$A$ particle of mass $2\, kg$ is initially at rest. $A$ force acts on it whose magnitude changes with time. The force-time graph is shown below. The velocity of the particle after $10\, s$ is ......... $ms^{-1}$.

If the curves $x^2 - 6x + y^2 + 8 = 0$ and $x^2 - 8y + y^2 + 16 - k = 0$ $(k > 0)$ touch each other at a point,then the largest value of $k$ is

Starting from rest, the time taken by a body sliding down on a rough inclined plane at $45^{\circ}$ with the horizontal is twice the time taken to travel on a smooth plane of the same inclination and same distance. Then the coefficient of kinetic friction is:

If $|a|=4, |b|=5, |a-b|=3$ and $\theta$ is the angle between the vectors $a$ and $b$, then $\tan^2 \theta=$

The current flowing through an inductor of self-inductance $L$ is continuously increasing at a constant rate. The variation of induced e.m.f. $(e)$ versus $dI/dt$ is shown graphically by which graph?

The glenoid cavity articulates: