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.

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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)]

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]

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]

Sol. (C)

Q. A value of b for which the equations



have one root in common is –

(A) $-\sqrt{2}$

(B) $-i \sqrt{3}$

(C) $\mathrm{i} \sqrt{5}$

(D) $\sqrt{2}$

[JEE 2011]

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]

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)]

Sol. (C)


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)]

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)]

Sol. (C)


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  • May 3, 2020 at 10:30 pm

    Excellent 👌👌👌