JEE Main 2012 — Binomial Theorem Question with Solution
From: AIEEE 2012
Question
If is a positive integer, then is :
Choose an option
Show full solutionCorrect option: A
Correct answer
Aan irrational number
Step-by-step explanation
Let = Odd trems(A) + Even terms(B)
So = Odd terms(A) - Even terms(B)
= (A + B) - (A - B)
= 2B
= 2[even terms]
= 2[ T2 + T4 + T6 + ....... ]
So in case of
= 2[ T2 + T4 + T6 + ....... ]
= 2[
Here in , 2n - 1 is odd number. So there will be always in .
So will be always irrational number.
So = Odd terms(A) - Even terms(B)
= (A + B) - (A - B)
= 2B
= 2[even terms]
= 2[ T2 + T4 + T6 + ....... ]
So in case of
= 2[ T2 + T4 + T6 + ....... ]
= 2[
Here in , 2n - 1 is odd number. So there will be always in .
So will be always irrational number.
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This is a previous-year question from JEE Main 2012, 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.