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JEE Math Practice Question

If the circles $${x^2}\, + \,{y^2} + \,2ax\, + \,cy\, + a\,\, = 0$$ and $${x^2}\, + \,{y^2} - \,3ax\, + \,dy\, - 1\,\, = 0$$ intersect in two ditinct points P and Q then the line 5x + by - a = 0 passes through P and Q for :

  1. A.exactly one value of a
  2. B.no value of a
  3. C.infinitely many values of a
  4. D.exactly two values of a

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