## 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.

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

### Q19. If ∫ sec²(7 – 4x)dx = a tan (7 – 4x) + C, then value of a is

(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.

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.

Option c – 9

We hope that the given** NCERT MCQ** **Questions for Class 12 Mathematics Chapter 7 Integrals** **Free Pdf download** will help you in gaining knowledge on the subject.