If $4$ moles of an ideal monoatomic gas at temperature $400 ~K$ is mixed with $2$ moles of another ideal monoatomic gas at temperature $700 ~K$,the temperature of the mixture is

$(\vec{a} \times \vec{b}) \times [(\vec{b} \times \vec{c}) \times (\vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a})]$ is

The equation of the line passing through the point of intersection of the lines $x-3y+2=0$ and $2x+5y-7=0$ and perpendicular to the line $3x+2y+5=0$ is:

In short-day plants,flowering is induced by:

$\int_2^3 \frac{dx}{x^2-x}$ is equal to

The efficiency of a Carnot engine is $50\%$ and the temperature of the sink is $500\, K$. If the temperature of the source is kept constant and its efficiency is to be raised to $60\%$,then the required temperature of the sink will be........ $K$.