The process of the isolation of a metal by dissolving the ore in a suitable chemical reagent followed by precipitation of the metal by a more electropositive metal is called:

Carbon,Silicon,and Germanium atoms have four valence electrons each. Their valence and conduction bands are separated by energy band gaps represented by $(E_g)_C$,$(E_g)_{Si}$,and $(E_g)_{Ge}$ respectively. Which one of the following relationships is true in their case?

If $m \begin{bmatrix} -3 & 4 \end{bmatrix} + n \begin{bmatrix} 4 & -3 \end{bmatrix} = \begin{bmatrix} 10 & -11 \end{bmatrix}$,then $3m + 7n$ is equal to

Six faces of an unbiased die are numbered with $2, 3, 5, 7, 11$ and $13$. If two such dice are thrown,then the probability that the sum on the uppermost faces of the dice is an odd number is

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 ${}^n P_r = 30240$ and ${}^n C_r = 252$,then the ordered pair $(n, r)$ is equal to