Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 9 Differential Equations. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Differential Equations MCQs Pdf with Answers to know their preparation level.

## 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:

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