In a $\triangle ABC$,if $a \cos^2 \frac{C}{2} + c \cos^2 \frac{A}{2} = \frac{3b}{2}$,then the sides of the triangle are in

Match the following genes of the $Lac$ operon with their respective products.
Select the correct option.

$(a)$ $i$ gene	$(i)$ $\beta$-galactosidase
$(b)$ $z$ gene	$(ii)$ Permease
$(c)$ $a$ gene	$(iii)$ Repressor
$(d)$ $y$ gene	$(iv)$ Transacetylase

The product of the lengths of perpendiculars drawn from any point on the hyperbola $x^2 - 2y^2 - 2 = 0$ to its asymptotes is

The maximum number of sub-levels,orbitals and electrons in $N$ shell of an atom are respectively

$A$ thin prism $P_1$ with angle $4^o$ and made from glass of refractive index $1.54$ is combined with another prism $P_2$ made from glass of refractive index $1.72$ to produce dispersion without deviation. The angle of prism $P_2$ is......$^o$

Which mineral element is present in the structure of the amino acids cysteine and methionine?