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Mathematics

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

MathematicsIf R is an equivalence relation on a set A, which statement about its equivalence classes is correct?Class 12Relations and FunctionsEquivalence relationLevel 25MediumMathematicsOn A = {1,2,3,4}, let R = {(a,b) : a^2 = b^2}. What type of relation is R?Class 12Relations and FunctionsEquivalence relationLevel 25MediumMathematicsOn A = {1,2,3,4,5}, R = {(1,2), (2,3), (4,5)}. How many ordered pairs are in the smallest equivalence relation containing R?Class 12Relations and FunctionsEquivalence relationLevel 27HardMathematicsHow many equivalence relations on a 4-element set have exactly 2 equivalence classes?Class 12Relations and FunctionsEquivalence relationLevel 27HardMathematicsOn A = {1,2,3,4,5}, for aRb when a ≡ b (mod 3), what is the equivalence class [2]?Class 12Relations and FunctionsEquivalence relationLevel 25HardMathematicsIf R = {(1, 2), (2, 4), (1, 4)}, which pair is required in the transitive check?Class 12Relations and FunctionsTransitive relationLevel 27MediumMathematicsIf R={(1,1),(1,2),(2,2)}, which pair is required from (1,2) and (2,2) in a transitive check?Class 12Relations and FunctionsTransitive relationLevel 26EasyMathematicsIf A={1,2,3} and R={(1,2),(2,3),(1,3)}, which fact shows the transitive property?Class 12Relations and FunctionsTransitive relationLevel 26EasyMathematicsIf \(A=\{1,2,3\}\), \(B=\{1,2,3,4\}\), and \(R=\{(x,y)\in A\times B:y=x+2\}\), what is \(R\)?Class 12Relations and FunctionsIntroduction to RelationsLevel 23EasyMathematicsIf \(A=\{1,2,3\}\) and \(B=\{2,4,6,8\}\), how many ordered pairs \((x,y)\) in \(A\times B\) have \(y/x\) as an integer?Class 12SetsLevel 23MediumMathematicsIf \(A=\{1,2,3,4\}\) and \(B=\{1,3,5,7\}\), how many ordered pairs \((x,y)\) in \(A\times B\) satisfy \(y=2x-1\)?Class 12Relations and FunctionsLevel 23MediumMathematicsIf U = {1, 2, ..., 45} and A = {x : x ∈ U, 9 divides x}, how many elements divisible by 3 are in A'?Class 12SetsLevel 21HardMathematicsIf \(A\cap B'=\varnothing\), which statement is correct?Class 12SetsLevel 10HardMathematicsIf A ∩ B′ = A, which of the following conclusions must be true?Class 12SetsLevel 20MediumMathematicsIf \(U=\{x:x\in\mathbb N, x\le 50\}\) and \(A=\{x:x\text{ is not a prime number}\}\), then \(A'\) is the set of what?Class 12SetsLevel 21EasyMathematicsIf \((A\cap B')\cup(A'\cap B')=B'\), this is an example of which rule?Class 12SetsLevel 20MediumMathematicsIf \(U=\mathbb{R}\), \(A=(-5,2]\), and \(B=[-1,6)\), what is \((A\cap B)'\)?Class 12SetsLevel 20HardMathematicsAccording to De Morgan's law, what is the value of \((A\cap B)^c\)?Class 12SetsLevel 10EasyMathematicsWhich expression is equal to \((A\cup B)\cap(A\setminus B)\)?Class 12SetsLevel 18MediumMathematicsIf A = (-∞, 3] and B = [0, 5), what is A ∩ B?Class 12SetsLevel 18Medium