The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is ........ $^o$

If $\left| {{{\vec v}_1} + {{\vec v}_2}} \right| = \left| {{{\vec v}_1} - {{\vec v}_2}} \right|$ and ${{{\vec v}_1}}$ and ${{{\vec v}_2}}$ are finite, then

Add vectors $\overrightarrow{ A }, \overrightarrow{ B }$ and $\overrightarrow{ C }$ each having magnitude of $50$ unit and inclined to the $X$-axis at angles $45^{\circ}, 135^{\circ}$ and $315^{\circ}$ respectively.

If the resultant of $n$ forces of different magnitudes acting at a point is zero, then the minimum value of $n$ is

The coordinates of a moving particle at any time $t$ are given by $x = a\, t^2$ and $y = b\, t^2$. The speed of the particle is

A cyclist starts from the centre $O$ of a circular park of radius $1\; km$, reaches the edge $P$ of the park, then cycles along the circumference, and returns to the centre along $QO$ as shown in Figure. If the round trip takes $10 \;min$, what is the

$(a)$ net displacement,

$(b)$ average velocity, and

$(c)$ average speed of the cyclist ?