QJEEM23Ma112b: JEE Main 2023 Mathematics - Class 11 JEEM23Ma112b Solution: The remainder, when 19 200 + 23 200 is divided by 49 , is…

Question

Verified Solution • 2025–26 Session moderate

The remainder, when $19^{200} + 23^{200}$ is divided by 49 , is ___________.

Accepted Answer

19^{200}+23^{200}

=

(21-2)^{200}+(21+2)^{200}=49 \lambda+2^{201}

Now,

2^{201}=8^{67}=(7+1)^{67}=49 \lambda+7 \times 67+1

=49 \lambda+470

=49(\lambda+9)+29

∴

Remainder

=29

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