The $Adaptation$ of eyes in the dark is due to

The gas used in the hydrogenation of vegetable oils in the presence of nickel as catalyst is

Black Jack is an ore of

The ends of an element of zinc wire are kept at a small temperature difference $\Delta T$ and a small current $I$ is passed through the wire. Then,the heat developed per unit time

Match the items of column $I$ with column $II$. Select the correct option from the following:

Column $I$	Column $II$
$(a)$ $XX-XO$ method of sex determination	$(i)$ Turner's syndrome
$(b)$ $XX-XY$ method of sex determination	$(ii)$ Female heterogametic
$(c)$ Karyotype-$45$	$(iii)$ Grasshopper
$(d)$ $ZW-ZZ$ method of sex determination	$(iv)$ Female homogametic

Observe the following statements:
$(I)$ In $\triangle ABC, b \cos^2 \frac{C}{2} + c \cos^2 \frac{B}{2} = s$
$(II)$ In $\triangle ABC, \cot \frac{A}{2} = \frac{b+c}{a} \Rightarrow B = 90^{\circ}$
Which of the following is correct?