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

MathematicsOn the power set \(\mathcal{P}(X)\) of \(X=\{1,2,3\}\), a relation \(R\) is defined by \(A R B\) if and only if \(A\subseteq B\). What type of relation is it?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsLet \(R=\{(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1)\}\) be a relation on \(A=\{1,2,3\}\). Why is \(R\) not an equivalence relation?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsOn (A={1,2,3,4}), (R={(1,2),(2,1),(2,4),(3,4)}). What is the minimum number of pairs to add to make it symmetric?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsOn (A={1,2,3,4}), (R={(1,1),(1,2),(2,3)}). What is the minimum number of pairs to add to make (R) reflexive?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsIf \(A=\{1,2,3,4\}\), \(B=\{3,4,5,6\}\), and \(R=\{(a,b)\in A\times B: b=a+2\}\), how many ordered pairs does \(R\) contain?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsWhat is the range of the relation \(R=\{(x,y): y=x^2,\ x\in\{-2,-1,0,1,2\}\}\)?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeLevel 27Hard MathematicsIf (R={(1,2),(2,4),(3,1)}), what is (R^{-1})?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsIf a relation (R) satisfies (R=R^{-1}), which property does (R) definitely have?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsIf (A) has (4) elements, how many relations on (A) are reflexive, symmetric and antisymmetric all together?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsIf (A) has (5) elements, how many relations on (A) are both symmetric and antisymmetric?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsOn the set \(A=\{1,2,3,\ldots,15\}\), a relation \(R\) is defined by \(aRb\) if and only if \(a\equiv b\pmod{6}\). Which of the following is the equivalence class \([8]\) in \(A\)?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsOn the real numbers, define aRb if and only if a^3 = b^3. What type of relation is R?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsOn real numbers, (aRb) if and only if (a+b=0). What type of relation is it?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsOn the set of real numbers, a relation R is defined by aRb if and only if \(|a-b|\leq 2\). Choose the correct statement.Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsOn (A=\mathbb{R}\setminus{0}), (aRb) if and only if (ab>0). What are its equivalence classes?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsOn non-zero integers, (aRb) if and only if (\frac{a}{b}>0). What type of relation is it?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsOn positive integers, (aRb) if and only if (a\mid b) and (b\mid a). Which relation is this?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsOn the set \(A=\{-2,-1,0,1,2,3\}\), define the relation \(R\) by \(aRb\) if and only if \(a\equiv b\pmod{3}\). What is the equivalence class \([-1]\)?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsOn the set \(A=\{0,1,2,3,4,5,6,7\}\), define a relation \(R\) by \(aRb\) if and only if \(a^2\equiv b^2\pmod{8}\). What is the equivalence class \([1]_R\) of 1 under \(R\)?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsWhat is the total number of equivalence relations on a set with (3) elements?Class 11Relations and FunctionsRelationsLevel 27Hard