$A$ circular disc is rolling on a horizontal plane. Its total kinetic energy is $300\,J$. What is its translational kinetic energy in $J$?

If a bar magnet of pole strength $m$ and magnetic moment $M$ is cut equally $5$ times parallel to its axis and again $3$ times perpendicular to its axis,then the pole strength and magnetic moment of each piece are respectively

If the centroid of the triangle formed by the lines $2y^2 + 5xy - 3x^2 = 0$ and $x + y = k$ is $\left(\frac{1}{18}, \frac{11}{18}\right)$,then the value of $k$ equals $............$

$A$ body of mass $M \ kg$ is at the top point of a smooth hemisphere of radius $5 \ m$. It is released to slide down the surface of the hemisphere. It leaves the surface when its velocity is $5 \ m/s$. At this instant,the angle made by the radius vector of the body with the vertical is: (Acceleration due to gravity $g = 10 \ m/s^2$) (in $^{\circ}$)

If the normal to the curve $y = f(x)$ at the point $(3, 4)$ makes an angle $\frac{3\pi}{4}$ with the positive $x$-axis,then $f'(3)$ is equal to

When a positively charged particle enters a uniform magnetic field with uniform velocity,its trajectory can be :
$(1)$ a straight line
$(2)$ a circle
$(3)$ a helix