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Question - 1

The value of \(\overset { \pi \over 2 }{ \underset { 0 }{ \int } } { \frac { { cos }^{ 5/3 } }{ { cos }^{ 5/3 }x+{ sin }^{ 5/3 }x } } dx\) is

  • A \(\pi /2\)
  • B \(\pi /4\)
  • C \(0\)
  • D \(\pi \)

Question - 2

The value of  \(\overset { \pi\over 2 }{ \underset { 0 }{ \int } } \ { \frac { sinx-cosx }{ 1+sinxcosx } } dx\) is.

  • A \(\pi /2\)
  • B \(0\)
  • C \(\pi /4\)
  • D \(\pi \)

Question - 3

The value  \(\overset { 1 }{ \underset { 0 }{ \int } }{ x\left( 1-x \right) ^{ 4 } } dx\) is.

  • A 1/12
  • B 1/30
  • C 1/24
  • D 1/20

Question - 4

The value of  \(\overset { \pi/2 }{ \underset { -{\pi/2} }{ \int } }{ \left( \frac { sinx }{ 2+cosx } \right) } dx\) is.

  • A \(0\)
  • B \(2\)
  • C \(\log { 2 } \)
  • D \(\log { 4 } \)

Question - 5

The value of  \(\overset { \pi }{ \underset { 0 }{ \int } }{ \sin ^{ 4 }{ xdx } } \) is

  • A \(3\pi /16\)
  • B \(3/16\)
  • C \(0\)
  • D \(3\pi /8\)

Question - 6

The value of  \(\int _{ 0 }^{ \pi /4 }{ \cos { ^{ 3 }2xdx } } \) is

  • A 2/3
  • B 1/3
  • C 0
  • D \(2\pi /3\)

Question - 7

The value of  \(\overset { \pi }{ \underset { 0 }{ \int } }{ \sin ^{ 2 }{ x\cos ^{ 3 }{ xdx } } } \) is

  • A \(\pi \)
  • B \(\pi /2\)
  • C \(\pi /4\)
  • D \(0\)

Question - 8

The area bounded by the line y = x, the x axis, the ordinates x = 1 , x = 2 is.

  • A 3 / 2
  • B 5 / 2
  • C 1 / 2
  • D 7/2

Question - 9

The area of the region bounded by the graph of \(y = sin x\) and \(y = cos x\) between \(x = 0\) and  \(x = \pi /4\)   is. 

  • A \(\sqrt { 2 } +1\)
  • B \(\sqrt { 2 } -1\)
  • C \(2\sqrt { 2 } +1\)
  • D \(2\sqrt { 2 } +2\)

Question - 10

The area between the ellipse  \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1\) and its auxillary circle is

  • A \(\pi b(a-b)\)
  • B \(2\pi a(a-b)\)
  • C \(\pi a(a-b)\)
  • D \(2\pi b(a-b)\)