If $x^2+y^2=t-\frac{1}{t}$ and $x^4+y^4=t^2+\frac{1}{t^2}$,then $\frac{dy}{dx}=$

If the difference between the roots of the equation $x^2 + ax + 1 = 0$ is less than $\sqrt{5}$,then what is the set of possible values of $a$?

If the roots of the equation $4x^3 - 12x^2 + 11x + k = 0$ are in arithmetic progression,then $k$ is equal to

$A$ car is moving along a straight line,say $OP$ in the given figure. It moves from $O$ to $P$ in $18 \; s$ and returns from $P$ to $Q$ in $6.0 \; s$. What are the average velocity and average speed of the car in going from $O$ to $P$?

Arrange $CCl_4, AlCl_3, PCl_5$ and $SiCl_4$ in the order of their ease of hydrolysis.

$A$ mass $M$ attached to a horizontal spring executes $S.H.M.$ of amplitude $A_1$. When the mass $M$ passes through its mean position,a smaller mass $m$ is placed over it and both of them move together with amplitude $A_2$. The ratio $\left(\frac{A_1}{A_2}\right)$ is