The area bounded by the curves $$y=\left|x^{2}-1\right|$$ and $$y=1$$ is

The odd natural number a, such that the area of the region bounded by y = 1, y = 3, x = 0, x = y^a is $${{364} \over 3}$$, is equal to :

The area of the region given by

$$A=\left\{(x, y): x^{2} \leq y \leq \min \{x+2,4-3 x\}\right\}$$ is :

Let the locus of the centre $$(\alpha, \beta), \beta>0$$, of the circle which touches the circle $$x^{2}+(y-1)^{2}=1$$ externally and also touches the $$x$$-axis be $$\mathrm{L}$$. Then the area bounded by $$\mathrm{L}$$ and the line $$y=4$$ is: