The molar heat capacity of water at constant pressure is $75 \ J \ K^{-1} \ mol^{-1}$. When $1.0 \ kJ$ of heat is supplied to $100 \ g$ of water which is free to expand,the increase in temperature of water is ............. $K$.

The number of ways that $8$ beads of different colours can be strung as a necklace is

The centre of mass of two masses $m$ and $m'$ moves by a distance $\frac{x}{5}$ when mass $m$ is moved by a distance $x$ and $m'$ is kept fixed. The ratio $\frac{m'}{m}$ is

$A$ concave mirror of focal length $f$ (in air) is immersed in water $(\mu = 4/3)$. The focal length of the mirror in water will be

The major product of the following reaction is

At $27^{\circ} C$,a closed vessel contains a mixture of equal weights of helium (mol. wt. = $4$),methane (mol. wt. = $16$) and sulphur dioxide (mol. wt. = $64$). The pressure exerted by the mixture is $210 \ mm$. If the partial pressures of helium,methane and sulphur dioxide are $p_1, p_2$ and $p_3$ respectively,which one of the following is correct?