Class 12

Odisha State Board Elements of Mathematics Class 12 Solutions CHSE Odisha Chapter 11 Differential Equations Ex 11(a) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 11 Differential Equations Exercise 11(a)

Question 1.
Determine the order and degree of each of the following differential equations.
(i) y sec² x dx + tan x dy = 0
Solution:
Order: 1, Degree: 1

(ii) \(\left(\frac{d y}{d x}\right)^4\) + y⁵ = \(\frac{d^3 y}{d x^3}\)
Solution:
Order: 3, Degree: 1

(iii) a\(\frac{d^2 y}{d x^2}\) = \(\left\{1+\left(\frac{d y}{d x}\right)^2\right\}^{\frac{3}{2}}\)
Solution:
Order: 2, Degree: 2

(iv) tan^-1\(\sqrt{\frac{d y}{d x}}\) = x
Solution:
Order: 1, Degree: 1

(v) ln\(\left(\frac{d^2 y}{d x^2}\right)\) = y
Solution:
Order: 2, Degree: 1

(vi) \(\frac{\frac{d y}{d t}}{y+\frac{d y}{d t}}\) = \(\frac{y t}{d y}\)
Solution:
Order: 1, Degree: 2

(vii) \(\frac{d^2 y}{d u^2}\) = \(\frac{3 y+\frac{d y}{d u}}{\sqrt{\frac{d^2 y}{d u^2}}}\)
Solution:
Order: 2, Degree: 3

(viii) \(e^{\frac{d z}{d x}}\) = x²
Solution:
Order: 1, Degree: 1

Question 2.
Form the differential equation by eliminating the arbitrary constants in each of the following cases.
(i) y = A sec x
Solution:
y = A sec x
Then \(\frac{d y}{d x}\) = A sec x tan x = y tan x

(ii) y = C tan^-1 x
Solution:

(iii) y = Ae^t + Be^2t
Solution:

(iv) y = Ax² + Bx
Solution:

(v) y = -acos x + b sin x
Solution:

(vi) y = a sin^-1 x + b cos^-1 x
Solution:

(vii) y = at + be^t
Solution:

(viii) y = a sin t + be^t
Solution:

(ix) ax² + by = 1
Solution:

Question 3.
Find the general solution ofthe following differential equations.
(i) \(\frac{d y}{d x}\) = \(\frac{e^{2 x}+1}{e^x}\)
Solution:
\(\frac{d y}{d x}\) = \(\frac{e^{2 x}+1}{e^x}\)
⇒ y = ∫(e^x + e^-x) dx = e^x – e^-x + C

(ii) \(\frac{d y}{d x}\) = x cos x
Solution:
\(\frac{d y}{d x}\) = x cos x
⇒ y = ∫x cos x dx
= x . sin x – ∫sin x dx – x sin x + cos x + C

(iii) \(\frac{d y}{d x}\) = t⁵ log t
Solution:

(iv) \(\frac{d y}{d x}\) = 3t² + 4t + sec² t
Solution:
\(\frac{d y}{d x}\) = 3t² + 4t + sec² t
⇒ y = t³ + 2t² + tan t + C

(v) \(\frac{d y}{d x}\) = \(\frac{1}{x^2-7 x+12}\)
Solution:

(vi) \(\frac{d y}{d u}\) = \(\frac{u+1}{\sqrt{3 u^2+6 u+5}}\)
Solution:

(vii) (x² + 3x + 2) dy – dx = 0
Solution:

(viii) \(\frac{d y}{d t}\) = \(\frac{\sin ^{-1} t e^{\sin ^{-1} t}}{\sqrt{1-t^2}}\)
Solution:

Question 4.
Solve the following differential equations.
(i) \(\frac{d y}{d x}\) = y + 2
Solution:

(ii) \(\frac{d y}{d t}\) = \(\sqrt{1-y^2}\)
Solution:
\(\frac{d y}{d t}\) = \(\sqrt{1-y^2}\)
⇒ \(\frac{d y}{\sqrt{1-y^2}}\) = dt
⇒ sin^-1 y = t + C

(iii) \(\frac{d y}{d z}\) = sec y
Solution:
\(\frac{d y}{d z}\) = sec y
⇒ cos y dy = dz
⇒ sin y = z + C

(iv) \(\frac{d y}{d x}\) = e^y
Solution:

(v) \(\frac{d y}{d x}\) = y² + 2y
Solution:

(vi) dy + (y² + 1) dx = 0
Solution:

(vii) \(\frac{d y}{d x}\) + \(\frac{e^y}{y}\) = 0
Solution:

(viii) dx + cot x dt = 0
Solution:
dx + cot x dt = 0
⇒ tan x dx + dt = 0
⇒ ∫tan x dx + ∫dt = C₁
⇒ In sec x + t = C₁
⇒ In sec x = C₁ – t
⇒ sec x = \(e^{C_1}\) . e^-t
⇒ cos x = \(e^{-C_1}\) . e^t
⇒ cos x = Ce^t where C = \(e^{-C_1}\)

Question 5.
Obtain the general solution of the following differential equations.
(i) \(\frac{d y}{d x}\) = (x² + 1) (y² + 1)
Solution:

(ii) \(\frac{d y}{d t}\) = e^2t+3y
Solution:

⇒ 2e^-3y + 3e^2t + 6C₁ = 0
⇒ 2e^-3y + 3e^2t = C
where C = -6C₁

(iii) \(\frac{d y}{d z}\) = \(\frac{\sqrt{1-y^2}}{\sqrt{1-z^2}}\)
Solution:

(iv) \(\frac{d y}{d z}\) = \(\frac{x \log x}{3 y^2+4 y}\)
Solution:

(v) x²\(\sqrt{y^2+3}\) dx + y\(\sqrt{x^3+1}\) dy = 0
Solution:

(vi) tan y dx + cot x dy = 0
Solution:
tan y dx + cot x dy = 0
⇒ tan x . dx + cot y dy = 0
⇒ ∫tan x dx + ∫cot y dy = 0
⇒ -ln cos x + ln siny = ln C
⇒ ln\(\frac{\sin y}{\cos x}\) = ln C
⇒ \(\frac{\sin y}{\cos x}\) = C
⇒ sin y = C cos x

(vii) (x² + 7x + 12) dy + (y² – 6y + 5) dx = 0
Solution:

(viii) y dy + e^-y x sin x dx = 0
Solution:
y dy + e^-y x sin x dx = 0
⇒ ye^y dy + x sin x dx = 0
⇒ ∫ye^y dy + ∫x sin dx = C
[Integrating by parts.
⇒ ye^y – ∫e^y dy + x(-cos x) – ∫(-cos x) dx = C
⇒ ye^y – e^y – x cos x + sin x = C
⇒ (y – 1) e^y – x cos x + sin x = C

Question 6.
Solve the following second order equations.
(i) \(\frac{d^2 y}{d x^2}\) = 12x² + 2x
Solution:

(ii) \(\frac{d^2 y}{d t^2}\) =e^2t +e^-t
Solution:

(iii) \(\frac{d^2 y}{d \vartheta^2}\) = -sin υ + cos υ + sec² υ
Solution:
\(\frac{d^2 y}{d \vartheta^2}\) = -sin υ + cos υ + sec² υ
Integrating we get
\(\frac{d y}{d υ}\) = ∫sin υ dυ + ∫cos υ dυ + ∫sec² υ dυ
= cos υ + sin υ + tan υ + A
Again integratingwe get
y = ∫(cos υ + sin υ + tan υ + A)dυ + B
where A, B are arbritrary constants.
⇒ y = sin υ – cos υ + ln |sec υ| + A.υ. + B

(iv) cosec x \(\frac{d^2 y}{d x^2}\) = x
Solution:
cosec x \(\frac{d^2 y}{d x^2}\) = x
\(\frac{d^2 y}{d x^2}\) = x sin x
Integrating we get
\(\frac{d y}{d x}\) = ∫x sin x dx + A
= x . (-cos x) – ∫(-cos x) dx + A
= -x cos x + ∫cos x dx + A
= -x cos x + sin x + A
Again integrating we get
y = -∫x cos x dx + ∫sin x + ∫A dx + B
= -{x sin x -∫1 . sin x dx} – cos x + Ax + B
= -x sin x – 2cos x + Ax + B

(v) x²\(\frac{d^2 y}{d x^2}\) + 2 = 0
Solution:

(vi) sec x \(\frac{d^2 y}{d x^2}\) = sec 3x
Solution:

(vii) \(\frac{d^2 y}{d x^2}\) = sec² x + cos² x
Solution:

(viii) e^-x\(\frac{d^2 y}{d x^2}\) = x
Solution:
e^–x\(\frac{d^2 y}{d x^2}\) = x
⇒ \(\frac{d^2 y}{d x^2}\) = xe^x
Integrating we get
\(\frac{d y}{d x}\) = ∫xe^x dx = ∫e^x dx + Ax + B
= xe^x – e^x – e^x + Ax + B
= (x – 2)e^x + Ax + B

Question 7.
Find the particular solutions of the following equations subject to the given conditions.
(i) \(\frac{d y}{d x}\) = cos x, given that y = 2 when x = 0.
Solution:
\(\frac{d y}{d x}\) = cos x
Integrating we get
y = ∫cos x dx = sin x + C
Given that when x = 0, y = 2
So 2 = C
∴ The particular solution is y = sin x + 2

(ii) \(\frac{d y}{d t}\) = cos² y subject to y = \(\frac{\pi}{4}\) when t = 0.
Solution:
\(\frac{d y}{d t}\) = cos² y
⇒ sec² y dy = dt
∫sec² dy = ∫dt
⇒ tan y = t + C
When t = 0, y = \(\frac{\pi}{4}\)
So tan \(\frac{\pi}{4}\) = C ⇒ C = 1
∴ The particular solution is tan y = t + 1

(iii) \(\frac{d y}{d x}\) = \(\frac{1+y^2}{1+x^2}\) given that y = √3 when x = 1.
Solution:

(iv) \(\frac{d^2 y}{d x^2}\) = 6x given that y = 1 and \(\frac{d y}{d x}\) = 2 when x = 0.
Solution:
\(\frac{d^2 y}{d x^2}\) = 6x ⇒ \(\frac{d y}{d x}\) = 3x² + 2
When x = 0, \(\frac{d y}{d x}\) = 2
So 2 = A
∴ \(\frac{d y}{d x}\) = 3x² + 2
Again integrating we get
y = x³ + 2x + B
When x = 0, y = 1
So B = 1.
∴ The particular solution is y = x³ + 2x + 1

Question 8.
(i) Solve : \(\frac{d y}{d x}\) = sec (x + y)
Solution:

(ii) Solve : \(\frac{d y}{d x}\) = sin(x + y) + cos(x + y)
Solution:

(iii) Solve : \(\frac{d y}{d x}\) = cos (x + y)
Solution:

(iv) Solve : \(\frac{d y}{d x}\) + 1 = e^x+y
Solution:

Odisha State Board CHSE Odisha Class 12 Math Solutions Chapter 12 Vectors Ex 12(d) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 12 Vectors Exercise 12(d)

Question 1.
Each question given below has four possible answers out of which only one is correct. Choose the correct one.
(i) \(\vec{a} \cdot \vec{b} \times \vec{a}\) = _______.
(a) \(\overrightarrow{0}\)
(b) 0
(c) 1
(d) \(\vec{a}^2 \vec{b}\)
Solution:
\(\vec{a} \cdot(\vec{b} \times \vec{a})\) = \((\vec{b} \times \vec{a}) \cdot \vec{a}\)
= \(\vec{b} \cdot(\vec{a} \times \vec{a})\) = \(\vec{b} \cdot \overrightarrow{0}\)
= 0 [∴ Dot product is commutative and in the scalar triple product the dot and cross can be interchanged.]

(ii) \((-\vec{a}) \cdot \vec{b} \times(-\vec{c}))\) = _______.
(a) \(\vec{a} \times \vec{b} \cdot \vec{c}\)
(b) \(-\vec{a} \cdot(\vec{b} \times \vec{c})\)
(c) \(\vec{a} \times \vec{c} \cdot \vec{b}\)
(d) \(\vec{a} \cdot(\vec{c} \times \vec{b})\)
Solution:
\((-\vec{a}) \cdot \vec{b} \times(-\vec{c})\) = \(\vec{a} \cdot(\vec{b} \times \vec{c})\)

(iii) For the non-zero vectors \(\vec{a}, \vec{b}\) and \(\vec{c}, \vec{a} \cdot(\vec{b} \times \vec{c})\) = 0 if
(a) \(\vec{b} \perp \vec{c}\)
(b) \(\vec{a} \perp \vec{b}\)
(c) \(\vec{a} \| \vec{c}\)
(d) \(\vec{a} \perp \vec{c}\)
Solution:
\(\vec{a} \cdot(\vec{b} \times \vec{c})\) = \((\vec{a} \times \vec{b}) \cdot \vec{c}\)
\(\vec{c} \perp(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}})\)
but \(\vec{a} \times \vec{b}\) is perpendicular to \(\vec{a}\) and \(\vec{b}\)
∴ \(\vec{a} \| \vec{b}\)

Question 2.
Find the scalar triple product \(\vec{b} \cdot(\vec{c} \times \vec{a})\) where \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) are respectively.
(i) î + ĵ, î – ĵ, 5î + 2ĵ + 3k̂
Solution:

= 1 (0 – 3) + 1 (0 – 3) + 0 (5 – 2)
= 3 – 3 = -6

(ii) 5î – ĵ + 4k̂, 2î + 3ĵ + 5k̂, 5î – 2ĵ
Solution:

= 5 (18 + 10) + 1 (12 – 25) + 4 (- 4 – 15)
= 140 – 13 – 76 = 140 – 89 = 51

Question 3.
Find the volume of the parallelopiped whose sides are given by the vectors.
(i) î + ĵ + k̂, k̂, 3î – ĵ + 2k̂
Solution:

= 1 (0 + 1) – 1 (0 – 3) + 1 (0 – 0)
= 1 + 3 = 4 cube units.

(ii) (1, 0, 0), (0, 1, 0), (0, 0, 1).
Solution:

Question 4.
Show that the following vector are co-planar
(i) î – 2ĵ + 2k̂, 3î + 4ĵ + 5k̂, -2î + 4ĵ – 4k̂
Solution:

(ii) î + 2ĵ + 3k̂, -2î – 4ĵ + 5k̂, 3î + 6
Solution:

Question 5.
Find the value of λ so that the three vectors are co-planar.
(i) î + 2ĵ + 3k̂, 4î + ĵ + λk̂ and λî – 4ĵ + k̂
Solution:

(ii) (2, -1, 1), (1, 2, -3) and (3, λ, 5)
Solution:

⇒ 2 (10 + 3λ) + 1 (5 + 9) + 1 (λ – 6) = 0
⇒ 20 + 6λ +14 + λ – 6 = 0
⇒ 7λ + 28 = 0 ⇒ λ = -4

Question 6.
If \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) mutually perpendiculars, show that \([\vec{a} .(\vec{b} \times \vec{c})]^2\) = a²b²c²
Solution:

Question 7.
Show that \([\vec{a}+\vec{b} \vec{b}+\vec{c} \vec{c}+\vec{a}]\) = 2\([\vec{a} \vec{b} \vec{c}]\)
Solution:

Question 8.
Prove that \([\vec{a} \times \vec{b} \vec{b} \times \vec{c} \vec{c} \times \vec{a}]\) = \([\vec{a} \vec{b} \vec{c}]^2\)
Solution:

Question 9.
For \(\vec{a}\) = î + ĵ, \(\vec{b}\) = -î + 2k̂, \(\vec{c}\) = ĵ + k̂ obtain \(\vec{a} \times(\vec{b} \times \vec{c})\) and also verify the formula \(\vec{a} \times(\vec{b} \times \vec{c})\) = \((\vec{a} \cdot \vec{c}) \vec{b}-(\vec{a} \cdot \vec{b}) \vec{c}\).
Solution:

Question 10.
Prove that \(\vec{a} \times(\vec{b} \times \vec{c})+\vec{b} \times(\vec{c} \times \vec{a})+\vec{c} \times(\vec{a} \times \vec{b})\) and hence prove that \(\vec{a} \times(\vec{b} \times \vec{c}), \vec{b} \times(\vec{c} \times \vec{a}), \vec{c} \times(\vec{a} \times \vec{b})\) are coplanar.
Solution:

Question 11.
If \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) unit vectors and \(\hat{a} \times(\hat{b} \times \hat{c})=\frac{1}{2} \hat{b}\) find the angles that â makes with b̂ and ĉ, where b̂, ĉ are not parallel.
Solution:

Odisha State Board Elements of Mathematics Class 12 Solutions CHSE Odisha Chapter 9 Integration Additional Exercise Textbook Exercise questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Additional Exercise

Question 1.
∫\(\sqrt{1-\sin 2 x}\) dx
Solution:
I = ∫\(\sqrt{1-\sin 2 x}\) dx
= ∫\(\sqrt{(\cos x-\sin x)^2}\) dx
= ∫(cos x – sin x) dx
= sin x + cos x + c

Question 2.
∫\(\frac{d x}{1+\sin x}\)
Solution:
I = ∫\(\frac{d x}{1+\sin x}\)
= ∫\(\frac{1-\sin x}{\cos ^2 x}\)
= ∫sec² x – sec x tan x dx
= tan x – sec x + c

Question 3.
∫\(\frac{\sin x}{1+\sin x}\) dx
Solution:

Question 4.
∫\(\frac{\sec x}{\sec x+\tan x}\) dx
Solution:
I = ∫\(\frac{\sec x}{\sec x+\tan x}\) dx
= ∫\(\frac{\sec x(\sec x-\tan x)}{\sec ^2 x-\tan ^2 x}\) dx
= ∫sec² x – sec x tan x dx
= tan x – sec x + c

Question 5.
∫\(\frac{1+\sin x}{1-\sin x}\) dx
Solution:
I = ∫\(\frac{1+\sin x}{1-\sin x}\) dx
= ∫\(\frac{(1+\sin x)^2}{\cos ^2 x}\) dx
= ∫[sec² x+ tan² x+ 2sec x tan x) dx
= ∫[2sec² x – 1 + 2sec x tan x) dx
= 2tan x – x + 2sec x + c

Question 6.
∫tan^-1 (sec x + tan x) dx
Solution:

Question 7.
∫\(\frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha}\) dx
Solution:
I = ∫\(\frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha}\) dx
= ∫\(\frac{\left(2 \cos ^2 x-1\right)-\left(2 \cos ^2 \alpha-1\right)}{\cos x-\cos \alpha}\) dx
= 2 ∫(cos x + cos α) dx
= 2 sin x + 2x cos α + c

Question 8.
∫tan-1\(\sqrt{\frac{1-\cos 2 x}{1+\cos 2 x}}\) dx
Solution:

Question 9.
∫\(\frac{d x}{\sqrt{x+1+} \sqrt{x+2}}\)
Solution:

Question 10.
∫\(\frac{2+3 x}{3-2 x}\) dx
Solution:

Question 11.
∫\(\frac{d x}{\sqrt{x}+x}\)
Solution:

Question 12.
∫\(\frac{d x}{1+\tan x}\)
Solution:

Question 13.
∫\(\frac{x+\sqrt{x+1}}{x+2}\) dx (Hints put : \(\sqrt{x+1}\) = t)
Solution:

Question 14.
∫sin^-1\(\sqrt{\frac{x}{a+x}}\) dx (Hints put : x = a tan² t)
Solution:

Question 15.
∫e^x\(\left(\frac{2+\sin 2 x}{1+\cos 2 x}\right)\) dx
Solution:

Question 16.
∫\(\frac{\left(x^2+1\right) e^x}{(x+1)^2}\) dx
Solution:

Question 17.
∫\(\frac{x^2-1}{x^4+x^2+1}\) dx
Solution:

Question 18.
∫\(\frac{x^2 d x}{x^4+x^2+1}\)
Solution:

Question 19.
∫\(\sqrt{\cot x}\) dx
Solution:

Question 20.
∫\((\sqrt{\tan x}+\sqrt{\cot x})\) dx
Solution:

Question 21.
∫\(\frac{\mathrm{dx}}{x\left(x^4+1\right)}\)
Solution:

Question 22.
∫\(\frac{\mathrm{dx}}{e^x-1}\)
Solution:

Question 23.
∫\(\frac{(x-1)(x-2)(x-3)}{(x+4)(x-5)(x-6)}\) dx
Solution:

Question 24.
∫\(\frac{d x}{\left(e^x-1\right)^2}\)
Solution:

Question 25.
∫\(\frac{d x}{\sin x \cos ^2 x}\)
Solution:

Question 26.
\(\int_2^4 \frac{\left(x^2+x\right) d x}{\sqrt{2 x+1}}\)
Solution:

Question 27.
\(\int_{-a}^a \sqrt{\frac{a-x}{a+x}}\) dx
Solution:

Let a² – x² = t²
-2x dx = 2t dt
x = -a ⇒ 0 t = 0
x = a ⇒ t = 0
= 0
I = aI₁ – I₂ = aπ

Question 28.
\(\int_0^{\pi / 2}(\sqrt{\tan x}+\sqrt{\cot x})\) dx
Solution:

Question 29.
\(\int_0^{\pi / 2} \frac{\cos x d x}{1+\cos x+\sin x}\)
Solution:

Question 30.
\(\int_0^1\)x (1 – x)ⁿ dx
Solution:

Question 31.
\(\int_0^{\pi / 2}\)sin 2x log (tan x) dx
Solution:

Question 32.
\(\int_0^{\pi / 2} \frac{\sin ^2 x d x}{\sin x+\cos x}\)
Solution:

Question 33.
\(\int_0^{\pi / 2} \frac{\sin ^2 x d x}{1+\sin x \cos x}\)
Solution:

Question 34.
\(\int_0^{\pi / 2} \frac{x d x}{\sin x+\cos x}\)
Solution:

Question 35.
Prove that \(\int_0^\pi\) x sin³ x dx = \(\frac{2 \pi}{3}\)
Solution:

