Mathematics Tes...

If α, β be roots of x² – x – 1 = 0 and A_n = αⁿ + βⁿ, then Arithmetic Mean of A_n–1 and A_n is

In the value of 100! the number of zeros at the end is

If n integers taken at random are multiplied together, then the probability that the last digit of the product is 1, 3, 7 or 9 is

The distance of the lines 2x – 3y = 4 from the point (1, 1) measured parallel to the line x + y = 1 is

In a triangle ABC, if A is (2, –1), and 7x – 10y + 1 = 0 and 3x – 2y + 5 = 0 are equations of an altitude and an angle bisector, respectively, drawn from B, then equation of BC is

Let f (x) = (x – 1)^p (x – 2)^q where p > 1, q > 1, each critical point of f (x) is a point of extremum when

A variable chord of circle x² + y² = 4 is drawn from the point P(3, 5) meeting the circle at the points A and B. A point Q is taken on this chord such that 2PQ = PA + PB. Locus of Q is

The angle between the tangents to the parabola y² = 4ax at the points where it intersects with the line x – y – a = 0 is