Where is the largest newsprint paper industry located in India?

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

What will be the volume of $CO_2$ at $NTP$ obtained on heating $10 \ g$ of ($90\%$ pure) limestone (in $L$)?

$A$ reaction,$3 X_{(g)} \rightarrow 2 Y_{(g)} + Z_{(g)}$,takes place in a closed vessel. What is the rate of formation of $Y$ (in $mol \ L^{-1} \ s^{-1}$) if the rate of disappearance of $X$ is $7.2 \times 10^{-3} \ mol \ L^{-1} \ s^{-1}$?

$A$ bar magnet has a coercivity of $4 \times 10^3 \, A/m$. It is desired to demagnetize it by inserting it inside a solenoid $12 \, cm$ long and having $60$ turns. The current that should be sent through the solenoid is . . . . . . $A$.

$\frac{\sin 1^{\circ}+\sin 2^{\circ}+\ldots+\sin 89^{\circ}}{2(\cos 1^{\circ}+\cos 2^{\circ}+\ldots+\cos 44^{\circ})+1} = $