Two springs have spring constants $K_A$ and $K_B$ such that $K_A > K_B$. If both springs are stretched by the same extension $x$,the work required will be:

$A$ block of mass $m=25 \ kg$ sliding on a smooth horizontal surface with a velocity $v=3 \ ms^{-1}$ meets a spring of spring constant $k=100 \ N/m$ fixed at one end as shown in the figure. The maximum compression of the spring and the velocity of the block as it returns to the original position are respectively:

Light waves producing interference have their amplitudes in the ratio $3: 2$. The intensity ratio of maximum and minimum of interference fringes is

$A$ Carnot engine having an efficiency of $1/10$ 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 .......... $J$.

The cyanobacteria are also referred to as

$A$ and $B$ are two substances undergoing radioactive decay in a container. The half-life of $A$ is $15 \ min$ and that of $B$ is $5 \ min$. If the initial concentration of $B$ is $4$ times that of $A$ and they both start decaying at the same time,how much time will it take for the concentration of both of them to be same? $.......... \ min$