Explore topic-wise MCQs in Partial Differential Equations.

This section includes 4 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 \(u=\frac{e^{x+y}}{e^x-e^y}\), 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
2.

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

A. \(\frac{-1}{2\sqrt x}×tan⁡(\sqrt x+\sqrt y)\)
B. \(\frac{-1}{2\sqrt x}×cos⁡(\sqrt x+\sqrt y)\)
C. \(\frac{-1}{2\sqrt x}×sin⁡(\sqrt x+\sqrt y)\)
D. \(\frac{-1}{\sqrt x}×sin⁡(\sqrt x+\sqrt y)\)
Answer» D. \(\frac{-1}{\sqrt x}×sin⁡(\sqrt x+\sqrt y)\)
Discussion
3.

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

A. 2xsin⁡x2
B. x sin2x
C. 2xsin⁡x2 cos⁡y2
D. 6xsin⁡x2 cos⁡y2
Answer» D. 6xsin⁡x2 cos⁡y2
Discussion
4.

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