The number $101^{100} - 1$ is divisible by

100

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1000

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

10000

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

100000

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Solution

The correct options are
A $100$
B $1000$
C $10000$
$(101)^{100} - 1$
$= (1 + 100)^{100} - 1$
$= 1 +^{100} C_{1} 100 +^{100} C_{2} 100^{2} ‘ + . . .^{100} C_{100} 100^{100} - 1$
$=^{100} C_{1} 100 +^{100} C_{2} 100^{2} ‘ + . . .^{100} C_{100} 100^{100}$
$= 100^{2} + 100^{2} * 99 + . . .$
$= 100^{2} [1 + m]$ where m is a positive integer.

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