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.
(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
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.
(b) log |3x + x3| + C
(c) 3x²+ 3x loge 3 +C
(d) log |3x² + 3x loge 3| + C
Option -d
Q22.
(b) I2 > I1
(c) I1 = I2
(d) I1 > 2I2
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.
(a) 3
(b) 6
(c) 9
(d) 1
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.