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If Ncr + Ncr + 1 = N + 1cx , Then X = (A) R (B) R − 1 (C) N (D) R + 1 - Mathematics

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MCQ

If nCr + nCr + 1 = n + 1Cx , then x =

Options

  •  r

  • r − 1

  • n

  • r + 1

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Solution

r + 1

\[n_{C_r} + n_{C_{r + 1}} = n + 1_{C_x}\] [Given]
We have:
\[{}^n C_r +^n C_{r + 1} = {}^{n + 1} C_x \]
[∵\[{}^n C_r +^n C_{r - 1} = {}^{n + 1} C_r\]]
\[\Rightarrow {}^{n + 1} C_{r + 1} = {}^{n + 1} C_x\]
\[\Rightarrow r + 1 = x\] [∵ \[{}^n C_x =^n C_y \Rightarrow n = x + y\ \text{or} x = y\]]
Concept: Combination
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Q 8 | Page 25

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