If the number of $5$-element subsets of the set $A = \{a_1, a_2, \ldots, a_{20}\}$ of $20$ distinct elements is $k$ times the number of $5$-element subsets containing $a_4$,then $k$ is

$A$ circular coil having $N$ turns is made from a wire of length $L$ meters. If a current of $I$ amperes is passed through it and placed in a magnetic field of $B$ tesla,the maximum torque on it is

All the diodes are ideal. The current flowing in the $2 \, \Omega$ resistor connected between the diodes $D_1$ and $D_2$ is .......... $A$

If $\alpha, \beta$ are the roots of $x^2 - px + q = 0$ and $\alpha', \beta'$ are the roots of $x^2 - p'x + q' = 0$,then find the value of $(\alpha - \alpha')^2 + (\beta - \alpha')^2 + (\alpha - \beta')^2 + (\beta - \beta')^2$.

Cultivation of $Bt$ Cotton has been much in the news. The prefix "$Bt$" means

Which of the following is the most important cause driving animals and plants to extinction?