The angle between the lines $x \cos \alpha_1 + y \sin \alpha_1 = p_1$ and $x \cos \alpha_2 + y \sin \alpha_2 = p_2$ is:

The greatest threat to genetic diversity in agricultural crops is

If $(1, 3), (2, 5),$ and $(3, 3)$ are three elements of $A \times B$ and the total number of elements in $A \times B$ is $6$,then the remaining elements of $A \times B$ are:

If $\alpha = \frac{5}{2! 3} + \frac{5 \cdot 7}{3! 3^2} + \frac{5 \cdot 7 \cdot 9}{4! 3^3} + \ldots$,then $\alpha^2 + 4\alpha$ is equal to

$A$ circular coil of area $200 ~cm^2$ and $50$ turns is rotating about its vertical diameter with an angular speed of $40 ~rad/s$ in a uniform horizontal magnetic field of magnitude $2 \times 10^{-2} ~T$. The maximum emf induced in the coil is (in $~V$)

The product of the perpendicular distances from any point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ to its asymptotes is