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)

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

Question. The value of 

(a) 1/√a
(b) 1/2√a
(c) √a/2
(d) 2√a

Question. If value of lim_x→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

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

Question. Evaluate :

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

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

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

Question.

(a) 3/2
(b) 1
(c) 1/2
(d) 4/5

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

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

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

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

Question. 

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

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

Question. The value of

(a) 2
(b) –2
(c) 1
(d) –1

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

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

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

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

Question. If value of lim_x→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

Question.

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

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

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

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

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

Question. Evaluate 

(a) 1
(b) 2
(c) –1
(d) –2

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

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.

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

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

Question. 

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

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

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

Question.

(a) 2
(b) –2
(c) 1
(d) –1

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

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

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

Question.

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

Question.

(a) 3
(b) −1
(c) 1
(d) 0

Question.

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

Question.

(a) 1
(b) 1/2
(c) 1/√2
(d) 0

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

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

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

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

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

Question.

(a) 5/4
(b) 4/5
(c) 1
(d) 0

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

Question. The derivative of

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

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

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

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)e^x, then dy/dx at x = 0 is equal to
(a) 0
(b) 1
(c) 2
(d) 3

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

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

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

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

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

Question.

(a) 9/8
(b) −(9/8)
(c) 3/2
(d) −(3/2)

Question.

Question.

(a) − 1
(b) 0
(c) 1
(d) 2

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.

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.

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

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

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

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