Question - 2

If \(u=\) \(\sin ^{ -1 }{ \left( \frac { { x }^{ 4 }+{ y }^{ 4 } }{ { x }^{ 2 }+{ y }^{ 2 } } \right) } \) and \(f =\) \(\sin { u } \) then f is a homogeneous function of degree

Question - 3

If \(u =\) \(\frac { 1 }{ \sqrt { { x }^{ 2 }+{ y }^{ 2 } } } \) , then \(x\frac { \partial u }{ \partial x } +y\frac { \partial u }{ \partial y } \) is equal to

Question - 4

The curve \({ y }^{ 2 }\left( x-2 \right) ={ x }^{ 2 }\left( 1+x \right) \) has

Question - 5

If \(x=r\cos { \theta } ,y=r\sin { \theta \quad ,\quad then\quad \frac { \partial r }{ \partial x } } \) is equal to

Question - 6

Identify the true statements in the following

i. if a curve is symmetrical about the origin, then it is symmetrical about  both axes.

ii. if a curve is symmetrical about the both the axes, then it is symmetrical about the origin.

iii. A curve \(f\left( x,y \right) =0\) is symmetrical about the line \( y = x\) if \(f\left( x,y \right) =f\left( y,x \right) \).

iv. for the curve \(f\left( x,y \right) =0, \),if \( f\left( x,y \right) =f\left( -y,-x \right) \)then it is symmetrical about the origin. 

Question - 7

If \(u=\log { \left( \frac { { x }^{ 2 }+{ y }^{ 2 } }{ xy } \right) } \) then \( x\frac { \partial u }{ \partial x } +y\frac { \partial u }{ \partial y } \)is

Question - 8

The percentage error in the 11^th root of the number 28 is approximately…………. times  the percentage error in 28.

Question - 9

The curve \({ a }^{ 2 }{ y }^{ 2 }= { x }^{ 2 }\left( { a }^{ 2 }-{ x }^{ 2 } \right) \)has

Question - 10

An asymptote to the curve \({ y }^{ 2 }\left( a+2x \right) ={ x }^{ 2 }\left( 3a-x \right) \) is ..