHSE Odisha Class 12 Invitation to English 3 Solutions Writing Reporting Events and Business Matters Textbook Activity Questions and Answers.

CHSE Odisha 12th Class English Writing Reporting Events and Business Matters

8.1 Reporting Events

Generally, we come across events in daily newspapers. Reporting events requires a special skill in presenting the event accurately, concisely, and authentically. Various types of events take different forms of expression.

Now read the following news report from a staff reporter of a newspaper.

Answer these questions on the news item :

Question 1.
Who has been sentenced?
Answer:
A doctor belonging to Ranchi has been sentenced.

Question 2.
How long is the sentence?
Answer:
The sentence is for five years’ rigorous imprisonment.

Question 3.
Why has he been sentenced?
Answer:
He has been sentenced because he was caught in the act of removing a kidney of one Nasir Ali when he was unconscious.

Question 4.
When was the case detected?
Answer:
The case was detected by the police on May 8, 2008.

Question 5.
What was the doctor doing?
Answer:
The doctor was trying to remove the kidney of the unconscious Nasir Ali.

Activity – 1

A report about smuggling of fake currency notes appeared in The Times of India on 2 March 2009. The bare facts are given below. Write the report, using these facts.
Three Pakistani nationals have been arrested.
They were arrested on Monday.
Place of arrest, Amritsar.
They were attempting to smuggle fake currency notes.
The value of the currency notes was Rs. 20 lakh.
They were travelling by the Samjhauta Express.
The customs officials seized the fake currency notes.
This was the fifth major seizure.

Answer:
Fake Currency Notes Siezed The Times of India News Service:
Amritsar March 2 : Custom officials seized currency notes worth Rs. 20 lakhs from three Pakistani nationals who were travelling by Samjhauta Express. They were arrested on Monday at Amritsar. This was the custom officials fifth major seizure.

Activity – 2

A newspaper reporter sent a report of an incident on March 12, 2009 over telephone. A sub-editor in the newspaper office, who received the telephone message, took the following notes. Use them to write up a report for the newspaper.
Five pick-pockets caught red-handed
In north Calcutta
Wednesday
Robbing passengers on a private bus
45 wallets and jewellery recovered
police arrested them.

Answer:
Pick-pockets caught Red-handed
Calcutta March 12 : Police caught five pick-pockets in north Calcutta this Wednesday while they were trying to flee after having robbed passengers on a private bus. 45 wallets and jewellery were recovered from them. Police arrested them.

Activity – 3

There was a train accident in the area where you work as a news reporter. You went to the spot and talked to different people including some of the passengers. You also met the railway officials. The following are the points you noted down.
Train accident at Retang at 7.30 p.m. on 11 April.
Three bogies of the East Coast Express derailed.
7 bodies recovered so far
25 injured sent to hospital in Cuttack; 5 serious cases.
Rescue operations still on.
More bodies suspected trapped inside wreakage.

Answer:
Train Derailed : Many Feared Dead, 25 Injured.
Retang, April 1 1 : Three bogies of the East Coast Express derailed here at 7 30 p.m. this morning. 7 bodies have been recovered so far but many are feared to be still trapped under the wreckage. The injured have been sent to the SC B Hospital Cuttack Oi 25 injured, five are in an extremely serious condition. Rescue operations are still on.

Activity – 4

Below you can see a picture of an incident that happened in front of Badanibadi Bus Stand, Cuttack. Report the incident, using the hints given below the picture.

Hints :
Badanibadi, Cuttack  12 December, 2008.  Morning 9
bulls ready to fight traffic held up
Answer:
Bulls Hold up Traffic
Cuttack 12 : Traffic was held up for almost an hour from 9.00 am this morning at Badanibadi as two bulls were poised to fight in the middle of the road. The bull had locked horns while bystanders cheered them.

Activity – 5

Very often, as a students ’ representative, you may have to read out a report in a function, ceremony, meeting etc. At that time, you don’t have to make the mention of the place, date, etc. as is done in writing a news report. It is normally written like an essay.

A. The Minister of Education was the Chief Guest in the Annual Day Celebration of your college. Write a news report to be sent to a newspaper.
Answer:

To,
The Chief Editor,
The Times of Odisha, Bhubaneswar

Report on Annual Day Celebration

Cuttack: 12 March
The Annual Day celebration of A.K.B. College, Govindpur came off smoothly. The Hon’ble Education Minister Sri N. K. Patra was the Chief Guest. The celebration started with the national anthem and devotional song. The local Collector and Dist. Magistrate presided over the meeting. After a short speech made by the Hon’ble Chief Guest on the all-round development of the college, gave away the prizes for curricular and extracurricular activities of the students. The celebration was a grand success.

B. During the Annual Day celebration, you were asked to present a report on the students’ activities during the year. Draft your report.
Answer:

A Report on Students’ Activities

The A.K.B. College, Govindpur has already been recognized as a unique educational institution imparting teaching on all branches/streams in the State. Elections to the students’ union, the dramatic society, the day-scholars’ Association, the +2 Cultural Association, etc. were held without any untoward incident. The performance of the students in curricular activities was excellent. Most of the students were awarded gold medals for their outstanding results in different streams. The mention of the co-operation and mutual understanding among the students in the college and outside would not be out of place here,

8.2 Business Reports

Business reports are mainly based on market condition, market surveys or market- analyses. We usually take into account the background information, method of investigation, findings, and recommendations while preparing business reports. Besides, we follow direct and factual language based on the market-surveys and market analyses. There is no scope of rendering personal feelings or attributing subjective interpretations.

Activity – 6

Here is a report about the introduction of a new mosquito-repellant. Read the report, paying attention to various parts.

Quality Marketing Agency
27 Janpath, Bhubaneswar

4 March, 2013

To
Mr. M. Pradhan
Managing Director
Home Products India Ltd.
Industrial Estate
Mancheswar, Bhubaneswar.
Dear Mr. Pradhan,
As requested by you, vide your letter No. MD/NS/2233 dated 2.2.2013, we have carried out a market survey to test the public acceptance of the mosquito repellant which your company plans to manufacture. We conducted an opinion poll covering 1000 families in the coastal districts of Odisha. Forty percent of these families use mosquito repellants, but most of them are unhappy with the existing products in the market. They find the electronic repellants too expensive while the coil-based ones emit too much smoke.

The preference is for a less expensive product, preferably one that produces no smoke. Our study suggests there may be a good market for a new repellant, provided these requirements are kept in mind. We recommend that your company should concentrate on manufacturing an improved kind of smoke-free mosquito coil, preferably one that produces a pleasant fragrance.
Yours sincerely,
S.K. Patnaik
Director of Research
Quality Marketing Agency

You must have observed that the report has been written in the format of a business letter. However, it could be written in a different format as given below.

Date : 4 March 20
To : Mr M Pradhan, Managing Director, Home Products India Ltd. Industrial Estate, Mancheswar, Bhubaneswar
From : S.K. Patnaik, Director of Research, Quality Marketing Agency 27 Janpath, Bhubaneswar
Subject : Survey report on the Introduction of a new mosquito repellant.

A Report On The Introduction Of A New Mosquito Repellant

A market survey to test the public’s acceptance of a new mosquito repellant was conducted in the coastal districts of Odisha on 20 February, 20 by Quality Marketing
Agency, Bhubaneswar.
An Opinion poll covering 100 families ……………………. etc.
______________________________________
______________________________________
______________________________________
An improved kind of smoke-free mosquito coil, preferably one that produces a pleasant fragrance is likely to be widely accepted by the public.
Sd/-
(Director of Research)

Activity – 7

Imagine that you are the President of the Literary Society of your College. Your Society plans to publish a journal. You have asked the Secretary of the Society to contact all the printing firms in town and to select one of them to print your journal.
Answer:

Literary Society, Kulailey College, Kailey

5 February 2012

To,
Prof. B. Pujari
President, Literary Society
Sir,
As desired by you a team consisting of the Secretary and Assistant Secretary of the society contacted all five printing firms in town and obtained quotations from them for printing of the proposed journal. All the firms quoted the same price, that is Rs. 5000/- for 1000 copies. Rasmita Printers, however, offered a discount of ten per cent, provided we allowed them an extra period of fifteen days for printing. Since we do not need the copies of the journal till a month later, we could consider the offer of Rasmita Printers as it will cost us Rs. 500/- less than the offers quoted by other printing firms.
Yours faithfully,
S. Pujari
Secretary

Activity – 8

A customer approached a bank for a house building loan. Before sanctioning the loan, the Branch Manager asked the Field Officer to examine the application and suggest whether the loan should be sanctioned.

The following is the report that the Field Officer wrote. Some parts of the report are missing. Re-write the missing parts, using the hints supplied. (See the letter at textbook page 75)
Answer:

SBI PD BRANCH
CRP Square
Bhubaneswar

3 March, 2012

To,
Prof. M. Mishra
Branch Manager
SBI PD Branch
CRP Square
Bhubaneswar
Sir,

1. As desired by you in your letter No. 254 dt. 24 February 2010, I examined the application of Mr. J.K. Panda for a house-building loan. I also personally inspected the site, interviewed Mr Panda and examined the documents relating to the plot.
2. My examination of the application and the relevant documents reveal that the site is an undisputed one. Till date all land cess has been paid and the plot is litigation free. Mr J.K. Panda is the owner of the plot and he has clear papers certifying its ownership. The plot is 112 decimals in size and its market value is around Rs. 8.00 lakhs. Mr Panda also has a regular income of Rs. 15,000 and has no outstanding loan to his account.
3. As Mr Panda is a deserving party, the sanction of the loan is recommended
Yours faithfully,
K.C. Panigrahy
Field Officer

Activity – 9

Imagine that you are the foreman in a factory. There has been a fire in the Factory and one of the workers has been badly burnt and is in hospital. Your General Manager has asked you to send him a report on the fire. Write a report.
Answer:

JAYASHREE CHEMICALS
Corporate Office, Metro Towers
Bhubaneswar – 751007

28.3. 2012

To,
Mr J.B. Sahu
General Manager
Jayashree Chemicals
Corporate Office, Bhubaneswar
Sir,
1. As desired by you vide your letter No. JC 289 dt. 20.3.2012, I conducted an enquiry into the fire that ravaged the factory at the Mancheswar Industrial Estate.
2. On inspection of the fire ravaged site and after interviewing the workers present during the incident, I discovered that the fire was caused by the Careless throwing of a lighted cigarette into the boiler room where it ignited a dry rope. The rope was lying in contact with a jar of petrol kept by an employee for his personal use. The jar of petrol caught fire immediately and broke into high flames that ravaged the electrical circuit. Fortunately, there was no one in the boiler room as it was lunch time except Mr Lingaraj Patra who was cleaning some machine part.
3. He has received 40 per cent bums in his body and has been admitted at the Kalinga hospital. He is presently out of danger and the personnel department has already sanctioned Rs. 50,000 for his treatment.
4. Damage to the boiler section of the factory was limited to the minimum by the quick action of our fire personnel. A few chairs and benches must be replaced and the Electrical circuit done up again.
This is for your kind information.
Yours faithfully
D.P. Dehury
Chief Security Officer
Jayashree Chemicals

Activity – 10

Your club wants to buy a CTV (Colour TV) set. You have been asked to contact various firms marketing such sets and make your recommendation on the brand to be bought. Make a comparative study of the price, quality and durability of different brands of CTV and make a report.
Answer:

YOUNG FOLKS CLUB
213 Kharvela Nagar
Bhubaneswar

21 April 2012

Mr P. Khuntia
The Secretary
Young Folks Club
213 Kharavela Nagar
Bhubaneswar
Dear Mr Khuntia,

As requested by you I contacted 10 dealers of colour television in the town and personally inspected several makes of colour televisions in their showrooms. LG, Samsung, Philips and Onida companies all offer 25” CTVs at competitive prices. Of course L.G. is the costliest at Rs. 58,000 but it employs the golden eye technology which is truly soothing to the eyes. Samsung and Onida brands are also good. The unique thing about the Samsung T V. is that it offers two games in its set but we cannot afford members fiddling with the game program of the T.V. while others want to watch programs.

Except for its woofer impacted quality the Videocon CTV’s picture quality is no match for those of other brands. The Onida brand is good. It commands a price tag of Rs. 50,000. However its after sales-service is doubtful as the dealer here does not guarantee qualified personnel from the company to give service. However with a price tag of Rs. 48,000/- and a 5 year warranty contract, quality picture and sound, the Philips flatron CTV is perhaps the best that our town has to offer.

The concerned dealer is offering a free Antennae along with booster as well as 10 VCD’s with the T.V. He has also agreed to transport the CTV and to install it in our conference Hall free of cost. It is therefore recommended that the Shanti Electronics, 105, Bapuji Nagar, Bhubaneswar be contacted and the Philips Flatron CTV be bought from them at the price as well as the terms and conditions offered by them.
Yours faithfully
Girish Mishra
Joint Secretary
Young Folks Club

Odisha State Board CHSE Odisha Class 12 Invitation to English 4 Solutions Grammar Tense Patterns Unit 5 Past Simple and Past Progressive Textbook Activity Questions and Answers.

CHSE Odisha 12th Class English Grammar Tense Patterns Unit 5 Past Simple and Past Progressive

SECTION – 1

Study the sentences below :
(a) It started to rain while we were walking home.
(b) My sister was tidying my room when I saw your letter.
(c) Anita was walking along the road when suddenly she heard footsteps behind her. Someone was following her. She was frightened and started to run.
What do you think the use of the Past Simple and the Past Progressive indicates in these sentences?
(Hint: Think of a point of time and a duration of time in the past and relate them to the action.)

Note:
The Past Simple tells us that the work/action started and finished in the past. The speaker has a definite time in mind. But in Past Progressive the time of beginning or completion of the activity is not mentioned. The activity was in progress for that hour.

Activity – 21
Put the verbs into the correct form, Past Progressive or Past Simple.
(a) My friend ______________(meet) Anima and Amiya at the bus stop four days ago. They ______________(go) to Paradeep and my friend ______________ (go) to Bolangir. They ______________(have) a chat while they ______________(wait) for their buses.
(b) My brother ______________ (cycle) to school last Monday when suddenly an old woman ______________(step) out into the road in front of him. He ______________(go) quite fast but luckily he ______________ (manage) to stop in time and ______________(not / hit) her.
Answer:
(a) My friend met Anima and Amiya at the bus stop four days ago. They were going to Paradeep and my friend was going to Bolangir. They had a chat while they were waiting for their buses.
(b) My brother was cycling to school last Monday when suddenly an old woman stepped out into the road in front of him. He was going quite fast but luckily he managed to stop in time and did not hit her.

Activity – 22
Here is a true story.
An old couple …………………………living in a flat in Bhubaneswar. ………………………… locked up in one room ………………………….. Some unknown people took away everything ………………………… police arrived ………………………… climbed ………………………… rescued ………………………… broke open a door ………………………… one dacoit was killed ………………………… detective was called …………………………interviewed a witness.
Imagine that you are being questioned by the police as if you were a witness to the crime. A police Inspector is recording your statements in a notebook. Think about the situation and write the appropriate answers.
Inspector: Where were you standing at that time?
Answer: _____________________________.
Inspector: Why did you come here?
Answer: _____________________________.
Inspector: What was the old man doing at the time?
Answer: _____________________________.
Inspector: How did you see that?
Answer: _____________________________.
Inspector: How long were you standing there?
Answer: _____________________________.

Answer:
An old couple _____ living in a flat in Bhubaneswar, _____ Orissa locked up in one room _____. Some unknown people took away everything. _____ police arrived _____, limbed _____ rescued _____ , broke open a door _____one dacoit killed, _____detective was called _____ interviewed a witness.
Inspector: Where were you standing at that time?
Answer: I was standing near the flat.
Inspector: Why did you come here?
Answer: I came here to play.
Inspector: What was the old man doing at that time?
Answer: The old man was shouting and trembling out of fear.
Inspector: How did you see that?
Answer: I heard him shouting and saw him trembling.
Inspector: How long were you standing there?
Answer: I stood there till your arrival.

Odisha State Board CHSE Odisha Class 12 Invitation to English 4 Solutions Grammar Tense Patterns Unit 4 Present Perfect and Past Simple Textbook Activity Questions and Answers.

CHSE Odisha 12th Class English Grammar Tense Patterns Unit 4 Present Perfect and Past Simple

Study the dialogue given below.
Susant: Have you ever ridden a horse?
Subir: Yes, I have.
Susant: When was that?
Subir: I rode one last summer.
Susant : What was it like?
Subir: Oh, it was awful.
Susant : Why? What happened?
Subir: I fell off and hurt my back.
Identify the Present Perfect and Past Simple sentences and examine their use carefully. How are they different in meaning?
{Hint: One of them answers the question ‘When’? and the other does not)
Except for the first two i.e. “Have you ever ridden a horse ?” and “Yes, I have”, the rest of the sentences in the above dialogue belong to Past Simple constructions.
When an action/event took place in the past but its result is still operative at the present moment of speaking/time, we generally use a Present Perfect tense and the Past Simple means that the action/happening occurred before the present moment.

Activity – 18
1. Complete the dialogue using the hints given.
(i) A: ever / see /a lion _______________?
B: Yes, _______________.
A: Where _______________?
B: In the zoo _______________.
A: What/look _______________?
B: terrible _______________.
A: You / afraid _______________?
B: No, _______________?

(ii) A : ever / be to / Dhauligiri ………………………?
B: Yes, _______________.
A: What! see /there _______________?
B: A temple I top/hill _______________.
A See / the inscriptions _______________?
B: Yes, _______________?
A: Able to read the inscriptions _______________?
B: No, _______________.

Answer:
(i) A: Have you ever seen a lion?
B: Yes, I have.
A: Where did you see it?
B: I saw it in the zoo.
A: What did it look like?
B: Yes, it was very terrible to look at.
A: Were you afraid?
B: No, I wasn’t.

(ii) A: Have you ever been to Dhauligiri?
B: Yes, I have been two times.
A: What did you see there?
B: I saw a temple at the top of the hill.
A: Did you see the inscriptions there?
B: Yes, I saw the inscriptions there.
A: Were you able to read the inscriptions there?
B: No, I wasn’t.

Activity – 19
Choose the right verb for each blank space and put it into the correct tense.
(do, wear, carry, ask, say, think)
A : _______________your grandfather _______________ something really crazy ?
B: He _______________ something really silly last summer. One one of the hottest days he _______________ a raincoat and _______________ an umbrella. Everyone _______________ him why. He _______________he _______________ it was going to rain.
Answer:
A: Did your grandfather wear something really crazy?
B: He wore something really silly last summer. On one of the hottest days, he wore a raincoat and carried an umbrella. Everyone asked him why. He said he thought it was going to rain.

Activity – 20
Complete the sentences, using the verbs in brackets either in Past Simple or Present Perfect form.
(a) She _______________ up her mind (made). She’s going to look for another college.
(b) Amulya : _______________me his pen but I’m afraid I _______________ it. (give, lose)
(c) A: It’s a little bit noisy in here, isn’t it?
B: Pardon? I can’t hear. What _______________ you _______________? (say)
(d) Where is my bike? It _______________ outside the classroom. It _______________! (be, disappear)
(e) Did you know that Umesh _______________ a new scooter? (buy)
(f) I did Sanskrit at school but I _______________ most of it. (forget)
(g) A : Sima, this is Rajesh.
B: Hello, Rajesh. Actually, we know each other. We _______________ already ___________ (meet).

Answer:
(a) She has made up her mind. She’s going to look for another college.
(b) Amulya gave me his pen but I’m afraid I have lost it.
(c) A: It’s a little bit noisy in here, isn’t it?
B: Pardon? I can’t hear. What did you say?
(d) Where is my bike? It was outside the classroom. It has disappeared!
(e) Did you know that Umesh has bought a new scooter?
(f) I did Sanskrit at school but I have forgotten most of it.
(g) A : Sima, this is Rajesh.
B: Hello, Rajesh. Actually, we know each other. We have already met.

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

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

Question 1.
(i) ∫\(\frac{d x}{\sqrt{11-4 x^2}}\)
Solution:

(ii) ∫\(\frac{e^{3 x}}{\sqrt{4-e^{6 x}}}\)dx
Solution:

(iii) ∫\(\frac{d x}{\sqrt{25-(\ln x)^2}}\)
Solution:

(iv) ∫\(\frac{\cos \theta}{\sqrt{4-\sin ^2 \theta}}\)dθ
Solution:

(v) ∫\(\frac{x^2}{\sqrt{36-x^6}}\)dx (x³ = z)
Solution:

(vi) ∫\(\frac{x+3}{\sqrt{9-x^2}}\)dx
Solution:

(vii) ∫\(\frac{d x}{\sqrt{5-x^2-4 x}}\) (x + 2 = z)
Solution:

(viii) ∫\(\frac{x+3}{\sqrt{5-x^2-4 x}}\)dx
Solution:

Question 2.
(i) ∫\(\frac{d x}{3 x^2+7}\)
Solution:

(ii) ∫\(\frac{e^{4 x}}{e^{8 x}+4}\)dx (e^4x = z)
Solution:

(iii) ∫\(\frac{d x}{x\left\{(\ln x)^2+25\right\}}\)
Solution:

(iv) ∫\(\frac{\sec \theta \tan \theta}{\sec ^2 \theta+4}\)dθ
Solution:

(v) ∫\(\frac{x^9}{x^{20}+4}\)dx (x¹⁰ = z)
Solution:

(vi) ∫\(\frac{3 x+4}{x^2+4}\)dx
Solution:

(vii) ∫\(\frac{d x}{x^2+6 x+13}\) (x + 3 = z)
Solution:

(viii) ∫\(\frac{x+5}{x^2+6 x+13}\)dx
Solution:

Question 3.
(i) ∫\(\frac{d x}{x \sqrt{4 x^2-9}}\)
Solution:

(ii) ∫\(\frac{d x}{\sqrt{e^{4 x}-5}}\) (e^2x = z)
Solution:

(iii) ∫\(\frac{d x}{x \ln x \sqrt{(\ln x)^2-4}}\)
Solution:

(iv) ∫\(\frac{\sec \theta d \theta}{\sin \theta \sqrt{3 \tan ^2 \theta-1}}\)
Solution:

(v) ∫\(\frac{d x}{x \sqrt{x^{14}-b^2}}\) (x⁷ = z)
Solution:

(vi) ∫\(\frac{x^2+3}{x \sqrt{x^2-4}}\)dx
Solution:

(vii) ∫\(\frac{d x}{(x+1) \sqrt{x^2+2 x-3}}\) (x + 1 = z)
Solution:

(viii) ∫\(\frac{x^2+2 x+4}{(x+1) \sqrt{x^2+2 x-3}}\) dx
Solution:

Question 4.
(i) ∫\(\frac{d x}{\sqrt{3 x^2+4}}\)
Solution:

(ii) ∫\(\frac{4 e^x}{\sqrt{3 e^x+4}}\)dx
Solution:

(iii) ∫\(\frac{d x}{x \sqrt{(\ln x)^2+8}}\)
Solution:

(iv) ∫\(\frac{d \theta}{\sin ^2 \theta \sqrt{\cot ^2 \theta+2}}\)
Solution:

(v) ∫\(\frac{x^2}{\sqrt{x^6+a^6}}\)dx
Solution:

(vi) ∫\(\frac{3 x+4}{\sqrt{5 x^2+8}}\)dx
Solution:

(vii) ∫\(\frac{e^x \cos e^x}{\sqrt{\sin ^2 e^x+9}}\)dx
Solution:

(viii) ∫\(\frac{2 x+11}{\sqrt{x^2+10 x+29}}\)dx (x + 5 = z)
Solution:

Question 5.
(i) ∫\(\frac{d x}{\sqrt{4 x^2-6}}\)
Solution:

(ii) ∫\(\frac{e^{5 x}}{\sqrt{e^{10 x}-4}}\)dx
Solution:

(iii) ∫\(\frac{d x}{x \sqrt{(\ln x)^2-4}}\); x > e²
Solution:

(iv) ∫\(\frac{\cos \theta d \theta}{\sin ^2 \theta \sqrt{{cosec}^2 \theta-4}}\)
Solution:

(v) ∫\(\frac{d x}{\sqrt{x} \sqrt{x-a^2}}\)
Solution:

(vi) ∫\(\frac{x-2}{\sqrt{3 x^2-8}}\)dx
Solution:

(vii) ∫\(\frac{3 x+4}{x \sqrt{2 x^2-5}}\)dx
Solution:

(viii) ∫\(\frac{x^2+2 x+2}{x \sqrt{x^2-4}}\)dx
Solution:

(ix) ∫\(\frac{d x}{\sqrt{x^2+8 x}}\)
Solution:

(x) ∫\(\frac{x+7}{\sqrt{x^2+8 x}}\)dx
Solution:

Odisha State Board CHSE Odisha Class 12 Invitation to English 4 Solutions Grammar Tense Patterns Unit 3 Past Simple Textbook Activity Questions and Answers.

CHSE Odisha 12th Class English Grammar Tense Patterns Unit 3 Past Simple

SECTION – 1
Read the passage below carefully.
Ramesh was bon in Baleswar in 1960. He was brought up in Cuttack by his uncle because of his parents in Bangalore. Then he went to Hyderabad to complete his studies. He got a first-class M.Sc. degree in Physics and became a lecturer at a college in Orissa. In 1985 he joined a university but soon went to the U.S.A. on a scholarship. He came back in 1990 and got married. He bought a house in Bhubaneswar in 1993. The happenings above took place in the past time. The basic element of meaning is: “the happening takes place before the present moment.” This means that the present moment is excluded.

Activity – 16
Answer the following questions which relate to the things you do every day. Answer in full sentences.
1. When do you wake up?
2. What do you eat before you go to college?
3. When do you leave home?
4. How do you get to college?
5. What do you pass on the way?
6. How long does it take you?
7. When do your classes start?
Answer:
1. I wake up early at 6 a.m. in the morning.
2. I usually eat rice, dal, and curry before I go to college.
3. I leave home at half past 9 (o’clock).
4. I get to college by bicycle.
5. I pass people, motor cars, etc. on the way to college.
6. It takes me twenty minutes time.
7. Our classes start at 10 o’clock.

Imagine that a friend of yours wants to know from you what you did last Wednesday, which was a very typical day in your life. What kind of questions would he ask you and what answers would you give him? Here are a few questions and answers for you to write.

Question 1.
When did you wake up last Wednesday?
Answer:
I woke up at 6. a.m. last Wednesday.

Question 2.
How did you enjoy the day?
Answer:
I went on merry-making with my friends as it was my birthday.

Question 3.
What did you do in the morning that day?
Answer:
I took a clean bath first and put on a new pair of clothes.

Question 4.
What did you do after wearing the pair of new clothes?
Answer:
I went to the temple to worship God.

Question 5.
What did you give your friends to eat?
Answer:
I gave them some cake, sweets, and other sumptuous food to eat.

Question 6.
What did they give you on the day?
Answer:
They presented me with fabulous gifts.

Question 7.
Were you really happy on that day?
Answer:
Yes. I was very happy on that day.

Activity – 17
The following years were related to important events in Gandhiji’s life. Can you write a sentence on each of these years? One has been done for you.
1. (1869) Gandhiji was born.
2. (1888) ____________________________________________.
3. (1891) ____________________________________________.
4. (1893) ____________________________________________.
5. (1906) ____________________________________________.
6. (1915) ____________________________________________.
7. (1917) ____________________________________________.
8. (1931) ____________________________________________.
9. (1942) ____________________________________________.
10. (1948) ____________________________________________.
Answer:
1. (1869) Gandhiji was bom.
2. (1888) He went to London to study law.
3. (1891) He passed the law examination and was admitted to the bar.
4. (1893) He went to South Africa.
5. (1906) He wrote a significant letter to his brother Laxmidas Gandhi.
6. (1915) He left for Rajkot and Porbandar to meet his relations.
7. (1917) He received a summons to appear before the sub-divisional officer on April 18.
8. (1931) Gandhi-Irwin pact was signed in Delhi.
9. (1942) He attended the All-India Congress Committee meeting at Wardha.
10. (1948) He was shot dead by Nathuram Binayak Godse an R.S.S. member.

Activity – 18
Imagine that you went for a picnic last Sunday with some friends. Write a letter to your friend telling him/her about the picnic. You may follow the hints given below.
1. when and how it was planned
2. the place selected
3. how you went there
4. what you saw on the way
5. what you did there
6. what you enjoyed most
7. when you returned

Dear ___________,
It was really nice to hear from you again. Thanks for telling me about your plans for an excursion. I’m afraid I won’t be able to make it. I have exams to sit for. But I have already made up for the loss.
Yesterday we went on a picnic, and I feel I must share the excitement of it all with you.
______________________________________________________
______________________________________________________
______________________________________________________
______________________________________________________

Yours truly,
___________.

Answer:
Dear Suresh,
It was really nice to hear from you again. Thanks for telling me about your plans for an excursion. I’m afraid I won’t be able to make it. I have exams to sit for. But I have already made up for the loss.
Yesterday we went on a picnic, and I feel I must share the excitement of it all with you.
Our classmates sat together a week ahead and decided to go on a picnic to Nandankanan. We got the permission of the Principal and gave each one hundred rupees for the purpose. We were 50 students and three lecturers too consented to go with us. All of us were of the opinion to see Nandankanan, the zoo. We hired a bus and it was about two hours journey from our college. We saw a lot of buses, cars, and trees full of flowers on our way to Nandankanan. We arrived at Nandankanan by 9 o’clock in the morning. On getting there, we first had our breakfast. Mohan, Sanjay, and Pravakar voluntarily agreed to take charge of cooking. They discharged their duty pretty well. Others went to see the beautiful march of colorful sights and sounds. Our menu was very simple. We had rice, mutton curry, and fruit salad. The preparation of the food was superb. We all enjoyed the food to our heart’s content. After finishing our lunch, we took a little rest and then went round the zoo again. We first returned to our college at 6 p.m. Then the day scholars went to their houses and we went to our hostel. It was really a pleasant outing. I felt your absence there.

With love
Yours truly
Sandeep.

Note:
We can use sentences in the past simply when ‘the speaker/writer has a definite time in mind’.
Examples :
Once this town was a beauty spot.
Mahatma was bom in 1869.
“Past simple” can also be used for “habit in the past”.

Example :
He always carried an umbrella.
They never drank tea.
Note that in most cases we use used to if we wish to emphasize that the habit has been discontinued.

Example :
He used to smoke, (which means that he smoked at one time but he doesn’t smoke now.)
Past Simple can also be used for hypothetical meaning.

Example :
It’s time we had a holiday.
If you caught the 9 o’clock train, you would get there by lunchtime, etc.

Odisha State Board CHSE Odisha Class 12 Invitation to English 3 Solutions Writing Interpreting Graph, Charts, Tables and Diagrams Textbook Activity Questions and Answers.

CHSE Odisha 12th Class English Writing Interpreting Graph, Charts, Tables and Diagrams

Graphs, charts, tables, diagrams, etc. generally have visual representations so as to enable us to present some information. Visual representations make us understand the information contained therein.

7.1. Diagrams

Given below is a diagram of the British School System. Examine it carefully and compare it with the passage given below:

(ii) To test whether you have understood what the diagram presents, see if you can answer the following questions :

Question (a)
How many types of schools there are in England?
Answer:
There are two types of schools in England, namely, Private Schools and State Schools.

Question (b)
What percentage of the pupils go to state-run schools?
Answer:
Ninety-five percent of the students go to state-run schools.

Question (c)
What percentage goes to private schools?
Answer:
Only five percent go to private schools.

Question (d)
When do children start primary education in England?
Answer:
Children start primary education in England at the age of five.

Question (e)
When do they get into secondary education?
Answer:
They get into secondary education at the age of eleven.

Question (f)
When do they take their first and second public examinations?
Answer:
They take their first and second public examinations at the age of 16 and 18 respectively.

Question (g)
Is pre-primary education compulsory in England?
Answer:
Pre-primary education is not compulsory in England. On the other hand, it is voluntary.

The information found in the diagram is presented below in words.

The British School System
In Britain most schools are financed by the state and for the children attending these schools, they are free. However, about 5 percent of the school population attends private schools, and these are financed from pupils’ fees. For state-run as well as private schools, the general pattern of schooling in Britain is as follows. All children must start school at the age of 5. At the age of 11 children move to different schools, called Secondary Schools, where they are made to go through a set timetable of subjects for a period of 5 years, after which they take their first public examination at the age of 16.

After the first public examination, most pupils leave school. Only about 30 percent continue. Those that stay on spend the next two years concentrating on a small number of subjects. They take their second public examination at the age of 18. In Britain, there is also a provision for pre-primary schooling. However, pre-primary schooling is not compulsory. It is, on the other hand, voluntary, and is offered both by state-run schools and private schools.

