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This mock test of Partial Differential Equation MCQ - 1 for IIT JAM helps you for every IIT JAM entrance exam.
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QUESTION: 1

The order of equation p tan y + q tan x = sec^{2}z is

Solution:

QUESTION: 2

Equation is of the order

Solution:

QUESTION: 3

Which of the following is one of the criterions for linearity of an equation?

Solution:

The two criterions for linearity of an equation are:

- The dependent variable y and its derivatives are of first degree.
- Each coefficient depends only on the independent variable.

QUESTION: 4

Solution:

QUESTION: 5

For a partial differential equation, in a function φ (x, y) and two variables x, y, what is the form obtained after separation of variables is applied?

Solution:

The method of separation of variables relies upon the assumption that a function of the form,

Φ (x, y) = X(x)Y(y)

will be a solution to a linear homogeneous partial differential equation in x and y. This is called a product solution and provided the boundary conditions are also linear and homogeneous this will also satisfy the boundary conditions.

QUESTION: 6

The equation P_{p} + Q_{q} + R is known as

Solution:

QUESTION: 7

The general solution of (y — z)p + (z — x)q = x — y is

Solution:

QUESTION: 8

The integral surface to the first order p. d. e 2 y (z — 3) through the curve x^{2} + y^{2} = 2x, z = 0 is

Solution:

QUESTION: 9

Complete integral for the partial differential equation z = px + gy — sin(pq) is

Solution:

QUESTION: 10

The general integral of the partial differential equation (y + z x) z_{x} — (x + yz)Z_{y} = x^{2} — y^{2} is

Solution:

QUESTION: 11

The complete integral of q(p — cosx) = cosy

Solution:

QUESTION: 12

Consider the following statement about the following p. d. e. p + q — pq = 0

(i) it has no singular solutions

(iv) It is a first order non — linear p. d. e. Then choose the

correct code.

Solution:

QUESTION: 13

Integral surface of (2x y — l)p + (z — 2x^{2})q = 2(x — yz) passing through the line x_{0} (s) = 1 y_{0}(s) = 0 z_{0}(s) = s

Solution:

QUESTION: 14

Integral surface of PDE x^{2}p + y^{2}q = —z^{2} which passes through hyperbola xy = x + y, z = 1 is given by

Solution:

QUESTION: 15

Consider 4xyz = pq + 2px^{2}y + 2qxy^{2}

(i) It can be reduced to Claerut's form by some suitable transformation.

(ii) z = ax + by + ab is complete integral

(iii) z = —x^{2}y^{2} is singular solution choose correct code.

Solution:

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