List of top Mathematics Questions on distance and displacement

The angle of elevation of the top P of a vertical tower PQ of height 10 from a point A on the horizontal ground is 45°, Let R be a point on AQ and from a point B, vertically above R, the angle of elevation of P is 60°. If
\(∠BAQ = 30°\)
, AB = d and the area of the trapezium PQRB is α, then the ordered pair (d, α) is :

Let ABC be a triangle such that \(\vec{BC}\)=\(\vec a\),\(\vec{CA} \)=\(\vec b\),\(\vec AB\)=\(\vec c\),|\(\vec a\)|=6\(\sqrt2\),|\(\vec b\)|=2\(\sqrt3\) and \(\vec b\)⋅\(\vec c\)=12 Consider the statements:
(S1):|(\(\vec a\)×\(\vec b\))+(\(\vec c\)×\(\vec d\))|−|\(\vec c\)|=6(2\(\sqrt2\)−1)
(S2):\(\angle\)ACB=cos−1⁡(\(\sqrt{\frac{2}{3}}\))
Then
An aeroplane flying at a constant speed, parallel to the horizontal ground, $\sqrt{3} \, km$ above it, is observed at an elevation of $60^{\circ}$ from a point on the ground. If, after five seconds, its elevation from the same point, is $30^{\circ}$, then the speed (in km/hr) of the aeroplane, is :