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.

If, 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 kind of curve is passing through (0, k)?

A. Parabola
B. Hyperbola
C. Ellipse
D. Circle
Answer» E.
Discussion
2.

What is the equation of the curve passing through (1, 0) of (y(dy/dx) + 2x)2 = (y2 + 2x2)[1 + (dy/dx)2]?

A. 2x<sup> 1/ 2</sup> = y/x + (y<sup>2</sup> + 2x<sup>2</sup>)/x<sup>2</sup>
B. 2x<sup> 1/2 2</sup> = y/x + (y<sup>2</sup> + 2x<sup>2</sup>)/x<sup>2</sup>
C. 2x<sup> 2</sup> = y/x + (y<sup>2</sup> + 2x<sup>2</sup>)/x<sup>2</sup>
D. 2x = y/x + (y<sup>2</sup> + 2x<sup>2</sup>)/x<sup>2</sup>
Answer» B. 2x<sup> 1/2 2</sup> = y/x + (y<sup>2</sup> + 2x<sup>2</sup>)/x<sup>2</sup>
Discussion
3.

What is the solution of (y(dy/dx) + 2x)2 = (y2 + 2x2)[1 + (dy/dx)2]?

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

A particle starts from the origin with a velocity 5cm/sec and moves in a straight line, its acceleration at time t seconds being (3t2 5t)cm/sec2. What will be the distance from the origin at the end of 4 seconds?

A. 30(4/3)
B. 30(2/3)
C. 30
D. Unpredictable
Answer» C. 30
Discussion
5.

A particle starts from the origin with a velocity 5cm/sec and moves in a straight line, its acceleration at time t seconds being (3t2 5t)cm/sec2. What will be the velocity of the particle?

A. 27cm/sec
B. 28 cm/sec
C. 29 cm/sec
D. 30 cm/sec
Answer» D. 30 cm/sec
Discussion
6.

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

A. 3x y + log|2x + 3y 3| = -c/3
B. 3x y + log|2x + 3y 3| = c/3
C. 3x + y + log|2x + 3y 3| = -c/3
D. 3x y log|2x + 3y 3| = c/3
Answer» B. 3x y + log|2x + 3y 3| = c/3
Discussion
7.

What will be the differential equation form of (a2 + x2)dy/dx + y = (a2 + x2) x?

A. a<sup>2</sup> log (x + (a<sup>2</sup> x<sup>2</sup>)) + c
B. a<sup>2</sup> log (x + ( a<sup>2</sup> + x<sup>2</sup>)) + c
C. a<sup>2</sup> log (x ( a<sup>2</sup> + x<sup>2</sup>)) + c
D. a<sup>2</sup> log (x ( a<sup>2</sup> x<sup>2</sup>)) + c
Answer» C. a<sup>2</sup> log (x ( a<sup>2</sup> + x<sup>2</sup>)) + c
Discussion
8.

What will be the value of dy/dx a/x * y = (x + 1)/x?

A. y = x/(1 a) 1/a + cx<sup>a</sup>
B. y = x/(1 + a) + 1/a + cx<sup>a</sup>
C. y = x/(1 a) 1/a cx<sup>a</sup>
D. y = x/(1 + a) 1/a + cx<sup>a</sup>
Answer» B. y = x/(1 + a) + 1/a + cx<sup>a</sup>
Discussion
9.

A curve passes through (1, 1) such that the triangle formed by the coordinate axes and the tangent at any point of the curve is in the first quadrant and has its area equal to 2. What will be the equation of the curve?

A. xy = 2
B. xy = -1
C. x y = 2
D. x + y = 2
Answer» E.
Discussion
10.

A curve passes through (1, 1) such that the triangle formed by the coordinate axes and the tangent at any point of the curve is in the first quadrant and has its area equal to 2. What is the differential equation?

A. dy/dx = [(xy + 2) (1 + xy)]/ x<sup>2</sup>
B. dy/dx = [(xy 2) (1 + xy)]/ x<sup>2</sup>
C. dy/dx = [(xy 2) (1 xy)]/ x<sup>2</sup>
D. dy/dx = [(xy + 2) (1 xy)]/ x<sup>2</sup>
Answer» D. dy/dx = [(xy + 2) (1 xy)]/ x<sup>2</sup>
Discussion