When the size of a spherical nanoparticle decreases from $30 \, nm$ to $10 \, nm$,the ratio of surface area to volume becomes:

$A$ $1 \, kg$ diatomic gas is at a pressure of $8 \times 10^4 \, N/m^2$. The density of the gas is $4 \, kg/m^3$. What will be the energy associated with the thermal motion of the gas?

The enthalpy of combustion of benzene from the following data will be
$(i) \ 6C_{(s)} + 3H_{2(g)} \to C_6H_{6(l)}; \Delta H = + 45.9 \ kJ$
$(ii) \ H_{2(g)} + \frac{1}{2}O_{2(g)} \to H_2O_{(l)}; \Delta H = - 285.9 \ kJ$
$(iii) \ C_{(s)} + O_{2(g)} \to CO_{2(g)}; \Delta H = - 393.5 \ kJ$
........$kJ$

Which of the following is a method of sexual reproduction in algae?

For $k=1, 2, 3$,the box $B_k$ contains $k$ red balls and $(k+1)$ white balls. Let $P(B_1)=\frac{1}{2}$,$P(B_2)=\frac{1}{3}$,and $P(B_3)=\frac{1}{6}$. $A$ box is selected at random and a ball is drawn from it. If a red ball is drawn,then the probability that it has come from box $B_2$ is:

If $A$ is any set,then: