The number of real-valued solutions of the equation 2^x + 2^(−x) = 2 − (x − 2)² is

How many distinct positive integer-valued solutions exist to the equation (x² − 7x + 11)^(x² − 13x + 42) = 1?

How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?

Let A, B and C be three positive integers such that the sum of A and the mean of B and C is 5. In addition, the sum of B and the mean of A and C is 7. Then the sum of A and B is

A solution, of volume 40 litres, has dye and water in the proportion 2 : 3. Water is added to the solution to change this proportion to 2 : 5. If one-fourths of this diluted solution is taken out, how many litres of dye must be added to the remaining solution to bring the proport…

A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remaining stock along with one extra to the second and continues giving away in this fashion. His total stoc…

On a rectangular metal sheet of area 135 sq in, a circle is painted such that the circle touches two opposite sides. If the area of the sheet left unpainted is two-thirds of the painted area then the perimeter of the rectangle in inches is

The mean of all 4-digit even natural numbers of the form ‘aabb’, where a > 0, is

Among 100 students, x₁ have birthdays in January, x₂ have birthdays in February, and so on. If x₀ = max(x₁, x₂, ..., x₁₂), then the smallest possible value of x₀ is