Free Printable B.Sc. Sem I Paper II Unit II

1.

If $z=f\left(x+ay\right)+g\left(x-ay\right)\$ then

a)

$\frac{\partial^2z}{\partial x^2}=a^2\frac{\partial^2z}{\partial y^2}$

b)

$\frac{\partial^2z}{\partial x^2}=-a^2\frac{\partial^2z}{\partial y^2}$

c)

$\frac{\partial^2z}{\partial y^2}=a^2\frac{\partial^2z}{\partial x^2}$

d)

$\frac{\partial^2z}{\partial y^2}=-a^2\frac{\partial^2z}{\partial x^2}$

2.

$u=\log\left[\frac{\left(x^4+y^4\right)}{x+y}\right]$

a)

Is non homogeneous function

b)

is homogeneous function of degree 3

c)

is homogeneous function of degree 4

d)

none of these

3.

If $z=f\left(x,\ y\right)$ be a homogeneous function of x, y of degree n then $x^2\frac{\partial^2z}{\partial x^2}+2xy\frac{\partial^2z}{\partial x\partial y}+y^2\frac{\partial^2z}{\partial y^2}=$

a)

nz

b)

(n-1)z

c)

$\frac{n\left(n-1\right)}{2}z$

d)

n(n-1)z

4.

If $G=f\left(y-z,\ z-x,\ x-y\right)$ then $\frac{\partial G}{\partial x}+\frac{\partial G}{\partial y}+\frac{\partial G}{\partial z}=$

a)

0

b)

1

c)

2

d)

G

5.

The asymptotes parallel to x-axis obtained by equating coefficients of highest power of --- to zero

(a)

6.

The asymptotes to any curve is

a)

always a circle

b)

always a parabola

c)

always a straight line

d)

y=mx+c

7.

An envelope is a curve that ----- to each member of the family of curves in a plane.

(a)

8.

The envelope of the curve $y=mx+\frac{a}{m}$

a)

$y^2=4ax$

b)

$x^2=4ay$

c)

$\frac{x^2}{a^2}+\frac{y^2}{a^2}=1$

d)

none of these

9.

$\left(x-a\right)^2+\left(y-b\right)^2=r^2$ is

a)

a two parameter family of curves

b)

a collection of all circles of radius 3

c)

a collection of all circles of radius r

d)

one parameter family of curves

10.

The envelope of $Pm^2+Rm+Q=0$ is

a)

$Q^2=\text{}4PR$

b)

$Q^2=4RP$

c)

$P^2=4RQ$

d)

$R^2=4PQ$

B.Sc. Sem I Paper II Unit II

Total questions: 10

Worksheet time: 7mins

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