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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 all ordered pairs in (R^2), ((a,b)S(c,d)) if and only if (a-b=c-d). Which is the equivalence class of ((4,1))?Class 12Relations and FunctionsEquivalence relationLevel 18ExpertMathematicsOn natural numbers, (aRb) if and only if (a) and (b) have the same greatest prime factor. What kind of numbers form the equivalence class of (18)?Class 12Relations and FunctionsEquivalence relationLevel 18ExpertMathematicsOn the set of all polynomials, (pRq) if and only if (p(1)=q(1)). By which condition is the equivalence class of (p(x)=x^2+x) formed?Class 12Relations and FunctionsEquivalence relationLevel 18ExpertMathematicsOn (A={1,2,3,4,5,6,7,8}), (aRb) if and only if (\lceil \frac{a}{2}\rceil=\lceil \frac{b}{2}\rceil). Which is the equivalence class of (5)?Class 12Relations and FunctionsEquivalence relationLevel 18ExpertMathematicsOn all complex numbers, (z_1Rz_2) if and only if (\operatorname{Re}(z_1)=\operatorname{Re}(z_2)). What does the equivalence class of (2+3i) represent?Class 12Relations and FunctionsEquivalence relationLevel 18ExpertMathematicsOn all real numbers, (aRb) if and only if (a^4=b^4). Which is the equivalence class of (2)?Class 12Relations and FunctionsEquivalence relationLevel 18ExpertMathematicsOn (A={1,2,3,4,5,6}), (aRb) if and only if (\operatorname{lcm}(a,6)=\operatorname{lcm}(b,6)). Which is the equivalence class of (4)?Class 12Relations and FunctionsEquivalence relationLevel 18ExpertMathematicsOn real numbers, (aRb) if and only if (\lfloor 2a\rfloor=\lfloor 2b\rfloor). Which is the correct equivalence class of (\frac{5}{4})?Class 12Relations and FunctionsEquivalence relationLevel 18ExpertMathematicsOn all real numbers, (aRb) if and only if (\lfloor 2a\rfloor=\lfloor 2b\rfloor). Which is the equivalence class of (\frac{5}{4})?Class 12Relations and FunctionsEquivalence relationLevel 18ExpertMathematicsOn (A={1,2,3,4,5,6,7}), (aRb) if and only if (a^2\equiv b^2 \pmod{7}). Which is the equivalence class of (3)?Class 12Relations and FunctionsEquivalence relationLevel 18ExpertMathematicsOn real numbers, (aRb) if and only if (a-b\in Z). Which is the equivalence class of (\frac{3}{4})?Class 12Relations and FunctionsEquivalence relationLevel 18ExpertMathematicsOn integers, (aRb) if and only if (a-b) is divisible by (7). How will the equivalence class of (-15) be written?Class 12Relations and FunctionsEquivalence relationLevel 18ExpertMathematicsOn (A={1,2,3,4,5,6,7,8,9,10,11,12}), (aRb) if and only if (a) and (b) leave the same remainder on division by (6). Which is the equivalence class of (5)?Class 12Relations and FunctionsEquivalence relationLevel 18ExpertMathematicsOn (A={1,2,3,4,5}), (aRb) if and only if the squares of (a) and (b) leave the same remainder on division by (5). Which is the equivalence class of (2)?Class 12Relations and FunctionsEquivalence relationLevel 17ExpertMathematicsOn positive integers, (aRb) if and only if (a) and (b) have the same last digit. What forms the equivalence class of (102)?Class 12Relations and FunctionsEquivalence relationLevel 17ExpertMathematicsOn all real numbers where tangent is defined, (aRb) if and only if (\tan a=\tan b). Which of the following is in the equivalence class of (0)?Class 12Relations and FunctionsEquivalence relationLevel 17ExpertMathematicsOn natural numbers, (aRb) if and only if (a) and (b) have the same sum of digits. Which of the following is in the equivalence class of (29)?Class 12Relations and FunctionsEquivalence relationLevel 17ExpertMathematicsOn (A={1,2,3,4,5,6}), (aRb) if and only if (a) and (b) are both multiples of (2) or both not multiples of (2). Which is the equivalence class of (5)?Class 12Relations and FunctionsEquivalence relationLevel 17ExpertMathematicsOn all positive real numbers, (aRb) if and only if (\log a-\log b\in Z). Which is the equivalence class of (1)?Class 12Relations and FunctionsEquivalence relationLevel 17ExpertMathematicsOn the set of all vectors in (R^2), (uRv) if and only if (|u|=|v|). Which is the equivalence class of the zero vector?Class 12Relations and FunctionsEquivalence relationLevel 17Expert