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JEE Main20236 Apr 2023Morning ShiftMathematicsBinomial TheoremActual

If C 3 2 n : C 3 n = 10 : 1 , then the ratio n 2 + 3 n : n 2 - 3 n + 4 is

Options

  1. A35 : 16
  2. B27 : 11
  3. C65 : 37
  4. D2 : 1

Correct answer

D. 2 : 1

Step-by-step solution

We have been given that C 3 2 n : C 3 n = 10 We know that C r n = n ! r ! n - r ! ⇒ 2 n ! 3 ! 2 n - 3 ! n ! 3 ! n - 3 ! = 10 ⇒ 2 n ! 3 ! 2 n - 3 ! × 3 ! n - 3 ! n ! = 10 ⇒ 2 n 2 n - 1 2 n - 2 2 n - 3 ! 2 n - 3 ! × n - 3 ! n n - 1 n - 2 n - 3 ! = 10 ⇒ 2 n 2 n - 1 2 n - 2 n n - 1 n - 2 = 10 ⇒ 4 2 n - 1 n - 2 = 10 ⇒ 8 n - 4 = 10 n - 20 ⇒ n = 8 Hence, the value of n 2 + 3 n n 2 - 3 n + 4 is = 8 2 + 3 8 8 2 - 3 8 + 4 = 88 44 = 2 Therefore, the value of n 2 + 3 n n 2 -

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