A) \[r\]
B) \[r-1\]
C) \[n\]
D) \[r+1\]
Correct Answer: D
Solution :
Given, \[^{n}{{C}_{r}}{{+}^{n}}{{C}_{r+1}}{{=}^{n+1}}{{C}_{x}}\] \[\Rightarrow \] \[^{n+1}{{C}_{r+1}}{{=}^{n+1}}{{C}_{x}}\] \[(\because \,\,{{\,}^{n}}{{C}_{r}}{{+}^{n}}{{C}_{r+1}}{{=}^{n+1}}{{C}_{r+1}})\] \[\therefore \] \[r+1=x\] \[(\because \,\,{{\,}^{n}}{{C}_{x}}{{=}^{n}}{{C}_{u}}\Rightarrow x=y)\] or \[x=r+1\]
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