Which of the following statements is correct?

$A$ body is moving up an inclined plane of angle $\theta$ with an initial kinetic energy $E$. The coefficient of friction between the plane and the body is $\mu$. The work done against friction before the body comes to rest is

When the coordinate axes are rotated by an angle $\tan ^{-1}\left(\frac{3}{4}\right)$ about the origin,then the equation $x^2+y^2=9$ is transformed to the equation.

If $\alpha = \frac{5}{2! 3} + \frac{5 \cdot 7}{3! 3^2} + \frac{5 \cdot 7 \cdot 9}{4! 3^3} + \ldots$,then $\alpha^2 + 4\alpha$ is equal to

$A$ motorcyclist of mass $m$ is to negotiate a curve of radius $r$ with a speed $v$. The minimum value of the coefficient of friction so that this negotiation may take place safely,is

The electric field $\vec{E}$ between two points is constant in both magnitude and direction. Consider a path of length $d$ at an angle $\theta = 60^o$ with respect to the field lines as shown in the figure. The potential difference between points $1$ and $2$ is