Class 11 Mathematics Limits And Derivatives MCQs

Question. lim_x→0 sinx / √(x + 1 - √(1- x) is      
(a) 2
(b) 0
(c) 1
(d) –1

Answer :  C
 

Question. lim_x→1 (√x +1) (2x - 3) /2x³ + x -3 is      
(a) 1/10
(b) 1/10
(c) 1
(d) None of these

Answer :  B
 

Question. lim_x→4 |x-4 | /x - 4 is equal to     
(a) 1
(b) –1
(c) does not exist
(d) None of these

Answer :  C
 

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

(a) 1
(b) 1/2
(c) 1/√2
(d) 0

 Answer :  D
 

Question. lim_x→0 |Sinx | /x  is      
(a) 1
(b) –1
(c) does not exist
(d) None of these

Answer :  C
 

Question. If y =

(a) -4x / (x² - 1)2

(b) -4x / (x² - 1)
(c)  1 - x² / 4x
(d) 4x / x² - 1
 

Answer :  A
 

Question. lim_x→0 tan2x - x / 3x - Sinx      
(a) 2
(b) 1/2
(c) -1/2
(d) 1/4

Answer :  B
 

Question. 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

Answer :  C
 

Question. 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

Answer :  A
 

Question. The derivative of (x sinx cosx) 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

Answer :  B
 

Question. 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

Answer :  B
 

Question. The derivative of x⁵ cos x /sinx is

Answer :  B

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

Answer :  A
 

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

Answer :  B
 

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

(a) 5/4
(b) 4/5
(c) 1
(d) 0

Answer :  A
 

Question. 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

Answer :  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

Answer :  A