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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}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}) is given. Which pairs are definitely needed to make it an equivalence relation?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn the set of all functions from (A={1,2,3}) to (A), (fRg) if and only if (f(1)=g(1)). Choose the correct statement about this relation.Class 12Relations and FunctionsEquivalence relationExpert MathematicsA relation (R) on a set is transitive. If ((x,y) \in R), ((y,z) \in R), ((z,u) \in R), and ((u,v) \in R), which pair must definitely be in (R)?Class 12Relations and FunctionsTransitive relationExpert MathematicsOn (A={1,2,3,4,5}), (R={(1,2),(2,4),(4,5),(1,4),(2,5)}). Which pair must be added to make it transitive?Class 12Relations and FunctionsTransitive relationExpert MathematicsOn a set, (R) and (S) are both transitive relations. Which statement is always true?Class 12Relations and FunctionsTransitive relationExpert MathematicsOn (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,3),(1,3),(3,4),(1,4),(2,4)}). What is the nature of this relation?Class 12Relations and FunctionsTransitive relationExpert MathematicsOn (A={1,2,3,4}), (R={(1,3),(3,2),(2,4),(1,2),(3,4)}). Which pair is compulsory to add to make it transitive?Class 12Relations and FunctionsTransitive relationExpert MathematicsOn non-zero integers, (aRb) is defined when (a) divides (b). What is the nature of this relation?Class 12Relations and FunctionsTransitive relationExpert MathematicsOn the set (A={1,2,3}), the relation (R={(1,1),(1,2),(1,3),(2,2),(2,3),(3,3)}) is given. What type of relation is it?Class 12Relations and FunctionsTransitive relationExpert MathematicsIf (A={1,2,3}) and (R={(1,1),(2,2),(1,2),(2,1)}), which statement about (R) is correct?Class 12Relations and FunctionsSymmetric relationExpert MathematicsIf a relation on (A={1,2,3,4}) is both symmetric and antisymmetric, how many such relations are possible?Class 12Relations and FunctionsSymmetric relationExpert MathematicsIf (R) and (S) are symmetric, what is true about (R\triangle S), where (R\triangle S=(R-S)\cup(S-R))?Class 12Relations and FunctionsSymmetric relationExpert MathematicsA set (A) has (n) elements. Which is the correct formula for the number of symmetric relations on (A)?Class 12Relations and FunctionsSymmetric relationExpert MathematicsIf (A={1,2,3}) and the relation matrix is (M=\begin{bmatrix}1&0&1\1&0&0\1&0&1\end{bmatrix}), what is the issue with symmetry?Class 12Relations and FunctionsSymmetric relationExpert MathematicsIf the matrix of a relation is (M=\begin{bmatrix}0&1&1\1&1&0\1&0&1\end{bmatrix}), choose the correct statement.Class 12Relations and FunctionsSymmetric relationExpert MathematicsIf (R) and (S) are symmetric relations, which additional condition is sufficient for (R\circ S) to be symmetric?Class 12Relations and FunctionsSymmetric relationExpert MathematicsA set (A) has (6) elements. How many relations on (A) are both symmetric and reflexive?Class 12Relations and FunctionsSymmetric relationExpert MathematicsLet (A={1,2,3,4,5,6,7,8}) and (R={(a,b)\in A\times A:a+b\text{ is divisible by }6}). What is the minimum number of pairs needed to make (R) reflexive?Class 12Relations and FunctionsReflexive relationExpert MathematicsIf (A={1,2,3,4,5,6}) and (R={(a,b):a\equiv 2b \pmod{3}}), how many diagonal pairs must be added to make (R) reflexive?Class 12Relations and FunctionsReflexive relationExpert MathematicsIf (A={1,2,3,4,5}) and (R={(a,b):a^2+b^2\text{ is divisible by }5}), how many diagonal pairs are in (R)?Class 12Relations and FunctionsReflexive relationExpert