JEE Main 2021 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 24 February 2021, Shift 1, Maths Q81

Question 81 of 90 in this shift, Maths question 21 of 30, Section B.

If the least and the largest real values of

\alpha

, for which the equation

z + \alpha|z - 1| + 2i = 0

(

z \in C

and

i = \sqrt{-1}

) has a solution, are p and q respectively; then

4(p^2 + q^2)

is equal to ___________.

Official answer

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Quadratic Roots
Idea tested: Nature of Roots

Same idea in other shifts

Asked 9× in all

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31 Jan 2024, Shift 2 · Q24Let $a, b, c$ be the lengths of three sides of a triangle satisfying the condition $(a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0$ . If the set of all…HardNumerical value
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27 Aug 2021, Shift 1 · Q61If $x^2+9y^2-4x+3=0$ , $x, y \in \mathbb{R}$ , then $x$ and $y$ respectively lie in the intervals :MediumSingle correct
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25 Feb 2021, Shift 1 · Q76The coefficients a, b and c of the quadratic equation, $ax^2 + bx + c = 0$ are obtained by throwing a dice three times. The probability…MediumSingle correct
8 Jan 2020, Shift 1 · Q71The least positive value of 'a' for which the equation, $2x^2+(a-10)x+\frac{33}{2}=2a$ has real roots is ______.EasyNumerical value
3 Sep 2020, Shift 1 · Q51Consider the two sets : $A=\{m\in\mathbf{R}$ : both the roots of $x^2-(m+1)x+m+4=0$ are real $\}$ and $B=[-3,5)$ . Which of the following is…MediumSingle 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.