To remove the second term of the equation $x^4-8x^3+x^2-x+3=0$,diminish the roots of the equation by

$A$ ball rolls without slipping. The radius of gyration of the ball about an axis passing through its center of mass is $K$. If the radius of the ball is $R$,what fraction of its total energy is associated with its rotational kinetic energy?

$A$ rifle of $20 ~kg$ mass can fire $4$ bullets per second. The mass of each bullet is $35 \times 10^{-3} ~kg$ and its final velocity is $400 ~ms^{-1}$. What force must be applied on the rifle so that it does not move backwards while firing the bullets (in $~N$)?

$A$ current of $5 ~A$ is flowing at $220 ~V$ in the primary coil of a transformer. If the voltage produced in the secondary coil is $2200 ~V$ and $50 \%$ of power is lost,then the current in the secondary coil will be: (in $~A$)

If $f: R \rightarrow R$ is defined by $f(x) = 7 + \cos(5x + 3)$ for $x \in R$,then the period of $f$ is

Let $f(x) = \int \frac{\sqrt{x}}{(1+x)^2} \, dx, x \geq 0$. Then $f(3) - f(1)$ is equal to