Four number-pairs are given, out of which three are

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

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

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

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 x⁴ + 2x³ + ax² + bx + 9 is a perfect square, where a and b are positive real numbers, then the value of a and b are

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

If (2x + 3y+ 4) (2x + 3y 5) is equivalent to (ax² + by² + 2hxy + 2gx + 2fy + c), then what is the value - of ((g + f – c) / abh}?

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 :