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

If $f(x) = \frac{\cos^2 x + \sin^4 x}{\sin^2 x + \cos^4 x}$,for $x \in R$,then $f(2002)$ is equal to

If $\alpha, \beta, \gamma, \delta$ are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity $k$,then the value of $4\sin \frac{\alpha}{2} + 3\sin \frac{\beta}{2} + 2\sin \frac{\gamma}{2} + \sin \frac{\delta}{2}$ is equal to

$\cot \frac{\pi}{16} \cdot \cot \frac{2 \pi}{16} \cdot \cot \frac{3 \pi}{16} \cdot \cot \frac{4 \pi}{16} \cdot \cot \frac{5 \pi}{16} \cdot \cot \frac{6 \pi}{16} \cdot \cot \frac{7 \pi}{16} = $

If $0 \leq x \leq 3$ and $0 \leq y \leq 3$,then the number of solutions $(x, y)$ of the equation $\left(\sqrt{\sin^2 x - \sin x + \frac{1}{2}}\right) 2^{\sec^2 y} = 1$ is

The value of $\cos \frac{\pi}{10} \cos \frac{2\pi}{10} \cos \frac{4\pi}{10} \cos \frac{8\pi}{10} \cos \frac{16\pi}{10}$ is