If a convex lens of focal length $80 \ cm$ and a concave lens of focal length $50 \ cm$ are combined together,what will be their resulting power?

If ${z_r} = \cos \frac{{r\alpha }}{{{n^2}}} + i\sin \frac{{r\alpha }}{{{n^2}}},$ where $r = 1, 2, 3, \dots, n$,then $\mathop {\lim }\limits_{n \to \infty } \,{z_1}{z_2}{z_3}\dots{z_n}$ is equal to

$\sec ^2(\tan ^{-1} 2) + \operatorname{cosec}^2(\cot ^{-1} 3)$ is equal to

Which of the following is a true acidic anhydride?

A short bar magnet placed with its axis at $30^{\circ}$ with an external field of $800$ $Gauss$, experiences a torque of $0.016 ext{ N.m}$. The work done in moving it from most stable to most unstable position is $\alpha \times 10^{-3} ext{ J}$. The value of $\alpha$ is . . . . . . . . . .

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