(2 × 4 × 8 × 16) / [(log₂4)² (log₄8)³ (log₈16)⁴] equals

The vertices of a triangle are (0, 0), (4, 0) and (3, 9). The area of the circle passing through these three points is

A person invested a certain amount of money at 10% annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs 18522. The amount, in rupees, that the person had invested is

Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick's age is 1 year less than the average age of all three, then Harry's age, in years, is

If logₐ30 = A, logₐ(5/3) = −B and log₂a = 1/3, then log₃a equals

In the final examination, Bishnu scored 52% and Asha scored 64%. The marks obtained by Bishnu is 23 less, and that by Asha is 34 more than the marks obtained by Ramesh. The marks obtained by Geeta, who scored 84%, is

Two alcohol solutions, A and B, are mixed in the proportion 1 : 3 by volume. The volume of the mixture is then doubled by adding solution A such that the resulting mixture has 72% alcohol. If solution A has 60% alcohol, then the percentage of alcohol in solution B is

Let N, x and y be positive integers such that N = x + y, 2 < x < 10 and 14 < y < 23. If N > 25, then how many distinct values are possible for N?

How many pairs (a, b) of positive integers are there such that a ≤ b and ab = 4²⁰¹⁷?