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Counting Pairs

Class 12 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsOn (A={1,2,3,4,5,6,7,8}), (aRb) if (a) and (b) lie in the same block among ({1,2}), ({3,4,5}), ({6,7,8}). How many pairs are in the relation?Class 12Relations and FunctionsEquivalence relationHard MathematicsOn (A={1,2,3,4,5}), (R) has classes ({1,2},{3},{4,5}). How many pairs are in the complement of (R)?Class 12Relations and FunctionsEquivalence relationHard MathematicsOn (A={1,2,3,4,5,6,7,8,9,10,11,12}), (aRb) holds when (a) and (b) have the same remainder on division by (6). How many pairs are in (R)?Class 12Relations and FunctionsEquivalence relationHard MathematicsOn (A={1,2,3,4,5,6,7}), relation (R) has classes ({1,7},{2,6},{3,5},{4}). How many pairs are in (R)?Class 12Relations and FunctionsEquivalence relationHard MathematicsOn (A={1,2,3,4,5,6}), for the relation where (a+b) is divisible by (7) or (a=b), how many ordered pairs are there?Class 12Relations and FunctionsEquivalence relationHard MathematicsOn (A={1,2,3,4,5,6,7,8,9}), (aRb) holds when (\gcd(a,9)=\gcd(b,9)). How many ordered pairs are in the relation?Class 12Relations and FunctionsEquivalence relationHard MathematicsOn (A={1,2,3,4,5,6,7}), (aRb) holds when (a) and (b) have the same divisibility status by (3) and the same divisibility status by (2). How many ordered pairs are in this relation?Class 12Relations and FunctionsEquivalence relationHard MathematicsIf (R) is an equivalence relation on a (7)-element set and (R) has (19) ordered pairs. Which class-size pattern is possible?Class 12Relations and FunctionsEquivalence relationHard MathematicsIf (R) is an equivalence relation on (A) and ([a]) has exactly (4) elements, how many ordered pairs of (R) come from inside ([a])?Class 12Relations and FunctionsEquivalence relationHard MathematicsOn (A={1,2,3,4,5,6}), (aRb) holds when (a) and (b) have the same remainder on division by (5). How many pairs are in the relation?Class 12Relations and FunctionsEquivalence relationHard MathematicsIf an equivalence relation on a (6)-element set has class sizes (3,2,1), how many pairs are in the relation?Class 12Relations and FunctionsEquivalence relationHard MathematicsOn (A={1,2,3,4,5,6,7,8}), how many ordered pairs are in the relation defined by (\gcd(a,8)=\gcd(b,8))?Class 12Relations and FunctionsEquivalence relationHard MathematicsOn (A={1,2,3,4,5,6}), (aRb) holds when (a\equiv b \pmod{3}). How many pairs are in this relation?Class 12Relations and FunctionsEquivalence relationMedium MathematicsOn (A={1,2,3,4}), (aRb) holds when (a+b) is even. How many ordered pairs are in the relation?Class 12Relations and FunctionsEquivalence relationMedium MathematicsIf (A) has (6) elements and the identity relation is taken, how many ordered pairs are in the relation?Class 12Relations and FunctionsEquivalence relationMedium MathematicsOn (A={1,2,3,4}), (aRb) holds when (a=b) or (a+b=5). How many ordered pairs are in the relation?Class 12Relations and FunctionsEquivalence relationMedium MathematicsIf an equivalence relation has class sizes (4) and (2), how many ordered pairs are in the relation?Class 12Relations and FunctionsEquivalence relationMedium MathematicsIf (A) has (5) elements and the sizes of the equivalence classes are (2,2,1), how many pairs are in the relation?Class 12Relations and FunctionsEquivalence relationMedium MathematicsIf an equivalence relation has classes ({p,q,r}) and ({s}), how many ordered pairs are in the relation?Class 12Relations and FunctionsEquivalence relationMedium MathematicsAn equivalence relation on (A={a,b,c,d}) has classes ({a,c}) and ({b,d}). How many ordered pairs are in this relation?Class 12Relations and FunctionsEquivalence relationMedium