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Divisibility

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

MathematicsIf \(A=\{1,2,3\}\) and \(B=\{2,4,6,8\}\), how many ordered pairs \((x,y)\) in \(A\times B\) have \(y/x\) as an integer?Class 12SetsLevel 23Medium MathematicsOn integers, (a*b=a+b+ab). For which (a) will inverses exist in integers under this operation?Class 12Relations and FunctionsBinary operationsLevel 29Hard MathematicsOn (A={1,2,3,4,5,6}), (aRb) if (a+b) is divisible by (3). Why is this not an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn integers, (aRb) if and only if (a^2-b^2) is divisible by (8). Which of the following pairs belongs to the relation?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn (A={1,2,3,4}), (aRb) if and only if (a^2-b^2) is divisible by (3). What is the equivalence class of (1)?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn integers, (aRb) holds when (a-b) is divisible by (8) or by (12). Why is this relation not an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 17Hard MathematicsOn integers, (aRb) holds when (a-b) is divisible by (4) or by (6). Why is this relation not an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsOn integers, (aRb) holds when (a^2-b^2) is divisible by (3). What type of relation is it?Class 12Relations and FunctionsEquivalence relationLevel 18Medium MathematicsOn (A={1,2,3,4,5}), (aRb) holds when (|a-b|) is divisible by (3). Which pair belongs to (R)?Class 12Relations and FunctionsEquivalence relationLevel 17Medium MathematicsOn (A={2,4,6,8}), (aRb) when (a) and (b) are both divisible by (2). What type of relation is (R)?Class 12Relations and FunctionsEquivalence relationLevel 18Easy MathematicsOn (A={1,2,3,4,5,6}), (aRb) when (a) and (b) are both divisible by (2) or both not divisible by (2). Which is the class of (2)?Class 12Relations and FunctionsEquivalence relationLevel 18Easy MathematicsOn integers, (aRb) when (a-b) is divisible by (4). What type of relation is this?Class 12Relations and FunctionsEquivalence relationLevel 18Easy MathematicsOn integers, (aRb) when (a-b) is divisible by (5). Which statement about (R) is correct?Class 12Relations and FunctionsEquivalence relationLevel 17Easy MathematicsOn integers, (aRb) if (a-b) is divisible by (5). This relation is connected with which idea?Class 12Relations and FunctionsEquivalence relationLevel 16Easy MathematicsOn integers, (aRb) is defined when (a-b) is divisible by (9). What is the nature of this relation?Class 12Relations and FunctionsTransitive relationLevel 15Expert MathematicsOn (A={1,2,3,4,5,6}), (R={(a,b):a\mid b\text{ and }b\mid a}). What is the nature of this relation?Class 12Relations and FunctionsTransitive relationLevel 14Expert MathematicsOn integers, (aRb) is defined when (a-b) is divisible by (7). Why is this relation transitive?Class 12Relations and FunctionsTransitive relationLevel 14Expert MathematicsOn (A={1,2,4,8}), (aRb) is defined when (b) is a multiple of (a). What is the nature of this relation?Class 12Relations and FunctionsTransitive relationLevel 13Expert MathematicsOn (A={1,2,3,4}), (R={(a,b):a) divides (b}). Which option correctly shows a transitivity check?Class 12Relations and FunctionsTransitive relationLevel 13Expert MathematicsOn the set of integers, (aRb) is defined when (a-b) is divisible by (3). What is the nature of this relation?Class 12Relations and FunctionsTransitive relationLevel 13Expert