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Saturday, 31 October

Same idea in other shifts

Asked 11× in all
  1. 8 Apr 2024, Shift 1 · Q3The sum of all the solutions of the equation (8)2x−16⋅(8)x+48=0(8)^{2x}-16\cdot(8)^x+48=0 is :EasySingle correct
  2. 1 Feb 2024, Shift 1 · Q2Let S={x∈R:(3+2)x+(3−2)x=10}S=\{x\in\mathbb{R}:(\sqrt{3}+\sqrt{2})^x+(\sqrt{3}-\sqrt{2})^x=10\}. Then the number of elements in S is :MediumSingle correct
  3. 24 Jun 2022, Shift 2 · Q2The sum of all the real roots of the equation (e2x−4)(6e2x−5ex+1)=0(e^{2x} - 4)(6e^{2x} - 5e^x + 1) = 0 isEasySingle correct
  4. 27 Jun 2022, Shift 1 · Q22If the sum of all the roots of the equation e2x−11ex−45e−x+812=0e^{2x}-11e^x-45e^{-x}+\frac{81}{2}=0 is log⁡ep\log_e p, then p is equal to ____________.MediumNumerical value
  5. 30 Jun 2022, Shift 1 · Q1Let S1={x∈R−{1,2}:(x+2)(x2+3x+5)−2+3x−x2≥0}S_1 = \left\{x \in \mathbf{R} - \{1, 2\} : \frac{(x+2)(x^2+3x+5)}{-2+3x-x^2} \geq 0\right\} and…MediumSingle correct
  6. 4 Aug 2021, Shift 1 · Q61The number of roots of the equation (3+5)∣x2−4∣+4(3−54)∣x2−4∣=6\left(3+\sqrt{5}\right)^{|x^2-4|}+4\left(\frac{3-\sqrt{5}}{4}\right)^{|x^2-4|}=6 isMediumSingle correct
  7. 31 Aug 2021, Shift 1 · Q62The number of real roots of the equation e4x+2e3x−ex−6=0\mathrm{e}^{4x}+2\mathrm{e}^{3x}-\mathrm{e}^{x}-6=0 is :MediumSingle correct
  8. 31 Aug 2021, Shift 2 · Q63The sum of the roots of the equation, x+1−2log⁡2(3+2x)+2log⁡4(10−2−x)=0x+1-2\log_2(3+2^x)+2\log_4(10-2^{-x}) = 0, 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.