Explore topic-wise MCQs in Mathematics.

This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics 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 u2061y)<sup>2</sup>+(log u2061x)<sup>2</sup>=0
B. (log u2061y)<sup>2</sup>-(log u2061x)<sup>2</sup>=0
C. log u2061y-log u2061x=0
D. 2 log u2061x+log u2061y=0
Answer» C. log u2061y-log u2061x=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. 7x<sup>2</sup>=2y<sup>3</sup>+5
B. 7x<sup>3</sup>=2y<sup>2</sup>+5
C. 7y<sup>2</sup>=2x<sup>3</sup>+5
D. 2y<sup>2</sup>=5x<sup>3</sup>+6
Answer» D. 2y<sup>2</sup>=5x<sup>3</sup>+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+x<sup>2</sup>+1
B. y=x-x<sup>2</sup>+4
C. y=5x-x<sup>2</sup>+1
D. y=5x-x<sup>2</sup>
Answer» D. y=5x-x<sup>2</sup>
Discussion
5.

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

A. y=3e<sup>x</sup>+2x+C
B. y=3e<sup>x</sup>-2x+C
C. y=2e<sup>x</sup>+3x+C
D. y=2e<sup>x</sup>-3x+C
Answer» B. y=3e<sup>x</sup>-2x+C
Discussion
6.

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

A. x<sup>3</sup>-y<sup>3</sup>-4y+C=0
B. x<sup>4</sup>+8x+y<sup>4</sup>-16y+C=0
C. 2x+y<sup>4</sup>-4y+C=0
D. x<sup>3</sup>+2x+C=0
Answer» C. 2x+y<sup>4</sup>-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 u2061x-2 cos u2061y=C
B. 3 sin u2061x+2 sin u2061y=C
C. 3 cos u2061x+2 tan u2061x=C
D. 3 cos u2061x+2 sin u2061y=C
Answer» E.
Discussion
8.

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

A. x<sup>4</sup>-2x<sup>2</sup>-4y+C=0
B. x<sup>4</sup>-2x<sup>2</sup>+C=0
C. 2x<sup>2</sup>+4x-4y+C=0
D. x<sup>4</sup>-2x<sup>2</sup>+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. 10x<sup>3</sup>+12x-3y<sup>2</sup>+C=0
B. 12x-3y<sup>2</sup>+C=0
C. 10x<sup>3</sup>+12x-y<sup>2</sup>+C=0
D. 10x<sup>2</sup>-3y<sup>2</sup>+C=0
Answer» B. 12x-3y<sup>2</sup>+C=0
Discussion