A={123},=B{456} then number of unordered pair is equal to please if you know then give me answer if you don't know answer and if you give me answer then I will report you this is jee advance leval question I want anwer of this question please help plz if you don't know answer then don't give me answer warning if you answered me wrong answer your account will be suspended
Answers
Answer:
AnswEr :
⠀⠀⠀⌬ Let the Unit's place digit = M
⠀⠀⠀⌬ And the ten's place digit = N
⠀⠀⠀⌬ Then, Original Number = 10(M + N)
⠀⠀⠀⌬ Also, Interchaged Number = 10(N + M)
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• F i r s t⠀C o n d i t i o n :
Sum of the two digits (M + N) number is 9.
\begin{gathered}\twoheadrightarrow\sf M + N = 9 \qquad\quad\qquad\quad\Bigg\lgroup\sf eq^{n}\;(1)\Bigg\rgroup\\\\\end{gathered}
↠M+N=9
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• S e c o n d⠀C o n d i t i o n :
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After Interchanging the digits, the new number is greater than the original number by 27.
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\begin{gathered}\longrightarrow\sf (10N + M) - (10M + N) = 27\\\\\\\end{gathered}
⟶(10N+M)−(10M+N)=27
\begin{gathered}\longrightarrow\sf 9N - 9M = 27\\\\\\\end{gathered}
⟶9N−9M=27
\begin{gathered}\longrightarrow\sf N - M = 3\\\\\\\end{gathered}
⟶N−M=3
\begin{gathered}\longrightarrow\sf N = 3 + M \qquad\quad\qquad\quad\Bigg\lgroup\sf eq^{n}\;(2)\Bigg\rgroup\\\\\end{gathered}
⟶N=3+M
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\begin{gathered}\underline{\bigstar\:\sf{Substitue \: the \: value \: of \: N \: from \: eq^n \: (2) \: to \: eq^n \: (1) : }} \\ \\ \\ \end{gathered}
★SubstituethevalueofNfromeq
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\begin{gathered}\longrightarrow\sf M + N = 9\\\\\\\end{gathered}
⟶M+N=9
\begin{gathered}\longrightarrow\sf M + 3 + M = 9\\\\\\\end{gathered}
⟶M+3+M=9
\begin{gathered}\longrightarrow\sf 2M = 9 - 3 \\\\\\\end{gathered}
⟶2M=9−3
\begin{gathered}\longrightarrow\sf 2M = 6\\\\\\\end{gathered}
⟶2M=6
\begin{gathered}\longrightarrow\sf M = \cancel\dfrac{6}{2}\\\\\\\end{gathered}
⟶M=
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\begin{gathered}\longrightarrow\sf M = 3\\\\\end{gathered}
⟶M=3
\begin{gathered}\underline{\bigstar\:\sf{Substituting\;value\;of\;M\;in\;\;eq^n\;(1)\;: }} \\ \\ \\ \end{gathered}
★SubstitutingvalueofMineq
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\begin{gathered}\longrightarrow\sf M + N = 9\\\\\\\end{gathered}
⟶M+N=9
\begin{gathered}\longrightarrow\sf 3 + N = 9\\\\\\\end{gathered}
⟶3+N=9
\begin{gathered}\longrightarrow\sf N = 9 - 3\\\\\\\end{gathered}
⟶N=9−3
\begin{gathered}\longrightarrow\sf N = 6\\\\\end{gathered}
⟶N=6
\begin{gathered}\underline{\bigstar\:\textsf{Now,\;Original\; Number\; :}}\\\\\end{gathered}
★Now,OriginalNumber:
\begin{gathered}\twoheadrightarrow\sf Original\; Number = 10(M + N)\\\\\\\end{gathered}
↠OriginalNumber=10(M+N)
\begin{gathered}\twoheadrightarrow\sf Original\; Number = 10(3) + 6\\\\\\\end{gathered}
↠OriginalNumber=10(3)+6
\begin{gathered}\twoheadrightarrow\sf Original\; Number = 30 + 6\\\\\\\end{gathered}
↠OriginalNumber=30+6
\begin{gathered}\twoheadrightarrow\underline{\boxed{\pmb{\sf{ Original\; Number =36}}}}\\\\\end{gathered}
↠
OriginalNumber=36
OriginalNumber=36
\;\;\;\;\;\qquad\therefore{\underline{\textsf{Hence, the Original number is \textbf{36}.}}}∴
Hence, the Original number is 36.