11 players of the Indian cricket team are sitting at a circular table. The number of ways they can sit so that two players, the wicket keeper and the captain never sit together is ___

In $\triangle ABC$, if $\angle C = \dfrac{\pi}{3}$, then the value of $\cos^2 A + \cos^2 B + \cos A\cos B$ is...

The line $L_1$ given by $\dfrac{x}{p} + \dfrac{y}{2} = 1$ passes through the point $(5,0)$. The line $L_2$ given by $\dfrac{x}{10} + \dfrac{y}{q} = 1$ is parallel to $L_1$. Then the distance between the lines $L_1$ and $L_2$ is...

Two lines are given by $x^2 - 4xy + 4y^2 + kx - 2ky = 0$, then the value of k so that the distance between them is 3 is