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binomial theoram — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSbinomial theoram1 Mark
MCQ
The last two digits of $2015! + 3^{2015}$ is-
  • A
    $03$
  • B
    $18$
  • C
    $13$
  • ✓
    $07$
✓

Answer

Correct option: D.
$07$
d
$2015! + {3^{2015}}$

$2015!$ has last two digits zero.

$3^{2015} \equiv 3 \cdot\left(3^{2014}\right)$

$\equiv 3.9^{1007}=(3)(10-1)^{1007}$

on expansion last two digits $\equiv 07$

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