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JEE Math Practice Question

Let $$a$$, b, c $$ \in R$$. If $$f$$(x) = ax2 + bx + c is such that $$a$$ + b + c = 3 and $$f$$(x + y) = $$f$$(x) + $$f$$(y) + xy, $$\forall x,y \in R,$$ then $$\sum\limits_{n = 1}^{10} {f(n)} $$ is equal to

  1. A.165
  2. B.190
  3. C.255
  4. D.330

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