JEE Main 2022 · 29 Jul · Shift 2 · Mathematics Q25

MathematicsInteger+4 / -1Question 25 of 90

If $\displaystyle\sum_{k=1}^{10}K^2\left({}^{10}C_K\right)^2=22000L$ , then L is equal to _______.

Your answer

Answer and worked solution

Official answer: 221

Identity. $k\binom{10}k=10\binom9{k-1}$ , so the sum is $100\sum\binom9{k-1}^2=100\binom{18}9=4862000=22000\times221$ .

Answer: 221

JEE Main 2022 · 29 Jul · Shift 2, Mathematics question 25