The distance between the lines represented by $4x^2 + 20xy + 25y^2 + 2x + 5y - 12 = 0$ is equal to

Which of the following gases has the highest heat of combustion?

Acetone on addition to methyl magnesium bromide forms a complex,which on decomposition with acid gives $X$ and $Mg(OH)Br$. Which one of the following is $X$?

$A$ magnet freely suspended in a vibration magnetometer makes $40$ oscillations per minute at place $A$ and $20$ oscillations per minute at a place $B$. If the horizontal component of earth's magnetic field at $A$ is $36 \times 10^{-6} ~T$,then its value at $B$ is

$A$ bus moving on a level road with a velocity $v$ can be stopped at a distance of $x$,by the application of a retarding force $F$. The load on the bus is increased by $25 \%$ by boarding the passengers. Now,if the bus is moving with the same speed and if the same retarding force is applied,the distance travelled by the bus before it stops is

If $u=\sin ^{-1}\left(\frac{x^2+y^2}{x+y}\right)$ then $x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}$ is equal to: