# Limits and Derivatives MCQ Questions for Class 11 Maths Chapter 13 with Answers

We have completed the NCERT/CBSE chapter-wise Multiple Choice Questions for Class 11 Mathematics book Chapter 13 Limits and Derivatives with Answers by expert subject teacher for latest syllabus and examination. You can Prepare effectively for the exam taking the help of the Class 11 Maths Objective Questions PDF free of cost from here. Students can take a free test of the Multiple Choice Questions of Limits and Derivatives. Each Questions has four options followed by the right answer. Download the Maths Quiz Questions with Answers for Class 11 free Pdf and prepare to exam and help students understand the concept very well.

## Q1. The value of Limx→a (a × sin x – x × sin a)/(ax² – xa²) is

(i) = (a × cos a + sin a)/a²
(ii) = (a × cos a – sin a)/a²
(iii) = (a × cos a + sin a)/a
(iv) = (a × cos a – sin a)/a

(ii) = (a × cos a – sin a)/a²

(i) 0
(ii) 1
(iii) 2
(iv) -2

(iii) 2

(i) 1
(ii) 1/2
(iii) 1/√2
(iv) 0

(iv) 0

(i) 0
(ii) 1
(iii) a
(iv) 1/a

(iii) a

## Q5. The value of limy→0 {(x + y) × sec (x + y) – x × sec x}/y is

(i) x × tan x × sec x
(ii) x × tan x × sec x + x × sec x
(iii) tan x × sec x + sec x
(iv) x × tan x × sec x + sec x

(iv) x × tan x × sec x + sec x

## Q6. The derivative of (3x + 5)(1 + tan x) is

(i) 3x sec² x 6 sec2 x 3 + 3 tan x
(ii) 3x sec² x 5 sec2 x 3 3 tan x
(iii) 3x sec² x + 5 sec2 x + 3 + 3 tan x
(iv) None of the above

(iii) 3x sec2 x + 5 sec2 x + 3 + 3 tan x

(i) 0
(ii) 1
(iii) -18
(iv) 18

(iv) 18

(i) 0
(ii) 1
(iii) 1/2
(iv) 3/2

(ii) 1

## Q9. The derivative of (x sinx cosx) 2 + 2 is

(i) x² cos x + 2x sin x sin 2x
(ii) x² cos x + 2x sin x sin 2x
(iii) x² cos x + x sin x sin 2x
(iv) x² cos x + 2x sin x + sin 2x

(ii) x² cos x + 2x sin x sin 2x

(i) 1/2
(ii) 1/3
(iii) 1/4
(iv) 1/9

(iv) 1/9

(i) 0
(ii) 1
(iii) a/b
(iv) b/a

(iii) a/b

## Q12. Find the differentiation of cos (x² + 1 ) by using first principle.

(i) 2x sin (x² + 1 )
(ii) 2x sin (x² + 1 )
(iii) -2x sin (x² – 1 )
(iv) None of these

(ii) 2x sin (x² + 1 )

## Q13. Differentiation of cos √x with respect to x is

(i) sin x /2√x
(ii) -sin x /2√x
(iii) sin √x /2√x
(iv) -sin √x /2√x

(iv) -sin √x /2√x

(i) 1/x
(ii) -1/x
(iii) -1/x²
(iv) 1/x²

(iii) -1/x²

(i) cos 9
(ii) sin 9
(iii) 0
(iv) 1

(i) cos 9

## Q16. Differentiation of log(sin x) is

(i) cosec x
(ii) cot x
(iii) sin x
(iv) cos x

(ii) cot x

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