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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 correct simplified form of (\sum_{r=0}^{n}{}^{n}C_r{}^{n-r}C_m)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsIf (\frac{{}^{n}C_{r+1}}{{}^{n}C_r}=\frac{2}{3}), what relation is formed between (n) and (r)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsIf ({}^{n}P_3=10{}^{n}P_2), what is (n)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsIf ({}^{20}C_{3r-1}={}^{20}C_{r+5}) and the indices are not equal, what is (r)?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 MathematicsIf (^{n}C_r) is a maximum term, which condition is useful for (\frac{{}^{n}C_{r+1}}{{}^{n}C_r})?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsIf (^{n}C_{r-2}:{}^{n}C_{r-1}:{}^{n}C_r) is given, which ratio is most useful first in the derivation?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhich advanced method is useful for separating sums like ({}^{n}C_0+{}^{n}C_3+{}^{n}C_6+\cdots)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsHow is the sum of even-index coefficients of ((1+x)^n) derived?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhat is the coefficient of (x^3y^2z^3) in ((x+y+z)^8)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhat is the coefficient of (a^p b^q c^r) in ((a+b+c)^n), if (p+q+r=n)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsLength (r) strings are formed from (n) distinct symbols and exactly (s) distinct symbols are used. Which count is correct?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsLength (r) strings are formed from (n) distinct symbols with repetition allowed, but at least one symbol repeats. What is the count?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsUsing digits (1,2,3,4,5,6,7) with repetition allowed, if exactly (2) positions contain even digits in a (4)-digit number, what is the count?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsUsing digits (0,1,2,3,4,5,6) without repetition, (4)-digit numbers divisible by (5) are formed. Which count expression is correct?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhy is the case with (0) as the last digit treated separately when forming (5)-digit even numbers without repetition from (0,1,2,3,4,5,6,7)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsIn a line of (10) people, (A) must come before (B) and (C) before (D). What is the count?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert Mathematics(n) distinct objects are arranged in a row and the relative order of (k) special objects is fixed. What is the count?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsThere are (n) men and (n) women among (2n) people. What is the count of alternate seating around a round table?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert