Mathematics Tes...

Let S be the focus of the parabola y^2 = 8x and let PQ be the common chord of the circle x^2 + y^2 − 2x − 4y = 0 and the given parabola. The area of the triangle PQS is

Four fair dice D1, D2, D3 and D4, each having six faces numbered 1, 2, 3, 4, 5, and 6, are rolledsimultaneously. The probability that D4 shows a number appearing on one of D1, D2 and D3 is

If y(x) satisfies the differential equation y′ − ytanx = 2x secx and y(0) = 0, then

Let PQR be a triangle of area ∆ with a = 2, b =7/2 and c = 5/2, where a, b, and c are the lengths of the sides of the triangle opposite to the angles at P, Q and R respectively. Then (2sin P - sin 2P)/(2sin + P sin 2P) equals

Consider the statements:P : There exists some x ∈ such that f(x) + 2x = 2(1 + x^2 )Q : There exists some x ∈ such that 2f(x) + 1 = 2x(1 + x) Then

A tangent PT is drawn to the circle x^2 + y^2 = 4 at the point P( √3,1). A straight line L, perpendicular to PT is a tangent to the circle (x - 3)^2 + y^2 = 1.A possible equation of L is

Let a-n denote the number of all n–digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0. Let b-n = the number of such n–digit integers ending with digit 1 and c-n = the number of such n–digit integers ending with digit 0. The value of b6 is

If the straight lines (x-1)/2 = (y + 1)/k = z/2 and (x+1)/5 = (y + 1)/2 = z/k are coplanar, then the plane(s) containing these two lines is(are)