MCQs of Series Solutions of ODEs and Special Functions (Mathematics - II - 3110015) | GTU MCQ

Mathematics - II (3110015) MCQs

MCQs of Series Solutions of ODEs and Special Functions

Showing 1 to 10 out of 40 Questions

1.

The gamma function of

n (n > 0)

is denoted by

Γ (n)

and defined as ......

(a)	$\int_{- \infty}^{\infty} e^{- x} x^{n - 1} d x$
(b)	$\int_{0}^{1} e^{- x} x^{n - 1} d x$
(c)	$\int_{0}^{\infty} e^{- x} x^{n - 1} d x$
(d)	none of these

2.

Γ (n + 1) = n!

, where

n

is ......

(a)	a positive integer
(b)	a negative integer
(c)	real number
(d)	none of these

3.

Γ (\frac{1}{2}) =

.....

(a)	$π$
(b)	$\sqrt{π}$
(c)	$Γ (π)$
(d)	1

4.

Γ (\frac{1}{4}) Γ (\frac{3}{4}) =

.....

(a)	$π$
(b)	$\sqrt{π}$
(c)	$\sqrt{2} π$
(d)	$\frac{π}{2}$

5.

Γ (n) Γ (n + \frac{1}{2}) =

.....

(a)	$\frac{\sqrt{π} Γ (2 n)}{2^{2 n - 1}}$
(b)	$\frac{\sqrt{π}}{2^{2 n - 1}}$
(c)	$\frac{Γ (2 n)}{2^{2 n - 1}}$
(d)	$\frac{\sqrt{π} Γ (2 n)}{2^{2 n}}$

6.

\int_{0}^{1} x^{m} (1 - x)^{n} d x =

........

(a)	$B (m, n)$
(b)	$B (m + 1, n)$
(c)	$B (m + 1, n + 1)$
(d)	$B (m, n - 1)$

7.

The relation between Beta function and Gamma function is

(a)	$B (m, n) = \frac{Γ (m) Γ (n)}{Γ (m + n)}$
(b)	$B (m, n) = \frac{Γ (n)}{Γ (m + n)}$
(c)	$B (m, n) = \frac{Γ (m + n)}{Γ (m) Γ (n)}$
(d)	$B (m, n) = \frac{Γ (m) Γ (n)}{Γ (m - n)}$

8.

B (\frac{1}{2}, \frac{1}{2}) =

......

(a)	0
(b)	$π$
(c)	$\sqrt{π}$
(d)	$\frac{1}{\sqrt{π}}$

9.

For a non-negative real constant

n

, an equation of the form

(1 - x^{2}) y^{''} - 2 x y^{'} + n (n + 1) y = 0

is called ....

(a)	Legendre's equation
(b)	Legendre's polynomial
(c)	Bessel's equation
(d)	None of these

10.

The value of Legendre's polynomial

P_{2} (x)

is .....

(a)	0
(b)	$\frac{1}{2} (3 x^{2} - 1)$
(c)	1
(d)	$\frac{1}{2} (5 x^{3} - 3 x)$

Showing 1 to 10 out of 40 Questions