$A$ bag contains $n$ white and $n$ black balls. Pairs of balls are drawn at random without replacement successively,until the bag is empty. If the number of ways in which each pair consists of one white and one black ball is $14400$,then $n$ is equal to

Five moles of hydrogen initially at $STP$ is compressed adiabatically so that its temperature becomes $673 \, K$. The increase in internal energy of the gas, in kilo joule is $(R=8.3 \, J/mol-K; \gamma=1.4$ for diatomic gas$)$

$A$ die is thrown four times. The probability of getting a perfect square in at least one throw is

$SiCl_4$ on hydrolysis forms '$X$' and $HCl$. Compound '$X$' loses water at $1000^\circ C$ and gives '$Y$'. Compounds '$X$' and '$Y$' respectively are:

The transformed equation of $x^2+6xy+8y^2=10$ when the axes are rotated through an angle $\frac{\pi}{4}$ is:

Two wires $A$ and $B$ are of lengths $40 \ cm$ and $30 \ cm$. $A$ is bent into a circle of radius $r$ and $B$ into an arc of radius $r$. $A$ current $i_1$ is passed through $A$ and $i_2$ through $B$. To have the same magnetic inductions at the centre,the ratio of $i_1: i_2$ is