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

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 

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 

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

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 

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 

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

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

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 

Question: If 

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 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Question. lim_x→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

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

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

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

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

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

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

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

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

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

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

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

We hope the above MCQ Questions Class 11 Mathematics Limits and Derivatives with answers based on the latest syllabus and examination guidelines issued by CBSE, NCERT and KVS are really useful for you. Limits and Derivatives is an important chapter in Class 11 as it provides very strong understanding about this topic. Students should go through the answers provided for the MCQs after they have themselves solved the questions. All MCQs have been provided with four options for the students to solve. These questions are really useful for benefit of class 11 students. Please go through these and let us know if you have any feedback in the comments section.