For any two real numbers a and b.

a-b2+b-a2 is

The centroid of an equilateral triangle ABC is G. If AB is 6 cms, the length of AG is

A and B together can finish a work in 30 days. They worked for it for 20 days and then B left the work. The remaining work was done by A alone in 20 days more. In how many days can A alone finish the work?

The lengths of the two diagonals of a rhombus are 5 cm and 12 cm. Find its area (in cm2)

The angle of elevation of the top of a pillar from the foot and the top of a building 20 m high, are 60° and 30° respectively. The height of the pillar is

A cylinderical container of 32 cm height and 18 cm radius is filled with sand. Now all this sand is used to form a conical heap of sand. If the height of theconical heap is 24 cm, what is the radius of its base?

If θ be positive acute angle and 5cosθ + 12sinθ = 13, then the value of cosθ is

In ΔABC, ∠B = 70° and ∠C = 60°. The internal bisectors of the two smallest angles of ΔABC meet at O. The angle so formed at O is

If a - b = 3 and a2+b2=25, then the value of ab is