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

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

The area, in sq. units, enclosed by the lines x = 2, y = |x – 2| + 4, the X-axis and the Y-axis is equal to

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

How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?

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

Let k be a constant. The equations kx + y = 3 and 4x + ky = 4 have a unique solution if and only if

(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