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 while their incomes increase by 10%, 12% and 15%, respectively. In October, the percentage of their total income that will be paid as house rent, is nearest to

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

The sum of all four-digit numbers that can be formed with the distinct non-zero digits a, b, c, and d, with each digit appearing exactly once in every number, is 153310 + n, where n is a single digit natural number. Then, the value of (a + b + c + d + n) 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

ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of incircle of ∆ADE is

When 10¹⁰⁰ is divided by 7, the remainder is

In the XY-plane, the area, in sq. units, of the region defined by the inequalities y ≥ x + 4 and −4 ≤ x² + y² + 4(x − y) ≤ 0 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…

If x is a positive real number such that 4log₁₀x + 4log₁₀₀x + 8log₁₀₀₀x = 13, then the greatest integer not exceeding x, is