JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 3 April 2025, Shift 1, Maths Q3

Question 3 of 75 in this shift, Maths question 3 of 25, Section A.

Let

\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

P_n = \alpha^n + \beta^n

and

Q_n = \gamma^n + \delta^n

, then

\frac{P_{25} + \sqrt{3}P_{24}}{2P_{23}} + \frac{Q_{25} - Q_{23}}{Q_{24}}

is equal to

(1)3
(2)4
(3)5Official answer
(4)7

Official answer

Option 3

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

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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
25 Jul 2021, Shift 1 · Q90If $\alpha,\beta$ 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,…MediumNumerical value
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.