VBQs Limits and Derivatives Class 11 Mathematics

VBQs Limits and Derivatives Class 11 Mathematics with solutions has been provided below for standard students. We have provided chapter wise VBQ for Class 11 Mathematics with solutions. The following Limits and Derivatives Class 11 Mathematics value based questions with answers will come in your exams. Students should understand the concepts and learn the solved cased based VBQs provided below. This will help you to get better marks in class 11 examinations.

Limits and Derivatives VBQs Class 11 Mathematics

Question. If a is a fixed non-zero constant, then the derivative of sin(x+a)/cosx is
(a) cosa / cos²x
(b) − cosa / cos²x
(c) sina / cos²x
(d) − sina / cos²x

Question. lim_x→0 2sin²3x/x² is equal to :
(a) 12
(b) 18
(c) 0
(d) 6

Question.

(a) 0
(b) 6
(c) 2
(d) 3

Question. If y = ax^{n +1} + bx ^{– n} , then value of x² d²y/dx² is
(a) n (n + 1) y
(b) n² (n + 1) y
(c) 2n (n – 1) y
(d) None of these

Question. 

(a) 2
(b) 4
(c) 6
(d) 8

Question. If lim_x→0 sin(2+x)−sin(2−x)/x is equal to p cos q, then sum of p and q is
(a) 2
(b) 1
(c) 3
(d) 4

Question. 

(a) 1/2
(b) −1/2
(c) 0
(d) ∞

Question. If a and b are fixed non-zero constants, then the derivative of (ax + b)ⁿ is
(a) n(ax + b)^{n – 1}
(b) na(ax + b)^{n – 1}
(c) nb(ax + b)^{n – 1}
(d) nab(ax + b)^{n – 1}

Question. If f (x) = x + | x |/x, then the value of lim_x→0 f (x) is
(a) 0
(b) 2
(c) does not exist
(d) None of these

Question. The function u = e^x sin x, v = e^x cos x satisfy the equation

Question.

and if lim_x→1 f (x) f (1) then the value of a + b is
(a) 0
(b) 2
(c) 4
(d) 8

Question. lim_x→0 sin 2x/x is equal to
(a) 2
(b) 0
(c) 1
(d) 3

Question.

(a) 1
(b) 2
(c) – 1
(d) – 2

Question. Derivative of the function f (x) = 7x^–3 is
(a) 21x^–4
(b) –21x^–4
(c) 21x⁴
(d) –21x⁴

Question. What is the derivative of 

Question. Evaluate lim_x→0 Sin² 2x/x² .
(a) 4
(b) – 4
(c) sin x
(d) cos x

Question. 

(a) 1/2
(b) 0
(c) 1
(d) Not defined

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

Question. If x³ + y³ = 3xy, then value of dy/dx is
(a) x−y²/x² − y
(b) x² − y/x−y²
(c) x² − y²/x−y
(d) x−y/x² − y²

Question.

(a) 1
(b) 0
(c) ∞
(d) None of these

Question. If lim_x→a[f (x)/g(x)] exists, then which one of the following correct ?
(a) Both lim_x→a f(x) and lim_x→a g(x) must exist
(b) lim_x→af (x) need not exist but lim_x→a g(x) must exist
(c) Both lim_x→a f (x) and lim_x→a g(x) need not exist
(d) lim_x→a f (x) must exist but lim_x→a g(x) need not exist

Question. Value of lim_x→0 sin 4x/sin 2x is
(a) 1
(b) 2
(c) 4
(d) None of these

Question. 

(a) ∞
(b) 1/8
(c) 0
(d) 1/32

Question. Evaluate: 

(a) 3
(b) – 3
(c) 1
(d) – 1

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 F
(a) 2 2 1 3 5 4
(b) 2 2 3 1 4 5
(c) 2 2 1 4 3 5
(d) 2 2 1 3 4 5

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

Question. The value of lim_x→0 x³ cot x / 1− cos x is
(a) 1
(b) –2
(c) 2
(d) 0

Question. If sin y = x sin (a + y), then value of dy/dx is
(a) sin(a+y)/sin a
(b) sin² (a+y)/sina
(c) sin² (a+y)
(d) cos² (a+y)/sin a

Question. What is the value of lim _x→0x sin 5x/sin²4x ?
(a) 0
(b) 5/4 
(c) 5/16 
(d) 25/4

Question.

(a) z/2^{11/ 3} 
(b) 1/2^{23/ 3}z
(c) 2^21/3 z
(d) None of these

Question.

(a) 1/2
(b) −1/2
(c) 1
(d) – 2

Question. Consider the function 

Then, left hand limit and right hand limit of f (x) at x = 0, are respectively
(a) 1, 2
(b) 2, 1
(c) 1,1
(d) 2, 2

Question. 

(a) −1/8
(b) 1/8
(c) 1/48
(d) −1/48

STATEMENT TYPE QUESTIONS

Question. Consider the function h (x) = x²−4/x−2 ,x≠2 Then,
I. h (2) is not defined.
II. lim_x→2h(x) = 4.
Which of the following is/are true?
(a) Both I and II are true
(b) Only I is true
(c) Only II is true
(d) Both I and II are false

Question. Which of the following is/are true?
I. The derivative of y = 2x−3/4 is 2.
II. The derivative of y = (5x³ + 3x – 1) (x – 1) is 20x³ + 15x² + 6x – 4
(a) Both I and II are true
(b) Only I is true
(c) Only II is true
(d) Both I and II are false

Question. Which of the following is/are true?

(a) Both I and II are true
(b) Only I is true
(c) Only II is true
(d) Both I and II are false

Question. Which of the following is/are true?
I. The derivative of f(x) = 1 + x + x² + … + x⁵⁰ at x = 1 is 1250.
II. The derivative of f (x) = x+1/x is 1/x² .
(a) Both I and II are true
(b) Only I is true
(c) Only II is true
(d) Both I and II are false

Question. Which of the following is/are true?
I. The derivative of – x is –1.
II. The derivative of (–x)^–1 is 1/x²
(a) Both I and II are true
(b) Only I is true
(c) Only II is true
(d) Both I and II are false

Question. Which of the following is/are true?

(a) Both I and II are true
(b) Only I is true
(c) Only II is true
(d) Both I and II are false

Question. Which of the following is/are true?
I. The derivative of f (x) = sin 2x is 2(cos² x – sin² x).
II. The derivative of g (x) = cot x is – cosec² x.
(a) Both I and II are true
(b) Only I is true
(c) Only II is true
(d) Both I and II are false