Correct Answer - Option 2 : 5

**Given:**

If 2nC3 : nC2 = 12 : 1

**Formula used :**

^{n}C_{r} = n!/r!(n - r)!

**Calculation:**

If 2nC3 : nC2 = 12 : 1 ----(1)

Using the formula

^{2n}C_{2} = {2n!/3! (2n - 3)!}

⇒ 2n(2n - 1)(2n - 2)(2n - 3)!/(2n - 3)! × 3 × 2

⇒ n(2n - 1)2(n - 1)/3 ----(2)

^{n}C_{2} = {n!/2! (n - 2)!

⇒ n(n - 1)(n - 2)!/(n - 2)! × 2

⇒ n(n - 1)/2 ----(3)

Putting equation 2 and 3 in equation 1

⇒ {n(2n - 1)2(n - 1)/3}/{n(n - 1)/2} = 12/1

⇒ 2n - 1 = 9

⇒ 2n = 10

⇒ n = 5

**∴ The value of n is 5.**