Explore topic-wise MCQs in Partial Differentiation.

This section includes 7 Mcqs, each offering curated multiple-choice questions to sharpen your Partial Differentiation knowledge and support exam preparation. Choose a topic below to get started.

1.

The determinant of the matrix whose eigen values are 6, 4, 3 is given by ___________

A. 3
B. 24
C. 72
D. 13
Answer» C. 72
Discussion
2.

Given \(∫_0^8x^{\frac{1}{3}}dx,\) find the error in approximating the integral using Simpson’s 1/3 Rule with n=4.

A. 1.8
B. 2.9
C. 0.3
D. 0.35
Answer» E.
Discussion
3.

What is the value of \(\frac{∂^2z}{∂x∂y}\) for the z=3x2y+5y?

A. 3xy
B. 6x
C. 3x+5
D. 6xy
Answer» C. 3x+5
Discussion
4.

Which of the following relations hold true for division rule of differentiation?

A. \((\frac{f(x)}{g(x)})’= \frac{f'(x)}{g'(x)} \)
B. \((\frac{f(x)}{g(x)})’= \frac{g(x) f'(x)- g'(x)f(x)}{(f(x))^2}\)
C. \((\frac{f(x)}{g(x)})’= \frac{g(x)f'(x)- g'(x)f(x)}{(g(x))^2} \)
D. \((\frac{f(x)}{g(x)})’= \frac{f(x)g'(x)-f'(x)g(x)}{(g(x))^2} \)
Answer» D. \((\frac{f(x)}{g(x)})’= \frac{f(x)g'(x)-f'(x)g(x)}{(g(x))^2} \)
Discussion
5.

Find the correct values for \(\frac{∂f}{∂x} \,and\, \frac{∂f}{∂y}\) for the function \(f=\frac{2}{x^3}y^2+4y^3.\)

A. \(\frac{∂f}{∂x}= \frac{-6}{x^2}, \frac{∂f}{∂y}= \frac{2}{x^3} y+8y^2\)
B. \(\frac{∂f}{∂x}= \frac{2}{x^4}, \frac{∂f}{∂y}= \frac{2}{x^3} y+12y^2\)
C. \(\frac{∂f}{∂x}= \frac{-6}{x^4}, \frac{∂f}{∂y}= \frac{4}{x^3} y+12y^2\)
D. \(\frac{∂f}{∂x}= \frac{-6}{x^4}, \frac{∂f}{∂y}= \frac{4}{x^3} y^2+12\)
Answer» D. \(\frac{∂f}{∂x}= \frac{-6}{x^4}, \frac{∂f}{∂y}= \frac{4}{x^3} y^2+12\)
Discussion
6.

The value of \(\frac{∂z}{∂y}\)=8x2+6xy2+4. What is the function z expressed as?

A. z=8x3+2x2 y2+4x
B. z=8x2 y+2xy3+4y
C. z=8y+2xy2+4y
D. z=16x+6y2
Answer» C. z=8y+2xy2+4y
Discussion
7.

If z=3xy+4x2, what is the value of \(\frac{∂z}{∂x}\)?

A. 3y+8x
B. 3x+4x2
C. 3xy+8x
D. 3y+3x+8x
Answer» B. 3x+4x2
Discussion