The negation of $\sim s \vee (\sim r \wedge s)$ is equivalent to

The horizontal acceleration that should be given to a smooth inclined plane of angle $\theta = \sin^{-1}\left(\frac{1}{l}\right)$ to keep an object stationary on the plane, relative to the inclined plane is:

If the curves $y^2=6x$ and $9x^2+by^2=16$ intersect each other at right angles,the value of $b$ is

The number of real solutions of $\tan ^{-1} \sqrt{x(x+1)}+\sin ^{-1} \sqrt{x^2+x+1}=\frac{\pi}{2}$ is

If $A$ and $B$ are square matrices of the same order and $|B| \neq 0$,then $(B^{-1}AB)^5 =$

Two spheres $S_{1}$ and $S_{2}$ have the same radii but temperatures $T_{1}$ and $T_{2}$ respectively. Their emissive power is the same and their emissivity is in the ratio $1: 4$. Then the ratio of $T_{1}$ to $T_{2}$ is: