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 acid by volume in the final solution obtained after these three replacements, is nearest to

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

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

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

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

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…

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 (x, y) coordinates of vertices P, Q and R of a parallelogram PQRS are (−3, −2), (1, −5) and (9, 1), respectively. If the diagonal SQ intersects the x-axis at (a, 0), then the value of a 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