# MCQ Questions Chapter 13 Limits and Derivatives Class 11 Mathematics

Please refer to MCQ Questions Chapter 13 Limits and Derivatives Class 11 Mathematics with answers provided below. These multiple-choice questions have been developed based on the latest NCERT book for class 11 Mathematics issued for the current academic year. We have provided MCQ Questions for Class 11 Mathematics for all chapters on our website. Students should learn the objective based questions for Chapter 13 Limits and Derivatives in Class 11 Mathematics provided below to get more marks in exams.

## Chapter 13 Limits and Derivatives MCQ Questions

Please refer to the following Chapter 13 Limits and Derivatives MCQ Questions Class 11 Mathematics with solutions for all important topics in the chapter.

### MCQ Questions Answers for Chapter 13 Limits and Derivatives Class 11 Mathematics

Question. Find f'(x), if f(x) = x2
(a) x
(b) 2x
(c) 4x
(d) x2/2

B

Question. Find the derivative of (x2 + 1) cos x
(a) 2xcosx – xsinx
(b) 2x cosx – x2 sinx – sinx
(c) 2xcosx
(d) xcosx – sinx

B

Question. Find f'(x), if f(x) = 1/x
(a) 1/x2
(b) -1/x2
(c) 0
(d) 1

B

Question. Compute the derivative of f(x) = sin2 x.
(a) sin 2x
(b) 2 sin x
(c) 2x sin 2x
(d) sin x

A

Question. If y = 1+1/x2 /1,1-x2 , then dy/dx =
(a) -4x/(x2-1)2
(b) -4x/x2-1
(c) 1-x2/4x
(d) dx/x2-1

A

Question. Find f'(x), if f(x) = 2x+3/x-2
(a) -7/(x-2)
(b) -7/(x-2)2
(c) 7/(x-2)
(d) None of these

B

Question. If f(x) = x-4/2√x , then f′(1) is
(a) 3/4
(b) -1/4
(c) 5/4
(d) 1/4

C

Question. If x √1 + y + y √1 + x = 0 , then dy/dx =
(a) x+1/x
(b) 1/1+x
(c) -1/(1+x)2
(d) x/1+x

C

Question. Find the derivative of f(x) = x+1/x
(a) 1/x
(b) 1/x2
(c) 0
(d) -1/x2

D

Question. If y = sin(x+9)/cosx , then dy/dx at x = 0 is
(a) cos 9
(b) sin 9
(c) 0
(d) 1

A

Question. Find the derivative of x5 – cosx/sinx
(a) x5 cosx/sin2x
(b) 1/sinx – x5 cosx/sin2x
(c) x/sin2x
(d) None of these

D

Question. Find the derivative of (x2 + 1) cos x.
(a) 2x cos x – (x2 + 1) sin x
(b) 2x sin x – x2 cos x
(c) x2(cos x – sin x)
(d) 2x(sin x + cos x)

A

Question. Find f'(x), if f(x) = 3, at x = 0 and at x = 3.
(a) 0, 0
(b) 1, 2
(c) 5, 1
(d) 2, 8

A

Question. Find the derivative of 2×4 + x.
(a) x3 + 1
(b) 8x3 + 1
(c) x3 – 1
(d) None of these

B

Question. If y = 1 + x/1! + x2/2! + x3/3! + ………, then dy/dx = ______ .
(a) 2y
(b) y
(c) –y
(d) –2y

B

Question. Find the derivative of 4 √x −2
(a) 2/x
(b) 2/x2
(c) 2/√x
(d) 1/√x

C

Question. If y = f(x) = –cosec x ⋅ cos x, then (dy/dx) x = π/2 is equal to
(a) 0
(b) 1/2
(c) 1
(d) 3

C

Question. If y = x2+sinx + 1/x2 , then dy/dx is equal to
(a) 2x – cosx + 2
(b) x – 2×2 + cosx
(c) 2x + cosx – (2/x3)
(d) (2/x3) – cosx

C

Question. Find the derivative of f(x) = 1 + x + x2 + x3 + … + x50 at x = 1.
(a) 1275
(b) 1200
(c) 1326
(d) 1542

A

Question. If f(x) = x sinx, then f'(π/x) is equal to
(a) 0
(b) 1
(c) –1
(d) 1/2

B

Question. If y = x tan x, then dy/dx is equal to
(a) tanx/x – x2 – y2
(b) y/x – x2 – ye
(c) tanx/y-x
(d) cos x sin x+ x/cos2x

D

Question. Find f'(x), if f(x) = sin x, at x = 0.
(a) 1
(b) 5
(c) 3
(d) 2

A

Question. Compute the derivative of 6×100 – x55 + x.
(a) x99 – x54 + 1
(b) 100×99 – 55×4 + 1
(c) 600×99 – 55×54 + 1
(d) None of these

C

Question. If y = √x + 1/√x , then dy/dx at x = 1 is
(a) 1
(b) 1/2
(c) 1/√2
(d) 0

D

Question. If h(x) = 2+x2/2-x2 , h'(1) =
(a) 2
(b) 4
(c) 6
(d) 8

D

Question. If f(x) = 1 + x/2+x2/3 + …..+x100/101 , then f ′(0) is equal to
(a) 1/100
(b) 100
(c) Does not exist
(d) 1/2

D

Question. If y = (x + 1)(x + 2)(x + 3)(x + 4)(x + 5), then the value of dy dx at x = 0 is equal to
(a) 374
(b) 742
(c) 472
(d) 274

D

Question. Find f'(x), if f(x) = 2×2 + 3x – 5, at x = –1.
(a) 0
(b) 1
(c) –1
(d) –2

C

Question. Find the derivative of (secx – 1)(secx + 1)
(a) 2 tanx sec2x
(b) tanx secx
(c) tanx sec2x
(d) tanx

A

Question. Find f'(x), if f(x) = a, where a is a real number.
(a) 4
(b) 1
(c) –1
(d) 0

D

Question. If f (x) =1√x +(1+ √x)2 , f (1) is equal to
(a) 1/2
(b) 1
(c) 3/2
(d) 2

C

Assertion & Reasoning Based Questions :

(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.

Question. Assertion : The derivative of y = 2x-3/4 is 2.
Reason : The derivative of y = cx is c.

A

Question. Assertion : The derivative of h(x) = x+cos x/tan x is (1-sinx) tanx – (x+cos x) sec2 x/(tanx)2
Reason : (u/v)’ = u’v-uv /(v)2

A

Question. Let u = f(x) and v = g(x). Then,
Assertion : (uv)′ = u′v + uv′ is a Leibnitz rule or product rule.
Question: (u/v)’ = u’v-uv /v’ a Leibnitz rule or quotient rule.