NCERT Class 11 Chapter 13 Maths Limits and Derivatives MCQ

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1. lim_x→0 sinx / √(x + 1 - √(1- x) is

A. 2

B. 0

C. 1

D. –1

2. lim_x→1 (√x +1) (2x - 3) /2x³ + x -3 is

A. 1/10

B. 1/10

C. 1

D. None of these

3. lim_x→4 |x-4 | /x - 4 is equal to

A. 1

B. –1

C. does not exist

D. None of these

4. If y = √x + 1/√x , then dy/dx at x = 1 is

A. 1

B. 1/2

C. 1/√2

D. 0

5. lim_x→0 |Sinx | /x is

A. 1

B. –1

C. does not exist

D. None of these

6. If y =

A. -4x / (x2 - 1)2

B. -4x / (x2 - 1)

C. 1 - x2 / 4x

D. 4x / x2 - 1

7. lim_x→0 tan2x - x / 3x - Sinx

A. 2

B. 1/2

C. -1/2

D. 1/4

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

A. 3x sec² x 6 sec2 x 3 + 3 tan x

B. 3x sec² x 5 sec2 x 3 3 tan x

C. 3x sec² x + 5 sec2 x + 3 + 3 tan x

D. None of the above

9. The derivative of (ax² + cot x)( p + q cos x) is

A. ax² cot (q sin ) + ( p+ q cosx )(2ax cosec²x )

B. ax² cot (q sin ) + ( p+ q cosx )(2ax cosec²x )

C. ax² cot (q sin ) + ( p q cosx )(2ax cosec²x )

D. None of the above

10. The derivative of (x sinxcosx) 2 + 2 is

A. x² cos x + 2x sin x sin 2x

B. x² cos x + 2x sin x sin 2x

C. x² cos x + x sin x sin 2x

D. x² cos x + 2x sin x + sin 2x

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11. The derivative of sin³x cos³x xis

A. 3 /5 sin² 2x cos 2x

B. 3 /4 sin² 2x cos 2x

C. 3 /4 sin 2x cos² 2x

D. 3 /2 sin² 2x cos 2x

12. The derivative of x5 cos x /sinx is

CBSE Class11 Limits and Derivatives (12 Q)

A. (a)

B. (b)

C. (c)

D. (d)

13. Question. Find the differentiation of x^{2/3^{by using first principle.}}

A. 2/3 x^-1/3

B. -2/3 x^-1/3

C. 2/3 x ^1/3

D. None of these

14. 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

15. If f (x )= x-4 /2√x then f '(1) is

A. 5/4

B. 4/5

C. 1

D. 0

16. Find the differentiation of x cos x by using first principle.

A. x sin x + cos x

B. x sin x + cos x

C. x cos x cos x

D. None of these

17. If y = Sin (x+9) / Cos x , then dy/dx at x = 0 is

A. cos 9

B. sin 9

C. 0

D. 1

18. The value of the limit Lim_x→0 (cos x)^cot2 x is

A. 1

B. e

C. e^1/2

D. e^-1/2

19. The value of limit Lim_x→0 {sin (a + x) – sin (a – x)}/x is

A. 0

B. 1

C. 2 cos a

D. 2 sin a

20. Lim_x→-1 [1 + x + x² + ……….+ x¹⁰] is

A. 0

B. 1

C. -1

D. 2

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21. The value of Lim_x→01 (1/x) × sin^-1 {2x/(1 + x²) is

A. 0

B. 1

C. 2

D. -2

22. Lim_x→0 log(1 – x) is equals to

A. 0

B. 1

C. 1/2

D. None of these

23. Lim_x→0 {(a^x – b^x)/ x} is equal to

A. log a

B. log b

C. log (a/b)

D. log (a×b)

24. The value of lim_y→0 {(x + y) × sec (x + y) – x × sec x}/y is

A. x × tan x × sec x

B. x × tan x × sec x + x × sec x

C. tan x × sec x + sec x

D. x × tan x × sec x + sec x

25. Lim_y→∞ {(x + 6)/(x + 1)}^(x+4) equals

A. e

B. e³

C. e⁵

D. e⁶