JEE Main 2019 — Binomial Theorem Question with Solution
From: JEE Main 2019 (Online) 11th January Evening Slot
Question
Let Sn = 1 + q + q2 + . . . . . + qn and Tn = 1 + + . . . . . .+ where q is a real number and q 1. If 101C1 + 101C2 . S1 + .... + 101C101 . S100 = T100 then is equal to
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Show full solutionCorrect option: C
Correct answer
C2100
Step-by-step explanation
101C1 + 101C2S1 + . . . . . . . + 101C101S100
T100
101C1 + 101C2(1 + q) + 101C3(1 + q + q2) +
. . . . . .+101C101(1 + q + . . . . . + q100)
101C1(1 q) + 101C2(1 q2) +
. . . . . . + 101C101(1 q101)
(2101 1) ((1 + q)101 1)
T100
101C1 + 101C2(1 + q) + 101C3(1 + q + q2) +
. . . . . .+101C101(1 + q + . . . . . + q100)
101C1(1 q) + 101C2(1 q2) +
. . . . . . + 101C101(1 q101)
(2101 1) ((1 + q)101 1)
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This is a previous-year question from JEE Main 2019, covering the Binomial Theorem chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.