If $x^2+\alpha y^2+2 \beta y=a^2$ represents a pair of perpendicular lines,then $\beta$ equals to

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A = 10 \, cm^2$ and length $\ell = 20 \, cm$. If one of the solenoids has $N_1 = 300$ turns and the other has $N_2 = 400$ turns,their mutual inductance is (given $\mu_0 = 4\pi \times 10^{-7} \, T \cdot m \cdot A^{-1}$):

The order and degree of the differential equation $\sqrt{\frac{dy}{dx}} - 4\frac{dy}{dx} - 7x = 0$ are

An important evidence in favour of organic evolution is the occurrence of

The value of $k$ for which the function $f(x) = \begin{cases} (\frac{4}{5})^{\frac{\tan 4x}{\tan 5x}}, & 0 < x < \frac{\pi}{2} \\ k + \frac{2}{5}, & x = \frac{\pi}{2} \end{cases}$ is continuous at $x = \frac{\pi}{2}$ is

Which complex is most stable?
Where $k_d = \text{Dissociation constant}$