NDA MATHS QUESTION BANK

38. What is ∫

(a)^

(^)

• C (b)


• C (c)


• C^
  (d)^
  (^)


• C^

39. What is ∫^

(^) ( )
( )^ dx equal to?^
(a) (b) cos ( )^ + C (c) tan
( ) + C
(d) x cosec ( ) + C
where C is a constant of integration.

40. What is ∫ sin x dx equal to?
    (a) (sin x – cos x) + C (b) (sin x – x
    cos x) + C (c) (x sin x + cos x) + C (d)
    (sin x + x cos x) – C
    where C is a constant of integration.


41. What is ∫^

(^)
dx equal to?^
(a)^
(^) (b)
(^) (c)^
(d)^
(^)

42. If ∫
    ,
    what are the values of m and n
    respectively?
    (a)^ and - (b) 3 and -9 (c) 3 and 9

(d) 3 and 3

43. What is ∫ dx equal to?

(a) x – log x + C (b) x – log (tan x) + C
(c) x – log (1+ ) + C (d) log (1+ ) + C
where C is a constant of integration.

44. What is ∫^ dx equal to?

(a) a sec x + b tan x + C (b) a tan x + b
sec x + C (c) a cosec x + b cot x + C (d)
a cosec x + b cot x + C

45. What is ∫( ) dx equal to?

(a) ( ) (b) ( ) (c)

( )^ (d)
( )^

46. A function f is such that f ’ (x)= 6- 4
    sin 2x and f(0)= 3. What is f(x) equal
    to?
    (a) 6x + 2 cos2x (b) 6x – 2 cos2x (c) 6x

• 2 cos2x + 1 (d) 6x + 2 cos2x + 1

47. What is ∫ equal to?
    (a)^

(^)
(b)
c)^
(^)
(d)

48. What is ∫ equal to?
    (a) tan Ѳ + C (b) cot Ѳ + C

(c)^ tan Ѳ + C (d)^ cot Ѳ + C

49. What is
    ∫^ (^ )^
    (a) cos x log tan x + log tan (x/2) + C
    (b) – cos x log tan x + log tan (x/2) + C
    (c) cos x log tan x + log cot (x/2) + C
    (d) - cos x log tan x + log cot (x/2) + C


50. What is ∫ ( ) is equal to?
    (a) x log (x+1) - x + C (b) (x + 1) log (x+

1. – x + C (c) + C (d)^ ( )

51. What is the value of ∫( )( )?
    (a) ,*^

(^) ( )+ ( )+ -
( )^
(b) ,^
(^) ( )+ ( )+ -
( )^
(c) ,^
(^) ( )+ ( )+ -
( )^
(d) ,^
(^) ( )+ * ( )+ -
( )^

52. What is the value of ∫(√ )
    dx?
    (a) In (√ ) + C

(b) 2 In ( (^) √ ) + C
(c) 2 In ( (^) √ ) + C