Check the below NCERT MCQ Questions for Class 12 Maths Chapter 9 Differential Equations with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Differential Equations Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

## Q.1 Which of the following is a second order differential equation?

(a) (y’)² + x = y²

(b) y’y” + y = sin x

(c) y” + (y”)² + y = 0

(d) y’ = y²

## Q.2 The curve for which the slope of the tangent at any point is equal to the ratio of the abcissa to the ordinate of the point is

(a) an ellipse

(b) parabola

(c) circle

(d) rectangular hyperbola

## Q.3 The number of arbitrary constants in the general solution of a differential equation of fourth order is:

(a) 0

(b) 2

(c) 3

(d) 4

## Q.4 The number of arbitrary constants in the particular solution of a differential equation of third order is:

(a) 3

(b) 2

(c) 1

(d) 0

## Q.5 Which of the following is a homogeneous differential equation?

(a) (4x + 6y + 5)dy – (3y + 2x + 4)dx = 0

(b) xy dx – (x³ + y²)dy = Q

(c) (x³ + 2y²) dx + 2xy dy = 0

(d) y² dx + (x² – xy – y²)dy = 0

## Q.6 The degree of the differential equation representing the family of curves (x – a)² + y² = 16 is

(a) 0

(b) 2

(c) 3

(d) 1

## Q.7 The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is

(a) (x – 2)² y’² = 25 – (y – 2)²

(b) (x – 2) y’² = 25 – (y – 2)²

(c) (y – 2) y’² =25 – (y – 2)²

(d) (y – 2)² y’² = 25 – (y – 2)²

## Q.8 The differential equation of all parabolas whose axis of symmetry is along the axis of the x-axis is of order

(a) 3

(b) 1

(c) 2

(d) none of these

## Q.9 The solution of the differential equation cos x sin y dx + sin x cos y dy = 0 is

(a) sinx/siny=c

(b) sin x sin y = c

(c) sin x + sin y = c

(d) cos x cos y = c

## Q.10 If y dx + y² dy = x dy, x ∈ R, y > 0 and y(1) = 1, then y(-3) =

(a) 3

(b) 2

(c) 1

(d) 5

## Q.11 The radius of a circle is increasing at the rate of 0.4 cm/ s. The rate of increasing of its circumference is

(a) 0.4 π cm/s

(b) 0.8 π cm/s

(c) 0.8 cm/s

(d) None of these

## Q.12 Solution of differential equation xdy – ydx = Q represents

(a) a rectangular hyperbola

(b) parabola whose vertex is at origin

(c) straight line passing through origin

(d) a circle whose centre is at origin

## Q.13 Family r = Ax + A³ of curves is represented by the differential equation of degree

(a) 1

(b) 2

(c) 3

(d) 4