$A$ rotating body has angular momentum $L$. If its frequency of rotation is halved and its rotational kinetic energy is doubled,what will be its new angular momentum?

$A$ bomb moving with velocity $(40 \hat{i} + 50 \hat{j} - 25 \hat{k}) \text{ m/s}$ explodes into two pieces of mass ratio $1:4$. After the explosion,the smaller piece moves away with velocity $(200 \hat{i} + 70 \hat{j} + 15 \hat{k}) \text{ m/s}$. The velocity of the larger piece after the explosion is:

Consider the following reactions at $1000\,^oC$:
$(I)$ $Zn_{(s)} + \frac{1}{2}O_{2(g)} \rightarrow ZnO_{(s)}; \Delta G^o = -360\,kJ\,mol^{-1}$
$(II)$ $C_{(s)} + \frac{1}{2}O_{2(g)} \rightarrow CO_{(g)}; \Delta G^o = -460\,kJ\,mol^{-1}$
Choose the correct statement at $1000\,^oC$.

If the direction cosines of two lines are given by $l+m+n=0$ and $l^2-5m^2+n^2=0$,then the angle between them is

If $\vec{a}, \vec{b}, \vec{c}$ are mutually perpendicular vectors having magnitudes $1, 2, 3$ respectively,then $[\vec{a}+\vec{b}+\vec{c} \quad \vec{b}-\vec{a} \quad \vec{c}]=$

Let $\alpha$ and $\beta$ be the roots of the equation $x^2 - x - 1 = 0$. If $p_k = (\alpha)^k + (\beta)^k$ for $k \geq 1$,then which one of the following statements is not true?