Explore topic-wise MCQs in Differential Calculus.

This section includes 8 Mcqs, each offering curated multiple-choice questions to sharpen your Differential Calculus knowledge and support exam preparation. Choose a topic below to get started.

1.

Half Range Fourier Series contains either sine or cosine terms.

A. True
B. False
Answer» B. False
Discussion
2.

A sphere with the dimensions is shown in the figure. What is the error that can be incorporated in the radius such that the volume will not change more than 8%?

A. 0.127%
B. 0.02546%
C. 0.002546%
D. 0.2546%
Answer» C. 0.002546%
Discussion
3.

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

A. 1.8
B. 2.9
C. 0.3
D. 0.35
Answer» E.
Discussion
4.

What is the derivative of \(\frac{3x^2}{(1-sinx)}\)?

A. \(\frac{6xsinx-3x^2 cosx}{(1-sinx)^2} \)
B. \(\frac{6x}{1-sinx} \)
C. \(\frac{6xsinx-3x^2 cosx-6x}{(1-sinx)^2} \)
D. \(\frac{6xsinx-3cosx-6}{(1-sinx)^2} \)
Answer» D. \(\frac{6xsinx-3cosx-6}{(1-sinx)^2} \)
Discussion
5.

Product Rule of the derivative is given by ________

A. \(\frac{d(fg)}{dx}=\frac{d(g)}{dx}*\frac{d(f)}{dx}\)
B. \(\frac{df}{dx}*\frac{dg}{dx}=\frac{d(g)}{dx}+\frac{d(f)}{dx}\)
C. \(\frac{d(fg)}{dx}=f \frac{d(g)}{dx}*g \frac{d(f)}{dx}\)
D. \(\frac{d(fg)}{dx}=f \frac{d(g)}{dx}+g \frac{d(f)}{dx}\)
Answer» E.
Discussion
6.

Which of the following trigonometric function derivatives is correct?

A. \(\frac{d(sinx)}{dx}=-cosx\)
B. \(\frac{d(secx)}{dx}=secxtanx\)
C. \(\frac{d(tanx)}{dx}=cot^2 x\)
D. \(\frac{d(cosx)}{dx}=sinx\)
Answer» C. \(\frac{d(tanx)}{dx}=cot^2 x\)
Discussion
7.

Power Rule of the derivative states that, \(\frac{d(x^n)}{dx}=nx^{n-1}.\)

A. True
B. False
Answer» C.
Discussion
8.

What is the maximum area of the rectangle with perimeter 620 mm?

A. 24,025 mm2
B. 22,725 mm2
C. 24,000 mm2
D. 24,075 mm2
Answer» B. 22,725 mm2
Discussion