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General — Medium JEE math MCQ

Let $S=\{1,2,3, \ldots, 9\}$. For $k=1,2, \ldots, 5$, let $N_{k}$ be the number of subsets of $S$, each containing five elements out of which exactly $k$ are odd. Then $N_{1}+N_{2}+N_{3}+N_{4}+N_{5}=$
  1. A. 210
  2. B. 252
  3. C. 125
  4. D. 126

Solution

The correct option is **D**.

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
Let S={1,2,3,…,9}S=\{1,2,3, \ldots, 9\}. For k=1,2,…,5k=1,2, \ldots, 5, let NkN_{k} be the number of subsets of SS, each containing five elements out of which exactly kk are odd. Then N1+N2+N3+N4+N5=N_{1}+N_{2}+N_{3}+N_{4}+N_{5}=
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General — Medium JEE Mathematics MCQ | MyGoalPrep