If the equation whose roots are $p$ times the roots of $x^4 - 2ax^3 + 4bx^2 + 8ax + 16 = 0$ is a reciprocal equation,then $|p| = $

$3.2$ moles of hydrogen iodide were heated in a sealed bulb at $444 \, ^oC$ until the equilibrium state was reached. Its degree of dissociation at this temperature was found to be $22 \%$. The number of moles of hydrogen iodide present at equilibrium are:

$A$ body projected vertically upwards crosses a point twice in its journey at a height $h$ just after $t_1$ and $t_2$ seconds. Maximum height reached by the body is

If the circle $x^2+y^2+8x-4y+c=0$ touches the circle $x^2+y^2+2x+4y-11=0$ externally and cuts the circle $x^2+y^2-6x+8y+k=0$ orthogonally,then $k$ is equal to

Two long conductors,separated by a distance $d$,carry currents $I_1$ and $I_2$ in the same directions. They exert a force $F$ on each other. Now,the current in one of them is increased to two times its original value and its direction is reversed. The distance is also increased to $3d$. The new value of the force between them is:

If $\sin ^{-1} x+\sin ^{-1}(1-x)=\cos ^{-1} x$,then $x \in$