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Partial Differential Equation MCQ - 1 - Mathematics MCQ


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15 Questions MCQ Test Topic-wise Tests & Solved Examples for Mathematics - Partial Differential Equation MCQ - 1

Partial Differential Equation MCQ - 1 for Mathematics 2024 is part of Topic-wise Tests & Solved Examples for Mathematics preparation. The Partial Differential Equation MCQ - 1 questions and answers have been prepared according to the Mathematics exam syllabus.The Partial Differential Equation MCQ - 1 MCQs are made for Mathematics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Partial Differential Equation MCQ - 1 below.
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Partial Differential Equation MCQ - 1 - Question 1

The order of equation p tan y + q tan x = sec2z is

Partial Differential Equation MCQ - 1 - Question 2

Equation  is of the order

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Partial Differential Equation MCQ - 1 - Question 3

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

Detailed Solution for Partial Differential Equation MCQ - 1 - Question 3

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.
Partial Differential Equation MCQ - 1 - Question 4

Partial Differential Equation MCQ - 1 - 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?

Detailed Solution for Partial Differential Equation MCQ - 1 - Question 5

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.

Partial Differential Equation MCQ - 1 - Question 6

The equation Pp + Qq + R is known as

Partial Differential Equation MCQ - 1 - Question 7

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

Partial Differential Equation MCQ - 1 - Question 8

The integral surface to the first order p. d. e 2 y (z — 3) through the curve x2 + y2 = 2x, z = 0 is

Detailed Solution for Partial Differential Equation MCQ - 1 - Question 8

 

Partial Differential Equation MCQ - 1 - Question 9

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

Partial Differential Equation MCQ - 1 - Question 10

The general integral of the partial differential equation (y + z x) zx — (x + yz)Zy = x2 — y2 is

Partial Differential Equation MCQ - 1 - Question 11

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

Partial Differential Equation MCQ - 1 - 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.

Partial Differential Equation MCQ - 1 - Question 13

Integral surface of (2x y — l)p + (z — 2x2)q = 2(x — yz) passing through the line x0 (s) = 1 y0(s) = 0 z0(s) = s

Partial Differential Equation MCQ - 1 - Question 14

Integral surface of PDE x2p + y2q = —z2 which passes through hyperbola xy = x + y, z = 1 is given by

Partial Differential Equation MCQ - 1 - Question 15

Consider 4xyz = pq + 2px2y + 2qxy2
(i) It can be reduced to Claerut's form by some suitable transformation.
(ii) z = ax + by + ab is complete integral
(iii) z = —x2y2 is singular solution choose correct code.

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