JEE Main 2021 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 25 July 2021, Shift 1, Maths Q90

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

\alpha,\beta

are roots of the equation

x^2+5(\sqrt2)x+10=0

\alpha>\beta

and

P_n=\alpha^n-\beta^n

for each positive integer n, then the value of

\left(\frac{P_{17}P_{20}+5\sqrt2P_{17}P_{19}}{P_{18}P_{19}+5\sqrt2P_{18}^2}\right)

is equal to _________.

Official answer

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Quadratic Roots
Idea tested: Newton's Sums

Same idea in other shifts

Asked 9× in all

6 Apr 2026, Shift 2 · Q3Let $S=\{z\in\mathbb{C}: z^2+\sqrt{6}\,iz-3=0\}$ . Then $\sum_{z\in S} z^8$ is equal to :MediumSingle correct
2 Apr 2025, Shift 1 · Q17Let $P_n=\alpha^n+\beta^n$ , $n\in\mathbf{N}$ . If $P_{10}=123$ , $P_9=76$ , $P_8=47$ and $P_1=1$ , then the quadratic equation having roots…MediumSingle correct
3 Apr 2025, Shift 1 · Q3Let $\alpha$ and $\beta$ be the roots of $x^2 + \sqrt{3}x - 16 = 0$ , and $\gamma$ and $\delta$ be the roots of $x^2 + 3x - 1 = 0$ . If…MediumSingle correct
6 Apr 2024, Shift 2 · Q21Let $\alpha,\beta$ be roots of $x^2+\sqrt{2}x-8=0$ . If $U_n=\alpha^n+\beta^n$ , then $\frac{U_{10}+\sqrt{2}U_9}{2U_8}$ is equal to ________.EasyNumerical value
9 Apr 2024, Shift 2 · Q3Let $\alpha, \beta;\ \alpha>\beta$ , be the roots of the equation $x^2-\sqrt{2}x-\sqrt{3}=0$ . Let $P_n=\alpha^n-\beta^n,\ n\in\mathbb{N}$ .…MediumSingle correct
11 Apr 2023, Shift 1 · Q24If $a$ and $b$ are the roots of the equation $x^2 - 7x - 1 = 0$ , then the value of…MediumNumerical value
13 Apr 2023, Shift 2 · Q3Let $\alpha, \beta$ be the roots of the equation $x^2-\sqrt{2}x+2=0$ . Then $\alpha^{14}+\beta^{14}$ is equal toMediumSingle correct
2 Sep 2020, Shift 1 · Q52Let $\alpha$ and $\beta$ be the roots of the equation, $5x^{2}+6x-2=0$ . If $S_n=\alpha^{n}+\beta^{n}$ , $n=1, 2, 3, \ldots$ , then :EasySingle correct

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.