Which of the following statements is true regarding the

Quantity I – In how many ways letters of MOBILE can be arranged when vowels are always together.

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

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.

Which is the largest six digit number, which when divided by 12, 15, 20, 24 and 30, leaves the remainders 8, 11, 16, 20 and 26 respectively.

If a³ = 117 + b³ and a = 3 + b, then the value of a + b is:

If a + b² + c² = 16, x² + y² + z² = 25 and ax + by + cz = 20, then the value of (a+b+c)/(x+y+z)

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

If x1x2x3 = 4(4 + x1 + x2 + x3), then what is the value of [1/(2 + x1)] + [1/(2 + x2)] + [1/(2 + x3)]?

The total number of even factors of 2⁵ × 3³ × 5² is: