Factors affecting the Hardy-Weinberg principle are:
$(I)$ Gene flow
$(II)$ Genetic drift
$(III)$ Mutation
$(IV)$ Genetic recombination
$(V)$ Natural selection
The correct combination is:

In a playground,there is a merry-go-round of mass $120 \ kg$ and radius $4 \ m$. The radius of gyration is $3 \ m$. $A$ child of mass $30 \ kg$ runs at a speed of $5 \ m/s$ tangent to the rim of the merry-go-round when it is at rest and then jumps on it. Neglecting friction,find the angular velocity of the merry-go-round and child in $rad/s$.

Chemical $A$ is used for water softening to remove temporary hardness. $A$ reacts with sodium carbonate to produce caustic soda. When $CO_2$ is passed through a solution of $A$,it turns milky. What is the chemical formula of $A$?

Each pair forms an ideal solution except:

If the roots of the equations $px^2 + 2qx + r = 0$ and $qx^2 - 2\sqrt{pr}x + q = 0$ are real,then

Two small spheres,each having an equal positive charge $Q$ (Coulomb),are suspended by two insulating strings of equal length $L$ (metre) from a rigid hook. The whole setup is taken into a satellite where there is no gravity. The two balls are now held by electrostatic forces in a horizontal position. The tension in each string is then: