# MCQs For NCERT Class 11 Mathematics Chapter 13 Limits and Derivatives

Please refer to the MCQ Questions for Class 11 Limits and Derivatives Maths Chapter 13 with Answers. The following Limits and Derivatives Class 11 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 11. Our experts have designed MCQ Questions for Class 11 Limits and Derivatives with Answers for all chapters in your NCERT Class 11 Mathematics book. You can access all MCQs for Class 11 Mathematics

## Limits and Derivatives Class 11 MCQ Questions with Answers

See below Limits and Derivatives Class 11 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

Question. The derivative of f (x) = tan (ax + b) is
(a) sec2 (ax + b)
(b) b sec2 (ax + b)
(c) a sec2 (ax + b)
(d) ab sec2 (ax + b)

C

Question. For the function f (x) = x100 /100 + x99/99 + …… x2/2 + x + 1, f ‘(1) = mf ‘ (0), where m is equal to
(a) 50
(b) 0
(c) 100
(d) 200

C

Question. The value of

(a) 1/√a
(b) 1/2√a
(c) √a/2
(d) 2√a

B

Question. If value of limx→0 sin x / x (1+ cos x) is equal to a/2 then the value of ‘a’ is
(a) 0
(b) 1
(c) 2
(d) 3

B

Question. Derivative of the function f (x) = (x – 1) (x – 2) is
(a) 2x + 3
(b) 3x – 2
(c) 3x + 2
(d) 2x – 3

D

Question. Evaluate :

D

Question. Find the derivative of f (x) = 1 + x + x2 + x3 …… x50 at x = 1
(a) 1275
(b) 2550
(c) 1276
(d) 675

A

Question. If 7 = 2x3 – 4x2 + 6x + 8, then dy/dx at x = 1 is equal to
(a) 4
(b) 12
(c) −8
(d) 6

A

Question. If y = 2x3 – 8x2 + 5x, then dy/dx at x = – 1 is equal to
(a) 5
(b) -5
(c) 1
(d) -1

B

Question.

(a) 3/2
(b) 1
(c) 1/2
(d) 4/5

A

Question. If y = x−4 (3 – 4x-5 ), and dy/dx at x = 1 is equal to 24K, then K is equal to
(a) 0
(b) 1
(c) 2
(d) 3

B

Question. If f (x) = x −5 (6 – 3x-2) Then, f’ (1) is equal to
(a) − 8
(b) 10
(c) 9
(d) − 9

D

Question. If y = (5x3 + 3x – 1) (x – 1) then dy/dx at x = 1 is equal to
(a) 7
(b) 0
(c) 1
(d) 8

A

Question. limx→1 [x – 1], where [.] is greatest integer function, is equal to
(a) 1
(b) 2
(c) 0
(d) does not exist

D

Question.

(a) 1
(b) –1
(c) zero
(d) does not exist

D

Question. The value of limx→0 1+x/3 − 1+x/3 /x is
(a) 2/3
(b) 1/3
(c) 2/5
(d) 1/5

A

Question. The value of

(a) 2
(b) –2
(c) 1
(d) –1

A

Question. Derivative of x2 + sin x + 1/xis
(a) 2x + cos x
(b) 2x + cos x + (–2) x–3
(c) 2x – 2x–3
(d) None of these

B

Question. The value of limΘ→π/4 cosΘ+ sinΘ / Θ + π/4 is
(a) π/4
(b) −π/4
(c) – √2
(d) √2

D

Question. Let 3f (x) – 2f(1/x) = x, then f ‘(2) is equal to
(a) 2/7
(b) 1/2
(c) 2
(d) 7/2

B

Question. If limx→2xn − 2n/x− 2 = 80 and n ∈ N, then the value of ‘n’ is
(a) 2
(b) 3
(c) 4
(d) 5

D

Question. If value of limx→a √a+2x −√3x / √3a+x −2√x is equal to 2√3/m , where m is equal to
(a) 2
(b) 8
(c) 9
(d) 3

C

Question.

(a) 1/5
(b) 1/6
(c) 1/4
(d) 1/2

B

Question. If lim x→0 ax – xa/xa – aa = –1, then a is equal to:
(a) –1
(b) 0
(c) 1
(d) 2

C

Question. If a is a non-zero constant, then the derivative of x + a is
(a) 1
(b) 0
(c) a
(d) None of these

A

Question. If y = x tan x/2 , then value of (1 + cosx) dy/dx – sin x is
(a) – x
(b) x2
(c) x
(d) None

C

Question. The value of limx→0 x(ex−1)/1−cos x is
(a) 0
(b) 2
(c) –2
(d) does not exist

B

Question. Evaluate

(a) 1
(b) 2
(c) –1
(d) –2

A

Question. If f (x) = 2sinx – 3x4 + 8, then f ‘(x) is
(a) 2sin x – 12x3
(b) 2cos x – 12x3
(c) 2cos x + 12x3
(d) 2sin x + 12x3

B

Question. A function f is said to be a rational function, if f (x) = g(x)/h(x), where g (x) and h (x) are polynomials such that h (x) ≠ 0, then
(a) h (a) ≠ 0 ⇒ lim x→a f (x) = g(a)/h (a)
(b) h (a) = 0 and g (a) ≠ 0 ⇒ lim x→a f (x) does not exist
(c) Both (a) and (b) are true
(d) Both (a) and (b) are false.

C

Question. If f (x) = xn and f ‘ (1) = 10, then the value of ‘n’ is
(a) 1
(b) 5
(c) 9
(d) 10

D

Question. Match the terms given in column-I with the terms given in column-II and choose the correct option from the codes given below.

Codes
A B C D E
(a) 5 2 1 4 3
(b) 2 5 1 3 4
(c) 5 2 1 3 4
(d) 2 5 3 1 4

B

Question.

