Mathematics Tes...

Let f : (-π/2, π/2 ), → R be given by f(x) = (log(sec x + tan x))^3. Then

A circle S passes through the point (0, 1) and is orthogonal to the circles (x - 1)^2 + y^2 = 16 and x^2 + y^2 = 1. Then

In a triangle the sum of two sides is x and the product of the same two sides is y. If x^2 - c^2 = y, where c is the third side of the triangle, then the ratio of the in-radius to the circum-radius of the triangle is

From a point P(λ, λ, λ), perpendiculars PQ and PR are drawn respectively on the lines y = x, z = 1 and y = -x, z = -1. If P is such that angle QPR is a right angle, then the possible value(s) of λ is(are)

If the coefficients of x^3 and x^4 in the expansion of (1 + ax + bx^2) (1 - 2x)^18 in powers of x are both zero, then (a, b) is equal to

Let a, r, s, t be non-zero real numbers. Let P(at^2 , 2at), Q, R(ar^2 , 2ar) and S(as^2, 2as) be distinct points on the parabola y^2 = 4ax. Suppose that PQ is the focal chord and lines QR and PK are parallel, where K is the point (2a, 0).If st = 1, then the tangent at P and the normal at S to the parabola meet at a point whose ordinate is