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

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

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

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

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

The ratio of expenditures of Lakshmi and Meenakshi is 2 : 3, and the ratio of income of Lakshmi to expenditure of Meenakshi is 6 : 7. If excess of income over expenditure is saved by Lakshmi and Meenakshi, and the ratio of their savings is 4 : 9, then the ratio of their incomes i…

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…

Two tangents drawn from a point P touch a circle with center O at points Q and R. Points A and B lie on PQ and PR, respectively, such that AB is also a tangent to the same circle. If ∠AOB = 50°, then ∠APB, in degrees, equals