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JEE Math Practice Question

Consider a region R = {(x, y) $$ \in $$ R : x2 $$ \le $$ y $$ \le $$ 2x}. if a line y = $$\alpha $$ divides the area of region R into two equal parts, then which of the following is true?

  1. A.3$$\alpha $$2 - 8$$\alpha $$ + 8 = 0
  2. B.$$\alpha $$3 - 6$$\alpha $$3/2 - 16 = 0
  3. C.3$$\alpha $$2 - 8$$\alpha $$3/2 + 8 = 0
  4. D.$$\alpha $$3 - 6$$\alpha $$2 + 16 = 0

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