Complex Variables and Partial Differential Equations (3140610) MCQs

MCQs of First order partial differential equations

Showing 1 to 10 out of 15 Questions
1.

The partial differential equation of z=x-a2+y-b2 is _____.

(a)

4z=p2+q2

(b)

z=p2+q2

(c)

4z=p2-q2

(d)

none of these

Answer:

Option (a)

2.

The partial differential equation of fx2+y2, z-xy=0 is _____.

(a)

x2-y2=qx-py

(b)

x2+y2=qx+py

(c)

x2-=qx-py

(d)

y2-=qx-py

Answer:

Option (a)

3.

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

(a)

fx, x-y-z=0

(b)

fxy, x-y-z=0

(c)

fxy, x+y+z=0

(d)

fxy, x-z=0

Answer:

Option (b)

4.

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

(a)

z=p+q

(b)

z=pq2

(c)

z=pq

(d)

none of these

Answer:

Option (c)

5.

Eliminating the arbitrary function from z=fx2+y2 , then the partial differential equation formed is _____ .

(a)

py=qx

(b)

px=qy

(c)

pq=xy

(d)

pq=1

Answer:

Option (a)

6.

The general solution of the equation xp+yq=z , p=zx & q=zy , is _____ .

(a)

fxy, z=0

(b)

fx-y, x+y=0

(c)

fxy, x+y=0

(d)

fxy, yz=0

Answer:

Option (d)

7.

The general solution of the equation p tan x+q tan y= tan z , where p=zx & q=zy , is _____ .

(a)

f sin xsin y, sin ysin z =0

(b)

f cos xcos y, cos ycos z =0

(c)

fsin x sin y, sin y sin z=0

(d)

none of these

Answer:

Option (a)

8.

The partial differential equation pq=4z is _____ .

(a)

linear

(b)

non-linear

(c)

higher order

(d)

non of these

Answer:

Option (b)

9.

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

(a)

pq=4z

(b)

p2+q=1

(c)

px2+qy2=z2

(d)

none of these

Answer:

Option (c)

10.

The partial differential equation z=px+qy+fp, 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

Answer:

Option (b)

Showing 1 to 10 out of 15 Questions