Let $A = \{2, 4, 6, 8\}$. $A$ relation $R$ on $A$ is defined by $R = \{(2, 4), (4, 2), (4, 6), (6, 4)\}$. Then $R$ is

$A$ force $\overrightarrow F = 6\hat i + 2\hat j - 3\hat k$ acts on a particle,causing a displacement of $\overrightarrow s = 2\hat i - 3\hat j + x\hat k$. If the work done is zero,find the value of $x$.

$A$ uniform chain of length $L$ is lying on a horizontal table. If the coefficient of friction between the chain and the table top is $\mu$, what is the maximum length of the chain that can hang over the edge of the table without disturbing the rest of the chain on the table?

$M_p$ denotes the mass of a proton and $M_n$ denotes the mass of a neutron. $A$ given nucleus,of binding energy $B$,contains $Z$ protons and $N$ neutrons. The mass $M(N, Z)$ of the nucleus is given by ($c$ is the velocity of light):

The ratio of the mass percentages of $C$ and $H$,and $C$ and $O$ of a saturated acyclic organic compound $X$ are $4:1$ and $3:4$ respectively. Then,the moles of oxygen gas required for the complete combustion of two moles of organic compound $X$ is:

Which of the following expressions corresponds to simple harmonic motion along a straight line,where $x$ is the displacement and $a, b, c$ are positive constants?