Important Questions for CBSE Class 12 Maths Chapter 9

CBSE Class 12 Maths Chapter-9 Important Questions – Free PDF Download

Free PDF download of Important Questions for CBSE Class 12 Maths Chapter 9 – Differential Equations prepared by expert Maths teachers from latest edition of CBSE(NCERT) books, On CoolGyan.Org to score more marks in CBSE board examination.
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CBSE Class 12 Mathematics Important Questions Chapter 9 – Differential Equations

1 Mark Questions

1. Find the order and degree. +y²+=0
Ans. order =3
Degree = not define.

2. Verify that the functions is a sol of the corresponding diff. req.
Ans.

Hence prove.

3.Form the differential equation of the family of hyper bolas having foci On x-axis and center at origin.
Ans.

4. Find the order and degree
Ans. order = 2
degree = 1

5. Verify that the function is a solution of the corresponding diff eq.

Ans.

proved.

6. Find order and degree.
Ans. order = 3
degree = not define

7. Verify that the function is a solution of the corresponding diff eq.

Ans.

8. Find order and degree.
Ans. order = 4
degree = not define

9. Verify that the function is a solution of the corresponding diff eq.
Ans.
Proved

10. Write the order and degree of the diff equation
Ans.

11. Verify that the given functions is a solution of the corresponding diff eq.
Ans. y = Cos x + c

4 Mark Questions

1. Form the differential equation of the family of circles having centre on y-axis and radius 3 units.
Ans.

2. Solve the diff. equ. sec²x.tan y dx + sec² y tan x dy = 0
Ans. Sec²x. tan y dx = -sec²y tan x dy

3. Solve the diff eq. y log y dx –x dy = 0
Ans.

4. Solve x cos
Ans.

0

5. Solve
Ans.

6. Form the differential equation representing the family of ellipses having foci on x – axis and centre at the origin.
Ans.

diff eq (i) w. r. t. x

diff w. r. t. x

7. Form the diff. eq of the family of circles touching the x – axis at origin.
Ans. Let (o, a) be
The coordinate of circle.

Put a and y – a in eq (1)

8. Solve the diff eq.
Ans.

9. Solve Cos
Ans.

10. Solve.
Ans.

11. Solve
Ans.

12. Form the differential equation representing the family of curves given by (x-a)² + 2y²= a², where a is an arbitrary constant.
Ans.
diff both side w.r.t.x

13. Form the diff. equation of the family of circles in the second quadrant and touching the coordinate axes.

Ans. Eq. of circle is

14. Solve the diff eq.
Ans.

15. Solve
Ans.

16. Solve
Ans.

17. Solve
Ans.

18. Form a differential equation representing the given family of curve by eliminating arbitrary constants a and b.
Ans.

19. Form a differential equation representing the given family of curve by eliminating arbitrary constants a and b. Y = e^x (a Cos x + b Sin x)
Ans.

20. Solve the diff eq.
Ans.

21. Find the equation of the curve passing through the point whose diff eq. is Sin x Cos y dx + Cos x . Sin y dy = 0
Ans. Sin x. Cos y dx = – Cos x. Sin y dy