The value of log₀.₀₀₈√5 + log√3 81 − 7 is equal to : (log₀.₀₀₈√5 is log of √5 to base 0.008; log√3 81 is log of 81 to base √3)

If x + 1 = x² and x > 0, then 2x⁴ is :

If 9^(2x−1) − 81^(x−1) = 1944, then x is

Suppose, log₃x = log₁₂y = a, where x, y are positive numbers. If G is the geometric mean of x and y, and log₆G is equal to :

The number of solutions (x, y, z) to the equation x – y – z = 25, where x, y, and z are positive integers such that x ≤ 40, y ≤ 12, and z ≤ 12 is

Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 km, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour is :

For how many integers n, will the inequality (n – 5) (n – 10) – 3(n – 2) ≤ 0 be satisfied?

A ball of diameter 4 cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is 3 cm, while its volume is 9π cm³. Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder is :

If f1(x) = x² + 11x + n and f2(x) = x, then the largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots, is :