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

1. Given ∫ 2x dx = f(x) + C, then f(x) is
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 1

Answer/Explanation

Answer: c
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 63


2.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 2
(a) sin² x – cos² x + C
(b) -1
(c) tan x + cot x + C
(d) tan x – cot x + C

Answer/Explanation

Answer: d
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 64
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 65


3.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 3
(a) 2(sin x + x cos θ) + C
(b) 2(sin x – x cos θ) + C
(c) 2(sin x + 2x cos θ) + C
(d) 2(sin x – 2x cos θ) + C

Answer/Explanation

Answer: a
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 66


4. ∫cot²x dx equals to
(a) cot x – x + C
(b) cot x + x + C
(c) -cot x + x + C
(d) -cot x – x + C

Answer/Explanation

Answer: d
Explaination: (d), ∫ (cosec²x -1)dx = -cot x – x + C


5.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 4
(a) log |sin x + cos x|
(b) x
(c) log |x|
(d) -x

Answer/Explanation

Answer: d
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 67


6. If ∫ sec²(7 – 4x)dx = a tan (7 – 4x) + C, then value of a is
(a) 7
(b) -4
(c) 3
(d) \(-\frac{1}{4}\)

Answer/Explanation

Answer: d
Explaination:
(d), ∫sec²(7 – 4x)dx = \(\frac{\tan (7-4 x)}{-4}\) + C = –\(\frac{1}{4}\) tan (7 – 4x) + C.


7. The value of X for which
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 13
(a) 1
(b) loge4
(c) loe4 e
(d) 4

Answer/Explanation

Answer: b
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 79


8.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 30

Answer/Explanation

Answer: c
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 105


9.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 31
then value of a is equal to
(a) 3
(b) 6
(c) 9
(d) 1

Answer/Explanation

Answer: c
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 106
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 107


10.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 38
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 39

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 114
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 115


11.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 40

Answer/Explanation

Answer: c
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 116


12.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 41
(a) I1 > I2
(b) I2 > I1
(c) I1 = I2
(d) I1 > 2I2

Answer/Explanation

Answer: b
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 117


13. If a is such that \(\int_{0}^{a} x d x\) ≤ a + 4, then
(a) 0 ≤ a ≤ 4
(b) -2 ≤ a ≤ 0
(c) a ≤ -2 or a ≤ 4
(d) -2 ≤ a ≤ 4

Answer/Explanation

Answer: d
Explaination:
(d), as \(\int_{0}^{a}\) x dx ≤ a + 4
⇒ \(\frac{a²}{2}\) ≤ a + 4
⇒ a² – 2a — 8 ≤ 0
⇒ (a – 1)² ≤ (3)²
⇒ -3 ≤ a – 1 ≤ 3
⇒ -2 ≤ a ≤ 4


14. If \(\frac{d}{dx}\) f(x) = g(x), then antiderivative of g(x) is ________ .

Answer/Explanation

Answer:
Explaination:
f(x), as \(\frac{d}{dx}\) f(x) = g(x)
⇒ ∫ g(x)dx = f(x).


15. Derivative of a function is unique but a function can have infinite antiderivatives. State true or false.

Answer/Explanation

Answer:
Explaination: True, as ∫ f(x)dx = g(x) + C, C is constant can take different values but \(\frac{d}{dx}\) [g(x) + C]
=f(x) only


16.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 5

Answer/Explanation

Answer:
Explaination: \(\frac{2}{3}\) ∫ cosec x . cot x dx = –\(\frac{2}{3}\) ∫ cosec x + C


17. Find ∫(ax + b)3dx [AI 2011]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 68


18. If ∫(ax + b)² dx = f(x) + C, find f(x)

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 69


19. We have \(\frac{d}{dx}\)(3x² + sin x – ex) = 6x + cos x -ex. Represent the expression in the form of anti derivative.

Answer/Explanation

Answer:
Explaination:
\(\frac{d}{dx}\) (3x² + sin x – ex) = 6x + cos x – ex
⇒ ∫ (6x + cos x – ex) = 3x² + sin x – ex


20.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 6

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 70


21.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 7

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 71


22. Evaluate ∫ (sin x + cos x)² dx

Answer/Explanation

Answer:
Explaination:
∫ (sin x + cos x)² dx = ∫ (sin²x + cos²x + 2sin x cos x)dx
= ∫(1 + sin 2x)dx = x – \(\frac{\cos 2 x}{2}\) + C


23.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 8

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 72


24.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 9

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 73


25. Find ∫(ex log a + ea log x + ea log a)dx

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 74


26. Evaluate \(\int e^{\frac{1}{2} \log x} d x\).

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 75


27.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 10
(a) 3x + x3 + C
(b) log |3x + x3| + C
(c) 3x²+ 3x loge 3 +C
(d) log |3x² + 3x loge 3| + C

