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 lim_x→0a^{sin x}−1 is
(a) log a
(b) sin x
(c) log (sin x)
(d) cos x

Question.

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

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

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

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

Question. If lim_x→0((a−n)nx − tan x) sin nx/x² = 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

Question.

(a) 1
(b) –1
(c) 0
(d) does not exist

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
(a) 4 1 2 3
(b) 4 2 3 1
(c) 2 4 1 3
(d) 4 2 1 3

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

Question. Derivative of (√x + 1/√x)² is
(a) 1/x²
(b) 1−1/x²
(c) 1
(d) 1+1/x²

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

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

Question.

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

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

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

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

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

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

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

Question.

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

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

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

Question. 

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

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

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

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

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

Question. lim_x→0cosax − cosbx / coscx − 1 is equal to m/n , where m and n are respectively
(a) a² + b^2, c²
(b) c² , a² + b²
(c) a² – b², c² 
(d) c² , a² – b²

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

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

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

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

Question. 

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

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

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

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

Question. Assertion: lim_x→0 log_e (sinx/x) = 0
Reason: lim_x→0 f (g(x)) = f(lim_x→0 g(x)).

Question. Assertion: Suppose f is real valued function, the derivative of ‘f’ at x is given by
f ‘ (x) = lim_h→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).

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

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

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.