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JEE Main20254 Apr 2025Evening ShiftMathematicsBinomial TheoremActual

If (1^2 ( ¹⁵ C₁ )+2^2 ( ¹⁵ C₂ )+3^2 ( ¹⁵ C₃ )+ ) (+15^2 ( 15 15 )=2^m 3^n 5^k ), where (m, n, k N ), then ( m + n + k ) is equal to :

Options

  1. A19
  2. B21
  3. C18
  4. D20

Correct answer

A. 19

Step-by-step solution

aligned & _ r =1 ¹⁵ r ^2 ( ¹⁵ C _ r ) 15 _ r =1 ¹⁵ r ¹⁴ C _ r -1 & 15 _ r =1 ¹⁵( r -1+1) ¹⁴ C _ r -1 & 15 14 _ r =1 ¹⁵ ¹³ C _ r -2 +15 _ r =1 ¹⁵ ¹⁴ C _ r -1 & 15 14 2¹³+15 2¹⁴ & 3^1 2¹³(70+10) & 3^1 2¹³ 80 & 3^1 5^1 2¹⁷ & ~m =17 n =1 k =1 & option (1) aligned

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