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Permutations And Combinations

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

MathematicsWhat is the simplified result of (\sum_{r=0}^{n}r^2{}^{n}C_r)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhich split of (r^2) is correct for deriving (\sum_{r=0}^{n}r^2{}^{n}C_r)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhat is (\sum_{r=0}^{n}(-1)^r r(r-1){}^{n}C_r) for (n>2)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhat is the value of (\sum_{r=0}^{n}(-1)^r r{}^{n}C_r) for (n>1)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhat condition is necessary to write ({}^{n}C_r{}^{r}C_s) as ({}^{n}C_s{}^{n-s}C_{r-s})?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsHow can ({}^{n}C_a{}^{a}C_b{}^{b}C_c) be written by changing the order correctly?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsIn (\sum_{r=0}^{n}r{}^{n}C_r{}^{r}C_2), what is the most useful form of (r{}^{r}C_2)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhat is the simplified form of (\sum_{r=0}^{n}{}^{n}C_r{}^{r}C_3)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhat is the combinatorial meaning of (\sum_{r=0}^{n}{}^{n}C_r{}^{r}C_2)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhat is the best way to recognize (\sum_{k=0}^{r}{}^{m+k}C_k={}^{m+r+1}C_r)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsThe identity (\sum_{k=r}^{n}{}^{k}C_r={}^{n+1}C_{r+1}) is proved by which counting idea?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert Mathematics(4) players are chosen from (9) players, and (A) and (B) are not selected together. Which count is correct?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsA committee of (5) is formed from (10) students, and (A) and (B) are either both included or both excluded. What is the count?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhen choosing (r) objects from (n) distinct objects, at least (2) special objects are required and there are (s) special objects. Which complement expression is correct?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsIf (\frac{{}^{n}C_{r}}{{}^{n}C_{r-1}}=\frac{5}{2}), which relation is formed?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsIf (\frac{{}^{n}C_{r+1}}{{}^{n}C_r}=\frac{3}{4}), which relation is correct?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsIf ({}^{n}P_4=12{}^{n}P_3), what is the value of (n)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsIf ({}^{24}C_{2r-1}={}^{24}C_{r+8}) and the lower indices are unequal, what is (r)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsIf ({}^{n}C_{r}= {}^{n}C_{r+4}) and the indices are not equal, what is the relation between (r) and (n)?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