Free Printable MCQ-SLIP TEST-BTECH

1.

A differential equation is said to be --------if the dependent variable and its differential coefficients occur only in the first degree and not multiplied together.

a)

linear

b)

non - linear

c)

homogeneous

d)

non-homogeneous

2.

The signature of the ordinary differential equation, $y'+Py=qy'',\ n\ne0$

a)

Bernoulli's equations

b)

Gaussian equations

c)

Besseles equations

d)

Legendre's equations

3.

Order of the differential equation representing the family of parabolas y2 = 4ax is ----

a)

2

b)

4

c)

1

d)

-2

4.

If the given equation on solving for x, takes the form x = f(y, p) then the assumed solution is --------

a)

F(y, p, c) = 0

b)

F(x, p, c) = 0

c)

F(y, dp, c) = 0

d)

F(dy, p, c) = 0

5.

The degree of the differential equation is $\left(\frac{\text{d}^2y}{\text{d}x^2}\right)+\left(\frac{\text{d}y}{\text{d}x}\right)^2+\sin\left(\frac{\text{d}y}{\text{d}x}\right)+1=0$

a)

3

b)

2

c)

1

d)

not defined

6.

Classify the following differential equation: dz/dt=1+z+t+zt.

a)

Linear and not separable

b)

Separable and not linear

c)

Both separable and linear

d)

Neither separable nor linear.

7.

Classify the following differential equation: dx/dt=(x+2xt+cost)/1+t²

a)

Linear and not separable

b)

Separable and not linear

c)

Both separable and linear

d)

Neither separable nor linear.

8.

The degree of the differential equation is $\left(1+\frac{\text{d}y}{\text{d}x}\right)^{3\ }=\ \left(\frac{\text{d}^2x}{\text{d}y^2}\right)^2$

a)

1

b)

2

c)

3

d)

4

9.

The order of the differential equation of all circles of given radius a is ---

a)

1

b)

2

c)

3

d)

4

10.

Classify the following differential equation $w\ \frac{\text{d}w}{\text{d}t}+3t\ =\ 10$

a)

Separable and not linear

b)

Linear and not separable

c)

both separable and Linear

d)

Neither separable nor Linear

11.

The differential equation is ------- $\left(y^2e^{xy^2}+6x\right)dx\ +\ \left(2xye^{xy^2}-4y\right)dy=0\$

a)

linear, homogeneous and exact

b)

non-linear, homogeneous and exact

c)

non-linear, non-homogeneous and exact

d)

non-linear, non-homogeneous and inexact

12.

The differential equations regarding the family of the curve . $y=e^{500x}$

a)

xy′ = y log y

b)

xy′ = x log x

c)

yy ′ = y log y

d)

y+x′ = y log y

13.

Integrating factor

$dy=\left\{e^{x-y}\left(e^x-e^y\right)\right\}dx$

a)

$e^{e^x}$

b)

e

c)

e^x

d)

e^2x

14.

If Mdx+Ndy=0, have the form fydx+gxdy=0 the I.F.

a)

$\frac{1}{Mx-Ny}$

b)

$\frac{1}{Mx+Ny}$

c)

$\frac{1}{Mx-Ny\ne0}$

d)

$\frac{1}{Mx-Ny=0}$

15.

The required solution of $\sec^2x\tan ydx\ +\sec^2y\tan xdy=0$

a)

$\tan x\tan y=k$

b)

$\tan x+\tan y=k$

c)

$\tan x-\tan y=k$

d)

$\frac{\tan x}{\tan y}=k$

MCQ-SLIP TEST-BTECH

Total questions: 15

Worksheet time: 8mins

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