Answer/Explanation

Answer: d
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 76


28.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 11

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 77


29.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 12

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 78


30.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 14

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 80


31. Find ∫ sec² (7 – x)dx

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 81


32. Find \(\int \frac{\sin \sqrt{x}}{\sqrt{x}} d x\)

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 82


33. Find ∫2x sin(x² + 1) dx

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 83


34.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 15

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 84


35.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 16

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 85


36.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 17

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 86


37.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 18

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 87


38.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 19

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 88


39.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 20

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 89


40.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 21

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 90


41.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 22

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 91


42.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 23

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 92


43.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 24

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 93


44. Evaluate ∫ sec4 x tan x dx

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 94


45.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 25

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 95


46.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 26

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 96


47. Find ∫ cot x . log(sin x) dx [NCERT]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 97Maths MCQs for Class 12 with Answers Chapter 7 Integrals 98


48.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 27

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 99


49. Find ∫(ex + 3x)² (ex + 3)dx

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 100


50.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 28

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 101


51.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 29

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 102


52. Find ∫ (cosx – sinx)² dx

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 103


53. Evaluate \(\int \sqrt{1+\sin \frac{x}{4}} d x\)

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 104


54.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 32

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 108


55.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 33

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 109


56.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 34

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 110


57.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 35

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 111


58.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 36

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 112


59.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 37

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 113


60. ∫ ex sec x(1 + tan x)dx = ________ + C.

Answer/Explanation

Answer:
Explaination:
ex sec x, as ∫ex (sec x + sec x tan x) dx,
i.e. f(x) = sec x
f'(x) = sec x tan x,
using formula ∫ ex {f(x) + f'(x)}dx
= ex f(x) + C


61. If \(\int_{-1}^{4}\) f(x) dx =4 and \(\int_{2}^{4}\) (3 – f(x))dx = 7, then the value of \(\int_{-2}^{-1}\) f(x) dx is ________ .

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 118
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 119


62.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 42

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 120


63.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 43

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 121


64.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 45

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 122


65.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 46

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 123


66. If \(\int_{0}^{a}\) 3x² dx = 8 write the value of a. [Foreign 2017]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 124


67. Evaluate. \(\int_{2}^{3}\) 3x dx [Delhi 2017]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 125


68.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 47

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 126


69. \(\int_{0}^{2a}\)f(x)dx = 2 \(\int_{0}^{a}\) f(x)dx if f(2a -x)= f(x). State true or false.

Answer/Explanation

Answer:
Explaination: True; result


70.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 48
then value of a is ________ .

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 127


71.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 49

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 128


72. \(\int_{-1}^{1}\) |(1 – x)| dx is equal to ________ .

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 129


73.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 50
is equal to 0.State true or false.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 130


74. The value of \(\int_{0}^{\pi}\) | cos x|dx is 2. State true or false.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 131


75. The value of \(\int_{-\pi}^{\pi}\) sin3x cos²x dx is ________ .

Answer/Explanation

Answer:
Explaination: 0, as f(x) = sin3 x. cos² x dx is an odd function


76.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 51

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 132


77.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 52

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 133


78.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 53

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 134


79.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 54

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 135


80. Evaluate \(\int_{-1}^{1}\) x|x|dx

Answer/Explanation

Answer:
Explaination:
Consider \(\int_{-1}^{1}\) x|x| dx
f(x) = x|x|, f(-x) = (-x)|-x| = -x|x| = -f(x)
Odd function.
∴ \(\int_{-1}^{1}\) x|x|dx = 0
[using \(\int_{-a}^{a}\) f(x) = 0, if f(x) is odd function]


81. Evaluate \(\int_{0}^{2\pi}\) cos5x dx [Foreign 2017]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 136


82.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 55

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 137


83. Evaluate \(\int_{0}^{1}\) [2x]dx

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 138


84. Evaluate \(\int_{1}^{4}\) f(x) dx, where
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 56

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 139


85.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 57

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 140


86. Evaluate \(\int_{-\pi}^{\pi}\) (sin-93 x + x295) dx

Answer/Explanation

Answer:
Explaination:
\(\int_{-\pi}^{\pi}\) (sin-93 x + x295)dx,f(x) is odd function as f(-x) = -f(x)
∴ \(\int_{-\pi}^{\pi}\) (sin-93 x + x295) dx=0


87.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 58

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 141


88.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 59

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 142


89.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 60

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 143


90. \(\int_{1}^{e}\) log x. dx

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 144


91. Evaluate \(\int_{0}^{1}\) x(1 – x)89dx

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 145


92.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 61

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 146


93. Evaluate \(\int_{0}^{1}\) x²(1 -x)ndx

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 147


94.
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 62

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 148


95. Evaluate \(\int_{0}^{\pi}\) |cos x|dx [DoE]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 7 Integrals 149


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