Class 12 differential equation multiple choice question

Multiple choice (Differential equation)

Choose and write the correct option in the following question:(differential equation multiple choice)

1.) The degree of differential equation $x^2\frac{d^2y}{dx^2} = (x\frac{dy}{dx}-y)^3$ is

(a) 1 (b) 2

Answer (a)

2.) The degree of differential equation $\frac{d^2y}{dx^2}+3(\frac{dy}{dx})^2=x^2\log(\frac{d^y}{dx^2})$ is

(a) 1 (b) 2

Answer (d)

3.) The order and degree of the differential eqution $\left[1+(\frac{dy}{dx})^2\right]^2=\frac{d^2y}{dx^2}$ respectively, are

(a) 1, 2 (b) 2, 2

Answer (c)

4.) The solution of $\log(\frac{dy}{dx}) = ax + by$ is

(a) $\frac{e^{by}}{b}=\frac{e^{ax}}{a}+C$

(b) $\frac{e^{-by}}{-b}=\frac{e^{ax}}{a}+C$

(d) 4

Answer (b)

5.) The solution of the differential equation $2x.\frac{dy}{dx}-y = 3$ represents a family of

(a) Straight lines (b) circles

Answer (c)

6.) The integrating factor of the differential equation $\frac{dy}{dx}(x\log x)+y = 2\log x$ is

(a) $e^x$ (b) $\log x$

Answer (b)

7.) A solution of differential equation $(\frac{dy}{dx})^2 - x\frac{dy}{dx}+y = 0$ is

(a) y = 2 (b) y = 2x

Answer (c)

8.) Which of the following is not a homogenuous function of x and y ?

(a) $x^2+2xy$

(b) $2x-y$

(d) $\sin x - \cos y$

Answer (d)

9.) Solution of the differential equation $\frac{dx}{x}+\frac{dy}{y}=0$

(a) $\frac{1}{x}+\frac{1}{y}=c$

(b) $\log x.\log y = c$

(d) x + y = c

Answer (c)

10.) The solution of differential equation $x\frac{dy}{dx}+2y = x^2$ is

(a) $y = \frac{x^2+C}{4x^2}$

(b) $y = \frac{x^2}{4}+C$

(d) $y = \frac{x^4+C}{4x^2}$

Answer (d)

11.) The degree of the differential equation $(\frac{d^2y}{dx^2})^2+(\frac{dy}{dx})^2 = x\sin x(\frac{dy}{dx})$ is

(a) 1 (b) 2

Answer (d)

12.) The degree of the differential equation $\left[1+(\frac{dy}{dx})^2\right]^{3/2}= \frac{d^y}{dx^2}$ is

(a) 4 (b) 3/2

Answer (d)

13.) The order and degree of differential equation $\frac{d^2y}{dx^2}+(\frac{dy}{dx})^{1/4}+x^{1/5}= 0$

(a) 2 and Not defined (b) 2 and 2

Answer (a)

14.) The solution of differential equation $\frac{dy}{dx}+\frac{2y}{x}=0$ with y(1) = 1 is given by

(a) $y = \frac{1}{x^2}$ (b) $x = \frac{1}{y^2}$

Answer (a)

15.) The general solution of $\frac{dy}{dx} = e^{x-y}+x^2e^{-y}$ is

(a) $y = e^{x-y}- x^2e^{-y}+C$

(b) $e^y - e^x = \frac{x^3}{3}+C$

(d) $e^x-e^y = \frac{x^3}{3}+C$

Answer (b)

16.) Integrating factor of $x\frac{dy}{dx}-y = x^4-3x$ is

(a) x (b) $\log x$

Answer (c)

17.) Solution of $\frac{dy}{dx}-y =1,y(0) = 1$ is given by

(a) $xy =-e^{x}$ (b) $xy =-e^{-x}$

Answe (d)

18.) The number of solution of $\frac{dy}{dx} = \frac{y+1}{x-1}$ when y(1) = 2 is

(a) None (b) one

Answer (b)

19.) which of the following is a second order differential equation ?

(a) $(y')^2+x =y^2$

(b) $y'' + y =\sin x$

(d) $y' = y^2$

Answer (b)

20.) Integrating factor of the differential equation $(1-x^2)\frac{dy}{dx}-xy = 1$ is

(a) -x (b) $\frac{x}{1+x^2}$

Answer (c)

Class 12 differential equation multiple choice question

Multiple choice (Differential equation)

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