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[JEE Main 2012] For a positive integer $n$, $(\sqrt3+1)^{2n}-(\sqrt3-1)^{2n}$ is

VAVidaara Admin Asked 1mo ago 2 views 1 answer
#PYQJEE#JEE#JEE Main#2012#divisibility-remainders#Binomial Theorem

For a positive integer $n$, $(\sqrt3+1)^{2n}-(\sqrt3-1)^{2n}$ is

(a) irrational
(b) an odd positive integer
(c) an even positive integer
(d) a non-integer rational

1 Answer

VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 1mo ago ▲ 0

Correct answer: (a) irrational

The difference keeps only odd powers of $\sqrt3$, each of which is irrational, so the value is irrational.

JEE Main 2012 · Binomial Theorem — verified solution by the Vidaara Team.

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