MCQs of First order partial differential equations (Complex Variables and Partial Differential Equations - 3140610)

Complex Variables and Partial Differential Equations (3140610) MCQs

MCQs of First order partial differential equations

Showing 1 to 10 out of 15 Questions

The partial differential equation of $z = {(x - a)}^{2} + {(y - b)}^{2}$ is _____.

(a)	$4 z = p^{2} + q^{2}$
(b)	$z = p^{2} + q^{2}$
(c)	$4 z = p^{2} - q^{2}$
(d)	none of these

The partial differential equation of $f (x^{2} + y^{2}, z - xy) = 0$ is _____.

(a)	$x^{2} - y^{2} = qx - py$
(b)	$x^{2} + y^{2} = qx + py$
(c)	$x^{2} - = qx - py$
(d)	$y^{2} - = qx - py$

The general solution of P.D.E. $xp + yq = x - y$ is _____.

(a)	$f (x, x - y - z) = 0$
(b)	$f (\frac{x}{y}, x - y - z) = 0$
(c)	$f (\frac{x}{y}, x + y + z) = 0$
(d)	$f (\frac{x}{y}, x - z) = 0$

Eliminating arbitrary constants a and b from $z = (x + a) (y + b)$ , the partial differential equation formed is _____ .

(a)	$z = p + q$
(b)	$z = {pq}^{2}$
(c)	$z = pq$
(d)	none of these

Eliminating the arbitrary function from $z = f (x^{2} + y^{2})$ , then the partial differential equation formed is _____ .

(a)	$py = qx$
(b)	$px = qy$
(c)	$pq = xy$
(d)	$pq = 1$

The general solution of the equation $xp + yq = z$ , $p = \frac{\partial z}{\partial x} & q = \frac{\partial z}{\partial y}$ , is _____ .

(a)	$f (\frac{x}{y}, z) = 0$
(b)	$f (x - y, x + y) = 0$
(c)	$f (xy, x + y) = 0$
(d)	$f (\frac{x}{y}, \frac{y}{z}) = 0$

The general solution of the equation $p \tan x + q \tan y = \tan z$ , where $p = \frac{\partial z}{\partial x} & q = \frac{\partial z}{\partial y}$ , is _____ .

(a)	$f (\|\frac{\sin x}{\sin y}\|, \|\frac{\sin y}{\sin z}\|) = 0$
(b)	$f (\|\frac{\cos x}{\cos y}\|, \|\frac{\cos y}{\cos z}\|) = 0$
(c)	$f (\sin x \sin y, \sin y \sin z) = 0$
(d)	none of these

The partial differential equation $pq = 4 z$ is _____ .

(a)	linear
(b)	non-linear
(c)	higher order
(d)	non of these

Which of the following is a Lagrange's partial differential equation?

(a)	$pq = 4 z$
(b)	$p^{2} + q = 1$
(c)	${px}^{2} + {qy}^{2} = z^{2}$
(d)	none of these

10.

The partial differential equation $z = px + qy + f (p, q)$ is known as _____ .

(a)	Lagrange's partial differential equation
(b)	Clairaut's partialdifferential equation
(c)	higher order partial differential equation
(d)	none of these

Showing 1 to 10 out of 15 Questions