The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is

Let k be the largest integer such that the equation (x − 1)² + 2kx + 11 = 0 has no real roots. If y is a positive real number, then the least possible value of k/(4y) + 9y is?

For some positive real number x, if log_√3(x) + logₓ(25)/logₓ(0.008) = 16/3, then the value of log₃(3x²) is

Let a, b, m and n be natural numbers such that a > 1 and b > 1. If aᵐbⁿ = 144¹⁴⁵, then the largest possible value of n − m is

Pipes A and C are fill pipes while Pipe B is a drain pipe of a tank. Pipe B empties the full tank in one hour less than the time taken by Pipe A to fill the empty tank. When pipes A, B and C are turned on together, the empty tank is filled in two hours. If pipes B and C are turne…

Any non-zero real numbers x, y such that y ≠ 3 and x/y < (x + 3)/(y − 3), will satisfy the condition

Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays Rs 10320 at the end of the first year and closes the loan by paying the outstanding amount at the end of the third year. Then, the total interest, in rupees, paid over the three years i…

The sum of all possible values of x satisfying the equation 2^(4x²) − 2^(2x² + x + 16) + 2^(2x + 30) = 0, is

Ravi is driving at a speed of 40 km/h on a road. Vijay is 54 meters behind Ravi and driving in the same direction as Ravi. Ashok is driving along the same road from the opposite direction at a speed of 50 km/h and is 225 meters away from Ravi. The speed, in km/h, at which Vijay s…