33. If + = , then what is^ equal

to?

(a)^
(b)

( )

(c)

(d)

34. If f(x)= , then what is f ’
    (x)equal to?
    (a) 4 x sin ( ) cos ( ) (b) 2 sin ( )
    cos ( )
    (c) 4 sin ( ) x (d) 2x ( )


35. If f(x)= cos x, g(x)=log x and y=

(gof) (x), then what is the value of^ at

x= 0?
(a) 0 (b) 1 (c) – 1 (d) 2

36. If f(x)= log | |, x= 0, then what is f ’ x
    equal to?

(a) | | (b)^ (c)^ (d) None of these

37. If , then^ is equal to

which one of the following?

(a) ( (^ )) (b) ( )

(c) ( ) (d) ( ( ))

38. If x= sin t- t cos t and y= t sin t + cos
    t, then what is^ at point t=^?
    (a) 0 (b)^ (c) - (d) 1


39. If y= √ , what is

equal to?^

(a) √ (b)

√ (c)

(d) 0^

40. 
    

    What is the derivative of
    . √ ⁄ / at x= 1?
    (a) - (b)^ (c)^ (d) 1

    
    


41. 
    

    If x√ (^) √ =0, what is^
    equal to?
    (a) - (b) - (^) ( ) (c) ( ) (d) √√

    
    


42. 
    

    If f(x)= √ √ √ (^) √ ,
    then what is f ‘ (x) equal to?
    (a) ( ) (b) ( ) (c) ( ) (d)
    ( )^

    
    


43. 
    

    If f(x)= (x+1). ( ), then the
    value of f ‘ (0) is
    (a)^ (b)^ (c)^ (d)^

    
    

INTEGRATION

1. ∫ ( )^ dx equals?
   (a) log ( )+c (b)^ log ( )+c

(c) – log ( )+c (d) none of these

2. ∫ (1-cot x+ x) dx equals:
   (a) cot x+c (b) cosec x+c (c) -
   cot x+c
   (d) - cosec x+c
   3. ∫ ( ) dx is equal to:
   (a) x cos a – sin a. log (x-a) + c (b) x sin
   a + c
   (c) x sin a + sin a. log sin (x-a) + c (d) x
   cos a + sin a. log sin (x-a) + c