JEE Main 2021 · MathsNumerical answerNumerical valueEasyCalculation

JEE Main 26 February 2021, Shift 2, Maths Q87

Question 87 of 90 in this shift, Maths question 27 of 30, Section B.

Let

\alpha

and

\beta

be two real numbers such that

\alpha+\beta=1

and

\alpha\beta=-1

. Let

p_n=(\alpha)^n+(\beta)^n

p_{n-1}=11

and

p_{n+1}=29

for some integer

n \ge 1

. Then, the value of

p_n^2

is __________.

Official answer

324

NTA final key.

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

Same idea in other shifts

Asked 16× 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 1 · Q4Let $\alpha, \beta$ be the distinct roots of the equation $x^2-(t^2-5t+6)x+1=0$ , $t \in \mathbb{R}$ and $a_n=\alpha^n+\beta^n$ . Then the…HardSingle 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
12 Apr 2023, Shift 1 · Q2Let $\alpha, \beta$ be the roots of the quadratic equation $x^2+\sqrt{6}x+3=0$ . Then…HardSingle 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 108 of the 174 JEE Main shifts held from 2017 to 2026.