Below you will find **MCQ Questions of Chapter 9 Differential Equations Class 12 Maths Free PDF Download** that will help you in gaining good marks in the examinations and also cracking competitive exams. These Class 12 MCQ Questions with answers will widen your skills and understand concepts in a better manner.

# MCQ Questions for Class 12 Maths Chapter 9 Differential Equations with answers

1. The dif is a:

(a) second order, third degree equation.

(b) second order, first degree equation

(c) third order, third degree equation.

(d) second order, second degree equation.

► (d) second order, second degree equation.

2. The solution of the initial value problem e^{dy/dx} = x + 1, y(0) = 3 is :

(a) y = (x – 1)log(x + 1) + 3

(b) y = (x + 1)log(x + 1) + 3

(c) y = (x + 1)log(x + 1) + 4

(d) y = (x + 1)log(x + 1) – 1

► (b) y = (x + 1)log(x + 1) + 3

3. Solution of the differential equation

(a) y sec x = tan x + c

(b) y tan x = sec x + c

(c) tan x = (sec x + c) y

(d) sec x = (tan x + c) y

► (d) sec x = (tan x + c) y

4. Differential equation of the family of circles touching the y-axis at origin is

(a) 2y′ − x^{2} = y^{2}

(b) 2xyy′ + x^{2} = y^{2}

(c) 2xyy′ − x^{2} = y^{2}

(d) 2yy′ + x^{2} = y^{2}

► (b) 2xyy′ + x^{2} = y^{2}

5. The solution of differential equation x^{2}dy + y(x + y)dx = 0 when x = 1, y = 1 is:

(a) 3x^{2}y = x+y

(b) x^{2}y = 2x+y

(c) 3x^{2}y = 2x-y

(d) 3x^{2}y = 2x+y

► (d) 3x^{2}y = 2x+y

6. Solution of the equation

(x - y) (2dy - dx) = 3dx - 5dy is

(a) 2y - x = log(x - y + 2) + c

(b) 2x - y = log(y - x + 2) + c

(c) 2y + x = log (x - y + 2) + c

(d) None of the above

► (a) 2y - x = log(x - y + 2) + c

6. The solution of satisfying y (1) = 0 is given by

(a) a hyperbola

(b) a circle

(c) y^{2} = x (1 + x) - 10

(d) (x - 2)^{2} + (y - 3)^{2} = 5

► (a) a hyperbola

7. The order of the equation

(a) 1

(b) 4

(c) 3

(d) 2

► (d) 2

8. The order of the differential equation:

(a) 4

(b) 2

(c) 3

(d) 1

► (c) 3

9. The solution of the initial value problem is :

(a) sec x = 2y

(b) x = 2cosy

(c) y = 2secx

(d) y = 2cosx

► (b) x = 2cosy

10. Find the particular solution of the differential equation log = 3x+4y, given that y = 0 and x = 0.

(a) 4e^{3x}+3^{e−4y}+7 = 0

(b) 4e^{3x}−3^{e−4y}−7 = 0

(c) 4e^{3x}+3^{e−4y}−7 = 1

(d) 4e^{3x}+3^{e−4}y−7 = 0

► (d) 4e^{3x}+3^{e−4}y−7 = 0

11. Differential equations are equations containing functions y = f(x), g(x) and

(a) tangent of y at zero

(b) maxima of y

(c) derivatives of y

(d) minima of y

► (c) derivatives of y

12. Which of the following is a homogeneous differential equation?

(a) (xy) dx − (x^{3}+ y^{3}) dy = 0

(b) (x^{3}+ 2y2) dx + 2xy dy = 0

(c) y^{2}dx + (x^{2}− xy − y^{2}) dy = 0

(d) (4x + 6y + 5) dy − (3y + 2x + 4) dx = 0

► (c) y^{2}dx + (x^{2}− xy − y^{2}) dy = 0

13. The equation of the curve for which the tangent at P(x, y) cuts the y-axis at (0, y^{3}) is

(a) xy^{2} = x+ y

(b) x^{2} (y^{2} - 1)= cy^{2}

(c) y (x^{2} - 1) = cx^{2}

(d) yx + x^{2} = c

► (b) x^{2} (y^{2} - 1)= cy^{2}

14. The order and degree of the differential equation, of which xy = cex + be-x + x^{2} is a solution, is

(a) 1, 3

(b) 2, 1

(c) 3, 2

(d) None of these

► (b) 2, 1

15. A ray of light coming from origin after reflection at the point P(x, y) of any curve becomes parallel to x-axis, if the curve passes through (8, 6) then its equation is

(a) y^{2} = x

(b) y^{2} = 4x+ 4

(c) y^{2} = 4x

(d) y^{2} = 4x+ 1

► (b) y^{2} = 4x+ 4

16. General solution of

(a) y = 2tan (x/2) − x+ c

(b) y = 2tan^{2}(x/2) − x+ c

(c) y = 2tan (x) – x + c

(d) y = 2tan (x/2) + x+ c

► (a) y = 2tan (x/2) − x+ c

17. The solution of sec y satisfying y (1) = 0, is

(a) tan y = (x- 2) ex log x

(b) sin y = ex (x- 1) x^{-4}

(c) tan y = (x- 1) ex x^{-3}

(d) sin y = ex (x - 1) x^{-3}

► (b) sin y = ex (x- 1) x^{-4}

18. The equation of the curve in which the portion of the tangent included between the coordinate axes is bisected at the point of contact, is

(a) a parabola

(b) an ellipse

(c) a circle

(d) a hyperbola

► (d) a hyperbola

Hope the given MCQ Questions will help you in cracking exams with good marks. These **Differential Equations MCQ Questions** will help you in practising more and more questions in less time.