Which of the following gases has the highest heat of combustion?

$A$ body of mass $2\,kg$ makes an elastic collision with another body at rest and continues to move in the original direction with one-fourth of its original speed. The mass of the second body which collides with the first body is .......... $kg$.

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 $rad/s$.

An eight-digit number divisible by $9$ is to be formed using digits from $0$ to $9$ without repeating the digits. The number of ways in which this can be done is: (in $(7!)$)

$A$ $TV$ transmitting antenna is $128 \ m$ tall. If the receiving antenna is at the ground level,the maximum distance between them for satisfactory communication in line-of-sight mode is (radius of the earth $R_e = 6.4 \times 10^6 \ m$):

$A$ mass $M$ hangs on a massless rod of length $l$ which rotates at a constant angular frequency $\omega$. The mass $M$ moves with steady speed in a circular path of constant radius $r$. The angular momentum of $M$ about point $A$ is $L_A$,which lies in the positive $z$-direction,and the angular momentum of $M$ about point $B$ is $L_B$. Which of the following statements is correct for this system?