Question
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2.
3.
4.
Answer (Detailed Solution Below)
Option 2 : $2$ / $2$
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Detailed Solution
सही उत्तर $2$ / $2$ है।
Key Points
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prepsnap.in • Part -AQuestion:
When $N = 7^{2026} + 5^{2026}$ is divided by $12$, what is the remainder? / जब $N = 7^{2026} + 5^{2026}$ को $12$ से भाग दिया जाता है, तो शेषफल क्या होगा?
1.
$0$ / $0$
2.
$2$ / $2$
3.
$1$ / $1$
4.
$3$ / $3$
Correct Answer: $2$ / $2$
$7^2 = 49 \equiv 1 \pmod{12}$ so $7^{2026} = (7^2)^{1013} \equiv 1 \pmod{12}$; similarly $5^2 = 25 \equiv 1 \pmod{12}$ so $5^{2026} \equiv 1 \pmod{12}$. Hence $N \equiv 1 + 1 = 2 \pmod{12}$. / $7^2 = 49 \equiv 1 \pmod{12}$ अतः $7^{2026} = (7^2)^{1013} \equiv 1 \pmod{12}$; इसी प्रकार $5^2 = 25 \equiv 1 \pmod{12}$ अतः $5^{2026} \equiv 1 \pmod{12}$। इसलिए $N \equiv 1 + 1 = 2 \pmod{12}$।
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