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.

A normal is drawn at a point P(x, y) of a curve. It meets the x-axis at Q. If PQ is of constant
length k. What is the equation of such curve passing through (0, k)?

A. x<sup>2</sup> + 2y<sup>2</sup> = k<sup>2</sup>
B. 2x<sup>2</sup> + y<sup>2</sup> = k<sup>2</sup>
C. x<sup>2</sup> y<sup>2</sup> = k<sup>2</sup>
D. x<sup>2</sup> + y<sup>2</sup> = k<sup>2</sup>
Answer» E.
Discussion
2.

A normal is drawn at a point P(x, y) of a curve. It meets the x-axis at Q. If PQ is of constant
length k. Then what is the differential equation describing such curve?

A. y(dy/dx) = (k<sup>2</sup> + x<sup>2</sup>)
B. y(dy/dx) = (k<sup>2</sup> 2y<sup>2</sup>)
C. y(dy/dx) = (k<sup>2</sup> y<sup>2</sup>)
D. Depends on the value of k
Answer» D. Depends on the value of k
Discussion
3.

What is the solution of the equation(y + x( xy)(x + y))dx (y + y( xy)(x + y))dy = 0?

A. x<sup>2</sup> + y<sup>2</sup> = 2tan<sup>-1</sup>( (y/x)) + c
B. x<sup>2</sup> + y<sup>2</sup> = 4tan<sup>-1</sup>( (y/x)) + c
C. x<sup>2</sup> + y<sup>2</sup> = tan<sup>-1</sup>( (y/x)) + c
D. x<sup>2</sup> + y<sup>2</sup> = 2tan<sup>-1</sup>( (x/y)) + c
Answer» C. x<sup>2</sup> + y<sup>2</sup> = tan<sup>-1</sup>( (y/x)) + c
Discussion
4.

What will be the value of x(x 1)dy/dx y = x2(x 1)2?

A. xy = (x + 1)(x<sup>3</sup>/3 + c)
B. depends on x
C. depends on y
D. xy = (x 1)(x<sup>3</sup>/3 + c)
Answer» E.
Discussion
5.

What will be the value of the differential equation dy/dx = (x + y)2/(x + 2)(y 2)?

A. ke<sup>Y/X</sup> where, X = x + 2 and Y = y 2
B. ke<sup>2Y/X</sup> where, X = x + 2 and Y = y 2
C. ke<sup>2Y/X</sup> where, X = x and Y = 2y
D. ke<sup>2X/Y</sup> where, X = x 2 and Y = y + 2
Answer» C. ke<sup>2Y/X</sup> where, X = x and Y = 2y
Discussion
6.

What will be the value of dy/dx = (x + 2y + 3)/(2x + 3y + 4)?

A. [(2 + 3)/2 3 * (log ( 3(y + 2) (x 1))) + (2 3)/2 3 * (log ( 3(y + 2) (x 1)))]
B. [(2 + 3)/2 3 * (log ( 3(y + 2) + (x 1))) (2 3)/2 3 * (log ( 3(y + 2) + (x 1)))]
C. [(2 + 3)/2 3 * (log ( 3(y + 2) (x 1))) (2 3)/2 3 * (log ( 3(y + 2) (x 1)))]
D. [(2 + 3)/2 3 * (log ( 3(y + 2) + (x 1))) (2 3)/2 3 * (log ( 3(y + 2) (x 1)))]
Answer» D. [(2 + 3)/2 3 * (log ( 3(y + 2) + (x 1))) (2 3)/2 3 * (log ( 3(y + 2) (x 1)))]
Discussion
7.

What will be the general solution of differential equation for 2x y dx + 2y x dy = 0?

A. 2<sup>2x</sup> + 2<sup>2y</sup> = c
B. 2(2<sup>2x</sup> + 2<sup>2y</sup>) = c
C. 3(2<sup>2x</sup> + 2<sup>2y</sup>) = c
D. 4(2<sup>2x</sup> + 2<sup>2y</sup>) = c
Answer» B. 2(2<sup>2x</sup> + 2<sup>2y</sup>) = c
Discussion
8.

What is the order of the differential equation of the family of circles with one diameter along the line y = x axis?

A. 3
B. 2
C. 1
D. 0
Answer» C. 1
Discussion
9.

What is the value of the solution of dy/dx = (6x + 9y 7)/(2x + 3y 6)?

A. -c/3
B. 3c/2
C. 2c/3
D. -2c/3
Answer» B. 3c/2
Discussion
10.

What is the differential equation whose solution represents the family c(y + c)2 = x3?

A. [2x/3 *(dy/dx) y][x/3 *dy/dx]<sup>2</sup> = x<sup>3</sup>
B. [x/3 *(dy/dx) y][x/3 *dy/dx]<sup>2</sup> = x<sup>3</sup>
C. [2x/3 *(dy/dx) y][ 2x/3 *dy/dx]<sup>2</sup> = x<sup>3</sup>
D. [x/3 *(dy/dx) y][ 2x/3 *dy/dx]<sup>2</sup> = x<sup>3</sup>
Answer» D. [x/3 *(dy/dx) y][ 2x/3 *dy/dx]<sup>2</sup> = x<sup>3</sup>
Discussion