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STD 11 - 7. binomial theoram — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 7. binomial theoram1 Mark
MCQ
When ${2^{301}}$ is divided by $5$, the least positive remainder is
  • A
    $4$
  • B
    $8$
  • ✓
    $2$
  • D
    $6$
✓

Answer

Correct option: C.
$2$
c
(c) ${2^4} \equiv 1$(mod 5);$ \Rightarrow {({2^4})^{75}} \equiv {(1)^{75}}$(mod5)
$i.e.$ ${2^{300}} \equiv 1$ (mod 5) $ \Rightarrow {2^{300}} \times 2 \equiv (1.2)$(mod 5)
$ \Rightarrow {2^{301}} \equiv 2$ (mod 5), $\therefore $ Least positive remainder is $2$.

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