A particle has displacement of $12 \,m$ towards east and $5 \,m$ towards north then $6 \,m $ vertically upward. The sum of these displacements is........$m$

A car travels $6 \,km$ towards north at an angle of $45^o $ to the east and then travels distance of $4 \,km$ towards north at an angle of $135^o $ to the east. How far is the point from the starting point. What angle does the straight line joining its initial and final position makes with the east

In the picture shown, a ball standing from rest rolls down a ramp $AB$, goes along at the horizontal bottom $BC$, and then backs up a smaller ramp $CD$, thereafter rolls on horizontal plane $DE$. Ignore friction and air resistance.Which of the following figure shows variation in speed with time ?

A fighter plane is flying horizontally at an altitude of $1.5\, km$ with speed $720\, km/h$. At what angle of sight (w.r.t. horizontal) when the target is seen, should the pilot drop the bomb in order to attack the target ?

A particle moves towards east with velocity $5\ m/s$ . After $10\ seconds$ its direction changes towards north with same velocity. The average acceleration of the particle is 

A particle moves with constant speed $v$ along a regular hexagon $ABCDEF$ in the same order. Then the magnitude of the average velocity for its motion from $A$ to