Bihar Board 12th Maths Objective Questions and Answers

## Bihar Board 12th Maths Objective Answers Chapter 7 Integrals

Question 1.
Evaluate: ∫(2tan x – 3cot x)2 dx
(a) -4tan x – 9cot x – 25x + C
(b) 4tan x – 9cot x – 25x + C
(c) -4tan x + 9 cot x + 25x + C
(d) 4tan x + 9cot x + 25x + C
(b) 4tan x – 9cot x – 25x + C

Question 2.

(a) $$\frac{a^{x}}{\log a}+\frac{x^{a+1}}{a+1}+a^{a} x+C$$

Question 3.

(a) $$-\frac{1}{4} \tan (7-4 x)+C$$

Question 4.

(a) $$\frac{1}{(\log 2)^{3}} 2^{2^{2^{x}}}+C$$

Question 5.

(b) $$-\frac{\cos ^{4} x}{4}+C$$

Question 6.

(a) $$\frac{-3}{\sqrt[3]{\sin x}}+C$$

Question 7.
Evaluate: ∫tan(x – θ) tan(x + θ) tan2x dx
(a) $$\frac { 1 }{ 2 }$$ log|cos2x| – log|cos(x – θ)| + log|cos(x + θ)| + C
(b) –$$\frac { 1 }{ 2 }$$ log|cos2x| + log|cos(x – θ)| + log|cos (x + θ)| + C
(c) –$$\frac { 1 }{ 2 }$$ log|cos2x| – log|cos(x – θ)| – log|cos(x + θ)| + C
(d) None of these
(b) –$$\frac { 1 }{ 2 }$$ log|cos2x| + log|cos(x – θ)| + log|cos (x + θ)| + C

Question 8.

(b) $$-\frac{2}{\sqrt{\tan x}}+\frac{2}{3}(\tan x)^{3 / 2}+C$$

Question 9.

(b) $$-\frac{3}{5} \tan ^{-5 / 3} x+3 \tan ^{1 / 3} x+C$$

Question 10.

(c) $$\frac{1}{4} \log \left|x^{4}-9\right|-\frac{1}{12}\left|\frac{x^{2}-3}{x^{2}+3}\right|+C$$

Question 11.

(b) $$-\log \left|e^{-x}+\sqrt{e^{-2 x}-1}\right|+C$$

Question 12.

(b) $$\frac{1}{n} \log \left|\frac{x^{n}}{x^{n}+1}\right|+C$$

Question 13.

(c) $$\frac{1}{6} \tan ^{-1}\left(\frac{2 \tan x}{3}\right)+C$$

Question 14.

(c) $$2 \sqrt{x}-3(\sqrt[3]{x})+6(\sqrt[6]{x})-6 \log (\sqrt[6]{x}+1)+C$$

Question 15.

(b) $$\begin{array}{l} -\frac{1}{3} \log |1+\tan \theta|+\frac{1}{6} \log \left|\tan ^{2} \theta-\tan \theta+1\right| \\ \quad+\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 \tan \theta-1}{\sqrt{3}}\right)+C \end{array}$$

Question 16.

(a) $$\log |\sec x+\tan x|-2 \tan (x / 2)+C$$

Question 17.

(c) $$\tan \frac{x}{2}$$

Question 18.

(a) $$\frac{e^{x} \cos x}{1+\sin x}+C$$

Question 19.

(b) $$e^{x}\left(\frac{x+2}{x+4}\right)+C$$

Question 20.

(b) \begin{aligned} \frac{1}{2}(x+1) \sqrt{x^{2}+2 x+5} & \\ +2 \log |(x+1)+\sqrt{x^{2}+2 x+5}|+C & \end{aligned}

Question 21.
$$\int_{1}^{2} x^{2} d x$$
(a) 1
(b) $$\frac{7}{3}$$
(c) $$\frac{1}{3}$$
(d) 0
(b) $$\frac{7}{3}$$

Question 22.
$$\int_{0}^{2}\left(x^{2}+3\right) d x$$
(a) $$\frac{25}{3}$$
(b) $$\frac{26}{3}$$
(c) $$\frac{24}{3}$$
(d) None of these
(b) $$\frac{26}{3}$$

Question 23.
Evaluate: $$\int_{0}^{\pi / 4} \sqrt{1-\sin 2 x} d x$$
(a) √2 – 1
(b) √2 + 1
(c) √2
(d) None of these
(a) √2 – 1

Question 24.
Evaluate: $$\int_{0}^{2 \pi} \sin \left(\frac{\pi}{4}+\frac{x}{2}\right) d x$$
(a) -2√2
(b) -2
(c) √2
(d) 2√2
(d) 2√2

Question 25.
Evaluate: $$\int_{1}^{2} \frac{d x}{x^{2}}$$
(a) $$\frac{1}{2}$$
(b) 1
(c) 2
(d) -1
(a) $$\frac{1}{2}$$

Question 26.
Evaluate: $$\int_{0}^{1} \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) d x$$
(a) $$\frac{\pi}{2}$$ – log2
(b) π
(c) $$\frac{\pi}{4}$$
(d) $$\frac{\pi}{2}$$ – log2
(a) $$\frac{\pi}{2}$$ – log2

Question 27.

(a) $$\log \left(\frac{4}{3}\right)$$

Question 28.

(c) $$\frac{4-\pi}{4 \sqrt{2}}$$

Question 29.

(c) $$\frac{2}{\sqrt{5}} \tan ^{-1}\left(\frac{1}{\sqrt{5}}\right)$$

Question 30.

(c) $$\frac{1}{\sqrt{5}} \log \left(\frac{3+\sqrt{5}}{2}\right)$$

Question 31.

(a) $$\frac{\pi}{2}$$

Question 32.

(a) $$\frac{8}{21}$$

Question 33.

(a) 2 – √2

Question 34.

(b) $$\frac{1}{2}+\frac{1}{\pi+2}-A$$

Question 35.

(d) $$\frac{\pi}{2}$$

Question 36.

(c) π2

Question 37.

(c) $$\operatorname{cosec}(b-a) \log \left|\frac{\sin (x-b)}{\sin (x-a)}\right|+C$$

Question 38.

(a) $$\frac{e^{x}}{1+x^{2}}+C$$

Question 39.

(d) $$x-\frac{x^{2}}{2}+\frac{x^{3}}{3}-\log |1+x|+C$$
(d) a = $$\frac{1}{3}$$, b = -1