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If (^{n}C_{r}=^{n}C_{r-2}) and (r>2), then (n) is equal to what?यदि (^{n}C_{r}=^{n}C_{r-2}) और (r>2) है, तो (n) किसके बराबर है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(2r-2\)\(2r-2\)
Using the symmetry property of combinations, if \(^{n}C_a=^{n}C_b\) and \(a\ne b\), then \(a+b=n\). Here, \(r\ne r-2\), so \(r+(r-2)=n\). Therefore, \(n=2r-2\). Taking \(2r\) would not make \(r-2\) the complementary index of \(r\). Exam tip: use the identity \(^{n}C_r=^{n}C_{n-r}\).संयोजन के सममिति गुण के अनुसार \(^{n}C_a=^{n}C_b\) होने पर, जब \(a\ne b\), तब \(a+b=n\) होता है। यहाँ \(r\ne r-2\), इसलिए \(r+(r-2)=n\)। अतः \(n=2r-2\)। \(2r\) लेने पर पूरक सूचकांक \(r\) के बजाय \(r-2\) नहीं मिलेगा। परीक्षा टिप: \(^{n}C_r=^{n}C_{n-r}\) पहचान का प्रयोग करें।
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