Let $$2{\sin ^2}x + 3\sin x - 2 > 0$$ and $${x^2} - x - 2 < 0$$ ($$x$$ is measured in radians). Then $$x$$ lies in the interval

The number of points of intersection of two curves y = 2 sin x and y $$ = 5{x^2} + 2x + 3$$ is

If p, q, r are + ve and are on A.P., the roots of quadratic equation $$p{x^2} + qx + r = 0$$ are all real for

Let $$p,q \in \left\{ {1,2,3,4} \right\}\,$$. The number of equations of the form $$p{x^2} + qx + 1 = 0$$ having real roots is