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 \(\int _{ 0 }^{ 1 }{ x{ (1-x) }^{ 99 }dx } \) is

(a)

\(\frac{1}{11000}\)

(b)

\(\frac{1}{10100}\)

(c)

\(\frac{1}{10010}\)

(d)

\(\frac{1}{10001}\)

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)

\(2\pi\)

If \(\frac{\Gamma(n+2)}{\Gamma(n)}=90\) then n is 

(a)

10

(b)

5

(c)

8

(d)

9

The value of \(\int _{ 0 }^{ \frac { \pi }{ 6 } }{ { cos }^{ 3 }3x\ dx }\ is\)

(a)

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

(b)

\(\frac{2}{9}\)

(c)

\(\frac{1}{9}\)

(d)

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