Suppose x₁, x₂, x₃, …, x₁₀₀ are in arithmetic progression such that x₅ = −4 and 2x₆ + 2x₉ = x₁₁ + x₁₃. Then, x₁₀₀ equals

If the equations x² + mx + 9 = 0, x² + nx + 17 = 0 and x² + (m + n)x + 35 = 0 have a common negative root, then the value of (2m + 3n) is

Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days working 5 hours per day to complete the same task. They decide to work together to complete this task. Seema agrees to work for double the number of hours per day as Renu, w…

Let x, y, and z be real numbers satisfying 4(x² + y² + z²) = a, 4(x − y − z) = 3 + a. Then a equals

When 10¹⁰⁰ is divided by 7, the remainder is

Consider two sets A = {2, 3, 5, 7, 11, 13} and B = {1, 8, 27}. Let f be a function from A to B such that for every element b in B, there is at least one element a in A such that f(a) = b. Then, the total number of such functions f is

The sum of all real values of k for which (1/8)ᵏ × (1/32768)^(1/3) = (1/8) × (1/32768)^(1/k), is

For any natural number n, let aₙ be the largest integer not exceeding √n. Then the value of a₁ + a₂ + … + a₅₀ is

In September, the incomes of Kamal, Amal and Vimal are in the ratio 8 : 6 : 5. They rent a house together, and Kamal pays 15%, Amal pays 12% and Vimal pays 18% of their respective incomes to cover the total house rent in that month. In October, the house rent remains unchanged wh…