Test: Differential Equations & Multiple Integrals- 2 - Mechanical Engineering MCQ

Consider the shaded triangular region P shown in the figure. What is 

A path AB in the form of one quarter of a circle of unit radius is shown in the figure. Integration of (x + y)² on path AB traversed in a counterclockwise sense is  

The value of 

A parabolic cable is held between two supports at the same level. The horizontal span between the supports is L. The sag at the mid-span is h. The equation of the parabola is     where x is the horizontal coordinate and y is the vertical coordinate with the origin at the centre of the cable. The expression for the total length of the cable is 

A surface S(x,y)=2x+5y-3 is integrated once over a  path consisting of the points that satisfy ( x +1)2+ (y − 1)2 = √2 . The integral evaluates to

The value of integral  

The order of the differential equation 

The solution of the differential equation    under the boundary conditions  

 (i) y =y₁  At x = 0 and  

(ii) y =y₂  At x = ∞, 

Where k,   y₁ and y₂ are constants, is 

A function n(x) satisfies the differential equation    where L is a constant. The boundary conditions are: n(0)=K and n(∞)= 0. The solution to this equation is 

The solution of the differential equation 

If     then what is y(e)?

The solution to the differential equation f’’(x)+4f’(x)+4f(x)=0 is      

The above equation is a  

 Which of the following is a solution of the differential equation   

The Blasius equation, 

The degree of the differential equation  

The solution for the differential equation  with the condition that y = 1 at x = 0 is  

A spherical naphthalene ball exposed to the atmosphere loses volume at a rate proportional to its instantaneous surface area due to evaporation. If the initial diameter of the ball is 2 cm and the diameter reduces to 1 cm after 3 months, the ball completely evaporates in  

Solution of the differential equation  represents a family of  

The general solution of 

A body originally at 60ºC cools down to 40ºC in 15 minutes when kept in air at a temperature of 25ºC. What will be the temperature of the body at the end of 30 minutes?

The partial differential equation that can be formed from z = ax + by + ab has the form 

With K as constant, the possible solution for the first order differential equation    is 

The boundary-value problem yⁿ + λy = 0, y(0) = y(λ) = 0 will have non-zero solutions if and only if the values of λ are  

The solution of the differential equation    with the condition that y = 1 at x = 1, is

Consider the differential equation  Which of the following is a solution to this differential equation for x > 0?

If y = e^3x + e^-5x find the value of

at x = 0