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JEE Main20207 Jan 2020Evening ShiftMathematicsBinomial TheoremActual

The number of ordered pairs r , k for which 6 . C r 35 = k 2 - 3 . C r + 1 36 , where k is an integer is

Options

  1. A3
  2. B2
  3. C6
  4. D4

Correct answer

D. 4

Step-by-step solution

Given, 6 . C r 35 = k 2 - 3 . C r + 1 36 ⇒ 36 r + 1 × 35 C r k 2 - 3 = 6 × 35 C r , using properties of binomial coefficient. ⇒ k 2 - 3 = r + 1 6 ⇒ k 2 = 3 + r + 1 6 r can be 5,35 For r = 5 , k = ± 2 r = 35 , k = ± 3 Hence, number of solution = 4

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