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

Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB. If the perpendicular distance of P from each of AB, BC, and CA is 4(√2 − 1) cm, then the area, in sq cm, of the triangle ABC is

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

If three sides of a rectangular park have a total length 400 ft, then the area of the park is maximum when the length (in ft) of its longer side is

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

ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120 degrees and ∠BAC = 30 degrees, then the value of ∠BCD (in degrees) 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

The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is

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