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Binomial Coefficients

Class 11 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIf ({}^{n}C_{r+1}<{}^{n}C_r), which inequality is correct?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsIf ({}^{n}C_{r+1}>{}^{n}C_r), which condition is correct?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsIf ({}^{n}C_{r+1}>{}^{n}C_r), which inequality is correct?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhen (n) is odd, which terms are maximum for ({}^{n}C_r)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhen (n) is even, at which (r) does ({}^{n}C_r) have a unique maximum?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsUsing Pascal's identity, how can \(\binom{n}{r}+\binom{n}{r+1}\) be written?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsFor integers 0 ≤ r, s ≤ n, if \(\binom{n}{r}=\binom{n}{s}\) and \(r\ne s\), what relation must hold?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsIf n is odd, which two binomial coefficients C(n,r) are largest?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsIf n is even, which binomial coefficient C(n,r) is uniquely largest?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsWhy do the binomial coefficients C(n,0), C(n,1), …, C(n,n) increase toward the middle and then decrease?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsWhich identity explains why C(n+r−1, r) equals C(n+r−1, n−1)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsWhich relation is most useful for identifying the largest binomial coefficient C(n, r) as r varies?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsIf C(n, r−1):C(n, r) = 3:5, which expression for the ratio is useful in deriving a relation between n and r?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsWhich combinatorial idea explains the identity \(\sum_{r=0}^{n}\binom{n}{r}=2^n\)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsIf \(\frac{^{n}C_r}{^{n}C_{r-1}}=4\), which equation is correct?Class 11Permutations and CombinationsDerivations of formulas and their connectionsMedium MathematicsIf \(\frac{^{n}C_r}{^{n}C_{r-1}}=3\), which equation is correct?Class 11Permutations and CombinationsDerivations of formulas and their connectionsMedium MathematicsIn \(^{n}C_r=\frac{n}{n-r},^{n-1}C_r\), which lower index remains the same?Class 11Permutations and CombinationsDerivations of formulas and their connectionsMedium MathematicsIf \(^{n}C_r=\frac{n-r+1}{r},^{n}C_{r-1}\) and \(n=10\), \(r=4\), what is the multiplier?Class 11Permutations and CombinationsDerivations of formulas and their connectionsMedium MathematicsIf \(^{10}C_4=^{10}C_m\) and \(m\neq4\) what is (m)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsEasy MathematicsWhy is nCᵣ taken as 0 when r > n?Class 11Permutations and CombinationsDerivations of formulas and their connectionsEasy