JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 25 February 2021, Shift 1, Maths Q64

Question 64 of 90 in this shift, Maths question 4 of 30, Section A.

0 < \theta, \phi < \frac{\pi}{2}

x = \sum_{n=0}^{\infty} \cos^{2n}\theta

y = \sum_{n=0}^{\infty} \sin^{2n}\phi

and

z = \sum_{n=0}^{\infty} \cos^{2n}\theta \cdot \sin^{2n}\phi

then :

(1) $xy - z = (x+y)z$
(2) $xy + z = (x+y)z$ Official answer
(3) $xy + yz + zx = z$
(4) $xyz = 4$

Official answer

Option 2

NTA final key.

Chapter: Sequences and Series
Topic: AP and GP
Idea tested: Infinite GP Sum

Same idea in other shifts

Asked 15× in all

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15 Apr 2023, Shift 1 · Q24If the sum of the series…HardNumerical value
27 Jul 2022, Shift 2 · Q7Let the sum of an infinite G.P., whose first term is a and the common ratio is r, be 5. Let the sum of its first five terms be…MediumSingle correct
26 Jun 2022, Shift 2 · Q3If $A = \sum_{n=1}^{\infty} \frac{1}{(3 + (-1)^n)^n}$ and $B = \sum_{n=1}^{\infty} \frac{(-1)^n}{(3 + (-1)^n)^n}$ , then $\frac{A}{B}$ is…MediumSingle correct
27 Jun 2022, Shift 1 · Q3If $x=\sum_{n=0}^{\infty} a^n$ , $y=\sum_{n=0}^{\infty} b^n$ , $z=\sum_{n=0}^{\infty} c^n$ , where a, b, c are in A.P. and $|a|<1$ , $|b|<1$ ,…MediumSingle correct
28 Jun 2022, Shift 2 · Q25Let for $n=1, 2, \ldots, 50$ , $S_n$ be the sum of the infinite geometric progression whose first term is $n^2$ and whose common ratio is…HardNumerical value

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 108 of the 174 JEE Main shifts held from 2017 to 2026.