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JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 28 July 2022, Shift 1, Maths Q19

Question 19 of 90 in this shift, Maths question 19 of 30, Section A.

Consider the sequence

a_1,a_2,a_3,\ldots

such that

a_1=1,\ a_2=2

and

a_{n+2}=\frac{2}{a_{n+1}}+a_n

for

n=1,2,3,\ldots

. If

\left(a_1+\frac{1}{a_2}\right)\left(a_2+\frac{1}{a_3}\right)\left(a_3+\frac{1}{a_4}\right)\cdots\left(a_{30}+\frac{1}{a_{31}}\right)=2^{\alpha}\left({}^{61}C_{31}\right)

, then

\alpha

is equal to :

(1) $-30$
(2) $-31$
(3) $-60$ Official answer
(4) $-61$

Official answer

Option 3

NTA final key (2022 Session 2).

Chapter: Sequences and Series
Topic: No close match in our taxonomy
Idea tested: No close match in our taxonomy

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.