# MCQs for Mathematics Class 11 with Answers Chapter 13 Limits and Derivatives

Students of class 11 Mathematics should refer to MCQ Questions Class 11 Mathematics Limits and Derivatives with answers provided here which is an important chapter in Class 11 Mathematics NCERT textbook. These MCQ for Class 11 Mathematics with Answers have been prepared based on the latest CBSE and NCERT syllabus and examination guidelines for Class 11 Mathematics. The following MCQs can help you to practice and get better marks in the upcoming class 11 Mathematics examination

## Chapter 13 Limits and Derivatives MCQ with Answers Class 11 Mathematics

MCQ Questions Class 11 Mathematics Limits and Derivatives with answers provided below have been prepared by expert teachers of grade 11. These objective questions with solutions are expected to come in the upcoming Standard 11 examinations. Learn the below provided MCQ questions to get better marks in examinations.

Question. If f x then right hand limit of f (x ) at x = 1is equal to
(a) 1
(b) 2
(c) 3
(d) 4

A

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

B

Question: Find the differentiation of cos x2+1)  by using first principle.
(a) 2x sin (x2+1)
(b) -2x sin (x2+1)
(c) -2x sin (x2-1)
(d) None of these

B

Question: Find the differentiation of x2/3 by using first principle.
(a) 2/3x-1/3
(b) -2/3x-1/3
(c) 2/3x1/3
(d) None of these

A

Question: Find the differentiation of x cos x by using first principle.
(a) -x sin x+ cos x
(b) x sin x + cosx
(c) -x cos x – cos x
(d) None of these

A

Question: If f(x)= 1+x+x2/2 +…+ x100/100′ then f’ (1)
is equal to
(a) 1/100
(b) 100
(c) does not exist
(d) 0

B

Question: If f (x)= x-4/2√x, , then f ‘(1 ) is
(a) 5/4
(b) 4/5
(c) 1
(d) 0

A

Question: If f(x) = x-4/2√x, then f'(1) is
(a) 1
(b) 1/2
(c) 1/2
(d) 0

D

Question: If y = sin x+ cos x/sin x – cos x , then dy/dx  at x=0 is
(a) –2
(b) 0
(c) 1/2
(d) does not exist

A

Question: If

A

Question: If y = sin (x+9)/cos x , then dy/dx at x=0  is
(a) cos 9
(b) sin 9
(c) 0
(d) 1

A

Question. limx→0 tanx-sinx/sin3x is equal to
(a) 1/2
(b) 0
(c) 1
(d) Not defined

A

Question. The value of lim x→1/2 [4x2 – 1/2x-1] is equal to
(a) 1
(b) 2
(c) 3
(d) 4

B

Question. limx→0 tan2x -x / sinx is equal to
(a) 2
(b) 1/2
(c) −1/2
(d) 1/4

B

Question. If f (x) , then the left hand limit of f (x ) at x = 2 is equal to
(a) 6
(b) 7
(c) 9
(d) 8

B

Question. If f (x) then left hand limit of f (x ) at x = 3 is equal to
(a) 1
(b) −1
(c) 2
(d) 0

B

Question. The value of lim x→0 is equal to
(a) 2
(b) √2
(c) 2√2
(d) √3

B

Question. The value of lim x→1 x – 4/3-√(13-x) is equal to
(a) 3+2√3
(b) 3−2√3
(c) 2+√3
(d) 2−√3

A

Question. lim x→1 (√x-1)(2x-3) /2x2+x-3 is equal to
(a) 1/10
(b) -1/10
(c) 1
(d) None of these

B

Question. The value of lim x→1 (2/1-x2 + 1/x-1) is equal to
(a) 1/2
(b) 1/3
(c) 1/4
(d) 1

A

Question. The value of lim x→1/2 (4x2 – 1)/(2x-1) is equal to
(a) 1
(b) 2
(c) 3
(d) 4

B

Question. The value of lim (4×3 – 2×2-x+1 ) equal to
(a) 40
(b) 20
(c) 38
(d) 88

D

Question. The value of lim x→0 x/√(1+x+1) is equal to
(a) 0
(b) 1
(c) 2
(d) 3

A

Question. lim x→0 3x-2x/x is equal to
(a) log3/2
(b) log2/3
(c) log1/2
(d) log1/3

A

Question. If lim x→2 (xn – 2n)/(x-2) 80, then n is equal to
(a) 1
(b) 3
(c) 5
(d) 7

C

Question. lim x→0 cosecx-cotx /x is equal to
(a) −1/2
(b) 1
(c) 1/2
(d) 1

C

Question. The value of lim x→0 [√1+x-1 /x] is equal to
(a) 1/3
(b) 1/2
(c) 1/4
(d) 1/5

B

Question. lim x→0 loge (1+2x) is equal to
(a) 1
(b) 2
(c) 3
(d) 4

B

Question. The value of lim x→0 sin 7x/tan 5x is equal to
(a) 5/7
(b) 7/5
(c) 2/7
(d) 7/2

B

Question. The value of lim x→0 Sin4x/sin2x is equal to
(a) 1
(b) 2
(c) 3
(d) 4

B

Question. lim x→0 1-cos4x /x is equal to
(a) 0
(b) 1
(c) 2
(d) 3

A

Question. The value of lim x→2 (x3-8)/(x-2) is equal to
(a) 10
(b) 11
(c) 12
(d) 13

C

Question. limx→0 sinx /x(1+cosx) is equal to
(a) 0
(b) 1/2
(c) 1
(d) −1

B

Question. limx→0 sin(2+x) – sin(2-x)/x is equal to p cos q, where p and q are respectively
(a) 1 , 2
(b) 2, 1
(c) 1, 1
(d) 2, 2

D

Question. lim x→0 ex-e-x-2 /x2 is equal to
(a) 1
(b) 2
(c) 3
(d) 4

A

Question. The value of   lim is equal to
(a) 1
(b) 3
(c) 4
(d) 2

D

Question. limx→π/4
(a) 3
(b) 1
(c) 0
(d) 2

D

Question. lim x→0 x2 cosx/1 – cosx is equal to
(a) 2
(b) 3/2
(c) −3/2
(d) 1

A

Question. The value of lim x→1 [x15 – 1/x10 – 1] is equal to
(a) 3/2
(b) 2/3
(c) 4/3
(d) 3/4

A

Question. lim x→0 e3x-1/x is equal to
(a) 1
(b) 2
(c) 3
(d) 4

C

Question. lim x→3 ex-e3/x-3 is equal to
(a) e
(b) e2
(c) e3
(d) e4

C

Question. lim x→0 esinx -1 /x is equal to
(a) 1
(b) 2
(c) 3
(d) 4

A

Question. lim x→0 tan x0/x0 is equal to
(a) 1
(b) 3
(c) 2
(d) −1

A

Question. lim x→0 2x-1/√1+x-1 is equal to
(a) log2
(b) 2log2
(c) 3log2
(d) 4log2

B

Question. The value of lim x→0 (x+2)1/3 – 21/3 /x is equal to
(a) 1/3(2)3/2
(b) 1/3(2)2/3
(c) 1/(2)2/3
(d) 1/3/√3