MCQs of Differential Equations

Differential Equations MCQs

MCQs of Differential Equations

Showing 111 to 120 out of 145 Questions

111.

If the product of the slope of tangent to curve at (x, y) and its y - co-ordinate is equal to the x - co-ordinate of the point, then it represent _____.

(a)	circle
(b)	parabola
(c)	ellipse
(d)	rectangular parabola

112.

The length of sub-normal of hyperbola x² - y² = 8 at point (3, 1) is _____.

(a)	3
(b)	$\frac{1}{3}$
(c)	8
(d)	$\frac{1}{8}$

113.

The particular solution of differential equation

\frac{d y}{d x} = - 4 x y^{2}, y (0) = 1

is _____ .

(a)	y = (2x² + 1)^-1
(b)	$x^{2} = \frac{1}{y^{2}}$
(c)	y = x² + logx
(d)	$4 e^{x} + \frac{1}{y^{2}} = 8$

114.

Integrating Factor of differential equation

\frac{d y}{d x} = y \tan x + e^{x}

is _____.

(a)	sinx
(b)	secx
(c)	cosx
(d)	cotx

115.

The degree of the differential equation

{(y_{2})}^{2} - \sqrt{y_{1}} = y^{3}

is _____ .

(a)	$\frac{1}{2}$
(b)	2
(c)	3
(d)	4

116.

The integrating factor of the differential equation

(1 + x) \frac{d y}{d x} - x y = 1 - x

is _____ .

(a)	xe^x
(b)	1 + x
(c)	log (1 + x)
(d)	e^-x(1+ x)

117.

If the differential equation

\frac{d y}{d x} = \frac{a x + b}{c y + d}

represents a parabola, then a and c are _____.

(a)	a = 1, c = -2
(b)	a = 0, c = 0
(c)	a = 1, c = 1
(d)	a = 0, c ≠ 0

118.

The integrating factor for the differential equation

\cos x \frac{d y}{d x} = y \sin x + e^{x} \cos x

is _____.

(a)	e^-cosx
(b)	cos x
(c)	e^cosx
(d)	sec x

119.

The particular solution of the differential equation

\log {}_{e}{(\frac{d y}{d x})} = 3 x + 4 y, y (0) = 0

is _____.

(a)	4e^3x + 3e^-4y = 7
(b)	e^3x + 3e^-4y = 4
(c)	4e^3x - e^-4y = 3
(d)	3e^3x + 4e^4y = 7

120.

\frac{d I}{d y} = 3^{\cos y} \cdot \sin y

, then I = _____.

(a)	$- \frac{3^{\cos y}}{\log 3}$
(b)	$3^{\cos y} + c$
(c)	siny + c
(d)	None of the above

Showing 111 to 120 out of 145 Questions