The area between y² = 4x and its latus rectum is

(a)

\(\frac{2}{3}\)

(b)

\(\frac{4}{3}\)

(c)

\(\frac{8}{3}\)

(d)

\(\frac{5}{3}\)

The value of \(\int _{ 0 }^{ \pi }{ \frac { dx }{ 1+{ 5 }^{ cos\ x } } } \) is

(a)

\(\frac{\pi}{2}\)

(b)

\(\pi\)

(c)

\(\frac{3\pi}{2}\)

(d)

\(2\pi\)

The volume of solid of revolution of the region bounded by y² = x(a − x) about x-axis is

(a)

\(\pi a^3\)

(b)

\(\frac { \pi { a }^{ 3 } }{ 4 } \)

(c)

\(\frac { \pi { a }^{ 3 } }{ 5 } \)

(d)

\(\frac { \pi { a }^{ 3 } }{ 6 } \)

The value of \(\int _{ -1 }^{ 2 }{ |x|dx } \) is

(a)

\(\frac{1}{2}\)

(b)

\(\frac{3}{2}\)

(c)

\(\frac{5}{2}\)

(d)

\(\frac{7}{2}\)

The value of \(\int _{ -\frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ { sin }^{ 2 }x\ cos \ x \ dx } \) is

(a)

\(\frac{3}{2}\)

(b)

\(\frac{1}{2}\)

(c)

0

(d)

\(\frac{2}{3}\)

The value of \(\int _{ \frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ \sqrt { \frac { 1-cos2x }{ 2x } } } \) dx is __________

(a)

\(\frac { 1 }{ 2 } \)

(b)

2

(c)

0

(d)

1

If \(\int _{ 0 }^{ 2a }{ f(x) } dx=2\int _{ 0 }^{ a }{ f(x) } \) then __________

(a)

f(2a -x) = - f(x)

(b)

f(2a - x) = f(x)

(c)

f(x) is odd

(d)

f(x) is even

The area enclosed by the curve y = \(\frac { { x }^{ 2 } }{ 2 } \) , the x - axis and the lines x = 1, x = 3 is __________

(a)

4

(b)

8\(\frac23\)

(c)

13

(d)

4\(\frac{1}{3}\)

The value of \(\int _{ 0 }^{ \frac { \pi }{ 3 } } { tan } x \ dx\) __________

(a)

-log 2

(b)

log 2

(c)

-log 3

(d)

log 3

The volume when  \(y=\sqrt { 3+{ x }^{ 2 } } \) from x = 0 to x = 4 is rotated about x-axis is .................

(a)

\(100\pi \)

(b)

\(\frac { 100\pi }{ 9 } \)

(c)

\(\frac { 100\pi }{ 3 } \)

(d)

\(\frac { 100 }{ 3 } \)