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.

Find the particular solution of the differential equation \(\frac{dy}{dx}=\frac{9y \,log⁡x}{5x \,log⁡y}\).

A. (log⁡y)2+(log⁡x)2=0
B. (log⁡y)2-(log⁡x)2=0
C. log⁡y-log⁡x=0
D. 2 log⁡x+log⁡y=0
Answer» C. log⁡y-log⁡x=0
Discussion
2.

Find the particular solution for the differential equation \(\frac{dy}{dx}=\frac{3x^2}{7y}\) given that, y=1 when x=1.

A. 7x2=2y3+5
B. 7x3=2y2+5
C. 7y2=2x3+5
D. 2y2=5x3+6
Answer» D. 2y2=5x3+6
Discussion
3.

Find the particular solution of the differential equation \(\frac{dy}{dx}+8x=16x^2+4\) given that y=\(\frac{1}{3}\) when x=1.

A. y=\(\frac{(2x+1)^2}{3}\)
B. y=\(\frac{(4x+1)^2}{12}\)
C. y=\(\frac{(4x-2)^2}{3}\)
D. y=\(\frac{(2x-1)^2}{3}\)
Answer» E.
Discussion
4.

Find the particular solution of the differential equation \(\frac{dy}{dx}\)+2x=5 given that y=5, when x=1.

A. y=5x+x2+1
B. y=x-x2+4
C. y=5x-x2+1
D. y=5x-x2
Answer» D. y=5x-x2
Discussion
5.

Find the general solution of the differential equation \(\frac{dy}{dx}=3e^x+2\)

A. y=3ex+2x+C
B. y=3ex-2x+C
C. y=2ex+3x+C
D. y=2ex-3x+C
Answer» B. y=3ex-2x+C
Discussion
6.

Find the general solution of the differential equation \(\frac{dy}{dx}=\frac{2+x^3}{4-y^3}\).

A. x3-y3-4y+C=0
B. x4+8x+y4-16y+C=0
C. 2x+y4-4y+C=0
D. x3+2x+C=0
Answer» C. 2x+y4-4y+C=0
Discussion
7.

Find the general solution of the differential equation \(\frac{dy}{dx}=\frac{3 \,sec\,⁡y}{2 \,cosec⁡\,x}\).

A. 3 cos⁡x-2 cos⁡y=C
B. 3 sin⁡x+2 sin⁡y=C
C. 3 cos⁡x+2 tan⁡x=C
D. 3 cos⁡x+2 sin⁡y=C
Answer» E.
Discussion
8.

Find the general solution of the differential solution \(\frac{dy}{dx}=2-x+x^3\).

A. x4-2x2-4y+C=0
B. x4-2x2+C=0
C. 2x2+4x-4y+C=0
D. x4-2x2+4x-4y+C=0
Answer» E.
Discussion
9.

Find the general solution of the differential equation \(\frac{dy}{dx}=\frac{y-3}{x-3}\) (x, y≠3).

A. x-3=0
B. y-3=0
C. y+3=0
D. x-3y=0
Answer» C. y+3=0
Discussion
10.

Find the general solution of the differential equation \(\frac{dy}{dx}=5x^2+2\).

A. 10x3+12x-3y2+C=0
B. 12x-3y2+C=0
C. 10x3+12x-y2+C=0
D. 10x2-3y2+C=0
Answer» B. 12x-3y2+C=0
Discussion