As observed from the top of a light house, 120 √3 m above the sea level, the angle of depression of a ship sailing towards it changes from 30° to 60°. The distance travelled by the ship during the period of observation is:

If 9x² + y² = 37 and xy = 2, x, y>0, then the value of (27x³+ y³) is:

ABCD is a cyclic quadrilateral. Diagonals BD and AC intersect each other at E. If <BEC = 128° and <ECD = 25°, then what is the measure of <BAC?

Amit sold an article for ₹369.60 after allowing 12% discount on the marked price. Had he not allowed any discount he would have earned a profit of 20%. What is the cost price of the article?

if $${secθ={a\over b},b≠0,then \ {{1-tan^2θ}\over 2-sin^2θ}  }=?$$

If (10 a³+4b³):(11a³-15b³)=7:5, then (3a+5b):(9a-2b)=?

$$\left({1\over cosecθ}-{1\over sinθ} \right)+{1\over {cosecθ-cotθ}} -{1\over secθ+tanθ} =?$$

The areas of three adjacent faces of a cuboidal tank are 3 m², 12 m² and 16 m². The capacity of the tank, in litres, is: