The number (101) 100 – 1 is divisible by

Explanation: ( 101 ) 100 − 1 = 100 C 1 100 + 100 C 2 100 2 + 100 C 3 100 3 + … … … … . . + 100 C 100 100 100 = 100 2 [ 1 + 100 C 2 + 100 C 3 100 + … . . ] = ( 10 4 )

Question:

The number (101)¹⁰⁰ – 1 is divisible by

WBJEE

Updated On: Jul 31, 2024

(A) 10⁴
(B) 10⁶
(C) 10⁸
(D) 10¹²

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The Correct Option is A

Solution and Explanation

Explanation:

\begin{aligned} (101)^{100} - 1 =^{100} C_{1} 100 +^{100} C_{2} 100^{2} +^{100} C_{3} 100^{3} + \dots \dots \dots \dots . . +^{100} C_{100} 100^{100} \\ = & 100^{2} [1 +^{100} C_{2} +^{100} C_{3} 100 + \dots . .] \\ = & (10^{4}) \end{aligned}

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