The set of all real values of x for which (x² − |x + 9| + x) > 0, is

If m and n are integers such that (m + 2n)(2m + n) = 27, then the maximum possible value of 2m − 3n is

The number of divisors of (2⁶ × 3⁵ × 5³ × 7²), which are of the form (3r + 1), where r is a non-negative integer, is

An item with a cost price of Rs. 1650 is sold at a certain discount on a fixed marked price to earn a profit of 20% on the cost price. If the discount was doubled, the profit would have been Rs. 110. The rate of discount, in percentage, at which the profit percentage would be equ…

Let f(x) = x/(2x − 1) and g(x) = x/(x − 1). Then, the domain of the function h(x) = f(g(x)) + g(f(x)) is all real numbers except

Rita and Sneha can row a boat at 5 km/h and 6 km/h in still water, respectively. In a river flowing with a constant velocity, Sneha takes 48 minutes more to row 14 km upstream than to row the same distance downstream. If Rita starts from a certain location in the river, and retur…

In a △ABC, points D and E are on the sides BC and AC, respectively. BE and AD intersect at point T such that AD : AT = 4 : 3, and BE : BT = 5 : 4. Point F lies on AC such that DF is parallel to BE. Then, BD : CD is

Let ABCDEF be a regular hexagon and P and Q be the midpoints of AB and CD, respectively. Then, the ratio of the areas of trapezium PBCQ and hexagon ABCDEF is

A loan of Rs.1000 is fully repaid by two installments of Rs.530 and Rs.594, paid at the end of first and second year, respectively. If the interest is compounded annually, then the rate of interest, in percentage, is