The angle between the lines $\vec{r}=(2 \hat{i}-3 \hat{j}+\hat{k})+\lambda(\hat{i}+4 \hat{j}+3 \hat{k})$ and $\vec{r}=(\hat{i}-\hat{j}+2 \hat{k})+\mu(\hat{i}+2 \hat{j}-3 \hat{k})$ is

Two stones of masses $m$ and $3m$ are whirled in horizontal circles,the heavier one in a radius $\left(\frac{r}{3}\right)$ and the lighter one in a radius $r$. The tangential speed of the lighter stone is '$n$' times the value of the heavier stone. When the magnitude of the centripetal force becomes equal,the value of $n$ is:

Velocity and acceleration vectors of a charged particle moving perpendicular to the direction of a magnetic field at a given instant of time are $\overrightarrow{v}=2 \hat{i}+c \hat{j}$ and $\overrightarrow{a}=3 \hat{i}+4 \hat{j}$ respectively. Then the value of $c$ is

If the extremities of a diagonal of a square are $(1, -2, 3)$ and $(2, -3, 5)$,then the length of its side is

Consider the following two statements $A$ and $B$ and identify the correct choice in the given answers:
$A$. Paramagnetism is explained by domain theory.
$B$. Susceptibility of a diamagnetic substance is independent of temperature.

Which of the following is true in the case of an adiabatic process,where $\gamma = C_p / C_V$?