If K^2 (10_C_K )^2=22000L, then L is equal to___.

Correct answer: 221. (221) K^2 (10C_K )^2 (K .^10C_K )^2= (10 .^9C_K-1 )^2 =100 9C_K-1 .^9C_10-K =100 (18C_9 )=100 ( 18 !9 !9 ! ) ⇒4862000=22000L Hence L = 221

JEE Previous Year Question

$If \sum K^{2} (1 0_{C_{K}})^{2} = 22000 L, then L is equal to___.$

Topic: JEE PYQ

Answer: 221. Full step-by-step solution below.

Correct answer: 221

Solution

(221) \sum K^{2} (10 C_{K})^{2} \sum (K .^{10} C_{K})^{2} = \sum (10 .^{9} C_{K - 1})^{2} = 100 \sum 9 C_{K - 1} .^{9} C_{10 - K} = 100 (18 C_{9}) = 100 (\frac{18 !}{9 ! 9 !}) \Rightarrow 4862000 = 22000 L Hence L = 221

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