Free Printable Quiz on module-03

1.

$_{\int_0^{\infty}e^{-x}x^{\left(n-1\right)}dx}$

a)

$\Gamma\left(n-1\right)$

b)

$\Gamma\left(n\right)$

c)

$\Gamma\left(n+1\right)$

d)

not defined

2.

$\Gamma\left(-\frac{3}{2}\right)$

a)

$\frac{4\sqrt{\pi}}{3}$

b)

$-\frac{4\sqrt{\pi}}{3}$

c)

$-\frac{\sqrt{\pi}}{3}$

d)

$\frac{\sqrt{\pi}}{3}$

3.

$\Gamma\left(\frac{1}{6}\right)\Gamma\left(\frac{5}{6}\right)$

a)

$4\pi$

b)

$-4\pi$

c)

$2\pi$

d)

2

4.

$\int_0^{\infty}e^{-x}x^4dx$

a)

24

b)

0

c)

$\infty$

d)

120

5.

$\int_0^{\infty}e^{-x^2}x^3dx$

a)

$\frac{1}{2}$

b)

1

c)

2

d)

$\Gamma\left(\frac{5}{2}\right)$

6.

$\int_0^1x^4\left[\log\left(\frac{1}{x}\right)\right]^3dx$

a)

$\frac{3}{625}$

b)

$\frac{3}{325}$

c)

$\frac{6}{325}$

d)

$\frac{6}{625}$

7.

B(4,3) is?

a)

1/35

b)

1/60

c)

12/7

d)

-1/35

8.

$If\ B\left(n,2\right)=\frac{1}{2}\ and\ n\ is\ a\ positive\ integer,\ find\ the\ value\ of\ n.$

a)

1

b)

-2

c)

1/2

d)

does not exist

9.

$\int_0^2x\left(8-x^3\right)^{\frac{1}{3}}dx$

a)

$\frac{4}{3}B\left(\frac{2}{3},\frac{4}{3}\right)$

b)

$\frac{8}{3}B\left(\frac{4}{3},\frac{4}{3}\right)$

c)

$\frac{8}{3}B\left(\frac{2}{3},\frac{4}{3}\right)$

d)

$\frac{4}{3}B\left(\frac{4}{3},\frac{4}{3}\right)$

10.

$\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\cos^3\theta\left(1+\sin\theta\right)^{ }d\theta$

a)

11/6

b)

11/3

c)

8/3

d)

4/3

11.

$\int_0^{\frac{\pi}{2}}\sqrt{\cot\theta}d\theta$

a)

$\frac{\pi\sqrt{2}}{2}$

b)

$\frac{\pi}{2}$

c)

$\frac{\pi\sqrt{2}}{4}$

d)

$\frac{\pi}{4}$

12.

$B\left(\frac{3}{4},\frac{9}{4}\right)$

a)

$\frac{\pi}{16\sqrt{2}}$

b)

$\frac{5\pi}{16\sqrt{2}}$

c)

$\frac{5\pi}{32}$

d)

$\frac{\pi}{32}$

13.

$\int_0^{\infty}\left(\frac{x^2}{\left(1+x\right)^5}\right)dx$

a)

B(2,3)

b)

B(2,5)

c)

B(3,5)

d)

B(3,2)

14.

$\int_0^{\frac{\pi}{2}}\sin^7\theta\ d\theta$

a)

$\frac{1}{2}B\left(\frac{9}{2},\frac{1}{2}\right)$

b)

$B\left(\frac{9}{2},\frac{1}{2}\right)$

c)

$\frac{1}{2}B\left(4,\frac{1}{2}\right)$

d)

$B\left(4,\frac{1}{2}\right)$

15.

$\frac{1}{\sqrt{2\pi}}\int_0^{\infty}e^{\left(-\frac{x^2}{8}\right)}dx$

a)

$1$

b)

$\pi$

c)

$2$

d)

$2\pi$

Quiz on module-03

Total questions: 15

Worksheet time: 2mins

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