Quadratic Equation – JEE Advanced Previous Year Questions with Solutions
JEE Advanced Previous Year Questions of Math with Solutions are available at eSaral. Practicing JEE Advanced Previous Year Papers Questions of mathematics will help the JEE aspirants in realizing the question pattern as well as help in analyzing weak & strong areas. eSaral helps the students in clearing and understanding each topic in a better way. eSaral also provides complete chapter-wise notes of Class 11th and 12th both for all subjects. Besides this, eSaral also offers NCERT Solutions, Previous year questions for JEE Main and Advance, Practice questions, Test Series for JEE Main, JEE Advanced and NEET, Important questions of Physics, Chemistry, Math, and Biology and many more. Download eSaral app for free study material and video tutorials.     Simulator   Previous Years JEE Advanced Questions
Q. The smallest value of $\mathrm{k},$ for which both the roots of the equation, $\mathrm{x}^{2}-8 \mathrm{kx}+16\left(\mathrm{k}^{2}-\mathrm{k}+1\right)=0$ are real, distinct and have values at least $4,$ is [JEE 2009, 4 (–1)]

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Sol. 2

Q. Let p and q be real numbers such that $p \neq 0, p^{3} \neq q$ and $p^{3} \neq-q .$ If $\alpha$ and $\beta$ are nonzero complex numbers satisfying $\alpha+\beta=-p$ and $\alpha^{3}+\beta^{3}=q$, then a quadratic equation having $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$ as its roots is (A) $\left(p^{3}+q\right) x^{2}-\left(p^{3}+2 q\right) x+\left(p^{3}+q\right)=0$ (B) $\left(\mathrm{p}^{3}+\mathrm{q}\right) \mathrm{x}^{2}-\left(\mathrm{p}^{3}-2 \mathrm{q}\right) \mathrm{x}+\left(\mathrm{p}^{3}+\mathrm{q}\right)=0$ (C) $\left(\mathrm{p}^{3}-\mathrm{q}\right) \mathrm{x}^{2}-\left(5 \mathrm{p}^{3}-2 \mathrm{q}\right) \mathrm{x}+\left(\mathrm{p}^{3}-\mathrm{q}\right)=0$ (D) $\left(p^{3}-q\right) x^{2}-\left(5 p^{3}+2 q\right) x+\left(p^{3}-q\right)=0$ [JEE 2010, 3]

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Sol. (B)

Q. Let $\alpha$ and $\beta$ be the roots of $\mathrm{x}^{2}-6 \mathrm{x}-2=0,$ with $\alpha>\beta .$ If $\mathrm{a}_{\mathrm{n}}=\alpha^{\mathrm{n}}-\beta^{\mathrm{n}}$ for $\mathrm{n} \geq 1,$ then the value of $\frac{\mathrm{a}_{10}-2 \mathrm{a}_{8}}{2 \mathrm{a}_{9}}$ is (A) 1              (B) 2             (C) 3             (D) 4 [JEE 2011]

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Sol. (C)

Q. A value of b for which the equations $\mathrm{x}^{2}+\mathrm{bx}-1=0$ $\mathrm{x}^{2}+\mathrm{x}+\mathrm{b}=0$ have one root in common is – (A) $-\sqrt{2}$ (B) $-i \sqrt{3}$ (C) $\mathrm{i} \sqrt{5}$ (D) $\sqrt{2}$ [JEE 2011]

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Sol. (B)

Q. Let S be the set of all non-zero numbers a such that the quadratic equation $\alpha \mathrm{x}^{2}$ – x + a = 0 has two distinct real roots $\mathrm{x}_{1}$ and $\mathrm{x}_{2}$ satisfying the inequality $\left|x_{1}-x_{2}\right|<1$. Which of the following intervals is(are) a subset(s) of S ? (A) $\left(-\frac{1}{2},-\frac{1}{\sqrt{5}}\right)$ (B) $\left(-\frac{1}{\sqrt{5}}, 0\right)$ (C) $\left(0, \frac{1}{\sqrt{5}}\right)$ (D) $\left(\frac{1}{\sqrt{5}}, \frac{1}{2}\right)$ [JEE 2015, 4M, –0M]

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Sol. (A,D)

Q. Let $-\frac{\pi}{6}<\theta<-\frac{\pi}{12}$. Suppose $\alpha_{1}$ and $\beta_{1}$ are the roots of the equation $\mathrm{x}^{2}-2 \mathrm{xsec} \theta+1=0$ and $\alpha_{2}$ and $\beta_{2}$ are the roots of the equation $\mathrm{x}^{2}+2 \mathrm{xtan} \theta-1=0$. If $\alpha_{1}>\beta_{1}$ and $\alpha_{2}>\beta_{2},$ then $\alpha_{1}+\beta_{2}$ equals (A) $2(\sec \theta-\tan \theta)$ (B) $2 \sec \theta$ (C) $-2 \tan \theta$ (D) 0 [JEE(Advanced)-2016, 3(–1)]

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Sol. (C)

PARAGRAPH 2 Let p,q be integers and let $\alpha, \beta$ be the roots of the equation, $x^{2}-x-1=0,$ where $\alpha \neq \beta .$ For $n=0,1,2, \ldots . .,$ let $a_{n}=p \alpha^{n}+q \beta^{n}$. FACT : If a and b are rational numbers and $a+b \sqrt{5}=0,$ then $a=0=b$.
Q. If $a_{4}=28,$ then $p+2 q=$ (A) 14 (B) 7 (C) 12 (D) 21 [JEE(Advanced 2017, 3(–1)]

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Sol. (C)

Q. $\mathrm{a}_{12}=$ (A) $2 \mathrm{a}_{11}+\mathrm{a}_{10}$ (B) $a_{11}-a_{10}$ (C) $\mathrm{a}_{11}+\mathrm{a}_{10}$ (D) $a_{11}+2 a_{10}$ [JEE(Advanced 2017, 3(–1)]

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Sol. (C)

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Comments
  • June 12, 2021 at 2:29 pm

    Sir my me is Vinit and I am taking lecture of Saransh sir and now I cracked jee advanced 2020 with self study and e saral YouTube videos got AIR 47

    0
  • hi
    May 12, 2021 at 9:25 pm

    awesome question

    0
  • May 11, 2021 at 9:31 pm

    Last one paragraph is best. But i am disappointed because there was only 7 or 8 question 😖.
    But thanks for that

    2
  • April 26, 2021 at 5:21 pm

    Good question🙋🙋🙋

    10
    • April 26, 2021 at 6:00 pm

      Paragraph 2 not understood

      21
  • March 9, 2021 at 5:03 pm

    Thank You very much for these questions

    10
    • April 8, 2021 at 8:32 pm

      It’s really helpful.. thanks

      10
  • GB
    October 19, 2020 at 9:30 am

    Awesome questions

    10
  • October 15, 2020 at 10:19 pm

    Really helpful and the solutions are really good and very concise.

    18
    • February 18, 2021 at 9:51 pm

      Mostly we can use theory of equation in solving these questions. Some objects are misprinted in questions, so kindly revert them to understanding text.

      10
  • October 14, 2020 at 10:47 am

    Really good

    1
  • September 19, 2020 at 4:58 pm

    Really very helpful

    11
  • September 14, 2020 at 9:27 am

    pretty good and nice questions

    2
  • September 13, 2020 at 7:45 am

    Good questions 👍👍

    2
  • May 3, 2020 at 10:30 pm

    Excellent 👌👌👌

    2