Test: Differential Equations & Multiple Integrals- 1

# Test: Differential Equations & Multiple Integrals- 1

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## 20 Questions MCQ Test GATE Mechanical (ME) 2023 Mock Test Series | Test: Differential Equations & Multiple Integrals- 1

Test: Differential Equations & Multiple Integrals- 1 for Civil Engineering (CE) 2023 is part of GATE Mechanical (ME) 2023 Mock Test Series preparation. The Test: Differential Equations & Multiple Integrals- 1 questions and answers have been prepared according to the Civil Engineering (CE) exam syllabus.The Test: Differential Equations & Multiple Integrals- 1 MCQs are made for Civil Engineering (CE) 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Differential Equations & Multiple Integrals- 1 below.
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Test: Differential Equations & Multiple Integrals- 1 - Question 1

### A triangle ABC consists of vertex points A (0,0) B(1,0) and C(0,1). The value of the integral over the triangle is

Detailed Solution for Test: Differential Equations & Multiple Integrals- 1 - Question 1

The equation of the line  AB is    Test: Differential Equations & Multiple Integrals- 1 - Question 2

### The area enclosed between the parabala y = x2 and the straight line     y = x is

Detailed Solution for Test: Differential Equations & Multiple Integrals- 1 - Question 2  Test: Differential Equations & Multiple Integrals- 1 - Question 3

### Changing the order of the integration in the double integral  Detailed Solution for Test: Differential Equations & Multiple Integrals- 1 - Question 3

When    Test: Differential Equations & Multiple Integrals- 1 - Question 4

The right circular cone of largest volume that can be enclosed by a sphere of 1 m radius has a height of

Detailed Solution for Test: Differential Equations & Multiple Integrals- 1 - Question 4  Test: Differential Equations & Multiple Integrals- 1 - Question 5

the parabolic arc is revolved around the x-axis. The volume of

Detailed Solution for Test: Differential Equations & Multiple Integrals- 1 - Question 5

Differential volume   Test: Differential Equations & Multiple Integrals- 1 - Question 6

What is the area common to the circles r = a and r = 2a cos θ?

Detailed Solution for Test: Differential Equations & Multiple Integrals- 1 - Question 6

Area common to circles r = a

And r = 2a cos θ is 1.228 a2

Test: Differential Equations & Multiple Integrals- 1 - Question 7

The expression for the volume of a cone is equal to

Detailed Solution for Test: Differential Equations & Multiple Integrals- 1 - Question 7

Choices (a) and (b)  be correct because

for the volume of a cone is equal to Test: Differential Equations & Multiple Integrals- 1 - Question 8

f ( x,y ) is a continuous defined over ( x,y ) ∈ [0,1]× [0,1] . Given two constrains, x > y 2 and y > x 2 , the volume under f ( x,y ) is

Detailed Solution for Test: Differential Equations & Multiple Integrals- 1 - Question 8  Test: Differential Equations & Multiple Integrals- 1 - Question 9

The following differential equation has Detailed Solution for Test: Differential Equations & Multiple Integrals- 1 - Question 9 Order of highest derivative = 2
Hence, most appropriate answer is (b)

Test: Differential Equations & Multiple Integrals- 1 - Question 10

A solution of the following differential equation is given by Detailed Solution for Test: Differential Equations & Multiple Integrals- 1 - Question 10

Let y = mx be the trial soln of the given differental equation
∴The corrosponding auxiliary equation is Test: Differential Equations & Multiple Integrals- 1 - Question 11

For the differential equation the boundary conditions are

(i)  y = 0 for x = 0, and

(ii) y = 0 for x = a

The form of non-zero solutions of y (where m varies over all integers) are

Detailed Solution for Test: Differential Equations & Multiple Integrals- 1 - Question 11

Here y = c1 coskx + c2 sinkx ........... (1) be the solution of the given differential equation.
Now use boundary conditions
For x = 0,y = 0 gives c1 = 0. Equation − (1) becomes      be the solution, n 0,1,2,3.......

Test: Differential Equations & Multiple Integrals- 1 - Question 12

Which of the following is a solution to the differential equation Detailed Solution for Test: Differential Equations & Multiple Integrals- 1 - Question 12

Hints : m + 3 = 0 ⇒m = −3 Test: Differential Equations & Multiple Integrals- 1 - Question 13

For the differential equation the general solution is

Detailed Solution for Test: Differential Equations & Multiple Integrals- 1 - Question 13 Test: Differential Equations & Multiple Integrals- 1 - Question 14

The solution of the differential equation Detailed Solution for Test: Differential Equations & Multiple Integrals- 1 - Question 14

It is a linear diff. equation   Test: Differential Equations & Multiple Integrals- 1 - Question 15

The solution of with the condition y(1) Detailed Solution for Test: Differential Equations & Multiple Integrals- 1 - Question 15 Which is 1st order linear differential equation   Test: Differential Equations & Multiple Integrals- 1 - Question 16

A technique by which problems in analysis, in particular differential equations, are transformed into algebraic problems is called

Test: Differential Equations & Multiple Integrals- 1 - Question 17

The general solution of (x2 D2 – xD), y= 0 is :

Test: Differential Equations & Multiple Integrals- 1 - Question 18

For the particular integrals is

Detailed Solution for Test: Differential Equations & Multiple Integrals- 1 - Question 18   Test: Differential Equations & Multiple Integrals- 1 - Question 19

It is given that y" + 2y' + y = 0, y(0) = 0, y(1)=0. What is y (0.5)?

Detailed Solution for Test: Differential Equations & Multiple Integrals- 1 - Question 19

Auxiliary equation is m2 + 2m +1 = 0⇒m = −1,−1 Using boundary condition y(0) = 0 and y(1) = 0
we get y = 0

Test: Differential Equations & Multiple Integrals- 1 - Question 20

The partial differential equation Detailed Solution for Test: Differential Equations & Multiple Integrals- 1 - Question 20

The order is the highest numbered derivative in the equation (which is 2 here), while the degree is the highest power to which a derivative is raised (which is 1 here).

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