The British School System
Most children attend the British School System where schools are directly financed by the State. But on the other hand, nearly 5 percent of children attending schools go to private institutions. But in Great Britain, in the State-run and private educational institutions, children start school at the age of 5 and when they are 11, they go to secondary school. There they are taught to go through a set timetable of subjects for a period of 5 years.

Afterward, they attain their first public examination towards the age of 16. Then after the completion of the first public examination, most students leave schools leaving only 30 percent student- population to continue their studies. Pre-primary education in Britain is yet another feature of education, though not compulsory. Pre-primary education is offered through State-run schools and private schools as well.

Activity – 1

Study the diagram below and write a short passage of about 3 paragraphs on it.

Answer:
Kinds of musical instruments :
Musical instruments are of three types, namely, wind instruments, percussion instruments and string instruments. Wind instruments are those which are played by blowing wind into them while percussion instruments are played by beating or striking them like the drums. String instruments, on the other hand, are those which have strings. Wind instruments can be further classified into wood wind instruments and brass wind instruments.

Examples of the former are the clarinet, the flute and the basson, while examples of the latter are the trumpet, the horn etc. Similarly, string instruments can be classified into two groups on the basis of the method by which music is produced through them. Instruments like the harp which produce music when its strings are plucked belong to one group while instruments like the violin and the cello which produce music when a bow is drawn across its strings belong to another group.

Activity -2

Draw a diagram to present the facts on the school system in Odisha. Then, present the same information in words, in two or there paragraphs, (as has been done above for, the British School System).
Answer:

• Only one public examination at the age of 15.
• First Board examination at the age of ten.
• Second Board examination at the age of 12.
• Third Board examination at the age of 15.

In Odisha there are Public schools which are mostly English medium shcools as well as Government-run schools which teach in the Oriya medium, whereas in the past, Odisha had only Govt, schools and a very few public schools. The gap between the two is closely narrowing as public schools are mushrooming all over the state. As of now, 60% students go to Govt-run schools, while the rest 40% go to public schools. Govt- run schools offer Primary education free of cost and charge very little for Middle-English and Secondary education whereas public schools charge high fees.

Govt. Schools do not offer any pre-primary education. Students start their Primary education at the age of 5 and continue upto class 5 when they take their first public examination. After this they move to Middle English schools where they study for two years till their second public examinations at the age of 12. From here they go to High schools where they study for three years to take the third public examination at the age of 15. Public Schools, on the other hand, offer pre-primary education in the Kinder Garten and Nursery which starts at the age of 3 or 3V4. After this children continue into primary schooling and then till class ten when they take their first public examination at the age of 15.

Activity – 3

Draw a diagram showing how many streams your college has at the +2 level. Also include information about subjects, papers, practicals etc. in your diagram. Then write a short passage covering all the information in your diagram.

The Khallikote College, Berhampur has three streams, namely Arts. Science and Commerce at the +2 level. All the streams offer teaching in compulsory and optional subjects. While the compulsory subjects are the same for every stream, the optional subjects differ from stream to stream. Among optional subjects too there is a choice of a combination of subjects in each stream with three subjects to be chosen as primary optional and another to be added as a fourth optional.

Further in the Arts stream while only two subjects namely, Education and Anthropology have theory and practical classes; in the Science stream all subjects, except Mathematics, have theory and practical classes. In the Commerce stream there are practicals in no subject. The compulsory subjects for all streams are General English and MIL (O) or Alt. English or Hindi or Telugu. The optional subjects offered in the Arts stream are Anthropology, Economics, Political Science, History, Sanskrit, Philosophy and Education.

The optionals offered in the Science stream are Physics, Chemistry, Mathematics, Biology, Electronics and Geology. The combinations offered in these subjects are PCM with Biology or Electronics or Geology as fourth optional and PCB with Mathematics or Electronics or Geology as fourth optional. In the Commerce stream, the Business Organisation, Office Management, Costing, Financial Accounting and Business Mathematics are the primary optionals offered. There is no choice in this matter. All the five are to be studied. This apart one is to choose between Economics or Salesmanship as fourth optional.

7.2 Graphs

In America, there are frequent reports about Unidentified Flying Objects (UFOs) which people claim to have seen flying in the sky and which are believed to be space-ships carrying visitors from other planets. The following is a graph showing the number of UFOs “sighted” (seen) during a particular year. Study the graph.
Graphs

(I). Hints :
(a) 16 Jan, a science fiction film shown on the TV.
(b) 30 Jan, an article was published by an Airforce officer, interpreting UFOs as the result of aircraft movements.
(c) 16 Feb, a science correspondent attacked the Airforce officer’s findings.
(d) 26 Feb, a public debate between the Airforce officer and the science correspondent arranged, but the latter didn’t show up.

(II). Now, here are some questions you need to answer if you have to write a report (in words), based on the diagram above.
(a) There was a sharp rise in the number of reported sightings of UFOs. When ? Why ?
(b) After the rise, there was a marked fall in the number of reported sightings. When ? Why ?
(c) There was another rise, following the fall. Why ?
(d) What brought about the final fall ?
(e) Was there any noticeable rise in reports after the debate ?

Answer:
(a) There was a sharp rise in the number of reported sightings of UFOs. As per the reports, the rise recorded more than twenty during the early part of January and February. An article was published on the sightings of UFOs, as a result of the less movement of aircraft in the air.
(b) After a rise, there was a marked fall in the number of reported sightings towards the early part of March. It was perhaps due to the frequent movement of aircraft in the air.
(c) There was another rise, though small in quantity following the fall, due to fewer movements of civil and military aircraft.
(d) The increased movement of civil and military aircraft brought about the final fall.
(e) No, there was no noticeable rise after the debate.

Activity -4

Now complete the report below by filling in the blank.

During the early part of _________ this year the rate of UFO sightings was steady at around _________ or _________ a week. On 16 __________ a science fiction film about visitors from outer space was screened on television and immediately after that there was a sharp increase in reported sightings. On 30 __________ an Airforce officer, who had been investigating all such reports made his findings known. He maintained that all UFO reports could be explained quite naturally as being due to civil and military aircraft movements. Following this explanation, there was a rapid ___________ in the number of reported sightings. But the rate did not return to the pre-broadcast level. Some people, however, were not convinced. On 16 ____________, a science correspondent published a highly critical article about the findings of the Airforce officer. He demanded an independent inquiry. This article caused a renewal of interest in the subject of ___________ and a corresponding steep ____________ in the number of sightings. The rise, however, was not as marked as the increase in January. The Airforce officer invited the science correspondent to meet him in a public debate ____________ days later. But the science correspondent did not show up on the appointed day. The Airforce officer, in turn, produced some very convincing evidence for his case. As a result, interest in UFOs ___________ and the sightings were even fewer than at the beginning of the year. As the weeks went by there was a little increase in the number of reports.
Answer:
January, three, four, January, January, rise, February, UFOs, rise, ten, decreased

Activity – 5

Have a close look at the graph below and write a report to accompany it.

Hints
a. Return of a group of migrant workers from an affected area.
b. Very dry summer, lack of drinking water.
c. Preventive measures introduced by the government.
d. WHO sends limited supplies of medicine.
e. Medicine loses effectiveness; virus develops resistance.
f. Vaccine produced; population vaccinated.

Answer:
Progress of Virus Epidemic in Bihar – A viral epidemic started in Bihar in December 1997. By February 1998 about 4000 people had died. It was then that a group of migrant workers returned from an affected area. This resulted in a sudden rise in the death toll. By the middle of March, the death toll stood at 7000 (approx.). This phenomenally escalated because of a very dry summer and lack of drinking water. Consequently, between the middle of March and April, the death toll rose to an all-time high of 18,000. Only then did the government wake up to introduce preventive measures. This saw a slight decrease in the death toll.

But towards the end of May when the WHO sent supplies of medicine, happily the death toll sharply decreased and by the middle of June, it had reduced to 5000. The decreasing trend, however, did not last long. The medicine soon lost its effectiveness as the virus developed resistance to the medicine and therefore once again the epidemic spread. As a result of this between mid-June and mid-September, almost 14,000 people died. By then a vaccine had been produced and the entire population was vaccinated. This proved effective and the death toll fell to 2000 by December 1998. By April 1999 the epidemic had been completely controlled.

Activity – 6

Write an account of a difficult night journey you made on a scooter from Sambalpur to Keonjhar. You may use the information in the diagram below.

Hints: Carefully mark the mountains and forests shown in the graph.

Answer:
Night Journey by Scooter from Sambalpur to Keonjhar I began my journey by scooter from Sambalpur at 10.00 pm in night. It was going to be a long and arduous journey. By 10.30 p.m. I had reached Padiabahal. The road was good and there was not much of traffic. Ten minutes after that I arrived at Badarama ghat. All around there was. pitch darkness. I had to slow down as I crossed this dangerous ghat. There were steep curves and hairpin bends.

Negotiating them was nerve-racking. It took me almost 25 minutes to cross the 5 km-long ghats. After crossing the ghat, I arrived at Balarama. It was almost 11.30 p.m. then. I decided to stop at a roadside Dhaba for tea. I was already feeling drowsy. The tea did me good as I started off at midnight steeling myself for the long journey through the thickly forested areas of the Deogarh and Palalahara districts. The roads were undulating and had plenty of pot-holes and whenever an occasional truck passed by I had to drive slow and was pushed to the edge of the road.

All this slowed me down during this 70 km-long journey between Badarama and Palalahara. At 1.30 a.m. I passed Deogarh. In spite of the bad roads, I covered it in one and a half hours. After passing Deogarh, I felt as if I had crossed a big milestone. The forest area was gradually coming to an end. Yet it took me an hour to reach Palalahara. At Palalahara, I had another cup of tea. It was really refreshing. I washed my face, eased myself, and started on again. After 5 km I reached the Plalahara ghat.

This was not as steep and rough as the Badarama ghat. But I was careful as I negotiated its bends. It took me just 20 minutes to cross the ghat. This time I arrived at the level road leading to Keonjhar. The milestone read 35 km. The road was good. It had been repaired a few months back by the L and T Company. I sped in the darkness of the night. As it was nearing dawn, traffic was extremely thin. By 4.40 a.m. Sodium Vapour lamps greeted me as I entered Keonjhar and my journey came to an end.

Activity – 7

The students of your college are dissatisfied about a number of things and sometimes resort to strikes, Dharana, etc.
Write a report on the different incidents of student unrest during recent years in your college and how a satisfactory solution was found. First, prepare a graph and then write the report.

Report on strikes during the years 2005-2009 at Rampur College
Deogarh college in Sambalpur was established in 1999. It provides education at the +2 level in the Arts, Science and Commerce streams. Since its inception, the college was incident free till the year 2004. But when college elections were held in 2005 for the first time, strikes were witnessed in the college. In 2005, one of the presidential candidates who lost by a very narrow margin went on a hunger strike. He had lost by 11 votes and therefore he requested for recounting. The panel of Appeals only assented to readdition.

