$A$ Carnot engine,having an efficiency of $\eta = 1/10$ as a heat engine,is used as a refrigerator. If the work done on the system is $10 \ J$,the amount of energy absorbed from the reservoir at a lower temperature is .......... $J$.

On a rainy day,a small oil film on water shows brilliant colours. This is due to

Consider the following anions:
$(I)$ $CF_{3}SO_{3}^{-}$
$(II)$ $C_{6}H_{5}SO_{3}^{-}$
$(III)$ $C_{6}H_{5}O^{-}$
$(IV)$ $CH_{3}COO^{-}$
When attached to $sp^{3}$-hybridized carbon,their leaving group ability in nucleophilic substitution reaction decreases in the order:

If $3$ is a root of $x^2+kx-24=0$,then it is also a root of which of the following equations?

If the angle between the circles $x^2+y^2-2x-4y+c=0$ and $x^2+y^2-4x-2y+4=0$ is $60^{\circ}$,then $c$ is equal to

$A$ bag $X$ contains $2$ white and $3$ black balls and another bag $Y$ contains $4$ white and $2$ black balls. One bag is selected at random and a ball is drawn from it. Then the probability for the ball chosen to be white is