The LCM of two natural numbers is 12 times their HCF.

If the nine-digit number 43x1145y2 is divisible by 88, then the value of (3x — 2y), for the smallest value of y, is:

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

If x + y + z = 0, then what is the value of (3y² + x² + z²)/(2y² – xz)?

If x + y = 7 and xy = 10, then the value of (1/x³ + 1/x³) is :

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

The simple interest accrued on a sum at the rate of 10% p.a. for two years is Rs. 5,000.

If 2y cos θ  = x sin θ  and 2x sec θ -  y cosec θ  = 3, then the value of x²+ 4y² is

If sec θ + tan θ = m(> 1), then the value of sin θ is (0° < θ < 90°)

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 x² + y² + 2x + 1 = 0, therefore the value of x³¹ + y³⁵ is