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JEE Main20209 Jan 2020Evening ShiftMathematicsBinomial TheoremActual

If C r ≡ C r 25 and C 0 + 5 ∙ C 1 + 9 ∙ C 2 + … + 101 ∙ C 25 = 2 25 ∙ k , then k is equal to ____________.

Correct answer

0

Step-by-step solution

∑ r = 0 25 4 r + 1 25 C r = 4 ∑ r = 0 25 r . 25 C r + ∑ r = 0 25 C r 25 = 4 ∑ r = 1 25 r × 25 r C r - 1 24 + 2 25 = 100 ∑ r = 1 25 C r - 1 25 + 2 25 = 100.2 24 + 2 25 = 2 25 50 + 1 = 51 .2 25 So, k = 51

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