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 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

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

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

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

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

The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are equal in length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar…

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