Let $P(3, 2, 6)$ be a point in space and $Q$ be a point on the line $\vec{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \mu(-3\hat{i} + \hat{j} + 5\hat{k})$. Then the value of $\mu$ for which the vector $\overrightarrow{PQ}$ is parallel to the plane $x - 4y + 3z = 1$ is

If three unit vectors $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ satisfy $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$, then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is

In a meter bridge,a $30 \Omega$ resistance is connected in the left gap and a pair of resistances $P$ and $Q$ in the right gap. Measured from the left,the balance point is $37.5 \text{ cm}$ when $P$ and $Q$ are in series,and $71.4 \text{ cm}$ when they are in parallel. The values of $P$ and $Q$ (in $\Omega$) are:

Two identical blocks $A$ and $B$,each of mass $m$,resting on a smooth floor,are connected by a light spring of natural length $L$ and spring constant $k$. $A$ third identical block $C$ (mass $m$) moving with a speed $v$ along the line joining $A$ and $B$ collides with $A$. The maximum compression in the spring is proportional to:

Identify the correct statement among the following options:

The binding energy of deuteron ${}_1^2H$ is $1.112 \text{ MeV}$ per nucleon and an $\alpha$-particle ${}_2^4He$ has a binding energy of $7.047 \text{ MeV}$ per nucleon. Then in the fusion reaction ${}_1^2H + {}_1^2H \to {}_2^4He + Q$,the energy $Q$ released is ........... $\text{MeV}$.