JEE Main 2020 — Binomial Theorem Question with Solution
From: JEE Main 2020 (Online) 7th January Morning Slot
Question
The greatest positive integer k, for which 49k + 1 is a factor of the sum
49125 + 49124 + ..... + 492 + 49 + 1, is:
49125 + 49124 + ..... + 492 + 49 + 1, is:
Choose an option
Show full solutionCorrect option: C
Correct answer
C63
Step-by-step explanation
1 + 49 + 492
+ ..... + 49125
sum of G.P. =
=
Also 4963 - 1
= (1 + 48)63 - 1
= [63C01 + 63C1 48 + 63C2 (48)2 + .... ] - 1
= [1 + 48] - 1 = 48
So = integer
4963 + 1 is a factor.
So k = 63.
sum of G.P. =
=
Also 4963 - 1
= (1 + 48)63 - 1
= [63C01 + 63C1 48 + 63C2 (48)2 + .... ] - 1
= [1 + 48] - 1 = 48
So = integer
4963 + 1 is a factor.
So k = 63.
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