(a) a ≠ 1
(b) a ≠ 0
(c) a ≠ –1
(d) a ≠ 2

B

Question. f (x) is a function such that f ” (x) = – f(x) and f ‘(x) = g(x) and h (x) is a function such that h (x) = [f(x)]2 + [g(x)]2 and h (5) = 11, then the value of h (10) is
(a) 5
(b) –5
(c) –11
(d) 11

D

Question. The derivative of sinn x is
(a) n sinn–1 x
(b) n cosn – 1 x
(c) n sinn – 1 x cos x
(d) n cosn – 1 x sin x

B

Question.

(a) 2
(b) –2
(c) 1
(d) –1

A

Question. If f (x) = |cos x – sin x|, then f'(π/4) Is equal to
(a) √2
(b) −√2
(c) 0
(d) None of these

D

Question. The derivative of the function f (x) = x is
(a) 0
(b) 1
(c) ∞
(d) None of these

B

Question. If y = f(2x−1/x2+1) and f ‘ (x) = sin x2, then value of dy/dx is

C

Question.

(a) 0
(b) n
(c) 2n
(d) None of these

A

Question.

(a) 3
(b) −1
(c) 1
(d) 0

D

Question.

(a) 1
(b) 4
(c) 5
(d) 6

C

Question.

(a) 1
(b) 1/2
(c) 1/√2
(d) 0

D

Question. Differential coefficient of xsin x/1+ cos x is
(a) −x − sin x/1 + cosx
(b) x − sin x/1 + cosx
(c) x + sin x/1 − cosx
(d) x + sin x/1 + cosx

D

Question. The derivative of sin x at x = 0 is
(a) 0
(b) 2
(c) 1
(d) 3

C

Question. The derivative of function 6×100 − x 55 + x is
(a) 600x100 – 55x55 + x
(b) 600x99 – 55x45 + 1
(c) 99x99 – 54x54 + 1
(d) 99x99 – 54x54

B

Question. The f ¢ (x) of f (x) = x cos x is
(a) cos x + xsin x
(b) cos x −xsin x
(c) xsin x − cos x
(d) x cos x + sin x

B

Question. The derivative of ax + b / cx + d is

A

Question.

(a) 5/4
(b) 4/5
(c) 1
(d) 0

A

Question. If a, b are fixed non-zero constants, then the

B

Question. The derivative of

B

Question. If y = sin x2 , then dy/dx at x = π/4 is equal to
(a) 0
(b) 2
(c) 1
(d) 3

C

Question. If y = eloge sin, then dy/dx at x = π/2 is equal to
(a) 1
(b) 0
(c) 2
(d) 3

B

Question. If f (x) = xsin x, = then f’ (π/2) is equal to
(a) 0
(b) 1
(c) − 1
(d) 1/2

B

Case Based Questions

Sam was learning ‘‘Algebra of Derivative of Functions’’ from his Tutor Rajesh.
Derivative of product of two functions is given by the following product rule.

This is also known as Leibnitz product rule of derivative.
Based on above information, answer the following questions.

Question. If y = (x + 1)ex, then dy/dx at x = 0 is equal to
(a) 0
(b) 1
(c) 2
(d) 3

C

Question. If y = x tan x, then dy/dx at π = 4 is equal to
(a) (π/2) + 1
(b) π/2
(c) (π/2) − 1
(d) π

B

Question. If y = x2 log x, then dy/dx is equal to
(a) x(1 + 3logx)
(b) x2 (1 + 3logx)
(c) x2 (1 − 3logx)
(d) None of these

B

Question. If y = ex (x3 + √x) then dy/dx at x = 1 is equal to
(a) (11/3) e
(b) 11e
(c) (11/2) e
(d) e/5

C

Question. If y = (x2 + 2x – 3) (x2 + 7x + 5) then dy/dx at x = 0 is equal to
(a) − 5
(b) 32
(c) 11
(d) − 11

D

Two friends Raj and Shyam of class XI standard were discussing on the topic derivative of quotient of two functions. Derivative of quotient of two functions is given by the following quotient rule.

Based on above information, answer the following questions

Question.

(a) 0
(b) 1
(c) − 1
(d) 2

A

Question.

(a) 9/8
(b) −(9/8)
(c) 3/2
(d) −(3/2)

B

Question.

D

Question.

(a) − 1
(b) 0
(c) 1
(d) 2

C

ASSERTION – REASON TYPE QUESTIONS

(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Question. Assertion: Derivative of f (x) = 2 is zero.
Reason: Differentiation of a constant function is zero.

A

Question. Assertion. For the function
f (x) = x100/100 + x99/99+…..+x2/2 … x+1,f'(1) = 100f ‘ (0).
Reason: d/dx (xn ) = n.xn−1.

A

Question. Assertion: Let limx→a f (x) = l and limx→a g (x) = m. If l and m both exist, then limx→a
(fg) (x) = limx→a f (x) limx→a g (x) = lm
Reason: Let f be a real valued function defined by f (x) = x2 + 1, then f ‘ (2) = 4.

B

Question. Assertion: limx→0 (cosec x – cot x) = 0
Reason: limx→π/2 tan 2x / x −π/2 = 1

C

Question. Assertion: limx→0tan x/ x= 1 where x0 means x degree.
Reason: If limx→0 f(x) = l, limx→0g(x) = m, limx→0{f(x)g(x)} = lm

B

Question. Let a1, a2, a3, …, an be fixed real numbers and define a function f (x) = (x – a1) (x – a2) … (x – an), then
Assertion: limx→a1 f (x) = 0.
Reason: limx→a f (x) = (x – a1) (x – a2) … (x – an), for some a ≠ a1, a2, …, an.