He agreed but after readdition when the result was the same, he went on dharma for a second time, sitting under the portico and prohibiting everyone from entering the college. No one paid any attention to him for 4 days but suddenly on- the fifth day he feigned unconsciousness. As a result, the panel of Appeals allowed the counting of votes in Ballot papers. Once again he was proved wrong and the college limped back to normalcy. After 2005, strikes became a regular feature.

In 2006, 6 incidents of striking and unrest during the whole academic year. The strikes were resorted to for several reasons like, such demand for a bus stop in front of the college, postponement of Examinations etc. In 2007, the spate of students unrest shot up to 12 separate incidents of dharnas and strikes because of the sudden increase in the tuition fees and corruption in the admission of students. This was perhaps the worst year of student unrest and all that was only settled with the intervention of the collector and the dismissal of a few clerks.

After this, an aura of fear was seven among the students as well as the staff. Besides this, the government appointed Dr R. K. Sahu a man of great integrity as the principal of the college. As a result strikes completely stopped in the college. The year 2009 was also a year of no strikes and the college witnessed a new spirit of amity among the staff and the students. Thus the graph shows that strikes reached their peak in the year 2007 and had their complete decline in the year 2009.

7.3 Charts

Look at the chart below. It shows the ownership pattern of durable goods by different families in India. Try to understand the facts presented in it and answer the questions that follow :
Ownership pattern of Durables (Percentage of the total owned by different income classes)

Now answer these questions :
a. What is the annual family income of the people belonging to the low category?
b. What percentage of which goods do they buy as shown in the chart?
c. Considering their limited income, do they buy a lot?
d. Would you call the people belonging to the high category “rich”? Do they spend enough on consumer durables, in proportion to their income? What percentage of goods do they buy? What do the rich prefer to buy?

Question (a)
What is the annual family income of the people belonging to the low category?
Answer:
The annual family income of people belonging to the low category is Rs 1,20,000.

Question (b)
What percentage of which goods do they buy as shown in the chart?
Answer:
The percentage of goods which the low category people buy is as follows: Bicycles – 47% Mopeds – 17% Scooters – 9% Motorcycles – 11% Colour TVs – 10% and Washing Machines – 6% Note – All are approximate figures.

Question (c)
Considering their limited income, do they buy a lot?
Answer:
Yes, in spite of earning Rs 1.20,000 annually, they hold 17 percent of the market share in durables which is equal to the market share of the higher-income group and more than the market share of the upper-middle group.

Question (d)
Would you call the people belonging to the high category “rich”? Do you spend enough on consumer durables, in proportion to your income? What percentage of goods do they buy? What do the rich prefer to buy?
Answer:
In comparison with the low-income group, the people of the high-income group are definitely richer but their market share is comparatively lower than the market share of the low-income group in proportion to their income. They buy only 3 percent Of bicycles, 7 percent of mopeds, 17 percent of scooters, 20 percent of motorcycles, 19 percent of color T.V.s, and 37 percent of washing machines. It is obvious that they prefer to buy goods like color T.V.s and washing machines.

Activity – 8

Fill in the blanks in the report below with the ideas from the chart above.
A short report on the Ownership pattern of consumer durables in India.

The poor in India do not have a lot of money: their annual family income, on average, comes to Rs. 20,000. But they make a lot of purchases and constitute the mainstay for most products in the country. For example, families belonging to this category own _____________ of all bicycles, __________of mopeds, __________ of scooters, ___________ of motorcycles, and 10 percent of color televisions. They even own washing machines. The rich, in contrast, have money, but their share of purchases of these products is comparatively much less. Despite the money they have, they buy only ___________ of bicycles ___________ of mopeds, ___________of scooters, ___________ of motorcycles, and _____________ of color TVs. The poor earn less but spend more. And the rich earn more but spend less.

Answer:
The poor in India do not have a lot of money: their annual family income, on average, comes to Rs. 20,000. But they make a lot of purchases and constitute the mainstay for most products in the country. For example, families belonging to this category own 47 percent of all bicycles, 17 percent of mopeds, 9 percent of scooters, 11 percent of motorcycles, and 10 percent of color televisions. They even own washing machines. The rich, in contrast, have money, but their share of purchases of these products is comparatively much less. Despite the money they have, they buy only 3 percent of bicycles, 7 percent of mopeds, 17 percent of scooters, 20 percent of motorcycles, and 19 percent of color TVs. The poor earn less but spend more. And the rich earn more but spend less.

Activity – 9

Look at the chart below and answer the questions that follow.
Four-wheelers that passed over the bridge :

Question 1.
When was the bridge least busy?
Answer:
The bridge was least busy between 7.30 and 8.30 a.m.

Question 2.
When did the rush hour begin? When was the bridge most busy?
Answer:
The rush hour began at 9.00 a.m. and continued till 10.00 a.m. The bridge was most busy at 9.30 a.m.

Question 3.
How many vehicles in total passed over the bridge by 10.30?
Answer:
A total of 420 (approx.) vehicles passed over the bridge by 10.30.

Question 4.
If you know that schools start at 9.30 and government offices at 10.00, can you think of a way to reduce the pressure of traffic between 9.00 and 10.00?
Answer:
The school timings can be changed from 9.30 to 8.00 to reduce the pressure of traffic.

Activity – 10

Use the information in the chart below and write a short report to show which course was popular and why. (No reason has been shown in the chart, you have to think of some).

(Students enrolled in the Civil Engineering and Electronics courses of an Engineering College.)

A short report on the popularity of Civil Engineering and Electronics courses between 1970 -1998.
Answer:
In the year 1970 students’ preference for Civil Engineering was very high. 900 students were admitted for Civil Engineering courses whereas only 610 had enrolled for Electronics. Civil Engineering was a traditionally demanded subject and with a lot of development works taking place then, jobs were aplenty. On the other hand, electronics had been newly introduced and did not have many employment opportunities.

Ten years later Civil Engineering was still popular but because of a slight decrease in employment opportunities student enrolment also saw a slight decrease. Enrolment in Electronics however did not register much change. By 1990, the introduction of computers all over India, boosted the popularity of electronics and as it provided better job opportunities there was an increase in student enrolment in courses on Electronics. Now 900 students have been enrolled in Electronics while only 700 are in Civil Engineering.

The popularity of Electronics soared to new heights with the entry of multinationals into India after 1995. The multinationals provide great job opportunities and with many job opportunities overseas for computer professionals with handsome pay packets, the Electronics courses witnessed an admission of more than a thousand students in 1998. By then jobs for Engineering students were completely saturated. Civil engineers remained unemployed and therefore. Civil Engineering courses were no more popular. In 1998 only 300 students got enrolled in Civil Engineering.

7.4 Tables

Look at the table below, showing the maximum temperature recorded at different places in Odisha.

II. Answer these questions.

Question (a)
What was the highest temperature recorded?
Answer:
The highest record temperature was 43.5.

Question (b)
Where was it recorded?
Answer:
It was recorded at Angul.

Question (c)
Which were the other places that recorded high temperatures?
Answer:
The other places which recorded high temperatures were Bhubaneswar, Bolangir, Cuttack, Phulbani, Sambalpur, and Jharsuguda.

Question (d)
What was the maximum temperature in Bhubaneswar?
Answer:
The maximum temperature in Bhubaneswar was 42.2.

Question (e)
Which other places were as warm as Bhubaneswar?
Answer:
Bolangir, Jharsuguda, Sambalpur and Cuttack were as warm as Bhubaneswar.

Question (f)
What was the weather like in Puri, Gopalpur, Paradip, and Balasore? Why?
Answer:
The weather in these places was considerably less warm. It stood between 32.00 to 33.5. This is because these towns are on the coast.

Activity-11

Fill in the blanks to complete the following report based on the table above.

A report on today’s weather in Odisha
It was the season’s hottest day, in Odisha today. The temperature in many places went beyond __________ Celsius. Of all places in Odisha, _________recorded the highest temperature of __________ The other places that experienced an equally hot day were Bolangir and Jharsuguda. In these two places, the mercury soared up to __________ Bhubaneswar, the capital city, recorded a high temperature of __________ The other places that were as hot as Bhubaneswar were ________ and __________ with a recording of __________ and ___________ respectively. However, ____________, __________, Paradip, and Balasore, places near the sea, were relatively cooler. They recorded maximum temperatures of around ___________ Celsius.

Answer:
A report on today’s weather in Odisha
It was the season’s hottest day, in Odisha. The temperature in many places went beyond 40° Celsius. Of all places in Odisha, Angul recorded the highest temperature of 43.5° Celsius. The other places that experienced an equally hot day were Bolangir and Jharsuguda. In these two places, the mercury soared up to 42.7° Celsius. Bhubaneswar, the capital city, recorded a high temperature of 42.2° Celsius. The other places that were as hot as Bhubaneswar were Cuttack and Sambalpur with a recording of 41.5° Celsius and 41.8° Celsius respectively. However, Gopalpur, Puri. Paradip and Balasore, places near the sea, were relatively cooler. They recorded maximum temperatures of around 33.5° Celsius.

Activity – 12

The following table presents a weather report on the basis of data recorded up to 8.30 a.m. on Friday, 8 December. Have a look at the table and answer the questions that follow. Then write a short report to go with the table.

(a) On 8 December, Mumbai had the highest maximum temperature.

Question (i)
Which City had the lowest maximum temperature?
Answer:
Delhi had the lowest maximum temperature on 8 December.

Question (ii)
What was the temperature?
Answer:
The temperature was 20° C.

(b). Question (i)
Which city had the highest minimum temperature?
Answer:
Chennai had the highest minimum temperature.

Question (ii)
How much was it?
Answer:
The temperature was 23°C.

Question (c)
Which city had rainfall during the past 24 hours?
Answer:
Chennai had rainfall during the past 24 hours.

Question (d)
Which city had recorded the highest amount of rainfall since 1 October?
Answer:
Chennai had recorded the highest amount of rainfall since 1 October.

Weather report of Metro Cities:
Even in winter, the Metro cities of India were quite warm. On 8 December, Mumbai was the hottest with a maximum temperature of 34° celsius, while the lowest maximum temperature, 26° celsius, was recorded at Delhi. The same day, New Delhi, recorded the lowest minimum temperature of 08° celsius. It was quite cold there but in spite of recording maximum temperatures of 29° and 33° Celsius, the lowest minimum temperatures at Chennai and Kolkata respectively remained constant at 23° Celsius.

Similarly, Chennai witnessed the highest amount of rainfall in a week since 1 Oct. The rainfall stood at 560 inches which was 52 inches less than normal. New Delhi recorded the least rainfall during the week. It was only 3 inches which were 27 inches less than normal. Mumbai and Kolkata too had 6 inches and 64 inches respectively, less rainfall than normal. On the whole, rainfall in all the Metro cities was less than normal.

Activity -13

Here is a table of figures showing the leisure habits of the people of Bhubaneswar.

Use the information given in the table above and write a short report.
The leisure habits of the people of Bhubaneswar in the last year and this year does not show significant change. Last year, 1 lakh books were bought by people and this increased to 1.5 lahks this year. Thus there was an increase of 50% in the sale of books. There was a similar rise in Cable – T.V. connections. While, last year, only 50,000 people subscribed to Cable.

T.V., this year, the subscribers had increased to 1 lakh which is a 50 percent increase. As a result of this cinema, attendance fell from 3.5 lahks to 3.25 lakh last year to this year. Happily however 10,000 more people went on picnics this year than last year. However, in comparison with leisure activities like reading books or watching Cable T.V. going on picnics is the least popular.

Activity -14

Look at the table below and write a paragraph based on the information given in it.

Answer:
A comparative study of the Moon, the Earth, and the Sun:
Among all the bodies in the solar system, the Moon, the Earth, and Sun are the most significant. But they differ in size, weight, distance, and description. The Moon is the smallest of heavenly bodies while the Earth is 50 times bigger than the Moon and the Sun 400 times bigger than the weight of Moon is also the least while the Earth and the Sun are 81 times and 27 million times more than the Moon. If Earth is taken as a center point, the distance of the Moon from the Earth is 384,000 km. In fine, the Moon is a satellite of the planet Earth.

7.5 Pie Charts/circle charts

Here is a chart showing how Ramesh spends his day, Look at the chart and answer the questions that follow.

Activity- 15

(i)Answer the following questions.
a. How many hours does Ramesh spend at school?
b. Does this include the time he spends on the way to and from school?
c. How long does he sleep? When do you think he goes to bed? When does he get up?
d. How much time does he spend on the play?
e. How much time does he spend on his studies at home?
f. Do you divide your time in the same way?
Answer:
(a) Ramesh spends five and a half (51/2) hours at school.
(b) Yes, the hours spent at school include the time on the way to and from school.
(c) He sleeps for eight (8) hours a day He is supposed to go to bed at 10 p.m. and gets up at 6 a.m.
(d) It is supposed that Ramesh spends about 61/2 hours in playing.
(e) He spends about 6V2 hours on his studies.
(f) Yes, I divide time in the same way.

(ii) Now complete the report below by filling in the blank spaces with ideas from the pie chart above.

(iii) A child’s daily routine.

Ramesh walks to school at 10. It takes him hardly 20 minutes to get there. After prayers, he attends classes from 10.30 to 4 p.m. which includes a tiffin break for half an hour, from 1 to 1.30. At 4, when the classes are over, he comes back home, with his friends. He greatly enjoys the return trip home as his friends and he usually amuses themselves with innocent jokes, makes fun, and indulges in different kinds of innocuous mischief. On reaching home, he gobbles up something and scampers away to join his friends either in volleyball or in some country games, which he plays for just one hour. At 6, he has a wash, says his prayers, and sits down to study from 6.30 to 9.30 in the evening. At 9.30 he has dinner, does some light reading, and goes to bed by 10.30 p.m. The next morning he is up by 6.30. Within one hour he brushes his teeth have a wash, etc. and by 7.30 he is at his study table. He does his homework for two hours. At 9.30 he has an early lunch, packs his books in the bag, and is ready to go to school.

Activity – 16

A. Look at the chart below. It tells us how Mrs. Pattnaik spends her money.

Does Mrs. Pattnaik spend her money wisely? Why do you think so?
Answer:
Mrs. Pattnaik receives net cash of Rs 6000/- from her husband. She spends Rs 2700/- that is 45% of it towards her children’s education. She sends Rs 1350/- each to her son, who is studying engineering, and daughter who is studying medicine. Besides this, she spends equally on her house rent and food. For a three-room apartment, she pays Rs 1320/ which is 22% of the money she receives. She spends the same amount on food for a month. In addition to all this, she spends 540/- on transport.

Of this, she gives Rs 300A to her husband for petrol and monthly maintenance of his scooter and uses the rest for transport needs. She spends the least on entertainment spending Rs 80/- for her cable T.V. connection and Rs 40/ – for an occasional picture along with her husband. In all this, she spends her money wisely investing largely in her children’s education.

B. Look at the following diagram :

Now write a few sentences explaining why milk is considered to be a well-balanced food.
Answer:
Milk is considered a well-balanced diet because it has proteins, fats, carbohydrates, vitamins, and minerals as well as water in the right proportions and as required by the body. Moreover, milk is a universal diet that is available everywhere. It can also be taken by people of all ages.

C. You have collected the opinions of 500 people through a random sample survey. The findings of the survey are presented in the chart below.
Now use the information in the chart

The subjects were asked whether India should adopt the presidential form of government.
Answer:
A random sample survey of 500 people in Metro cities was conducted by the Operations Research Group to find the people’s opinion on changing over to a Presidential form of Government. The respondents were chosen from a cross-section of society. The results of the survey reveal that the majority were in favor of a Presidential form of Government.

However, they only consist of 40% of the respondents. 35 percent of the respondents are against a Presidential form of Government while 25 percent opined that they could not say anything about it. Thus though the majority calls for a Presidential form of Government, it is only a small majority as far as the percentage of respondents is concerned.

7.6. Maps

You are traveling by bus to Bhubaneswar. After reaching the new bus stand at Baramunda, you hire an auto-rickshaw to take you to Vani Vihar for an interview. But the highway is blocked at a point between Jayadev Vihar and Acharya Vihar. The auto-driver tells you he is new to Bhubaneswar and does not know all the roads. Which route would you ask him to take? Use the map below to decide on a route to Vani Vihar and then write down the instructions you would give the driver.

A. Answer the following questions.

Question 1.
How many possible routes are available to you?
Answer:
There are three routes available to go to Vanivihar.

Question 2.
Which route would you prefer?
(i) CRP square – Power house square – Assembly and Station square – R.D. Women’s College.
(ii) CRP square – Jayadev Vihar – Power house – Assembly – Acharva Vihar.
(iii) CRP square – Jayadev Vihar – Nalco Chhak – Vani Vihar.
Answer:
I would prefer the CRP square – Jayadav Vihar – Nalco Chhak – Vani Vihar route.

Question 3.
Would you take the CRP – Power house – Jayadev Vihar Acharya Vihar traffic route? If not, why?
Answer:
It would not be of any use to take this route because the traffic is blocked between Jayadev Vihar and Acharya Vihar. Another man, under similar circumstances, chose the route Jayadev Vihar – NALCO Chhak – Vani Vihar and gave the following instructions. Read the instructions before you write your own instructions.

B. instructions were given to the auto driver.

Go straight along the National Highway up to _________. Then turn left and take the Nandankanan Road. Keep going for about two kilometers and then turn right at ___________. Continue until you come to the ___________ on the left. Don’t stop. Go straight ahead. YOU will reach Vani Vihar after half a kilometer. You can see the gates of Vani Vihar on the left, just 1(X) meters before the Acharya Vihar traHie post. Enter and go straight to the Administrative Block.

Activity – 17

Fill in the blanks in the paragraph above with ideas from the map above.

Some common expressions used in giving instructions to reach someplace.
Turn right / left. Go straight ahead. Pass two roads on the right / left. On your left, you will see ……………. etc.
Go straight along the National Highway up to Javadev Vihar. Then turn left and take the Nandankanan Road. Keep going for about two kilometers and then turn right at Nalco Chhak. Continue until you come to the Sainik School, on the left. Don’t stop. Go straight ahead. You will reach Vani Vihar after half a kilometer. You can see the gates of Vani Vihar on the left, just 100 meters before the Acharya Vihar traffic post. Enter and go straight to the Administrative Block.

Activity – 18

Look at the map of a town given below. A car and a bus have collided on Bridge Road, causing a road block. Another car (shown on the map) has to reach the railway office. Write down the instructions that you would give the driver of the car.

Answer:
Turn right towards the shops and then go along the boundary of the Convent School again on the right till you reach Second Avenue. Here take a turn to the right till you reach the temple which you can see on the left. Here take a turn to the left and drive on till you cross the temple and the post office. The third building on this street is the Railway Office.

Activity – 19

The following is a map of your college. Write a letter to a friend, describing the things shown on the map.

Bhubaneswar
15.04.2012

Dear Gautam,
How are you? It is a long time since 1 wrote to you. In your last letter, you asked me to describe my college. Now that I am completely familiar with my college 1 can very vividly describe it. Our college faces the west and its front boundary runs along the main road. It has two gates that open onto the main road, one at the north end and another at the south end. The north gate leads to the library and the playground right in front of it. Beyond the library is the Commerce Block.

It is the smallest Block. Beside it on the south side is the Arts Block which constitutes the biggest building of the college. Further south, down the Arts Block, is the Science Block, it is bigger than the Commerce Block but smaller than the Arts Block. The Commerce and Science Blocks have twelve rooms and galleries each but the rooms and galleries of the Science Block are bigger than that of the Commerce Block.

The Arts Block has even huger rooms and galleries numbering fourteen in all. Near the Science Block towards the southwest are the Physics, Chemistry, and Biology laboratories. The entrance to the laboratories is in the north. They face the road leading to the Library from the north gate. The Biology Lab. is the closest from the Science Block. After the Biology Lab is the Chemistry Lab and then the Physics Lab which borders the main road. The back of these Laboratories runs along the road leading from the south gate to the Science Block.

Beyond this road on the south, are the office and staff common rooms. They lie adjacent to each other. Of course, the entrance to the office is from the West while the entrance to the staff rooms is on the south. All the Blocks, Laboratories, staff rooms, and office buildings are rectangular in structure. I hope, 1 have given a clear picture of the layout of my college. 1 am sending a photocopy of a map which found in the college calendar to make things more clear.
Do write to me,
Love,
Sanjay

Activity – 20

Use the information in the chart below and write a report stating which courses are popular in Odisha, which courses are popular among women, what percentage of boys and girls get enrolled in each course, etc.
Students taking admission in different branches of study in Odisha.

Students’ Enrolment and popularity of courses in Odisha.
Answer:
In Odisha, courses in the humanities stream are the most popular. Almost sixty students of every 100 opt for humanities. In addition, the largest number of girls enroll in humanities courses where the proportion between girls and boys is 60: 40. Courses in science stand second in popularity. In such courses the proportion between boys and girls is 50: 50.

Engineering courses take third place in popularity. This course is more popular with boys than with girls. Hence the enrolment of boys to girls in this course is 70: 30. Commerce courses are next in terms of popularity. This course is preferred more by boys than by girls. The proportion between boys and girls in this course is 80: 20. Agriculture, Forestry and Vet Science stand next in popularity. Here too the boys dominate over girls with a proportion of 80: 20. After this, vocational subjects are preferred.

In this course there are more boys than girls with the proportion being 75: 25. Finally, the Medical science course is the least popular. This course too has more boys than girls and the proportion between them is 90: 10. On the whole, while humanities and science courses are the most popular, the Medical science course is the least popular. Moreover, while more girls are enrolled in humanities, the proportion of boys in all other courses is larger than that of girls.

Activity – 21

The graphs below represent the spending habit of the young and old people of Odisha. Compare the information in both graphs and write a paragraph.

