In the set of consecutive odd numbers {1, 3, 5, ..., 57}, there is a number k such that the sum of all the elements less than k is equal to the sum of all the elements greater than k. Then, k equals

A container holds 200 litres of a solution of acid and water, having 30% acid by volume. Atul replaces 20% of this solution with water, then replaces 10% of the resulting solution with acid, and finally replaces 15% of the solution thus obtained, with water. The percentage of aci…

Let 3 ≤ x ≤ 6 and [x²] = [x]², where [x] is the greatest integer not exceeding x. If set S represents all feasible values of x, then a possible subset of S is

The number of distinct pairs of integers (x, y) satisfying the inequalities x > y ≥ 3 and x + y < 14 is

For any natural number k, let aₖ = 3ᵏ. The smallest natural number m for which {(a₁)¹ × (a₂)² × … × (a₂₀)²⁰} < {a₂₁ × a₂₂ × … × a₍₂₀₊ₘ₎}, is

The number of distinct integers n for which log₍₁/₄₎(n² − 7n + 11) > 0, is

In a 3-digit number N, the digits are non-zero and distinct such that none of the digits is a perfect square, and only one of the digits is a prime number. Then, the number of factors of the minimum possible value of N is

Shruti travels a distance of 224 km in four parts for a total travel time of 3 hours. Her speeds in these four parts follow an arithmetic progression, and the corresponding time taken to cover these four parts follow another arithmetic progression. If she travels at a speed of 96…

If a − 6b + 6c = 4 and 6a + 3b − 3c = 50, where a, b and c are real numbers, the value of 2a + 3b − 3c is