Explore topic-wise MCQs in Mathematics Questions and Answers.

This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics Questions and Answers knowledge and support exam preparation. Choose a topic below to get started.

1.

Differentiate x3ex with respect to x.

A. 3e3x (3 log⁡x+\(\frac{1}{x}\))
B. x3e3x.3e3x (3 log⁡x-\(\frac{1}{x}\))
C. x3e3x (3 log⁡x+\(\frac{1}{x}\))
D. x3e3x.3e3x (3 log⁡x+\(\frac{1}{x}\))
Answer» E.
Discussion
2.

Differentiate \(\sqrt{\frac{x+1}{3x-1}}\) with respect to x.

A. \(\frac{-2}{(3x-1)\sqrt{(3x-1)(x+1)}}\)
B. \(\frac{2}{(3x-1)\sqrt{(3x-1)(x+1)}}\)
C. \(\frac{1}{(3x-1)\sqrt{(3x-1)(x+1)}}\)
D. \(\frac{-2}{\sqrt{(3x-1)(x+1)}}\)
Answer» B. \(\frac{2}{(3x-1)\sqrt{(3x-1)(x+1)}}\)
Discussion
3.

Differentiate (3 cos⁡x)x with respect to x.

A. (3 cos⁡x)x (log⁡(3 cos⁡x)+x tan⁡x)
B. (3 cos⁡x)x (log⁡(3 cos⁡x)+tan⁡x)
C. (cos⁡x)^x (log⁡(3 cos⁡x)-x tan⁡x)
D. (3 cos⁡x)x (log⁡(3 cos⁡x)-x tan⁡x)
Answer» E.
Discussion
4.

Differentiate 2(tan⁡x)cot⁡x with respect to x.

A. 2 csc2⁡x.tan⁡xcot⁡x (1-log⁡(tan⁡x))
B. csc2⁡x.tan⁡xcot⁡x (1-log⁡(tan⁡x))
C. 2 csc2⁡x.tan⁡xcot⁡x (1+log⁡(tan⁡x))
D. 2tan⁡xcot⁡x (1-log⁡(tan⁡x))
Answer» B. csc2⁡x.tan⁡xcot⁡x (1-log⁡(tan⁡x))
Discussion
5.

Differentiate \(e^{4x^5}.2x^{log⁡x^2}\) with respect to x.

A. \(e^{4x^5}.x^{log⁡x^2-1} (10x^5+log⁡2x^2)\)
B. \(4e^{4x^5}.x^{log⁡x^2-1} (10x^5+log⁡2x^2)\)
C. \(4e^{4x^5}.x^{log⁡x^2-1} (10x^5-log⁡2x^2)\)
D. \(x^{log⁡x^2 -1} (10x^4+log⁡2x^2)\)
Answer» C. \(4e^{4x^5}.x^{log⁡x^2-1} (10x^5-log⁡2x^2)\)
Discussion
6.

Differentiate 7x(2e2x) with respect to x.

A. 14e2x x(2e2x) (2 log⁡x+\(\frac{1}{x}\))
B. 14x(2e2x) (2 log⁡x+\(\frac{1}{x}\))
C. 14e2x x(2e2x) (2 log⁡x-\(\frac{1}{x}\))
D. 14e2x x(2e2x) (log⁡x-\(\frac{1}{x}\))
Answer» B. 14x(2e2x) (2 log⁡x+\(\frac{1}{x}\))
Discussion
7.

Differentiate (cos⁡3x)3x with respect to x.

A. (cos⁡3x)x (3 log⁡(cos⁡3x) – 9x tan⁡3x)
B. (cos⁡3x)3x (3 log⁡(cos⁡3x) + 9x tan⁡3x)
C. (cos⁡3x)3x (3 log⁡(cos⁡3x) – 9x tan⁡3x)
D. (cos⁡3x)3x (log⁡(cos⁡3x) + 9 tan⁡3x)
Answer» D. (cos⁡3x)3x (log⁡(cos⁡3x) + 9 tan⁡3x)
Discussion
8.

Differentiate 9tan⁡3x with respect to x.

A. 9tan⁡3x (3 log⁡9 sec2⁡x)
B. 9tan⁡3x (3 log⁡3 sec2⁡⁡x)
C. 9tan⁡3x (3 log⁡9 sec⁡x)
D. -9tan⁡3x (3 log⁡9 sec2⁡⁡x)
Answer» B. 9tan⁡3x (3 log⁡3 sec2⁡⁡x)
Discussion
9.

Differentiate 4xex with respect to x.

A. xex e-x (x log⁡x+1)
B. -4xex-1 ex (x log⁡x+1)
C. 4xex ex (x log⁡x+1)
D. 4xex-1 ex (x log⁡x+1)
Answer» E.
Discussion
10.

Differentiate (log⁡2x)sin⁡3x with respect to x.

A. (3 cos⁡3x log⁡(log⁡2x)+\(\frac{sin⁡3x}{x log⁡2x}\))
B. \(log⁡2x^{sin⁡3x} \,(3 \,cos⁡3x \,log⁡(log⁡2x)+\frac{sin⁡3x}{x \,log⁡2x})\)
C. –\((3 \,cos⁡3x \,log⁡(log⁡2x)+\frac{sin⁡3x}{x log⁡2x})\)
D. \(\frac{3 \,cos⁡3x \,log⁡(log⁡2x)+\frac{sin⁡3x}{x log⁡2x}}{log⁡2x^{sin⁡3x}}\)
Answer» C. –\((3 \,cos⁡3x \,log⁡(log⁡2x)+\frac{sin⁡3x}{x log⁡2x})\)
Discussion