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

Mathematics - II (3110015) MCQs

MCQs of Series Solutions of ODEs and Special Functions

Showing 21 to 30 out of 40 Questions

21.

J_{(\frac{3}{2})} (x) =

......

(a)	$\sqrt{\frac{2}{πx}} \sin (x)$
(b)	$\sqrt{\frac{2}{πx}} (\frac{\sin (x)}{x} - \cos (x))$
(c)	$- \sqrt{\frac{2}{πx}} (\frac{\cos (x)}{x} + \sin (x))$
(d)	$\sqrt{\frac{2}{πx}} \cos (x)$

22.

The power series is that series which include……… powers.

(a)	Negative
(b)	Fractional
(c)	Zero 'or' Positive
(d)	None of these

23.

The D.E.

y^{''} + P (x) y^{'} + Q (x) y = 0

in which if both terms

P (x)

and

Q (x)

are analytic at

x = x_{0}

then that point is called ....... point.

(a)	Ordinary
(b)	Irregular Singular
(c)	Regular Singular
(d)	Singular

24.

For the D.E.

x^{2} y^{''} + x y^{'} + y = 0

, point

x = 1

is called ..... point.

(a)	Ordinary
(b)	Irregular Singular
(c)	Regular Singular
(d)	Singular

25.

The D.E.

y^{''} + P (x) y^{'} + Q (x) y = 0

in which if both terms

(x - x_{0}) P (x) & (x - x_{0})^{2} Q (x)

are analytic at

x = x_{0}

, where

x = x_{0}

is a singular point, then

x_{0}

is called ........ point.

(a)	Ordinary
(b)	Irregular Singular
(c)	Regular Singular
(d)	Singular

26.

For the D.E.

y^{''} + P (x) y^{'} + Q (x) y = 0

if only one out of

(x - x_{0}) P (x) & (x - x_{0})^{2} Q (x)

are analytic at

x = x_{0}

then that point is called ........ point, where

x = x_{0}

is a singular point.

(a)	Irregular Singular
(b)	Ordinary
(c)	Regular Singular
(d)	Singular

27.

For the D.E.

x^{2} y^{''} - x y^{'} - 3 y = 0

, the singular point is ........

(a)	$x = 0$
(b)	$x = 1$
(c)	$x \neq 0$
(d)	None

28.

For the D.E.

(1 - x^{2}) y^{''} - 6 x y^{'} - 4 y = 0

, point

x = 0

is called ....... point.

(a)	Ordinary
(b)	Irregular Singular
(c)	Regular Singular
(d)	Singular

29.

For the D.E.

y^{''} + e^{x} y^{'} + \sin (x^{2}) y = 0, \forall x \in ℝ

is called .........

(a)	Irregular Singular
(b)	Singular
(c)	Regular Singular
(d)	Ordinary

30.

For the D.E.

(x^{2} + 4) y^{''} + 2 x y^{'} - 12 y = 0

, singular points are .......

(a)	$x = \pm 2$
(b)	$x = 0, 2$
(c)	$x = \pm 2 i$
(d)	None

Showing 21 to 30 out of 40 Questions