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Equivalence Class

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

MathematicsOn real numbers, (aRb) if and only if (\cos a=\cos b). Which of the following numbers must be in the equivalence class of (0)?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn (A={1,2,3,4,5,6}), (aRb) if and only if the greatest common divisor of (a) and (6) equals the greatest common divisor of (b) and (6). Which is the equivalence class of (5)?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn natural numbers, (aRb) if and only if (a) and (b) have the same number of digits. What forms the equivalence class of (125)?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn (A={1,2,3,4,5,6,7,8,9,10}), (aRb) if and only if (a) and (b) are both prime or both not prime. Which is the equivalence class of (4)?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn all complex numbers, (z_1Rz_2) if and only if (|z_1|=|z_2|). What does the equivalence class of (3+4i) represent?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn the set of all non-zero polynomials, (pRq) if and only if (\deg(p)=\deg(q)). What forms the equivalence class of (x^2+1)?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn real numbers, (aRb) if and only if (\lfloor a\rfloor=\lfloor b\rfloor). Which is the equivalence class of (-1.2)?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn the set of all real ordered pairs, ((a,b)R(c,d)) if and only if (a+b=c+d). How can the equivalence class of ((2,5)) be written?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn real numbers, (aRb) if and only if (a^2=b^2). Which is the equivalence class of (-5)?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsA partition of (A={1,2,3,4,5,6}) is ({{1,2,6},{3,5},{4}}). Choose the correct statement about ((2,6)) and ((3,4)) in the equivalence relation formed by it.Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn real numbers, (aRb) if and only if (a-b\in Q). Which is the equivalence class of (\sqrt{2})?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn (A={1,2,3,4,5,6,7,8}), (aRb) if and only if (a-b) is divisible by (4). Which is the equivalence class of (3)?Class 12Relations and FunctionsEquivalence relationLevel 17Expert MathematicsOn (A={1,2,3,4,5}), (aRb) if and only if (\min(a,3)=\min(b,3)). What is the equivalence class of (5)?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn real numbers, (aRb) if and only if (a-b\in Z). Which is the correct form of the equivalence class of (1.7)?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn (A={1,2,3,4,5,6}), (aRb) if and only if (a) and (b) are both multiples of (3) or both not multiples of (3). What is the equivalence class of (3)?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn (A={1,2,3,4}), (R=A\times A). Which statement about its equivalence classes is correct?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn natural numbers, (aRb) if and only if (a) and (b) have the same set of prime factors. Which of the following belongs to the equivalence class of (12)?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn (A={1,2,3,4,5}), (R={(a,b):|a-b|\text{ is even}}). What is the equivalence class of (4)?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn all subsets of (A={1,2,3,4}), (XRY) if and only if (|X|=|Y|). How many subsets are in the equivalence class of ({1,2})?Class 12Relations and FunctionsEquivalence relationLevel 16Expert MathematicsOn integers, (aRb) if and only if (a-b) is divisible by (4). Which is the equivalence class of (-1)?Class 12Relations and FunctionsEquivalence relationLevel 16Expert