Explore topic-wise MCQs in Partial Differential Equations.

This section includes 5 Mcqs, each offering curated multiple-choice questions to sharpen your Partial Differential Equations knowledge and support exam preparation. Choose a topic below to get started.

1.

If ( theta=t^n e^ frac{-r^2}{2t} ), find the value of n that satisfies the equation, ( frac{ partial theta}{ partial t}= frac{1}{r^2} frac{ partial}{ partial r}(r^2 frac{ partial theta}{ partial r}) ).

A. 0
B. -1
C. 1
D. 3
Answer» C. 1
Discussion
2.

If (u= frac{e^{x+y}}{e^x-e^y} ), what is ( frac{ partial u}{ partial x}+ frac{ partial u}{ partial y} )?

A. ( frac{2((e^x-e^y) e^{x+y})-(e^{x+y}) (e^x+e^y)}{(e^x-e^y)^2} )
B. ( frac{2((e^x-e^y) e^{x+y})-(e^{x+y}) (e^x+e^y)}{(e^x+e^y)^2} )
C. ( frac{2((e^x-e^y) e^{x+y})-(e^{x+y}) (e^x-e^y)}{(e^x-e^y)^2} )
D. u
Answer» B. ( frac{2((e^x-e^y) e^{x+y})-(e^{x+y}) (e^x+e^y)}{(e^x+e^y)^2} )
Discussion
3.

Find ( frac{ partial u}{ partial x} ) where (u=cos ( sqrt x+ sqrt y) ).

A. ( frac{-1}{2 sqrt x} tan u2061( sqrt x+ sqrt y) )
B. ( frac{-1}{2 sqrt x} cos u2061( sqrt x+ sqrt y) )
C. ( frac{-1}{2 sqrt x} sin u2061( sqrt x+ sqrt y) )
D. ( frac{-1}{ sqrt x} sin u2061( sqrt x+ sqrt y) )
Answer» D. ( frac{-1}{ sqrt x} sin u2061( sqrt x+ sqrt y) )
Discussion
4.

Find ( frac{ partial z}{ partial x} ) where (z=sin x^2 cos y^2 ).

A. 2xsin u2061x<sup>2</sup>
B. x sin2x
C. 2xsin u2061x<sup>2</sup> cos u2061y<sup>2</sup>
D. 6xsin u2061x<sup>2</sup> cos u2061y<sup>2</sup>
Answer» D. 6xsin u2061x<sup>2</sup> cos u2061y<sup>2</sup>
Discussion
5.

Find ( frac{ partial z}{ partial x} ) where (z=ax^2+2by^2+2bxy ).

A. 3by
B. 2ax
C. 3(ax+by)
D. 2(ax+by)
Answer» E.
Discussion