Two satellites of earth,$S_1$ and $S_2$ are moving in the same orbit. The mass of $S_1$ is four times the mass of $S_2.$ Which one of the following statements is true?

If the coefficients of the $(2r+1)$-th term and the $(r+2)$-th term in the expansion of $(1+x)^{43}$ are equal,then $r$ is equal to:

The volume of one mole of the gas is changed from $V$ to $2 V$ at constant pressure $p$. If $\gamma$ is the ratio of specific heats of the gas,what is the change in internal energy of the gas?

$\int_{-\pi / 2}^{\pi / 2} \sin ^4 x \cos ^6 x \, dx$ is equal to

The most important method of preparation of hydrocarbons of lower carbon number is

$A$ cylinder of height $h$ is filled with water and is kept on a block of height $h / 2$. The level of water in the cylinder is kept constant. Four holes numbered $1, 2, 3$ and $4$ are at the side of the cylinder and at heights $0, h / 4, h / 2$ and $3h / 4$ respectively from the base of the cylinder. When all four holes are opened together,the hole from which water will reach the farthest distance on the plane $PQ$ is the hole number