If $\log 2=a, \log 3=b, \log 7=c$ and $6^x=7^{x+4}$,then $x$ is equal to:

One hundred identical coins,each with probability $p$ of showing heads,are tossed once. If $0 < p < 1$ and the probability of heads showing on $50$ coins is equal to that of heads showing on $51$ coins,then the value of $p$ is

The solution of the differential equation $\frac{dy}{dx} - 2y \tan 2x = e^x \sec 2x$ 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?

$100 \ g$ of water is heated from $30^\circ C$ to $50^\circ C$. Ignoring the slight expansion of the water,the change in its internal energy is ...... $kJ$ (specific heat of water is $4184 \ J/kg/K$).

The point collinear with $(1, -2, -3)$ and $(2, 0, 0)$ among the following is