# Limits and Derivatives MCQ Questions for Class 11 Math’s Chapter 13 with Answers

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

(ii) cot x

## Q2. 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) cos 9
(ii) sin 9
(iii) 0
(iv) 1

(i) cos 9

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

(iii) 2

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

(iii) -1/x²

(i) 1
(ii) 1/2
(iii) 1/√2
(iv) 0

(iv) 0

## Q7. 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) 0
(ii) 1
(iii) a
(iv) 1/a

(iii) a

## Q9. 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 )

## Q10. 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

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

(iii) a/b

## Q12. 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) 1/2
(ii) 1/3
(iii) 1/4
(iv) 1/9

(iv) 1/9

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

(iv) 18

## Q15. 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

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