# NCERT Solutions : Class 12 Maths with Answers MCQs Chapter 7

## NCERT Solutions for Class 12 Maths Chapter 7 MCQ’s with Answers

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## NCERT Maths MCQs for Class 12 Question and Answers Chapter 7 Integrals of Derivatives PDF

### Q1. ∫log10 xdx =

(a) loge 10.x loge (x/e) + c
(b) log10 e.x loge (x/e) + c
(c) (x – 1) loge x + c
(d) 1/x+ c

Option b – log10 e.x loge (x/e) + c

### Q2. ∫tan-1 √xdx is equal to

(a) (x + 1)tan-1 √x – √x + C
(b) x tan-1 √x – √x + C
(c) √x – x tan-1 √x + C
(d) √x – (x + 1)tan-1 √x + C

Option a – (x + 1)tan-1 √x – √x + C

### Q3. ∫ |x| dx is equal to

(a) 1/2 x² + C
(b) – 1/2+ C
(c) x|x| + C
(d) 1/2x|x| + C

Option d – 1/2x|x| + C

### Q4. ∫ cos(loge.x)dx is equal to

(a)1/2 x[cos (logex) + sin(logex)]
(b) x[cos (logex) + sin(logex)]
(c) 1/2x[cos (logex) – sin(logex)]
(d) x[cos (logex) – sin(logex)]

Option b – x[cos (logex) + sin(logex)]

### Q5. Evaluate: ∫ sec4/3 x cosec8/3 xdx

(a) 3/5tan-5/3 x – 3 tan1/3 x + C
(b) –3/5 tan-5/3 x + 3 tan1/3 + C
(c) –3/5 tan-05/3 x – 3 tan1/3 + C
(d) None of these

Option b – –3/5 tan-5/3 x + 3 tan1/3 + C

### Q6. Evaluate: ∫ sec²(7 – 4x)dx

(a) –1/4 tan(7 – 4x) + C
(b)1/4 tan(7 – 4x) + C
(c) 1/4tan(7 + 4x) + C
(d) – 1/4tan(7x – 4) + C

Option a – –1/4 tan(7 – 4x) + C

### Q7. Evaluate: ∫(2 tan x – 3 cot x)² dx

(a) -4tan x – cot x – 25x + C
(b) 4 tan x – 9 cot x – 25x + C
(c) – 4 tan x + 9 cot x + 25x + C
(d) 4 tan x + 9 cot x + 25x + C

Option b – 4 tan x – 9 cot x – 25x + C

### Q8. ∫1.dx =

(a) x + k
(b) 1 + k
(c) x/2+ k
(d) log x + k

Option a – x+k

Q9.

Option b –

Q10.

Option a –

Q11.

Option a –

Q12.

Option b –

Q13.

Option a –

Q14.

Option a –

Q15.

Option c –

Q16.

(a) sin² x – cos² x + C
(b) -1
(c) tan x + cot x + C
(d) tan x – cot x + C

Option d –

Q17. (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

Option a –

### Q18. ∫cot²x dx equals to

(a) cot x – x + C
(b) cot x + x + C
(c) -cot x + x + C
(d) -cot x – x + C

Option d – -cot x – x + C

(a) 7
(b) -4
(c) 3
(d)-1/4

Option d – -1/4

### Q20. Derivative of a function is unique but a function can have infinite antiderivatives. State true or false

Option – True, as ∫ f(x)dx = g(x) + C, C is constant can take different values but [g(x) + C] =f(x) only

Q21. (a) 3x + x3 + C(b) log |3x + x3| + C(c) 3x²+ 3x loge 3 +C(d) log |3x² + 3x loge 3| + C

Option -d

Q22.

Option -b

### Q23. If d/dx f(x) = g(x), then antiderivative of g(x) is __ .

Option -f(x), d/dx as f(x) = g(x) ⇒ ∫ g(x)dx = f(x).

Q24.

Option -c

Q25.