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?

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

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

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

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

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

For any natural numbers m, n and k, such that k divides both m + 2n and 3m + 4n, k must be a common divisor of

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…