A – Housing, fuel, light, and power
B – Clothing, footwear, and durable goods
C – Other goods and services
D – Food

Comparative spending habits of the young and old in Odisha.
Answer:
A comparative study of the spending habits of the young and old people of Odisha reveals that both groups spend the most on other goods and services which exclude food, shelter, and clothing. While young people spend 40% of their income on other goods and services, old people spend 33% on this. Items that constitute other goods and services include household items like Refrigerators, Washing Machines.

Air Coolers, Grinders, and the like. Services in this category mainly consist of transport and entertainment. Similarly, both groups spend the least on clothing, footwear, and durable goods. However, young people spend more than old people on this item. The former spend 17% of their income while the latter spend 4% less that is, 13% of their income on clothing, footwear, and durable goods. The old people spend equally on housing and food. They give more priority to these items on their budget than the young.

54% of their income, that is 27% is spent each on food and housing. The young people, on the other hand, spend 24% and 19% respectively on food and housing. They give more priority to food than to housing. However, the amount they spend on each of these items is less than what the old spend on it. In short, the young and the old give top priority to other goods and services while giving the least priority to clothing, footwear, and other durable goods. But the old people give more priority to food and housing than the young.

Activity – 22

Prepare a newspaper report on the basis of the information presented in the graph below.

Answer:
Alarming rise in Road Accidents
By our correspondent :
Bhubaneswar, Aug 18: There has been an alarming rise in road accidents in Bhubaneswar since 1991. Talking to our correspondent, Mr. Sudhansu Mohanty. the traffic SP. Bhubaneswar pointed out that since the last decade, road accidents have occurred in Bhubaneswar with alarming frequency. Quoting statistics available in his department he is reported to have said that between 1987 to the middle of 1988 almost 3500 people were reported to have died due to road accidents. The sudden spurt in accidents and the number of fatalities forced the government to enforce traffic laws especially, the donning of helmets.

As a result deaths due to accidents decreased gradually and touched a low of 1700 in mid ’90. However, changes in the Government and relaxation of traffic rules after this saw a dramatic rise in fatalities caused by road accidents. Thus, in ’92 the number of fatalities rose to 3600, in ’94 to 4800, and in ‘98 to 7200. Thus from the middle of 1990 to the end of 1998, almost 5400 people died as a result of road accidents in Bhubaneswar. It is hoped that law enforcement agencies will take steps to enforce laws and traffic rules, NGOs will educate people on traffic rules and the public will cooperate to ensure that the roads of Bhubaneswar are safe for one and all.

Activity – 23

An influential person has applied for permission to set up a stone crusher unit at a place indicated with dots on the map below. As a resident of the area, you have serious objections. Write a letter to the appropriate authority expressing your objections.

Answer:

80 Saheed Nagar, Bhubaneswar
17 April 2012

The Collector and District Magistrate
Collectorate
Puri Road, Bhubaneswar
Dt. Khurda
Sir,
I wish to invite your attention to a stone-crusher unit that is proposed to be set up in the center of the city.
As you may be aware that there are two acres of government land right in front of the Head Post Office beside the Convent School on Janpath road, Bhubaneswar. This piece of land is being reportedly leased to an extremely influential person to set up a stone crusher unit. Such a step is highly objectionable.

First of all, the Honourable High Court of Odisha had in an already judged P.I.L. petition stated that no stone-crushers unit should be set up within 20 km of the city limits. Consequently, stone-crusher units beyond Khandagiri have now moved beyond Khurda. Therefore building a unit here is entirely illegal. Secondly, stone-crusher units cause great environmental pollution and bring with it numerous health hazards.

The stone-crusher units spread a pall of dust which is especially dangerous for people with respiratory problems like Asthma. Thirdly, the stone crusher unit is being proposed in an area that is heavily populated, though you may call it a floating population. It is situated right in the middle of a school and a women’s college which is on either side of it. Thus, it will not only affect our young ones in the school but also the girls in the women’s college. The proposed unit can cause a lot of sound pollution besides dust pollution.

This is really unwelcome in an educational block of buildings. Finally, the land on which the proposed crusher unit is being proposed to be set up has a lot of evergreen trees and serves as an environmental cushion for the whole city. Cutting down trees to set up a stone-crusher unit on it is therefore the least desirable thing that could be done there. I request you to therefore prohibit the lease of the land for the proposed stone-crusher unit and instead develop it into a park in which all the members of the public are with you. Yours faithfully (Suman Priyadarshini)
Member-Secretary
Odisha Environmental Society.
Bhubaneswar

Odisha State Board CHSE Odisha Class 12 Invitation to English 4 Solutions Grammar Tense Patterns Unit 1 The Present Simple and the Present Progressive Textbook Activity Questions and Answers.

CHSE Odisha 12th Class English Grammar Tense Patterns Unit 1 The Present Simple and the Present Progressive

SECTION-I

We might have heard two English words, i.e., Time and Tense. They are not regarded as the same in the English language. The word ‘Tense’ is a purely grammatical term. But we use the words yesterday, today, and tomorrow. We use ‘yesterday’ for past time, ‘today’ for the present time, and ‘tomorrow’ for future time. We can experience the time and say what time it is. The term ‘tense’ in grammar is used to refer to a verb form. An English verb basically has two forms/categories. Let’s take the verb go. We say: go — present tense, went — past tense, gone — past participle tense.
Some of us have a wrong notion that the verb ‘go’ has three forms.
Observe all the forms of the verb (go)-
(i) present (go),
(ii) past (went), and
(iii) past participle (gone).

The past participle is the sub-class/form of the past form. So there are basically two forms of a verb i.e., present and past. These two forms express all the various kinds of meanings in the present, past, and future times. If a verb has two forms, then there are two tenses — (not three tenses). That is why there is no ‘Future Tense’ in the English language.
Let’s have some ideas on Tense patterns.
The Present Simple and Present Progressive.
Look at the following sentences.
(a) Satish: What are you doing?
Manish: I am writing a letter to my friend. I write to him every Sunday.
(b) I don’t understand why my dog is barking at you this morning. He is usually quite friendly.
(c) You are very gentle normally, so why are you acting in such a violent manner now?

In the above examples, 7 write to him every Sunday.’ 7 don’t understand’. ‘He is usually quite friendly.’ ‘’You are very gentle normally.’ the verb phrases underlined belong to ‘Simple Present Tense’.They are used to describe persons and things in their normal or usual state or they talk about some activity that takes place habitually or regularly.
But the examples: ‘Why my dog is barking at you this morning.’ ‘Why are you acting… ?’ and 7 am writing a letter….’ the verb phases (be + ing form) belong to ‘Present Progressive/Continuous Tense’. They are used to talking about some activity that is going on at the present moment of speaking. The activity/event is going on or continuing now.

Activity – 1
Study the sentences below and fill in the gaps, using the Present Simple / Present Progressive form of the verb in brackets, as required.
(a) They boy next door ______________(water) the plants this morning, but he normally ______________(do) it in the evening.
(b) My sister ______________(play) badminton now, but she ______________ (not play) here everyday.
(c) My brother ______________(search) for his pen. He always ______________ (misplace) it.
(d) We ______________(get) ready to go to school; we ______________ (go) to school every morning.
(e) I usually ______________ (enjoy) reading books in the library, but I ______________ (not enjoy) this one very much.
(f) My grandfather rarely ______________(carry) an umbrella, but he ______________(carry) one now because there are dark clouds in the sky.
(g) I’m sorry, but you can’t see the Minister. He ______________ (sleep) still, although he usually ______________(wake up) very early.
(h) Hari ______________ (do) his homework still. His brother, who always ______________(work) very fast ______________ (play) in the garden already.
Answer:
(a) The boy next door is watering the plants this morning, but he normally does it in the evening.
(b) My sister is playing badminton now, but she does not play here every day.
(c) My brother is searching for his pen. He always misplaces it.
(d) We are getting ready to go to school; we go to school every morning.
(e) I usually enjoy reading books in the library, but I am not enjoying this one very much.
(f) My grandfather rarely carries an umbrella, but he is carrying one now because there are dark clouds in the sky.
(g) I’m sorry, but you can’t see the Minister. He is sleeping still, although he usually wakes up very early.
(h) Hari is doing his homework still. His brother, who always works very fast, is playing in the garden already.

Activity -2:
The time is 8 p.m. Everyone in your family is busy, but each person is doing something which is different from what he/she usually does at this time. The members of your family, including yourself, are listed below. Write what each one of them is doing, and also mention what they usually do at this time. (One example has been given)
1. Father
Ans. ______________________________________________________
2. Mother
Ans. ______________________________________________________
3. My uncle
Ans. ______________________________________________________
4. My aunt
Ans. ______________________________________________________
5. My sister
Ans. ______________________________________________________
6. My brother
Ans. ______________________________________________________
7. I
Ans. ______________________________________________________
Answer:
1. Father
Answer:
Father is having a shave, but he usually goes for a walk at this time.
2. Mother
Answer:
She is knitting now, but she normally works at this time.
3. My uncle
Answer:
My brother is sleeping still, but he usually goes to school at this time.
4. My aunt
Answer:
My aunt is having a bath now, but she usually sleeps at this time.
5. My sister
Answer:
My sister is playing now, but she generally studies her lessons at this time.
6. My brother
Answer:
My brother is playing cards now, but he usually goes to the fields at this time.
7. I
Answer:
I am doing morning exercise now, but I usually do not do it every day.

Section -2:
Examine the following sentences :
(a) We usually have a football match in our village every Sunday, but this year we aren’t having any matches.
(b) He usually avoids going to the library but he is going there regularly this month as he is preparing for an exam.
The above examples show that the Present Progressive does not specify either the time of beginning or the time of completing the activity. All we know is the activity is in progress now (the moment of speaking). Expressions like nowadays, this month, these days, etc. are used to refer to the period of time during which the activity takes place. In order to distinguish the Progressive from the Non-Progressive form, we have to see its three separate meanings. It indicates :
(i) Temporary duration,
(ii) Limited duration,
(iii) the happenings need not be complete.
Simple present, on the other hand, refers to a relatively permanent activity or state.

Activity – 3
Fill in the blank spaces below, using the appropriate forms of the verbs in brackets.
(a) Our neighbours ______________(go) to Puri every winter but this winter they ______________ (go) to Sambalpur.
(b) My father generally______________ (take) the bus but today he ______________(walk) to work.
(c) They usually ______________(play) football on Sundays but this month they ______________ (play) cricket instead.
(d) My brother always ______________(work) on the day shift but this summer he ______________(work) on the night shift.
(e) My teacher ______________(go) abroad every year but she ______________ (visit) Kanyakumari this year.
Answer:
(a) Our neighbors go to Puri every winter but this winter they are going to Sambalpur.
(b) My father generally takes the bus but today he is walking to work.
(c) They usually play football on Sundays but this month they are playing cricket instead.
(d) My brother always works the day shift but this summer he is working on the night shift.
(e) My teacher goes abroad every year but she is visiting Kanyakumari this year.

Activity -4
Imagine that you have an examination next month. You are working very hard for your examination and have been forced to change your daily routine. Describe seven things that you usually do and the things you are required to do now. You can use expressions such as these days, nowadays, this month, this summer, etc. An example is given in (i).
(i) ______________________________________________________.
(ii) ______________________________________________________.
(iii) ______________________________________________________.
(iv) ______________________________________________________.
(v) ______________________________________________________.
Answer:
(i) I normally get up at 7 o’clock but I am getting up at 5 a.m. these days.
(ii) I usually go to tuition but I am preparing my lessons myself these days.
(iii) I normally read my books but I’m writing out my lessons this month.
(iv) I generally study the textbooks but I’m studying the key books these days.
(v) I study for my lessons two hours a day but I’m studying ins ten hours this month.

Activity – 5
Imagine that panchayat elections are going to be held in your village and as a result, a lot of development work is taking place. Write five sentences, mentioning in each what the present condition in the village is and what new work is going on right now. Look at the example in (i) and use the hints provided in the other bits of your sentences.

(i) Drinking water.
______________________________________________________
(ii) Electricity
______________________________________________________
(iii) Roads
______________________________________________________
(iv) Medical facilities
______________________________________________________
(v) Education
______________________________________________________
Answer:
(i) Drinking water.
Our village has no water supply but now the government is providing piped water to every home.
(ii) Electricity
Our village has no electricity facilities but the government is fixing poles in our village for electricity.
(iii) Roads
Our village has no concrete road but the government is making a concrete road for the villagers.
(iv) Medical facilities
Our village has no dispensary but the government is providing a dispensary for us.
(v) Education
Our village has no primary school but the government is constructing a building for a primary school.

SECTION-III

Verbs that do not normally take the Progressive form.
Examine the pairs of sentences below.
(a) (i) I like to fish.
(ii) I am liking fish.
(b) (i) He feels very happy.
(ii) He is feeling the heat now.
(c) (i) Sugar tastes sweet.
(ii) The sugar in the market is tasting less sweet these days.
Verbs like feel, like, taste, love, hate, want, need, prefer, know; realize, suppose, mean, understand, believe, remember, belong, contain, consist, depend, seem, think, see, etc. are known as stative verbs. They refer to states rather than to events or actions. We use the Simple Present to refer to states that exist at the present moment. Some of these verbs can be used as dynamic or action-oriented. In that case, they go with an —ing form i.e., the Progressive form. Then the usual character of the verb
becomes action-oriented.

Activity — 6
Choose the correct alternative to fill in the blanks.
(a) Costs / is costing
(i) Gold ________ more and more these days.
(ii) Gold ________a great deal of money.
(b) thinks/is thinking
(i) He ________Don’t disturb him.
(ii) He ________very highly of you.
(c) enjoy/am enjoying
(i) I ________ games.
(ii) I ________this game.
Answer:
(a) (i) is costing
(ii) costs
(b) (i) is thinking
(ii) thinks
(c) (i) enjoy
(ii) am enjoying

Activity -7
Rewrite the sentences below without changing the meaning. Use the word given in capital letters, which must not be altered in any way.
Example :
These shoes are the wrong size for me. FIT
These shoes do not fit me.
(a) There are four gallons of petrol in the tank. CONTAINS
______________________________________________________
(b) I intend to go to Koraput next summer. THINKING OF
______________________________________________________
(c) The life of the Rajput family forms the subject of the story. DESCRIBES
______________________________________________________
(d) The doctor is looking at the X-Ray. HAVING A LOOK
______________________________________________________
(e) When I see this village I remember my childhood. REMINDS ME OF
______________________________________________________
(f) I am fond of sweets. LIKE
______________________________________________________
(g) In my opinion you should meet him again. THINK
______________________________________________________
Answer:
(a) The tank contains four gallons of petrol.
(b) I am thinking of going to Koraput next summer.
(c) The life of the Rajput family describes the subject of the story.
(d) The doctor is having a look at the X-Ray.
(e) This village reminds me of my childhood.
(f) I like sweets.
(g) I think you should meet him again.

Activity – 8
Use the verbs in brackets in the Simple Present or Present Progressive forms.
This year I ________ (study) English at Delhi University. I ________ (work) part-time in a public library. I’m lucky to have this job. I ________(not have to) get up early. The library ________ (open) at 10 and ________ (close) at 7. The work is interesting because people ________ (always come in) and ________ (ask) me to help them, so I ________ (learn) a lot about different subjects. I ________ (enjoy) the job and ________ (find) it very amusing too. People ________ (use) the strangest things as bookmarks. I have found a lock of black hair inside books. Matchsticks ________ (be) common and so ________ (be) bus tickets. My colleagues ________ (always find) things – even a ten rupee note, but I haven’t been so lucky! I often ________ (think) of a photograph I once found inside a book. It was the photograph of a beautiful girl, and on the back were the words ‘I ________ (love) you, and I ________ (miss) you very much.’
Answer:
This year I am studying English at Delhi University. I am working part-time in a public library. I’m lucky to have this job. I do not have to get up early. The library opens at 10 and closes at 7. The work is interesting because people always come in and ask me to help them, so I learn a lot about different subjects. I enjoy the job and find it very amusing too. People use the strangest things as bookmarks. I have found a lock of black hair inside books. Matchsticks are common and so is bus tickets. My colleagues always find things – even a ten rupee note, but I haven’t been so lucky! I often think of a photograph I once found inside a book. It was the photograph of a beautiful girl, and on the back were the words ‘I love you, and I miss you very much.

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

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

Evaluate the following Integrals.
Question 1.
(i) \(\int_{-2}^3\)x⁴ dx
Solution:

(ii) \(\int_0^1 x^{\frac{1}{3}}\) dx
Solution:
\(\int_0^1 x^{\frac{1}{3}}\) dx = \(\left[\frac{x^{\frac{4}{3}}}{\frac{4}{3}}\right]_0^1\) = \frac{3}{4}\(\)

(iii) \(\int_1^4 \frac{d x}{\sqrt{x}}\) dx
Solution:

(iv) \(\int_1^3 \frac{d x}{x^3}\) dx
Solution:

(v) \(\int_1^2\left(4 x+\sqrt{x}+\frac{1}{x^{\frac{1}{3}}}+\frac{1}{x^2}\right)\) dx
Solution:

(vi) \(\int_{-1}^2\)(2x + 1)(x – 2) dx
Solution:

(vii) \(\int_0^1\)(x + 1)⁴ dx
Solution:

(viii) \(\int_0^1 x^7\left(1+x^8\right)^{\frac{1}{3}}\) dx
Solution:

(ix) \(\int_1^4 \frac{x^2-3 x+5}{\sqrt{x}}\) dx
Solution:

(x) \(\int_1^4 \frac{(x+2)\left(x^2+3\right)}{\sqrt{x}}\) dx
Solution:

Question 2.
(i) \(\int_0^{\frac{\pi}{2}}\)(cos x – sin x) dx
Solution:

(ii) \(\int_0^{\frac{\pi}{2}}\)cos 2x dx
Solution:

(iii) \(\int_0^{\frac{\pi}{4}}\)tan² x dx
Solution:

(iv) \(\int_0^\pi 3 \sin \frac{x}{2} \cos \frac{x}{2}\) dx
Solution:

(v) \(\int_0^{\frac{\pi}{4}}\)sin 2x cos x dx
Solution:

(vi) \(\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{1+\cos 2 x}{1-\cos 2 x}\) dx
Solution:

(vii) \(\int_{\frac{\pi}{4}}^{\frac{\pi}{2}}\)cos x dx
Solution:

(viii) \(\int_0^{\frac{\pi}{4}}\) cos² 2x sin³ 4x dx
Solution:

Question 3.
(i) \(\int_1^2\)e^4x+1 dx
Solution:
\(\int_1^2\)e^4x+1 dx = \(\left[\frac{e^{4 x+1}}{4}\right]_1^2\) = \(\frac{1}{4}\){e⁹ – e⁵}

(ii) \(\int_0^2\)3^x+2 dx
Solution:
\(\int_0^2\)3^x+2 dx = \(\left[\frac{3^{x+2}}{\ln 3}\right]_0^2\) = \(\frac{1}{\ln 3}\){3⁴ – 3²} = \(\frac{72}{\ln 3}\)

(iii) \(\int_0^1\)cos h 2x dx
Solution:

(iv) \(\int_0^1 \frac{e^x-e^{-x}}{e^x+e^{-x}}\) dx
Solution:

(v) \(\int_0^2 x^2 e^{x^3}\) dx
Solution:

Question 4.
(i) \(\int_0^1 \frac{d x}{\sqrt{1-x^2}}\)
Solution:

(ii) \(\int_{\frac{2}{\sqrt{3}}}^2 \frac{d x}{x \sqrt{x^2-1}}\)
Solution:

(iii) \(\int_0^{\sqrt{3}} \frac{d x}{1+x^2}\)
Solution:

(iv) \(\int_0^{\ln 2} \frac{d x}{\sqrt{e^{2 x}-1}}\) dx
Solution:

Question 5.
(i) \(\int_0^1 \frac{d x}{3 x+2}\)
Solution:

(ii) \(\int_0^4 \frac{d x}{\sqrt{x^2+9}}\)
Solution:

(iii) \(\int_2^3 \frac{d x}{\sqrt{x^2-2}}\)
Solution:

(iv) \(\int_0^4 \sqrt{x^2+9}\) dx
Solution:

Question 6.
(i) \(\int_{-2}^1\)(|x| + x) dx
Solution:

(ii) \(\int_2^5\)[x] dx
Solution:

(iii) \(\int_0^{\frac{3}{2}}\)[2x] dx
Solution:

(iv) \(\int_0^2\)[x²] dx
Solution:

Question 7.
(i) \(\int_1^2\)e^x . (x + 1) dx
Solution:

(ii) \(\int_0^{\frac{\pi}{4}}\)x sin x dx
Solution:

(iii) \(\int_1^2\)x log x dx
Solution:

(iv) \(\int_0^1\)x tan^-1 x dx
Solution:

(v) \(\int_0^1 \frac{x d x}{(2x+1)(x+1)}\)
Solution:

(vi) \(\int_0^{\frac{\pi}{2}} \frac{\cos x d x}{(\sin x+1)(\sin x+2)}\)
Solution:

(vii) \(\int_\theta^{\frac{\pi}{2}}\)e^x cos x dx
Solution:

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

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

Evaluate the following Integrals.
Question 1.
I = \(\int_1^3\)5x² dx
Solution:
Here a = 1, b = 3, f(x) = 5x²
⇒ nh = b – a = 3 – 1 = 2

Question 2.
I = \(\int_{-1}^1\)ex dx
Solution:
Here a = -1, b = 1, f(x) = x, nh = b – a = 2

Question 3.
I = \(\int_0^6\)x dx
Solution:
Here a = 0, b = 6, f(x) =x, nh = b – a = b

Question 4.
I = \(\int_0^4\)(x² + 2x + 4) dx
Solution:
Here a = 0, b = 4, f(x) = x² + 2x + 4 and nh = b – a = 4