$50 \, g$ 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 .......... $g$.

The standard reduction potentials of $Zn^{2+}|Zn$,$Cu^{2+}|Cu$ and $Ag^{+}|Ag$ are respectively $-0.76 \ V$,$0.34 \ V$ and $0.8 \ V$. The following cells were constructed:
$(1)$ $Zn|Zn^{2+}||Cu^{2+}|Cu$
$(2)$ $Zn|Zn^{2+}||Ag^{+}|Ag$
$(3)$ $Cu|Cu^{2+}||Ag^{+}|Ag$
What is the correct order of $E_{cell}^{\circ}$ of these cells?

An air-cored coil has a self-inductance of $0.1 \ H$. $A$ soft iron core of relative permeability $1000$ is introduced,and the number of turns is reduced to $\left(\frac{1}{10}\right)^{\text{th}}$. The value of the new self-inductance is:

The number of subsets of $\{1, 2, 3, \ldots, 9\}$ containing at least one odd number is

$A$ man slides down a telegraphic pole with an acceleration equal to one-fourth of the acceleration due to gravity. The frictional force between the man and the pole is equal to which of the following in terms of the man's weight $w$?

The thermo emf of a thermocouple is given by $E = aT + bT^2$,where $\frac{a}{b} = -200^{\circ}C$. If the cold junction is kept at $30^{\circ}C$,then the inversion temperature is ($\varepsilon$ in volt,$T$ in centigrade). (in $K$)