Last three digits of the number N = 7^ 100 - 3^ 100 are - Vidyadip

MCQ

Last three digits of the number $N = 7^{100} - 3^{100}$ are

A
$100$
B
$300$
C
$500$
✓
$0$

✓

Answer

Correct option: D.

$0$

d
consider $(5 + 2)^{100} - (5 - 2)^{100}$

$= 2 [^{100}C_1 5^{99} · 2 + ^{100}C_3 5^{97} · 2^3 + ....... + ^{100}C_{99}5 · 2^{99}]$

$= 2 [1000 · 5^{98} + ^{100}C_3 5^{94} + ....... + 1000 · 2^{98}]$

$\Rightarrow$ minimum $000$ as last three digits.

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