A school has 100 students and every student plays

The value of = 3/4 ÷ 3/4  of 4/3 + 5/2 ÷ 2/5 of 5/4 – (2/3 + 2/3 of 5/6) is :

If α and β are the roots of equation x² – x + 1 = 0, then which equation will have roots α³ and β³?

If (a² − b²)sin θ + 2ab cos θ = a² + b², then tan θ =

If x sin³ θ + y cos³ θ = sin θ cos θ and x sin θ − y cos θ = 0, then the value of x² + y² equals

Quantity I – ³

Quantity II – 25⁴

If > 0 and < 0

An urn contains 3 green, 5 blue, 6 black and 4 yellow marbles.

If a + 1/a = -2 then the value of a¹⁰⁰⁰ + a^{- 1000} is

Find x, given 5 (√5)^x+6 = (√5)^2x+7 :

10 women and 12 men complete a certain piece of work in 30 days, if each women takes thrice the time taken by a man to finish the work.

If (a + b)/c = 6/5 and (b + c)/a = 9/2, then what is the value of (a + c)/b?