Which of the following statements is correct?

Suppose $\overrightarrow{a}=\lambda \hat{i}-7 \hat{j}+3 \hat{k}$ and $\overrightarrow{b}=\lambda \hat{i}+\hat{j}+2 \lambda \hat{k}$. If the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is greater than $90^{\circ}$,then $\lambda$ satisfies the inequality

If $\tan A$ and $\tan B$ are the roots of the quadratic equation $x^2-px+q=0$,then $\sin^2(A+B)$ is equal to

$A$ 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?

$A$ sound source is moving towards a stationary observer with $(1/10)$ of the speed of sound. The ratio of apparent to real frequency is .........

Three liquids of densities $\rho_1, \rho_2$ and $\rho_3$ (with $\rho_1 > \rho_2 > \rho_3$) having same value of surface tension $T$,rise to the same height in three identical capillaries. Angle of contact $\theta_1, \theta_2$ and $\theta_3$ respectively obey