# Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations

## Differential Equations Class 12 Maths MCQs Pdf

1. Order of differential equation correspon- ding to family of curves y = Ae^{2x} + Be^{2x} is ______ .

**Answer/Explanation**

Answer:

Explaination: 2, as there are two arbitrary constants and we have to differentiate twice.

2. The order of the differential equation corresponding to the family of curves y = c(x – c)², c is constant is ______ .

**Answer/Explanation**

Answer:

Explaination: One, as there is one arbitrary constant.

3. The degree of differential equation

is not defined. State true or false.

**Answer/Explanation**

Answer:

Explaination: Three, as equation cannot be represented as polynomial of derivatives.

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

then the value of 2p – 3q is

(a) 7

(b) -7

(c) 3

(d) -3

**Answer/Explanation**

Answer: b

Explaination:

(b), as degree p = 1 and order q = 3

∴ 2p – 3q = 2 – 9 = -7

5. The degree of the differential equation

(a) 1

(b) 2

(c) 3

(d) 4

**Answer/Explanation**

Answer: c

Explaination:

(c), as differential equation is

Exponent of highest order derivative is 3.

6. The degree of the differential equation

(a) 1

(b) 2

(c) 3

(d) not defined

**Answer/Explanation**

Answer: d

Explaination:

(d), as equation cannot be represented as a polynomial of derivatives.

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

(a) 1

(b)2

(c) 3

(d) 4

**Answer/Explanation**

Answer: b

Explaination:

(b), as centre is arbitrary (h, k), two arbitrary constants so we have to differentiate twice to eliminate h, k

∴ order is 2.

8. Degree of the differential equation

is not defined. State true or false.

**Answer/Explanation**

Answer:

Explaination:

False, as equation can be written as

Further it can be written as a polynomial of derivatives. 9.

9. Write the degree of the differential equation

**Answer/Explanation**

Answer:

Explaination: Degree 1

10. Write the degree of the differential equation

**Answer/Explanation**

Answer:

Explaination: Degree 3.

11. Find the value of m and n, where m and n are order and degree of differential equation

**Answer/Explanation**

Answer:

Explaination:

Order of differential equation (m) = 3

Degree of differential equation (n) = 2

12. Write the order and degree of the differential equation \(\frac{d y}{d x}+\sin \left(\frac{d y}{d x}\right)\) = 0. [HOTS]

**Answer/Explanation**

Answer:

Explaination:

Highest order derivative is \(\frac{dy}{dx}\). Hence, order of differential equation is 1. Equation cannot be written as a polynomial’ in derivatives. Hence, degree is not defined.

13. The differential equation of the family of lines passing through ongrn is

(a) y = mx

(b) \(\frac{dy}{dx}\) = m

(c) x dy – y dx = 0

(d) \(\frac{dy}{dx}\) = 0

**Answer/Explanation**

Answer: c

Explaination:

(c), as general equation of line through origin is

y = mx

⇒ \(\frac{dy}{dx}\) = m

Substituting in (i), we get dy

y = \(\frac{dy}{dx}\).x

⇒ x dy – y dx = 0

14. Find the differential equation representing the family of curves y = ae^{bx + 5}, where a and b are arbitrary constants. [CBSE 2018]

**Answer/Explanation**

Answer:

Explaination:

Consider y = ae^{bx + 5}

.On differentiating both sides, w.r.t, x

\(\frac{dy}{dx}\) = abe^{bx + 5} = by …..(i)

Again differentiating w.r.t. x, we get

\(\frac{d^{2} y}{d x^{2}}=b \cdot \frac{d y}{d x}\) …..(ii)

From (i) and (ii), eliminating b, we get

\(y \cdot \frac{d^{2} y}{d x^{2}}=\left(\frac{d y}{d x}\right)^{2}\) as required equation.

15. Form the differential equation representing the family of parabolas having vertex at origin and axis along positive direction of the x-axis. [NCERT; DoE]

**Answer/Explanation**

Answer:

Explaination:

General equation of parabola is y² = 4ax …..(i)

Differentiating, we get 2yy’ = 4a

⇒ yy’ = 2a.

Substituting in (i), we gety2 = 2xyy’.

16. Form the differential equation of the family of parabolas having vertex at the origin and axis along positive y-axis. [Delhi 2011]

**Answer/Explanation**

Answer:

Explaination:

x² = 4 ay

⇒ 2x = 4 ay’

⇒ \(\frac{x^{2}}{2 x}=\frac{4 a y}{4 a y^{\prime}}\)

⇒ xy’ – 2y = 0 is the required equation.

17. General solution of the differential equation log\(\frac{dy}{dx}\) = 2x +y is _______ .

**Answer/Explanation**

Answer:

Explaination:

18. Solve the differential equation \(\frac{dy}{dx}\) = e^{x – y} + x^{3}e^{-y}.

**Answer/Explanation**

Answer:

Explaination:

19. Find the particular solution of the differential equation \(\frac{dy}{dx}\) =y tanx, given that y= 1 when x = 0.

**Answer/Explanation**

Answer:

Explaination:

∫ \(\frac{dy}{y}\) = ∫tan x dx

⇒ log |y| = log|sec x| + log C

⇒ y = C sec x ….(i)

Given y = 1, x = 0

⇒ 1 = C sec 0

⇒ C = 1

∴ solution is y = sec x [from (i)]

20. Find the general solution of the differential equation \(\frac{dy}{dx}\) = \(\frac{x+1}{2-y}\), (y ≠ 2). [NCERT]

**Answer/Explanation**

Answer:

Explaination: