# 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

A

Question. limx→0 2sin23x/xis equal to :
(a) 12
(b) 18
(c) 0
(d) 6

B

Question.

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

D

Question. If y = axn +1 + bx – n , then value of x2 d2y/dxis
(a) n (n + 1) y
(b) n2 (n + 1) y
(c) 2n (n – 1) y
(d) None of these

A

Question.

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

C

Question. If limx→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

D

Question.

(a) 1/2
(b) −1/2
(c) 0
(d) ∞

A

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

B

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

C

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

D

Question.

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

C

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

A

Question.

(a) 1
(b) 2
(c) – 1
(d) – 2

B

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

B

Question. What is the derivative of

A

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

A

Question.

(a) 1/2
(b) 0
(c) 1
(d) Not defined

A

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

D

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

B

Question.

(a) 1
(b) 0
(c) ∞
(d) None of these

B

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

A

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

B

Question.

(a) ∞
(b) 1/8
(c) 0
(d) 1/32

D

Question. Evaluate:

(a) 3
(b) – 3
(c) 1
(d) – 1

B

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

D

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

B

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

C

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

B

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

C

Question.

(a) z/211/ 3
(b) 1/223/ 3z
(c) 221/3 z
(d) None of these

B

Question.

(a) 1/2
(b) −1/2
(c) 1
(d) – 2

B

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

A

Question.

(a) −1/8
(b) 1/8
(c) 1/48
(d) −1/48

D

STATEMENT TYPE QUESTIONS

Question. Consider the function h (x) = x2−4/x−2 ,x≠2 Then,
I. h (2) is not defined.
II. limx→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

A

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

B

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

A

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

D

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

A

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

B

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