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What is the value of (\binom{11}{5}-\binom{10}{5})?(\binom{11}{5}-\binom{10}{5}) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 210210
Using Pascal’s identity, \(\binom{n}{r}-\binom{n-1}{r}=\binom{n-1}{r-1}\). Therefore, \(\binom{11}{5}-\binom{10}{5}=\binom{10}{4}=210\). The value 252 is \(\binom{10}{5}\), not the required difference. Exam tip: apply Pascal’s identity directly when consecutive binomial coefficients are subtracted.पास्कल के सर्वसमिका के अनुसार \(\binom{n}{r}-\binom{n-1}{r}=\binom{n-1}{r-1}\)। अतः \(\binom{11}{5}-\binom{10}{5}=\binom{10}{4}=210\)। विकल्प 252, \(\binom{10}{5}\) का मान है, अंतर का नहीं। परीक्षा टिप: ऐसे क्रमागत द्विपद गुणांकों के अंतर में पास्कल की सर्वसमिका सीधे लागू करें।
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