If $x^2+2px-2p+8>0$ for all real values of $x$,then the set of all possible values of $p$ is

If $p \rightarrow (\sim p \vee q)$ is false,then the truth values of $p$ and $q$ are respectively

The transformed equation of $3x^2 - 4xy = r^2$ when the coordinate axes are rotated about the origin through an angle of $\operatorname{Tan}^{-1}(2)$ in the positive direction is:

$A$ polaroid is placed at $45^{\circ}$ to an incoming light of intensity $I_0$. Now,the intensity of light passing through the polaroid after polarization would be:

The minimum force required to start pushing a body up a rough (frictional coefficient $\mu$) inclined plane is $F_1$,while the minimum force needed to prevent it from sliding down is $F_2$. If the inclined plane makes an angle $\theta$ with the horizontal such that $\tan \theta = 2 \mu$,then the ratio $\frac{F_1}{F_2}$ is:

If $f(x) = \frac{1}{1+\frac{1}{x}}$ and $g(x) = \frac{1}{1+\frac{1}{f(x)}}$,then $g^{\prime}(2)$ is equal to