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Saturday, 31 October

JEE Main 2024 · MathsMultiple choiceTwo statementsHardConceptual

JEE Main 5 April 2024, Shift 1, Maths Q2

Question 2 of 90 in this shift, Maths question 2 of 30, Section A.

Consider the following two statements : Statement I : For any two non-zero complex numbers z1,z2z_1, z_2, (∣z1∣+∣z2∣)∣z1∣z1∣+z2∣z2∣∣≤2(∣z1∣+∣z2∣)(|z_1|+|z_2|)\left|\frac{z_1}{|z_1|}+\frac{z_2}{|z_2|}\right| \le 2(|z_1|+|z_2|), and Statement II : If x,y,zx, y, z are three distinct complex numbers and a,b,ca, b, c are three positive real numbers such that a∣y−z∣=b∣z−x∣=c∣x−y∣\frac{a}{|y-z|}=\frac{b}{|z-x|}=\frac{c}{|x-y|}, then a2y−z+b2z−x+c2x−y=1\frac{a^2}{y-z}+\frac{b^2}{z-x}+\frac{c^2}{x-y}=1. Between the above two statements,
  1. (1)both Statement I and Statement II are correct.
  2. (2)both Statement I and Statement II are incorrect.
  3. (3)Statement I is correct but Statement II is incorrect.Official answer
  4. (4)Statement I is incorrect but Statement II is correct.

Official answer

Option 3

NTA final key.

Chapter
Complex Numbers and Quadratic Equations
Topic
Complex Numbers - Polar Form
Idea tested
Modulus and Argument

Same idea in other shifts

Asked 13× in all
  1. 6 Apr 2024, Shift 2 · Q3If z1,z2z_1, z_2 are two distinct complex number such that ∣z1−2z212−z1z2ˉ∣=2\left|\frac{z_1-2z_2}{\frac{1}{2}-z_1\bar{z_2}}\right|=2, thenHardSingle correct
  2. 1 Feb 2024, Shift 1 · Q1Let S={z∈C:∣z−1∣=1S=\{z\in\mathbb{C}:|z-1|=1 and (2−1)(z+zˉ)−i(z−zˉ)=22}(\sqrt{2}-1)(z+\bar{z})-i(z-\bar{z})=2\sqrt{2}\}. Let z1,z2∈Sz_1, z_2\in S be such that…HardSingle correct
  3. 29 Jan 2024, Shift 1 · Q3If z=12−2iz=\frac{1}{2}-2i is such that ∣z+1∣=αz+β(1+i)|z+1|=\alpha z+\beta(1+i), i=−1i=\sqrt{-1} and α,β∈R\alpha,\beta\in\mathbb{R}, then α+β\alpha+\beta is…EasySingle correct
  4. 30 Jan 2024, Shift 1 · Q2If z=x+iy, xy≠0z=x+iy,\ xy\neq0, satisfies the equation z2+izˉ=0z^2+i\bar{z}=0, then ∣z2∣|z^2| is equal to :MediumSingle correct
  5. 31 Jan 2024, Shift 1 · Q22If α\alpha denotes the number of solutions of ∣1−i∣x=2x|1-i|^x=2^x and β=(∣z∣arg⁡(z))\beta=\left(\frac{|z|}{\arg(z)}\right), where…MediumNumerical value
  6. 8 Apr 2023, Shift 1 · Q2If for z=α+iβz=\alpha+i\beta, ∣z+2∣=z+4(1+i)|z+2|=z+4(1+i), then α+β\alpha+\beta and αβ\alpha\beta are the roots of the equationMediumSingle correct
  7. 28 Jul 2022, Shift 2 · Q88Let z=a+ib, b≠0z=a+ib,\ b\neq 0 be complex numbers satisfying z2=zˉ⋅21−∣z∣z^2=\bar{z}\cdot 2^{1-|z|}. Then the least value of n∈Nn\in\mathbb{N}, such that…HardNumerical value
  8. 30 Jul 2022, Shift 2 · Q62Let z1=1+2iz_1 = 1 + 2i, z2=2+iz_2 = 2 + i, 1z1+1z2=6w\frac{1}{z_1}+\frac{1}{z_2}=\frac{6}{w}, and z=iw2−w‾z = \frac{iw}{2-\overline{w}}. Consider the statements…MediumTwo statements

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.