JEE Main 2019 — Binomial Theorem Question with Solution
From: JEE Main 2019 (Online) 8th April Evening Slot
Question
If the fourth term in the binomial expansion of
is equal to 200, and x > 1, then the value of x is :
is equal to 200, and x > 1, then the value of x is :
Choose an option
Show full solutionCorrect option: C
Correct answer
C10
Step-by-step explanation
Fourth term (T4)
=
=
=
=
Given, T4 = 200
= 200
= 10
Taking log10 on both sides
= 1
put log10 x = t
= 1
= 1
t2 + 7t = 4 + 4t
t2 + 3t - 4 = 0
(t + 4)(t - 1) = 0
t = 1 or t = - 4
log10 x = 1
x = 10
or log10 x = - 4
x = 10-4
But as x > 1 so x 10-4
x = 10
=
=
=
=
Given, T4 = 200
= 200
= 10
Taking log10 on both sides
= 1
put log10 x = t
= 1
= 1
t2 + 7t = 4 + 4t
t2 + 3t - 4 = 0
(t + 4)(t - 1) = 0
t = 1 or t = - 4
log10 x = 1
x = 10
or log10 x = - 4
x = 10-4
But as x > 1 so x 10-4
x = 10
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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.