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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) 2022 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) 2022 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  

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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

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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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