The coefficient of $x^4$ in the expansion of $\frac{(1-3x)^2}{(1-2x)}$ is equal to

Two bodies $A$ and $B$ start from the same point at the same instant and move along a straight line. $A$ moves with uniform acceleration $a$ and $B$ moves with uniform velocity $V$. They meet after time $t$. The value of $t$ is:

$A$ plane passes through $(2,3,-1)$ and is perpendicular to the line having direction ratios $3,-4,7$. The perpendicular distance from the origin to this plane is

If $\frac{\cos x}{\cos (x-2y)} = \lambda$,then $\tan (x-y) \tan y$ is equal to

In any $\triangle ABC$,$r_1 r_2 + r_2 r_3 + r_3 r_1$ is equal to

Let $a \neq 0$ and $p(x)$ be a polynomial of degree greater than $2$. If $p(x)$ leaves remainders $a$ and $-a$ when divided respectively by $x+a$ and $x-a$,then the remainder when $p(x)$ is divided by $x^2-a^2$ is: