Test: Differential Equations & Multiple Integrals- 1 - Mechanical Engineering MCQ

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

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

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

The expression    for the volume of a cone is equal to

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  

The following differential equation has 

 A solution of the following differential equation is given by  

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 

Which of the following is a solution to the differential equation 

For the differential equation    the general solution is  

The solution of the differential equation 

The solution of    with the condition y(1) 

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

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

For    the particular integrals is

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

The partial differential equation