Question 36.
\(\int_{\pi / 5}^{3 \pi / 10} \frac{\sin x d x}{\sin x+\cos x}\)
Solution:

Question 37.
\(\int_0^\pi\)|cos x| dx
Solution:

Question 38.
\(\int_1^4\)(|x – 1| + |x – 2| + |x – 3|) dx
Solution:

Question 39.
\(\int_{-\pi / 2}^{\pi / 2}\)(sin |x| + cos |x|) dx
Solution:

Question 40.
\(\int_0^\pi\)log (1 + cos x) dx
Solution:

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

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

Question 1.
\(\int_0^{\frac{\pi}{2}}\)sin¹⁰ θ dθ
Solution:
\(\int_0^{\frac{\pi}{2}}\)sin¹⁰ θ dθ = \(\frac{9}{10} \cdot \frac{7}{8} \cdot \frac{5}{6} \cdot \frac{3}{4} \cdot \frac{1}{2} \cdot \frac{\pi}{2}\) = \(\frac{405 \pi}{7680}\)

Question 2.
\(\int_0^{\frac{\pi}{2}}\)cos¹² θ dθ
Solution:
\(\int_0^{\frac{\pi}{2}}\)cos¹² θ dθ = \(\frac{11}{12} \cdot \frac{9}{10} \cdot \frac{7}{8} \cdot \frac{5}{6} \cdot \frac{3}{4} \cdot \frac{1}{2} \cdot \frac{\pi}{2}\) = \(\frac{4455 \pi}{92160}\)

Question 3.
\(\int_0^{\frac{\pi}{2}}\)sin¹¹ θ dθ
Solution:
\(\int_0^{\frac{\pi}{2}}\)sin¹¹ θ dθ = \(\frac{10}{11} \cdot \frac{8}{9} \cdot \frac{6}{7} \cdot \frac{4}{5} \cdot \frac{2}{3}\) = \(\frac{3840}{4455}\)

Question 4.
\(\int_0^{\frac{\pi}{2}}\)cos⁹ θ dθ
Solution:
\(\int_0^{\frac{\pi}{2}}\)cos⁹ θ dθ = \(\frac{8}{9} \cdot \frac{6}{7} \cdot \frac{4}{5} \cdot \frac{2}{3}\) = \(\frac{384}{405}\)

Question 5.
\(\int_0^1 \frac{x^7}{\sqrt{1-x^2}}\) dx
Solution:

Question 6.
\(\int_0^1 \frac{x^5\left(4-x^2\right)}{\sqrt{1-x^2}}\) dx
Solution:

Question 7.
\(\int_0^a x^3\left(a^2-x^2\right)^{\frac{5}{2}}\) dx
Solution:

Question 8.
\(\int_0^1 x^5 \sqrt{\frac{1+x^2}{1-x^2}}\) dx
Solution:

Question 9.
\(\int_0^{\infty} \frac{x^2}{\left(1+x^6\right)^n}\) dx
Solution:

Question 10.
\(\int_0^\pi\)sin⁸ θ dθ
Solution:

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

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

Evaluate the following Integrals:
Question 1.
(i) \(\int_0^{\frac{\pi}{2}} \frac{d x}{1+\tan x}\)dx
Solution:

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

(iii) \(\int_0^1 \frac{\ln (1+x)}{2+x^2}\)dx (x = tan θ)
Solution:

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

Question 2.
(i) \(\int_{-a}^a\)x⁴ dx
Solution:

(ii) \(\int_{-a}^a\)(x⁵ + 2x² + x) dx
Solution:

(iii) \(\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\)cos² x dx
Solution:

(iv) \(\int_{-\frac{\pi}{6}}^{\frac{\pi}{6}}\)sin⁵ x dx
Solution:
Let f(x) = sin⁵ x
Then f(-x) = sin⁵ (-x)
= -sin⁵ x = -f(x)
So f(x) is an odd function.
Thus \(\int_{-a}^a\)f(x) dx = 0
\(\int_{-\frac{\pi}{6}}^{\frac{\pi}{6}}\)sin⁵ x dx = 0

Question 3.
(i) \(\int_0^\pi\)cos³ x dx
Solution:

(ii) \(\int_0^\pi\)cos² x dx
Solution:

(iii) \(\int_0^\pi\)sin³ x cos x dx
Solution:
\(\int_0^\pi\)sin³ x cos x dx
[Put sin x = t, then cos x dx = dt
When x = 0, t = 0, when x = π, t = 0
\(\int_0^\pi\)t³ dt = 0

(iv) \(\int_0^\pi\)sin x cos² x dx
Solution:

Question 4.
Show that
(i) \(\int_0^1 \frac{\ln x}{\sqrt{1-x^2}}\) dx = \(\frac{\pi}{2} \ln \frac{1}{2}\)
Solution:

(ii) \(\int_0^{\frac{\pi}{2}} \frac{\cos x-\sin x}{1+\sin x \cos x}\) dx = 0
Solution:

(iii) \(\int_0^\pi\)x ln sin x dx = \(\frac{\pi^2}{2} \ln \frac{1}{2}\)
Solution:

Question 5.
(i) \(\int_0^{\pi / 2}\)ln (tan x + cot x) dx
Solution:

(ii) \(\int_0^\pi \frac{x \tan x-\sin x}{1+\sin x \cos x}\) dx
Solution:

(iii) \(\int_1^3 \frac{\sqrt{x} d x}{\sqrt{4-x}+\sqrt{x}}\)
Solution:

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

(v) \(\int_0^1\)x (1 – x)¹⁰⁰ dx
Solution:

(vi) \(\int_{\pi / 6}^{\pi / 3} \frac{d x}{1+\sqrt{\cot x}}\)
Solution:

(vii) \(\int_0^{50}\)e^x-[x] dx
Solution:

Odisha State Board Elements of Mathematics Class 12 Solutions CHSE Odisha Chapter 11 Differential Equations Ex 11(c) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 11 Differential Equations Exercise 11(c)

Find the solutions of the following differential equations:
Question 1.
(x + y) dy + (x – y) dx = 0
Solution:
Given equation can be written as

Question 2.
\(\frac{d y}{d x}\) = \(\frac{1}{2}\left(\frac{y}{x}+\frac{y^2}{x^2}\right)\)
Solution:

Question 3.
(x² – y²) dx + 2xy dy = 0
Solution:
Given equation can be written as

Question 4.
x\(\frac{d y}{d x}\) + \(\sqrt{x^2+y^2}\) = y
Solution:
Given equation can be written as

Question 5.
x (x + y) dy = (x² + y²) dx
Solution:


This is the required solution.

Question 6.
y² + x² \(\frac{d y}{d x}\) = xy \(\frac{d y}{d x}\)
Solution:
Given equation can be written as

This is the required solution.

Question 7.
x sin\(\frac{y}{x}\) dy = \(\left(y \sin \frac{y}{x}-x\right)\)dx
Solution:
Given equation can be written as

Question 8.
x dy – y dx= \(\sqrt{x^2+y^2}\) dx
Solution:

This is the required solution.

Question 9.
\(\frac{d y}{d x}\) = \(\frac{y-x+1}{y+x+5}\)
Solution:
Given equation is


This is the required solution.

Question 10.
(x – y) dy = (x + y + 1) dx
Solution:
Given equation can be written as


This is the required solution.

Question 11.
(x – y – 2) dx + (x – 2y – 3) dy = 0
Solution:
Given equation can be written as


This is the required solution.

Question 12.
\(\frac{d y}{d x}\) = \(\frac{3 x-7 y+7}{3 y-7 x-3}\)
Solution:
Given equation can be written as


This is the required solution.

Question 13.
(2x + y + 1) dx + (4x + 2y – 1) dy = 0
Solution:
Given equation can be written as

⇒ 2z + ln (z – 1) = 3x + C
⇒ 2 (2x + y) + ln (2x + y – 1 ) = 3x + C
⇒ (x + 2y) + ln (2x + y – 1 ) = C
This is the required solution.

Question 14.
(2x + 3y – 5)\(\frac{d y}{d x}\) + 3x + 2y – 5 = 0
Solution:
Given equation can be written as

Question 15.
(4x + 6y + 5) dx – (2x + 3y + 4) dy = 0
Solution:
Given equation can be written as


This is the required solution.

CHSE Odisha 12th Class Political Science Book Solutions (+ 2 2nd Year)

CHSE Odisha Class 12 Political Science Book Solutions in English Medium

Unit 1 Democracy in India

• Democracy in India Objective Questions
• Democracy in India Short Answer Questions
• Democracy in India Long Answer Questions

Unit 2 Democratic Process in India-I

• Democratic Process in India-I Objective Questions
• Democratic Process in India-I Short Answer Questions
• Democratic Process in India-I Long Answer Questions

Unit 3 Democratic Process in India-II

• Democratic Process in India-II Objective Questions
• Democratic Process in India-II Short Answer Questions
• Democratic Process in India-II Long Answer Questions

Unit 4 India in World Politics

• India in World Politics Objective Questions
• India in World Politics Short Answer Questions
• India in World Politics Long Answer Questions

Unit 5 Issues in International Politics

• Issues in International Politics Objective Questions
• Issues in International Politics Short Answer Questions
• Issues in International Politics Long Answer Questions

CHSE Odisha Class 12 Political Science Book Solutions in Odia Medium

Chapter 1 ଗଣତନ୍ତ୍ର

• Objective Questions
• Short Answer Questions
• Long Answer Questions

Chapter 2 ଭାରତରେ ରାଜନୈତିକ ଦଳୀୟ ବ୍ୟବସ୍ଥା

• Objective Questions
• Short Answer Questions
• Long Answer Questions

Chapter 3 ଭାରତରେ ସଂଘୀୟବାଦ

• Objective Questions
• Short Answer Questions
• Long Answer Questions

Chapter 4 ଭାରତରେ ଗ୍ରାମାଞ୍ଚଳ ଓ ସହରାଞ୍ଚଳ ସ୍ୱାୟତ୍ତ ଶାସନ ବ୍ୟବସ୍ଥା

• Objective Questions
• Short Answer Questions
• Long Answer Questions Part-1
• Long Answer Questions Part-2

Chapter 5 ଜାତି ଗଠନରେ ପ୍ରତିବନ୍ଧକ

• Objective & Short Answer Questions
• Long Answer Questions

Chapter 6 ଭାରତୀୟ ରାଜନୀତିରେ ସାଂପ୍ରତିକ ପ୍ରସଙ୍ଗ-ଜନପ୍ରିୟ ଆନ୍ଦୋଳନ

• Objective Questions
• Short Answer Questions
• Long Answer Questions

Chapter 7 ଭାରତର ବୈଦେଶିକ ନୀତି

• Objective Questions
• Short & Long Answer Questions

Chapter 8 ଆନ୍ତର୍ଜାତୀୟ ସଙ୍ଗଠନ

• Objective & Short Answer Questions
• Long Answer Questions

Chapter 9 ସାଂପ୍ରତିକ ବିଶ୍ଵରେ ନିରାପତ୍ତା ପ୍ରସଙ୍ଗର ପରିବର୍ତ୍ତିତ ପୃଷ୍ଠଭୂମି

• Objective Questions
• Short Answer Questions
• Long Answer Questions

Chapter 10 ପରିବେଶ ଓ ପ୍ରାକୃତିକ ସମ୍ପଦ

• Objective Questions
• Short Answer Questions
• Long Answer Questions

CHSE Odisha Class 12 Political Science Syllabus (+2 2nd Year)

There shall be two papers in Political Science modeled on the Syllabi of CBSE. Paper-I: TitleFoundation of Political Theory and Indian Government at work (For First Year). Paper-II: Title-Democracy and Nation Building in India and International affairs (For Second Year).

The subject of Political Science modeled on the Syllabi of CBSE consists of two papers as mentioned above. Paper-I is to be covered in the +2 First Year class and Paper-ll is to be covered in the +2 Second Year class. Each paper is divided into two sections and each section is further subdivided into two/three units. Thus there are five units in both Paper-I and Paper II. Periods have been allocated for the respective units approximately. Teachers are advised to take at least those numbers of periods to cover the particular unit. The major concepts and principles should be taught in such a manner as to stimulate higher mental abilities among students like application, logical thinking, analysis, etc., and not factual information. Paper-setters and Examiners are requested to keep the above in mind while setting questions and examining, respectively. Questions should of short (one word/ multiple-choice/ one sentence), medium (50/100 words/ five sentences), and long (500 words or thereabout). Also, Questions of the final/AHS Examination shall cover all five units of Paper -II.

Objectives of the course/syllabus are, as briefly mentioned above are:

• To enable the students to acquire knowledge about the important concepts, theories, principles, provisions, processes and Institutions of the Indian constitution, and some rudimentary knowledge about International affairs;
• To acquaint the students with the changing dimension of politics and political theory both in the national and international knowledge domain;
• To develop an interest among the students regarding problems of the political domain and to find out the possible solution to those problems.

Suggested Reading:

1. Political Theory- For Class-XI (Published by NCERT, New Delhi)
2. Indian Constitution at Work- For Class-XI (Published by NCERT, New Delhi)
3. Contemporary World Politics, For Class-XII (Published by NCERT, New Delhi)
4. Politics in India, For Class-XII (Published by NCERT, New Delhi)

Second Year CHSE (2022-2023)
Political Science Paper-II
(DEMOCRACY IN INDIA AND INTERNATIONAL POLITICS)

Part A: Politics in India

Unit I Democracy in India

1. Democracy: Meaning, Types, and Features; Challenge to Democratic Process in India – Inequality, Illiteracy, Regionalism, Naxalite Problem, Gender Inequality. (8 Periods)
2. Party System in India: Meaning, Types; One Party Dominance, Coalition Politics; Regional Parties. (8 Periods)

Unit II Democratic Process in India-I

1. Federalism in India: Features, Centre-State relation, Recent Trends in Indian Federalism. (8 Periods)
2. Local Government in India – Rural and Urban Local Bodies, Composition and Functions. (8 Periods)

Unit III Democratic Process in India-II

1. Challenges to Nation-Building: Meaning, Communalism, Casteism, Regionalism, Terrorism; Remedies. (8 Periods)
2. Contemporary issues in Indian Politics: Popular Movements – Women Movement, Environment protection Movement, Development – Displacement Movements. (8 Periods)

Part B: Contemporary World Politics

UNIT-IV (India in World Politics)

1. Indian Foreign Policy: Basic Features; India and its neighbours-China, Pakistan. (8 Periods)
2. International Organizations: UN: Major Organs-General Assembly; Security Council; International Court of Justice; Reforms of the UN. India’s position in the UN. International Economic Organizations- World Bank and the IMF. (8 Periods)

UNIT-IV (Issues in International Politics)

1. Changing Dimension of Security in Contemporary World: Traditional Security Concerns: Arms Race and Disarmament. Non-Traditional Security Concerns: Human security: Global Poverty, Inequality, Health, and Education. (8 Periods)
2. Environment and Natural Resources: Global Environmental Concerns; Development and Environment; Global Warming and Climate Change. (8 Periods)

BOOK PRESCRIBED:
Bureau’s Higher Secondary (+2) Political Science, Paper-II (English & Odia) Published by Odisha State Bureau of Textbook Preparation & Production, Bhubaneswar.

