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

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

Let f(x) = x² and g(x) = 2x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is

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

If x is a real number such that log₃5 = log₅(2 + x), then which of the following is true?

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

If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers 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?