JEE Main 2022 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 25 June 2022, Shift 1, Maths Q26

Question 26 of 90 in this shift, Maths question 26 of 30, Section B.

For a natural number n, let

\alpha_n=19^n-12^n

. Then, the value of

\frac{31\alpha_9-\alpha_{10}}{57\alpha_8}

is __________.

Official answer

NTA final key.

Chapter: Sequences and Series
Topic: Quadratic Roots
Idea tested: Higher Degree Evaluation via Root Substitution

Same idea in other shifts

Asked 2× in all

29 Jan 2024, Shift 1 · Q21Let $\alpha,\beta$ be the roots of the equation $x^2-x+2=0$ with $Im(\alpha)>Im(\beta)$ . Then $\alpha^6+\alpha^4+\beta^4-5\alpha^2$ is…MediumNumerical 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.