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

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

The number of non-negative integer values of k for which the quadratic equation x² − 5x + k = 0 has only integer roots, 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

Stocks A, B and C are priced at rupees 120, 90 and 150 per share, respectively. A trader holds a portfolio consisting of 10 shares of stock A, and 20 shares of stocks B and C put together. If the total value of her portfolio is rupees 3300, then the number of shares of stock B th…

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

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…

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