The temperature in $K$ at which $\Delta G = 0$ for a given reaction with $\Delta H = -20.5 \ kJ \ mol^{-1}$ and $\Delta S = -50.0 \ J \ K^{-1} \ mol^{-1}$ is:

An $LCR$ series circuit with a resistance of $100\,\Omega$ is connected to an ac source of $200\,V$ (r.m.s.) and angular frequency $300\,rad/s$. When only the capacitor is removed,the current lags behind the voltage by $60^\circ$. When only the inductor is removed,the current leads the voltage by $60^\circ$. The average power dissipated is......$W$.

The equation of the radical axis of the pair of circles $7x^2+7y^2-7x+14y+18=0$ and $4x^2+4y^2-7x+8y+20=0$ is

Which of the following is not correctly matched?

Chitin is an example of which of the following?

$A$ point source emits sound equally in all directions in a non-absorbing medium. Two points $P$ and $Q$ are at distances of $2 \ m$ and $3 \ m$ respectively from the source. The ratio of the intensities of the waves at $P$ and $Q$ is