$50 \, g$ of ice at $0^{\circ} C$ is dropped into a calorimeter containing $100 \, g$ of water at $30^{\circ} C$. If the thermal capacity of the calorimeter is zero,then the amount of ice left in the mixture at equilibrium is .......... $g$.

$A$ transverse wave is travelling along a stretched string from right to left. The figure shown represents the shape of the string at a given instant. At this instant,

An inductor $(L = 100 \, mH)$,a resistor $(R = 100 \, \Omega)$,and a battery $(E = 100 \, V)$ are initially connected in series as shown in the figure. After a long time,the battery is disconnected by short-circuiting the points $A$ and $B$. The current in the circuit $1 \, ms$ after the short circuit is:

What is the membrane surrounding the heart called?

If the ionic product of water $(K_w)$ is $1.96 \times 10^{-14}$ at $35^{\circ} C$,what is its value at $10^{\circ} C$?

When acetylene is passed through a red-hot iron tube,compound $X$ is formed. Which one of the following reactions will yield $X$ as the major product?