For a gas $\frac{R}{C_V} = 0.67$. This gas is made up of molecules which are

If the distance $s$ travelled by a particle in time $t$ is given by $s=t^2-2t+5$, then its acceleration is

Two particles of mass $m$ each are tied at the ends of a light string of length $2a$. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance $a$ from the centre $P$ (as shown in the figure). Now,the mid-point of the string is pulled vertically upwards with a small but constant force $F$. As a result,the particles move towards each other on the surface. The magnitude of acceleration,when the separation between them becomes $2x$,is

The bond angles of $NH_3$,$NH_4^+$,and $NH_2^-$ are in the order :-

If $f$ is a differentiable function such that $f(2x+1) = f(1-2x)$ for all $x \in R$,then find the minimum number of roots of the equation $f'(x) = 0$ in the interval $x \in (-5, 10)$,given that $f(2) = f(5) = f(10)$.

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 $\vec{PQ}$ is parallel to the plane $x - 4y + 3z = 1$ is: