Quadratic Equation and Inequalities PYQs - Last 10 Years
JEE Advanced / Mathematics / Algebra / 10 recent questions
MathematicsAlgebra2017-2026
Practice 10 JEE Advanced Mathematics questions from Quadratic Equation and Inequalities. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
10
PYQs on Page
Mathematics / Algebra
2017-2026
Year Range
Based on indexed question metadata
4
Last 5 Years
2022-2026
10
Last 10 Years
2017-2026
Recent Year Trend
2020
2021
2022
2024
2025
2026Latest year
20201 max PYQs/year2026
Question Types
10PYQs
INTEGER40%
MCQ40%
MCQM20%
Difficulty Mix
#1 Medium6
#2 Hard3
#3 Easy1
4 in last 5 years10 in last 10 years
Last 10 Years Quadratic Equation and Inequalities Questions
Showing 10 of 10 filtered questions.
1Quadratic Equation And Inequalities
Let a, b, c be positive integers in arithmetic progression such that the equation\(ax^2 + bx + c = 0\)has only integer solutions.Then which of the following statements is (are) TRUE?
MCQM+4 / -12026
2Quadratic Equation And Inequalities
Let $\mathbb{R}$ denote the set of all real numbers. Let $a_i, b_i \in \mathbb{R}$ for $i \in \{1, 2, 3\}$.
Define the functions $f: \mathbb{R} \to \mathbb{R}$, $g: \mathbb{R} \to \mathbb{R}$, and $h: \mathbb{R} \to \mathbb{R}$ by
$f(x) = a...
Define the functions $f: \mathbb{R} \to \mathbb{R}$, $g: \mathbb{R} \to \mathbb{R}$, and $h: \mathbb{R} \to \mathbb{R}$ by
$f(x) = a...
MCQ+3 / -12025
3Quadratic Equation And Inequalities
Let $a=3 \sqrt{2}$ and $b=\frac{1}{5^{1 / 6} \sqrt{6}}$. If $x, y \in \mathbb{R}$ are such that
$$ \begin{aligned} & 3 x+2 y=\log _a(18)^{\frac{5}{4}} \quad \text { and } \\ & 2 x-y=\log _b(\sqrt{1080}), \end{aligned} $$
then $4 x+5 y$ is...
$$ \begin{aligned} & 3 x+2 y=\log _a(18)^{\frac{5}{4}} \quad \text { and } \\ & 2 x-y=\log _b(\sqrt{1080}), \end{aligned} $$
then $4 x+5 y$ is...
INTEGER+4 / -02024
4Quadratic Equation And Inequalities
The product of all positive real values of $x$ satisfying the equation
\(x^{\left(16\left(\log _{5} x\right)^{3}-68 \log _{5} x\right)}=5^{-16}\)
is __________.
\(x^{\left(16\left(\log _{5} x\right)^{3}-68 \log _{5} x\right)}=5^{-16}\)
is __________.
INTEGER+3 / -12022
5Quadratic Equation And Inequalities
For x \(\in\) R, the number of real roots of the equation \(3{x^2} - 4\left| {{x^2} - 1} \right| + x - 1 = 0\) is ________.
INTEGER+4 / -02021
6Quadratic Equation And Inequalities
Suppose a, b denote the distinct real roots of the quadratic polynomial x2 + 20x \(-\) 2020 and suppose c, d denote the distinct complex roots of the quadratic polynomial x2 \(-\) 20x + 2020. Then the value of ac(a \(-\) c) + ad(a \(-\) d) ...
MCQ+3 / -12020
7Quadratic Equation And Inequalities
Let \(\alpha\) and \(\beta\) be the roots of\({x^2} - x - 1 = 0\), with \(\alpha\) > \(\beta\). For all positive integers n, define\({a_n} = {{{\alpha ^n} - {\beta ^n}} \over {\alpha - \beta }},\,n \ge 1\)$${b_1} = 1\,and\,{b_n} = {a_{...
MCQM+4 / -12019
8Quadratic Equation And Inequalities
Let a, b, c three non-zero real numbers such that the equation \(\sqrt 3 a\cos x + 2b\sin x = c,x \in \left[ { - {\pi \over 2},{\pi \over 2}} \right]\), has two distinct real roots \(\alpha\) and \(\beta\) with $$\alpha + \beta = {\pi...
INTEGER+3 / -02018
9Quadratic Equation And Inequalities
If a4 = 28, then p + 2q =
MCQ+3 / -02017
10Quadratic Equation And Inequalities
a12 = ?
MCQ+3 / -02017