If the angles made by a straight line with the coordinate axes are $\alpha, \frac{\pi}{2}-\alpha, \beta$,then $\beta$ is equal to

The hybridisation of $Xe$ and the number of lone pairs of electrons on it in $XeF_6$ are

If $\log_e \left( \frac{a + b}{2} \right) = \frac{1}{2}(\log_e a + \log_e b)$,then the relation between $a$ and $b$ is:

$A$ spherical solid ball of volume $V$ is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_2$ (where $\rho_2 < \rho_1$). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$,i.e.,$F_{viscous} = -kv^2$ (where $k > 0$). Then the terminal speed of the ball is:

$y=A e^x+B e^{2 x}+C e^{3 x}$ satisfies the differential equation

If $\int \frac{dx}{x^2+2x+2} = f(x) + c$, then $f(x)$ is equal to :