CHSE Odisha Class 12 Text Book Solutions

CHSE Odisha 12th Class Psychology Book Solutions (+ 2 2nd Year)

CHSE Odisha 12th Class Psychology Book Solutions in English Medium

Unit 1 Life Span Development & Self and Personality

• Unit 1 Objective & Short Answer Type Questions
• Unit 1 Long Answer Questions Part-1
• Unit 1 Long Answer Questions Part-2
• Unit 1 Long Answer Questions Part-3
• Unit 1 Long Answer Questions Part-4

Unit 2 Stress: Meeting Life Challenges & Physical Environment and Behaviour

• Unit 2 Objective & Short Answer Type Questions
• Unit 2 Long Answer Questions Part-1
• Unit 2 Long Answer Questions Part-2

Unit 3 Group Processess and Leadership & Counselling Process

• Unit 3 Objective & Short Answer Type Questions
• Unit 3 Long Answer Questions Part-1
• Unit 3 Long Answer Questions Part-2

Unit 4 Psychological Disorder & Therapeutic Approaches

• Unit 4 Objective & Short Answer Type Questions
• Unit 4 Long Answer Questions Part-1
• Unit 4 Long Answer Questions Part-2
• Unit 4 Long Answer Questions Part-3
• Unit 4 Long Answer Questions Part-4

Unit 5 Statistics in Psychology

• Unit 5 Objective Questions and Answers

CHSE Odisha 12th Class Psychology Book Solutions in Odia Medium

Unit 1 ଜୀବନବ୍ୟାପୀ ବିକାଶ & ସ୍ଵୟଂ ତଥା ବ୍ୟକ୍ତିତ୍ଵ

• Objective Questions
• Short Answer Questions
• Long Answer Questions

Unit 2 ମନୋ-ସାମାଜିକ ଚାପ & ଭୌତିକ ପରିବେଶ ଓ ବ୍ୟବହାର

Unit 3 ସମୂହ ପ୍ରକ୍ରିୟା ଓ ନେତୃତ୍ଵ & ପରାମର୍ଶ ପ୍ରକ୍ରିୟା

• Objective Questions
• Short & Long Answer Questions

Unit 4 ମାନସିକ ବିକାର & ମାନସିକ ବିକାର ଚିକିତ୍ସା

• Objective Questions
• Short & Long Answer Questions

Unit 5 ମନୋବିଜ୍ଞାନରେ ପରିସଂଖ୍ୟାନର ବ୍ୟବହାର

• Objective Questions
• Short & Long Answer Questions

CHSE Odisha Class 12 Psychology Syllabus (+2 2nd Year)

Psychology is introduced as an elective subject at the higher secondary stage of education. The course deals with Psychological knowledge and practices which are contextually rooted, It emphasizes the complexity of cognitive and behavioural processes of human beings within a socio-cultural context. It encourages critical reasoning, allowing students to appreciate the role of social factors in behaviour and illustrates how biology and experience shape behaviour.

In the second year, there will be a council examination and the theory paper carries 70 marks and the practical paper carries 30 marks. The question paper pattern for both papers is same.

QUESTION PAPER PATTERN

Theory Paper:
Group-A: Objective type (Compulsory)
Q.No.1: Multiple choice (Fill up the blanks from all units) 1 mark each × 10 = 10 marks
Q.No.2: Statements “True” or “False” 1 mark each × 10 = 10 marks

Group-B: Short Type
Q.No.3: Short type answer (Answer within two /three sentences) and one has to answer 10 bits out of 12 bits.
2 marks each × 10 = 20 marks
Q.No.4: Short type answer (Answer within six sentences) and one has to answer 3 bits out of 5 bits.
3 mark each × 3 = 09 marks

Group-C: Long Type
Q.No.5: Question No-5 to Q.No-10 (Questions will be from all the units and one has to answer any three questions).
7 marks each × 3 = 21 marks

PRACTICAL
There will be 4 number of questions and the examinee is to choose/draw 2 number of questions through the lottery and is to conduct any one question out of the two questions.
Distribution of marks :
Record – 03
Viva -Voce – 07
Conduction & Report writing – 20
Total marks – 30

PSYCHOLOGY IN APPLICATION
SECOND YEAR
Total Marks – 100
Theory – 70 marks
Practical – 30 marks

Theory
UNIT-I
1. Life span development [10 Periods]
This chapter deals with variations in development and developmental tasks across the life span.
a) Meaning of development – Life span perspective
b) Principles of development
c) Stages of development: Pre-natal stage, Infancy, childhood stage, Adolescence, Adulthood and old age.

2. Self and Personality [9 Periods]
This chapter focuses on the study of self and personality in the context of different approaches in an effort to appraise the person. The assessment of personality will also be discussed.
a) Concept of self and personality
b) Personality types and traits
c) Assessment of Personality
This chapter deals with the nature of stress and strategies to cope with stress.
a) Meaning, Nature and causes of stress.
b) Coping strategies to deal with stress.

UNIT-II
3. Stress: Meeting life challenges [6 Periods]
This chapter deals with the nature of stress and strategies to cope with stress.
a) Meaning, Nature and causes of stress.
b) Coping strategies to deal with stress.

4. Physical environment and behaviour. [6 Periods]
This chapter focuses on the application of psychological understanding of human-environment relationship.
a) Human impact on the environment: Noise Pollution, Crowding, Natural disasters.
b) Impact of environment on human behaviour.

UNIT-III
5. Group Processes and leadership. [7 Periods]
This chapter deals with the concept of a group and the role of the leader in a group.
a) Groups: Nature, types and formation.
b) Leadership: Nature, functions and styles of leadership.

6. Counselling Processes [6 Periods]
This chapter focuses on helping the client in living a meaningful and fulfilling life.
a) Meaning and concept of counselling; Goals of counselling.
b) Characteristics of an effective counsellor.

UNIT-IV
7. Psychological disorder [10 Periods]
This chapter discusses the concept of normality and abnormality and the major psychological disorders.
a) Concept of normality and abnormality, criteria of studying abnormal behaviour
b) Causal factors associated with abnormal behaviour.
c) Major Psychological disorders: Anxiety disorders, somatoform disorders and mood disorders.

8. Therapeutic Approaches [6 Periods]
This chapter discusses the purpose and processes to treat Psychological disorders:
a) Nature and Processes of therapy
b) Types of therapy: Psychotherapy, Behaviour therapy, Cognitive therapy and Biomedical therapy.

UNIT-V
9. Statistics in Psychology [10 Periods]
This chapter deals with some basic statistical methods to be used in psychological studies.
a) Frequency distribution
b) Measures of Central Tendency: Computation and uses of mean, median and mode.

PRACTICALS

1. RCPM (Children) / RPM (Adults)
2. Case History Method (Preparation of at least one case profile)
3. Personality Test (Type A/B)
4. Piagetian Task (Conservation of Liquid Quantity)

Books Recommended:
1. Bureau’s Higher Secondary +2 Psychology Part-II Published by Odisha State Bureau of Test Book Preparation and Production, Bhubaneswar.
2. Psychology Part-II, NCERT.

CHSE Odisha Class 12 Text Book Solutions

CHSE Odisha 12th Class Education Book Solutions (+ 2 2nd Year)

CHSE Odisha Class 12 Education Book Solutions in English Medium

Unit 1 Contribution of Educators

• Contribution of Educators Objective Questions
• Contribution of Educators Short Answer Questions
• Contribution of Educators Long Answer Questions

Unit 2 Learning and Motivation

• Learning and Motivation Objective Questions
• Learning and Motivation Short Answer Questions
• Learning and Motivation Long Answer Questions

Unit 3 Current Issues in Education

• Current Issues in Education Objective Questions
• Current Issues in Education Short Answer Questions
• Current Issues in Education Long Answer Questions

Unit 4 Educational Statistics

• Educational Statistics Questions and Answers

CHSE Odisha Class 12 Education Book Solutions in Odia Medium

Unit 1 ଶିକ୍ଷାବିତମାନଙ୍କର ଦାନ

• Chapter 1 ମହାତ୍ମା ଗାନ୍ଧି
• Chapter 2 ପଣ୍ଡିତ ଗୋପବନ୍ଧୁ ଦାସ
• Chapter 3 ଶ୍ରୀ ଅରବିନ୍ଦ
• Chapter 4 ଜିନ୍ ଜାକୁଏସ୍ ଋଷୋ
• Chapter 5 ଜନ୍ ନ୍ୟୁଇ

Unit 2 ଶିକ୍ଷଣ ଏବଂ ଅଭିପ୍ରେରଣା

• Chapter 6 ଶିକ୍ଷଣ ପ୍ରକ୍ରିୟା ଓ ଶିକ୍ଷଣ ତତ୍ତ୍ବ
• Chapter 7 ପର୍ଯ୍ୟବେକ୍ଷଣାତ୍ମକ ଶିକ୍ଷଣ
• Chapter 8 ଶିକ୍ଷଣରେ ଅଭିପ୍ରେରଣା

Unit 3 ବିଦ୍ୟାଳୟ ଶିକ୍ଷା ସମସ୍ୟା

• Chapter 9 ପ୍ରାଥମିକ ଶିକ୍ଷାର ସାର୍ବଜନୀନୀକରଣ ଓ ଶିକ୍ଷାଧିକାର
• Chapter 10 ଜାତୀୟ ସଂହତି ଓ ଆନ୍ତର୍ଜାତିକ ବୁଝାମଣା ପାଇଁ ଶିକ୍ଷା
• Chapter 11 ପରିବେଶ ଶିକ୍ଷା
• Chapter 12 ମୂଲ୍ୟବୋଧ ଶିକ୍ଷା ଓ ମାନବାଧିକାର ଶିକ୍ଷା
• Chapter 13 ଶିକ୍ଷାରେ ସୂଚନା ଓ ସଞ୍ଚାର ପ୍ରଯୁକ୍ତି ବିଦ୍ୟା
• Chapter 14 ଜୀବନ ନୈପୁଣ୍ୟ (ଦକ୍ଷତା) ଶିକ୍ଷା

Unit 4 ଶୈକ୍ଷିକ ପରିସଂଖ୍ୟାନ

• Chapter 15 ଶୈକ୍ଷିକ ପରିସଂଖ୍ୟାନ (ପରିସଂଖ୍ୟାନ, ପୌନଃପୁନଃ ବିତରଣ, ତଥ୍ୟର ରେଖଚିତ୍ର ବା ଗ୍ରାଫୀୟ ପ୍ରଦର୍ଶନ, କେନ୍ଦ୍ରୀୟ ପ୍ରବଣତା ମାପ)

CHSE Odisha Class 12 Education Syllabus (+2 2nd Year)

EDUCATION ELECTIVE (Second Year)
Theory – 70 marks & Practical – 30 marks.
Theory Paper – II
FOUNDATIONS OF EDUCATION – II

Unit-I Fundamentals of Education (20 periods)
Contribution of Educators: Mahatma Gandhi, Pandit Gopabandhu Das, Sri Aurobindo, Jena Jacques Rousseau, John Dewey.

Unit-II Learning and Motivation (20 Periods)
Meaning, Nature and Factors of Learning, Theories of Learning: Trial and Error Theory and Laws of Learning, Classical Conditioning Theory, Insightful Learning, Learning and Construction of knowledge, Motivation in Learning: Meaning, Types, and Techniques of motivation.

Unit-III Current Issues in Education (20 Periods)
Universalisation of Elementary Education (UEE) and RTE, Education for National Integration and International Understanding, Environmental Education, Value Education, Human Rights Education, Information and Communication Technology (ICT) in education, and Life-skills Education.

Unit-IV Educational Statistics (20 Periods)
Statistics: Meaning, Nature and uses, Frequency Distribution, Graphical Representation of Data: Histogram, Polygon, and Pie-Chart, Measures of Central Tendency: Mean, Median, and mode – meaning, calculation, and uses.

Practical (60 Periods)
(To be examined by both external and Internal Examiners)
A. Practice Teaching Five Lessons in Classroom in the selected subject (30 Periods)
B. Preparation of Five Improvised Teaching Aids relating to the Five lessor plane along with their improvised teaching aids records (30 Periods)
For the Final Practical examination, the students shall deliver one lesson in his/her method subject.
Practice teaching records and improvised teaching aids records will be submitted during the final examination.

BOOKS RECOMMENDED:
1. Bureau Uchcha Madhyamik Siksha 2 (in Odia)
2. Bureau’s Higher Secondary Education II. Published by Odisha State Bureau of Textbook Preparation & Production, Bhubaneswar.

CHSE Odisha Class 12 Text Book Solutions

+2 2nd Year MIL Odia Book Solutions Pdf Download – Sahitya Jyoti Part 2 Question Answer ସାହିତ୍ୟ ଜ୍ୟୋତି

ସାହିତ୍ୟ ଜ୍ୟୋତି Sahitya Jyoti Part 2 Question Answer | MIL Odia Class 12 Question Answer Pdf 2022-2023

Unit 1 ପ୍ରଥମ ଏକକ (ଗଦ୍ୟ)

• Chapter 1 ଇତିହାସ
• Chapter 2 ପୁଷ୍ପପୁରରେ ବର୍ଷାବରଣ
• Chapter 3 ତିନି ତୁଣ୍ଡରେ
• Chapter 4 ସ୍ଵାଧୀନ ଦେଶରେ ଶିକ୍ଷାଚିନ୍ତା

Unit 2 ଦ୍ବିତୀୟ ଏକକ (ପଦ୍ୟ)

• Chapter 5 ବଡ଼ପଣ
• Chapter 6 ତପସ୍ବିନୀର ପତ୍ର
• Chapter 7 ବନ୍ଦୀର ବିରହ ବ୍ୟଥା
• Chapter 8 ପିଙ୍ଗଳାର ଅଭିସାର
• Chapter 9 ବାର୍ତା

Unit 3 ତୃତୀୟ ଏକକ (ଗଳ୍ପ)

• Chapter 10 ସଭ୍ୟ ଜମିଦାର
• Chapter 11 ପତାକା ଉତ୍ତୋଳନ
• Chapter 12 ରୂପନାରାୟଣ ସାହା
• Chapter 13 ଆକାଶ କଇଁଛ

BSE Odisha Class 12 Odia Grammar ବ୍ୟାକରଣ ବିଭାଗ

Unit 4 ଚତୁର୍ଥ ଏକକ (ବୋଧଜ୍ଞାନ ପରୀକ୍ଷଣ)

• ଅବବୋଧ ପରୀକ୍ଷଣ – (କ) ଗଦ୍ୟାଂଶ
• ଅବବୋଧ ପରୀକ୍ଷଣ – (ଖ) ପଦ୍ୟାଂଶ
• ସର୍ଜନାତ୍ମକ ରଚନା

Unit 5 ପଞ୍ଚମ ଏକକ (ପ୍ରବନ୍ଧ ଓ ବ୍ୟାକରଣ)

• ଦରଖାସ୍ତ ଓ ପତ୍ରଲିଖନ
• ସଂକ୍ଷିପ୍ତକରଣ Sankhiptakarana
• ବ୍ୟାକରଣ

CHSE Odisha Class 12 Text Book Solutions

CHSE Odisha 12th Class Sociology Book Solutions (+ 2 2nd Year)

CHSE Odisha 12th Class Sociology Book Solutions in English Medium

Unit 1 Introducing Indian Society

• Introducing Indian Society Objective Questions
• Introducing Indian Society Short Answer Questions
• Introducing Indian Society Long Answer Questions

Unit 2 Indian Social Structure

• Indian Social Structure Objective Questions
• Indian Social Structure Short Answer Questions
• Indian Social Structure Long Answer Questions Part-1
• Indian Social Structure Long Answer Questions Part-2

Unit 3 The Challenges of Cultural Diversity

• The Challenges of Cultural Diversity Objective Questions
• The Challenges of Cultural Diversity Short Answer Questions
• The Challenges of Cultural Diversity Long Answer Questions

Unit 4 Social Inequality, Exclusion and Movement

• Social Inequality, Exclusion and Movement Objective & Short Answer Type Questions
• Social Inequality, Exclusion and Movement Long Answer Questions

Unit 5 Change and Development in India

• Change and Development in India Objective Questions & Short Answer Questions
• Change and Development in India Long Answer Questions

CHSE Odisha 12th Class Sociology Book Solutions in Odia Medium

Unit 1 ଭାରତୀୟ ସମାଜର ପରିଚୟ

• ଭାରତୀୟ ସମାଜର ପରିଚୟ Objective Questions
• ଭାରତୀୟ ସମାଜର ପରିଚୟ Short Answer Questions
• ଭାରତୀୟ ସମାଜର ପରିଚୟ Long Answer Questions

Unit 2 ଭାରତୀୟ ସାମାଜିକ ସଂରଚନା

• ଭାରତୀୟ ସାମାଜିକ ସଂରଚନା Objective Questions
• ଭାରତୀୟ ସାମାଜିକ ସଂରଚନା Short Answer Questions
• ଭାରତୀୟ ସାମାଜିକ ସଂରଚନା Long Answer Questions

Unit 3 ସାଂସ୍କୃତିକ ବିବିଧତାର ଆହ୍ଵାନ

• ସାଂସ୍କୃତିକ ବିବିଧତାର ଆହ୍ଵାନ Objective Questions
• ସାଂସ୍କୃତିକ ବିବିଧତାର ଆହ୍ଵାନ Short Answer Questions
• ସାଂସ୍କୃତିକ ବିବିଧତାର ଆହ୍ଵାନ Long Answer Questions

Unit 4 ସାମାଜିକ ବୈଷମ୍ୟ, ବହିଷ୍କରଣ ଓ ଆନ୍ଦୋଳନ

• ସାମାଜିକ ବୈଷମ୍ୟ, ବହିଷ୍କରଣ ଓ ଆନ୍ଦୋଳନ Objective Questions
• ସାମାଜିକ ବୈଷମ୍ୟ, ବହିଷ୍କରଣ ଓ ଆନ୍ଦୋଳନ Short Answer Questions
• ସାମାଜିକ ବୈଷମ୍ୟ, ବହିଷ୍କରଣ ଓ ଆନ୍ଦୋଳନ Long Answer Questions

Unit 5 ଭାରତରେ ପରିବର୍ତ୍ତନ ଓ ବିକାଶ

• ଭାରତରେ ପରିବର୍ତ୍ତନ ଓ ବିକାଶ Objective Questions
• ଭାରତରେ ପରିବର୍ତ୍ତନ ଓ ବିକାଶ Short Answer Questions
• ଭାରତରେ ପରିବର୍ତ୍ତନ ଓ ବିକାଶ Long Answer Questions

CHSE Odisha Class 12 Sociology Syllabus (+2 2nd Year)

Sociology is introduced as an elective subject at Higher Secondary Education. This subject studies the processes and patterns of individual and group interaction, the forms of organization of social groups, the relationships among them, and group influences on individual behaviour. lt has focused on the understanding of group or other collective factors in human behavior. This syllabus is designed to help the learners to know about society and develop a constructive attitude towards different facets of life.

Objectives:

1. To enable learners to relate classroom teaching to their outside environment,
2. To introduce them to the basic concepts of sociology that would enable them to observe and interpret social life,
3. To make them aware of the complexity of social processes.
4. The overall objective of this syllabus is to provide learners with knowledge and understanding of the main sociological theories, concepts, and methods.

Distribution of Marks will be as follows: (Total Marks-100)

GROUP-A: Objective type (Compulsory)
Q.1 Multiple Choice (From all Units)
1 mark each × 15 marks = 15 marks
Q.2 One word answer/ (From all Units)
Very short answer/ Correct the sentence/ Filling in the blanks
1 mark each × 15 marks = 15 marks

GROUP-B: Short Answer Type
Q.3 Answer within Two/Three sentences (Out of 14 bits, one has to answer 11 bits)
2 marks each × 11 = 22 marks
Q.4 Answer within six sentences (Out of 8 bits, one has to answer 6 bits)
3 mark each × 6 = 18 marks

GROUP-C: Long Answer Type
Q.5 (out of 6 Questions from all units, one has to answer 4 questions)
7.5 marks each × 4 = 30 marks

SOCIOLOGY
Paper-II
Indian Society

Unit-I Introducing Indian Society
Composition of Indian Society – Demographic, Geographical, Racial, Linguistic, Religious, Tribal
Unity & Diversity – Factors of Unity & Diversity 4

Unit-II Indian Social Structure
Caste System – Meaning, Characteristics, Functions, Dysfunctions, Recent Changes, Caste and Class
Hindu Joint family – Meaning, Characteristics Merits, Demerits, Recent Changes
Village Community – Meaning and Characteristics/ Rural-Urban Linkages and Divisions

Unit-III The Challenges of Cultural Diversity
National Integration: Concept and obstacles – Communalism, Regionalism, Casteism, Terrorism

Unit-IV Social Inequality, Exclusion and Movement
Caste and Social Inequality, Class and Social Inequality, Marginalized Classes: Scheduled Castes, Scheduled Tribes, Constitutional Safeguards, Tribal Movements, Peasant Movements.

Unit-V Change and Development in India
Industrialization – Meaning, Characteristics, Impact
Urbanization – Meaning, Characteristics, Impact
Modernization – Meaning, Characteristics, Impact
Globalization – Meaning, Characteristics, Impact

BOOK PRESCRIBED:
1. Bureau’s Higher Secondary (+2) Sociology, Part-II Published by Odisha State Bureau of Textbook Preparation & Production, Bhubaneswar.
2. Sociology, Part-II, NCERT.

CHSE Odisha Class 12 Text Book Solutions