Mathematics Tes...

Interval in which tan^–1 (sinx + cosx) is increasing

From points on a given circle tangents are drawn to another circle. Then the locus of the mid-points of the chord of contact is will be :

The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is

The tangent \(\mathrm{P} \mathrm{T}\) and the normal \(\mathrm{P} \mathrm{N}\) to the parabola \(\mathrm{y}^{2}=4 \mathrm{ax}\) at a point \(\mathrm{P}\) on it meet its axis at points \(\mathrm{T}\) and \(\mathrm{N}\), respectively. The locus of the centroid of the \(\triangle \mathbf{P T} \mathrm{N}\) is a parabola whose-

If the function f(x) = x^3 + e^x/2 and g(x) = f^−1 (x), then the value of g′(1) is

In a triangle ABC with fixed base BC, the vertex A moves such that cosB + cosC = 4sin^2 A/2 . If a, b and c denote the lengths of the sides of the triangle opposite to the angles A, B and C, respectively, then

The domain of the function \(f: R \rightarrow R\) defined by \(\sqrt{x^{2}-x-110}\) is: