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Limits and Derivatives MCQ Class 11 Mathematics

Please refer to Chapter 13 Limits and Derivatives MCQ Class 11 Mathematics with answers below. These multiple-choice questions have been prepared based on the latest NCERT book for Class 11 Mathematics. Students should refer to MCQ Questions for Class 11 Mathematics with Answers to score more marks in Grade 11 Mathematics exams. Students should read the chapter Limits and Derivatives and then attempt the following objective questions.

MCQ Questions Class 11 Mathematics Chapter 13 Limits and Derivatives

The Limits and Derivatives MCQ Class 11 Mathematics provided below covers all important topics given in this chapter. These MCQs will help you to properly prepare for exams.

Question. Value of limx→0asin x−1 is
(a) log a
(b) sin x
(c) log (sin x)
(d) cos x

Answer

A

Question.

Limits and Derivatives MCQ Class 11 Mathematics

if limx→-1 f(x) exists, then c is equal to
(a) 1
(b) 0
(c) 2
(d) 3

Answer

A

Question. limΘ→0 2sin2Θ/Θ is equal to :
(a) 0
(b) 1
(c) m
(d) m2

Answer

D

Question. limx→4 lx−4l/x−4 is equal to
(a) 1
(b) 0
(c) – 1
(d) does not exist

Answer

D

Question. Derivative of x sin x
(a) x cos x
(b) x sin x
(c) x cos x + sin x
(d) sin x

Answer

C

Question. If limx→0((a−n)nx − tan x) sin nx/x= 0 where n is non-zero real number, then a is equal to
(a) 0
(b) n+1/n
(c) n
(d) n+1/n

Answer

D

Question.

Limits and Derivatives MCQ Class 11 Mathematics

(a) 1
(b) –1
(c) 0
(d) does not exist

Answer

A

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. 

Limits and Derivatives MCQ Class 11 Mathematics

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

Answer

D

Question. Derivative of logxx is
(a) 0
(b) 1
(c) 1/x
(d) x

Answer

A

Question. Derivative of (√x + 1/√x)is
(a) 1/x2
(b) 1−1/x2
(c) 1
(d) 1+1/x2

Answer

B

Question. If f be a function given by f (x) = 2x2 + 3x – 5. Then, f ‘(0) = mf ‘(–1), where m is equal to
(a) – 1
(b) – 2
(c) – 3
(d) – 4

Answer

C

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

Answer

B

Question.

Limits and Derivatives MCQ Class 11 Mathematics

(a) 0
(b) 1
(c) 2
(d) 3

Answer

C

Question. If f (t) = 1−t/1+t , then the value of f ‘ (1/t) is
(a) −2t2/(t+1)2
(b) 2t/(t+1)2
(c) 2t2/(t−1)2
(d) −2t2/(t−1)2

Answer

A

Question. If f (x) = | x | – 5, then the value of limx→5 f (x) is
(a) 9
(b) 1
(c) 0
(d) None of these

Answer

C

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

Answer

D

Question. limx→0 x tan 2x − 2x tan x / (1 − cos 2x )2 is
(a) 2
(b) –2
(c) 1/2
(d) –1/2

Answer

C

Question. Let f and g be two functions such that limx→a f(x) and a limx→ag(x) exist. Then, which of the following is incomplete?

Limits and Derivatives MCQ Class 11 Mathematics
Answer

D

Question. If a, b are fixed non-zero constant, then the derivative of a/x4 − b/x2 + cos x is ma + nb – p, where

Limits and Derivatives MCQ Class 11 Mathematics
Answer

B

Question.

Limits and Derivatives MCQ Class 11 Mathematics

(a) 1/8√3
(b) 1/4√3
(c) 0
(d) None of these

Answer

A

Question. If limx→3  xn − 3/x − 3 = 108, the positive integer n is equal to
(a) 3
(b) 5
(c) 2
(d) 4

Answer

D

Question. The limit of f (x) = x2 as x tends to zero equals
(a) zero
(b) one
(c) two
(d) three

Answer

A

Question. 

Limits and Derivatives MCQ Class 11 Mathematics

(a) equals √2
(b) equals – √2
(c) equals 1/√2
(d) does not exist

Answer

D

Question. limx→π/2(sec x – tan x) is equal to
(a) 0
(b) 2
(c) 1
(d) 3

Answer

A

Question. Let f : R → [0, ∞) be such that lim x→5 f(x) exists and

Limits and Derivatives MCQ Class 11 Mathematics

(a) 0
(b) 1
(c) 2
(d) 3

Answer

D

Question. The derivative of f (x) = 3 at x = 0 and at x = 3 are
(a) negative
(b) zero
(c) different
(d) not defined

Answer

B

Question. limx→0cosax − cosbx / coscx − 1 is equal to m/n , where m and n are respectively
(a) a2 + b2, c2
(b) c2 , a2 + b2
(c) a2 – b2, c2 
(d) c2 , a2 – b2

Answer

C

Question. If limx→5 xk − 5/ x− 5 = 500, then k is equal to :
(a) 3
(b) 4
(c) 5
(d) 6

Answer

B

Question. limx→0 x/tan x is
(a) 0
(b) 1
(c) 4
(d) not defined

Answer

B

Question. The derivative of 4√x − 2 is
(a) 1/√x
(b) 2√x
(c) 2/√x 
(d) √x

Answer

C

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.

Limits and Derivatives MCQ Class 11 Mathematics

Codes
A B C
(a) 3 1 2
(b) 1 3 2
(c) 1 2 3
(d) 2 3 1

Answer

B

Question. 

(a) 0
(b) 1/2 
(c) −1/2
(d) does not exist

Answer

C

Question. Let α and β be the distinct roots of ax2 + bx = c = 0, then 

Answer

A

Question. If f (x) = αxn, then α =
(a) f ‘(1)
(b) f'(1)/n
(c) n · f ‘(1)
(d) n/f'(1)

Answer

B

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: limx→0 sin ax/bx = a/b
Reason: limx→0 sin ax/sin bx = b/a = (a, b ≠ 0)

Answer

C

Question. Assertion: limx→0 loge (sinx/x) = 0
Reason: limx→0 f (g(x)) = f(limx→0 g(x)).

Answer

C

Question. Assertion: Suppose f is real valued function, the derivative of ‘f’ at x is given by
f ‘ (x) = limh→0 f (x+h) − f (x)/h.
Reason: If y = f (x) is the function, then derivative of ‘f’ at any x is denoted by f ‘ (x).

Answer

B

Question. Assertion: limx→0 (1+3x)1/x = e3.
Reason: Since limx→0(1 + x)1/x = e .

Answer

A

Question. Assertion: Derivative of f (x) = x | x | is 2 | x |.
Reason: For function u and v, (uv)’ = uv’ + vu’.

Answer

A

Question. Assertion: If a and b are non-zero constants, then the derivative of f (x) = ax + b is a.
Reason: If a, b and c are non-zero constants, then the derivative of f (x) = ax2 + bx + c is ax + b.

Answer

C

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