Mathematics Tes...

The equation of the common tangent touching the circle (x-3)² + y² = 9 and the parabola y² = 4x above the x-axis, is

If for a variable line  the condition a^–2 + b^–2 = c^–2 (c is a constant), is satisfied, then the locus of foot of the perpendicular drawn from origin to this is:

If A and B are two square matrices such that B = –A^–1 BA, then (A+B)² is equal to-

a, b, c are positive numbers and abc2 has the greatest value 1/64 Then

The altitude of a cone is 20cm and its semi-vertical angle is 30°. If the semi-vertical angle is increasing at the rate of 2° per second, then the radius of the base is increasing at the rate of-

The value of K, for which the equation (K–2)x² + 8x + K + 4 = 0 has both the roots real distinct and negative is:

The area bounded by curves y = f(x), the x-axis and the ordinates x = 1 and x = b is (b - 1) sin (3b + 4). Then f(x) is-