How many different pairs (a, b) of positive integers are there such that a ≤ b and 1/a + 1/b = 1/9?

Let a₁, a₂, a₃, a₄, a₅ be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with 2a₃. If the sum of the numbers in the new sequence is 450, then a₅ is

In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?

If log(2^a × 3^b × 5^c) is the arithmetic mean of log(2² × 3³ × 5), log(2⁶ × 3 × 5⁷), and log(2 × 3² × 5⁴), then a equals

How many four digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, 6, such that no digit is used more than once and 0 does not occur in the left-most position?

If 9^(x − 1/2) − 2^(2x − 2) = 4^x − 3^(2x − 3), then x is

If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is

The minimum possible value of the (sum of the) squares of the roots of the equation x² + (a + 3)x − (a + 5) = 0 is

Let f(x) = 2x − 5 and g(x) = 7 − 2x. Then |f(x) + g(x)| = |f(x)| + |g(x)| if and only if