NCERT Class 12 Chapter 9 Maths Differential Equations MCQ

NCERT Class 12 Chapter 9 Maths Differential Equations MCQ | Questions & Answers: Now is the best time for students of NCERT Class 12 to improve their basics about the Chapter 9 Maths Differential Equations topic. In this article, we have accommodated a series of MCQ questions that will definitely help you guys in enhancing your existing knowledge.

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1. The number of arbitrary constants in the general solution of differential equation of fourth order is

A. 4

B. 3

C. 2

D. 0

2. Integration factor of differential equation dydx + py = Q, where P and IQ are functions of x is

A. ∫epdx

B. e∫pdx

C. e-∫pdx

D. None of these

3. 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

CBSE Class12 Maths Differentials Equation (4Q)

A. second order, third degree equation

B. second order, first degree equation

C. third order, third degree equation.

D. second order, second degree equation.

5. The order of the differential equation of all the circles of given radius 4 is

A. 2

B. 3

C. 4

D. 5

6. 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

7. 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

8. The differential equation for the equation

CBSE Class12 Maths Differentials Equation (8Q)

A. (A)

B. (B)

C. (C)

D. (D)

9. The degree of the differential equation

A. not defined

B. 2

C. 3

D. None of these

10. The solution of dydx = 1 + x + y + xy is

A. x – y = k(1 + xy)

B. log (1 + y) = x + x22 + k

C. log (1 + x) + y + y22 = k

D. None of these

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11. 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

12. Formation of the differential equation of the family of curves represented by y=Ae^2x+Be^-2x is :

CBSE Class12 Maths Differentials Equation (12q)

A. (A)

B. (B)

C. (C)

D. (D)

13. The degree of the differential equation
(d2ydx)² + (dydx)² = x sin dydx is

A. 1

B. 2

C. 3

D. not defined

14. 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

15. The degree of the differential equation CBSE Class12 Maths Differentials Equation (15Q)

A. 2

B. 1

C. 3

D. 0

16. If p and q are the degree and order of the differential equation

A. -7

B. -8

C. 8

D. 7

17. The degree of differential equation
[1 + (dydx)²]³² = d2ydx2 is

A. 4

B. 32

C. 2

D. not defined

18. 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

19. Differential equation representing the family of curves given by y = ax + x² is:

CBSE Class12 Maths Differentials Equation(19q)

A. (A)

B. (B)

C. (C)

D. (D)

20. The order the differential equation

A. one

B. two

C. four

D. zero

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21. The order and degree of the differential equation
d2ydx2 + (dydx)¹⁴ + x¹³ = 0 respectvely, are

A. 2 and not defined

B. 2 and 2

C. 2 and 3

D. 3 and 3

22. 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

23. The degree of the differential equation CBSE Class12 Maths Differentials Equation (23Q)

A. one

B. two

C. half

D. four

24. If y = e^-x (A cos x + B sin x), then y is a solution of

A. d2ydx2 + 2dydx = 0

B. d2ydx2 – 2dydx + 2y = 0

C. d2ydx2 + 2dydx + 2y = 0

D. d2ydx2 + 2y = 0

25. 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