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JEE Math Practice Question

Let $$\Delta$$ be the area of the region $$\left\{ {(x,y) \in {R^2}:{x^2} + {y^2} \le 21,{y^2} \le 4x,x \ge 1} \right\}$$. Then $${1 \over 2}\left( {\Delta - 21{{\sin }^{ - 1}}{2 \over {\sqrt 7 }}} \right)$$ is equal to

  1. A.$$2\sqrt 3 - {1 \over 3}$$
  2. B.$$2\sqrt 3 - {2 \over 3}$$
  3. C.$$\sqrt 3 - {4 \over 3}$$
  4. D.$$\sqrt 3 - {2 \over 3}$$

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