If $A$ and $B$ are events of a random experiment such that $P(A \cup B) = \frac{4}{5}$,$P(\bar{A} \cup \bar{B}) = \frac{7}{10}$ and $P(B) = \frac{2}{5}$,then $P(A)$ equals

If $2.2 \, kW$ power is transmitted through a $10 \, \Omega$ line at $22000 \, V$,the power loss in the form of heat will be ............. $W$.

Let $A = \{2, 4, 6, 8\}$. $A$ relation $R$ on $A$ is defined by $R = \{(2, 4), (4, 2), (4, 6), (6, 4)\}$. Then $R$ 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

The angle between the lines represented by $y^2 \sin^2 \theta - xy \sin^2 \theta + x^2(\cos^2 \theta - 1) = 0$ is

There are two identical small holes of cross-sectional area $a$ on the opposite sides of a tank containing a liquid of density $\rho$. The difference in height between the holes is $h$. The tank is resting on a smooth horizontal surface. The horizontal force which will have to be applied on the tank to keep it in equilibrium is