The coordinates of the focus of the parabola described parametrically by $x = 5t^2 + 2, y = 10t + 4$ are

If $\alpha, \beta, \gamma$ are the roots of $2x^3 - 2x - 1 = 0$,then $(\Sigma \alpha \beta)^2$ is equal to

Four capacitors marked with their capacitances and breakdown voltages are connected as shown in the figure. Find the maximum $EMF$ of the source such that no capacitor breaks down. (in $kV$)

Which of the following statements is true?

The path of a projectile is given by the equation $y = ax - bx^2$,where $a$ and $b$ are constants and $x$ and $y$ are respectively horizontal and vertical distances of the projectile from the point of projection. The maximum height attained by the projectile and the angle of projection are respectively:

$A$ thin rod of length $L$ is bent to form a semicircle. The mass of the rod is $M$. What will be the gravitational potential at the centre of the circle?