$A$ crystal is made up of metal ions $M_1$ and $M_2$ and oxide ions. Oxide ions form a $ccp$ lattice structure. The cation $M_1$ occupies $50 \%$ of octahedral voids and the cation $M_2$ occupies $12.5 \%$ of tetrahedral voids of the oxide lattice. The oxidation numbers of $M_1$ and $M_2$ are,respectively:

$A$ lead bullet at $27\,^oC$ just melts when stopped by an obstacle. Assuming that $25\%$ of the heat produced is absorbed by the obstacle,the velocity of the bullet at the time of striking is ........ $m/s$. (Melting point of lead $= 327\,^oC$,specific heat of lead $= 0.03\,cal/g\,^oC$,latent heat of fusion of lead $= 6\,cal/g$,and $J = 4.2\,J/cal$)

Which of the following is logically equivalent to $\sim(\sim p \Rightarrow q)$?

When one end of a capillary tube is dipped in water,the height of the water column is $h$. The upward force of $105 \text{ dyne}$ due to surface tension is balanced by the force due to the weight of the water column. What is the inner circumference of the capillary (in $text{ cm}$)? (Surface tension of water $= 7 \times 10^{-2} \text{ N m}^{-1}$)

In a mass spectrometer used for measuring the masses of ions,the ions are initially accelerated by an electric potential $V$ and then made to describe semicircular paths of radius $R$ using a magnetic field $B$. If $V$ and $B$ are kept constant,the ratio $\left( \frac{\text{charge on the ion}}{\text{mass of the ion}} \right)$ will be proportional to

Let $S$ be the sample space of the random experiment of throwing simultaneously two unbiased dice with six faces (numbered $1$ to $6$) and let $E_k = \{(a, b) \in S : ab = k\}$ for $k \geq 1$. If $p_k = P(E_k)$ for $k \geq 1$,then which of the following is correct?