Consider an infinite geometric series with first term a and common ratio $$r$$. If its sum is 4 and the second term is 3/4, then

Let $$PS$$ be the median of the triangle with vertices $$P(2, 2),$$ $$Q(6, -1)$$ and $$R(7, 3).$$ The equation of the line passing through $$(1, -1)$$ and parallel to $$PS$$ is

Let $$f\left( \theta \right) = \sin \theta \left( {\sin \theta + \sin 3\theta } \right)$$. Then $$f\left( \theta \right)$$ is

The triangle PQR is inscribed in the circle $${x^2}\, + \,\,{y^2} = \,25$$. If Q and R have co-ordinates (3, 4) and ( - 4, 3) respectively, then $$\angle \,Q\,P\,R$$ is equal to