Class 12 differential equation multiple choice question

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Multiple choice (Differential equation)

Class 12 differential equation multiple choice

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

(c)3                              (d) 6

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

(c) 3                               (d) Not defined

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

(c) 2, 1                            (d) 4, 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

(c) \frac{e^{-by}}{a}=\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

(c) Prabolas                     (d) Ellipse

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

(c) \log(\log x)           (d) 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

(c) y = 2x – 4                    (d) y = 2x² – 4

Answer (c)

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

(a) x^2+2xy

(b) 2x-y

(c) \cos^2(\frac{y}{x})+\frac{y}{x}

(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

(c) xy = 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

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

(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

(c) 3                            (d) Not defined

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

(c) Not defined        (d) 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

(c) 2 and 3                              (d) 3 and 3

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}

(c) x = \frac{1}{y}              (d) y = \frac{1}{x}

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

(c) e^x+e^y = \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

(c) \frac{1}{x}    (d) -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}

(c) xy = -1                    (d) -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

(c) two                          (d) ifinite

Answer (b)

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

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

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

(c) y''' + (y'')^2+y=0

(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}

(c) \sqrt{1-x^2}     (d) \frac{1}{2}\log(1-x^2)

Answer (c) 

 

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