The number of divisors of $n = 38808$ (excluding $1$ and $n$) is

The spring balance $A$ reads $2 \ kg$ with a block $m$ suspended from it. $A$ balance $B$ reads $5 \ kg$ when a beaker with liquid is placed on the pan of the balance. The two balances are now arranged such that the hanging mass is inside the liquid in the beaker as shown in the figure. In this situation:

$A$ closed pipe is suddenly opened and changed to an open pipe of the same length. The fundamental frequency of the resulting open pipe is less than that of the $3^{rd}$ harmonic of the earlier closed pipe by $55 ~Hz$. Then,the value of the fundamental frequency of the closed pipe is: (in $~Hz$)

The maximum value of $Z=x+y$,subjected to $x+y \leq 10$,$5x+3y \geq 15$,$x \leq 6$,$x, y \geq 0$.

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

Suppose,the acceleration due to gravity at the Earth's surface is $10\, m\, s^{-2}$ and at the surface of Mars it is $4.0\, m\, s^{-2}$. $A$ $60\, kg$ passenger goes from the Earth to the Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which part of the figure best represents the weight (net gravitational force) of the passenger as a function of time?