Consider the arithmetic progressions 3, 7, 11, ... and let Aₙ denote the sum of the first n terms of this progression. Then the value of (1/25) ∑ₙ₌₁²⁵ Aₙ is

There are two containers of the same volume, first container half-filled with sugar syrup and the second container half-filled with milk. Half the content of the first container is transferred to the second container, and then the half of this mixture is transferred back to the f…

If a and b are non-negative real numbers such that a + 2b = 6, then the average of the maximum and minimum values of (a + b) is:

Suppose for all integers x, there are two functions f and g such that f(x) + f(x − 1) − 1 = 0 and g(x) = x². If f(x² − x) = 5, then the value of the sum f(g(5)) + g(f(5)) is

Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is

The number of integers greater than 2000 that can be formed with the digits 0, 1, 2, 3, 4, 5, using each digit at most once, is

Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5 : 8 : 10. They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However, Anu and Tanu work together for the first 6 days, working 6 hours 40 minu…

The number of distinct integer values of n satisfying (4 − log₂ n)/(3 − log₄ n) < 0, is

For some natural number n, assume that (15,000)! is divisible by (n!)!. The largest possible value of n is: