Maths MCQs for Class 12 with Answers Chapter 7 Integrals

Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 7 Integrals. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Integrals MCQs Pdf with Answers to know their preparation level.

Integrals Class 12 Maths MCQs Pdf

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

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

Question 3.
Evaluate: \(\int_{0}^{\pi / 4} \sqrt{1-\sin 2 x} d x\)
(a) √2 – 1
(b) √2 + 1
(c) √2
(d) None of these
Answer:
(a) √2 – 1

Question 4.
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
Answer:
(d) 2√2

Question 5.
Evaluate: \(\int_{1}^{2} \frac{d x}{x^{2}}\)
(a) \(\frac{1}{2}\)
(b) 1
(c) 2
(d) -1
Answer:
(a) \(\frac{1}{2}\)

Question 6.
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
Answer:
(a) \(\frac{\pi}{2}\) – log2

Question 7.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q27
Answer:
(a) \(\log \left(\frac{4}{3}\right)\)

Question 8.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q28
Answer:
(c) \(\frac{4-\pi}{4 \sqrt{2}}\)

Question 9.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q29
Answer:
(c) \(\frac{2}{\sqrt{5}} \tan ^{-1}\left(\frac{1}{\sqrt{5}}\right)\)

Question 10.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q30
Answer:
(c) \(\frac{1}{\sqrt{5}} \log \left(\frac{3+\sqrt{5}}{2}\right)\)

Question 11.
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
Answer:
(b) 4tan x – 9cot x – 25x + C

Question 12.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q2
Answer:
(a) \(\frac{a^{x}}{\log a}+\frac{x^{a+1}}{a+1}+a^{a} x+C\)

Question 13.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q3
Answer:
(a) \(-\frac{1}{4} \tan (7-4 x)+C\)

Question 14.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q4
Answer:
(a) \(\frac{1}{(\log 2)^{3}} 2^{2^{2^{x}}}+C\)

Question 15.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q5
Answer:
(b) \(-\frac{\cos ^{4} x}{4}+C\)

Question 16.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q6
Answer:
(a) \(\frac{-3}{\sqrt[3]{\sin x}}+C\)

Question 17.
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
Answer:
(b) –\(\frac { 1 }{ 2 }\) log|cos2x| + log|cos(x – θ)| + log|cos (x + θ)| + C

Question 18.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q8
Answer:
(b) \(-\frac{2}{\sqrt{\tan x}}+\frac{2}{3}(\tan x)^{3 / 2}+C\)

Question 19.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q9
Answer:
(b) \(-\frac{3}{5} \tan ^{-5 / 3} x+3 \tan ^{1 / 3} x+C\)

Question 20.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q10
Answer:
(c) \(\frac{1}{4} \log \left|x^{4}-9\right|-\frac{1}{12}\left|\frac{x^{2}-3}{x^{2}+3}\right|+C\)

Question 21.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q31
Answer:
(a) \(\frac{\pi}{2}\)

Question 22.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q32
Answer:
(a) \(\frac{8}{21}\)

Question 23.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q33
Answer:
(a) 2 – √2

Question 24.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q34
Answer:
(b) \(\frac{1}{2}+\frac{1}{\pi+2}-A\)

Question 25.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q35
Answer:
(d) \(\frac{\pi}{2}\)

Question 26.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q36
Answer:
(c) π2

Question 27.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q37
Answer:
(c) cosec(b-a) \(\log \left|\frac{\sin (x-b)}{\sin (x-a)}\right|\) + C

Question 28.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q38
Answer:
(a) \(\frac{e^{x}}{1+x^{2}}+C\)

Question 29.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q39
Answer:
(d) \(x-\frac{x^{2}}{2}+\frac{x^{3}}{3}-\log |1+x|+C\)

Question 30.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q40
Answer:
(d) a = \(\frac{1}{3}\), b = -1

Question 31.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q41
Answer:
(a) 1

Question 32.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q11
Answer:
(b) \(-\log \left|e^{-x}+\sqrt{e^{-2 x}-1}\right|+C\)

Question 33.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q12
Answer:
(b) \(\frac{1}{n} \log \left|\frac{x^{n}}{x^{n}+1}\right|+C\)

Question 34.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q13
Answer:
(c) \(\frac{1}{6} \tan ^{-1}\left(\frac{2 \tan x}{3}\right)+C\)

Question 35.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q14
Answer:
(c) \(2 \sqrt{x}-3(\sqrt[3]{x})+6(\sqrt[6]{x})-6 \log (\sqrt[6]{x}+1)+C\)

Question 36.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q15
Answer:
(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 37.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q16
Answer:
(a) \(\log |\sec x+\tan x|-2 \tan (x / 2)+C\)

Question 38.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q17
Answer:
(c) \(\tan \frac{x}{2}\)

Question 39.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q18
Answer:
(a) \(\frac{e^{x} \cos x}{1+\sin x}+C\)

Question 40.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q19
Answer:
(b) \(e^{x}\left(\frac{x+2}{x+4}\right)+C\)

Question 41.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals Q20
Answer:
(b) \(\begin{aligned} \frac{1}{2}(x+1) \sqrt{x^{2}+2 x+5} & \\ +2 \log |(x+1)+\sqrt{x^{2}+2 x+5}|+C & \end{aligned}\)

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