Quadratic Equation and Inequalities PYQs - Last 10 Years
JEE Main / Mathematics / Algebra / 165 recent questions
MathematicsAlgebra2017-2026
Practice 165 JEE Main 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.
165
PYQs on Page
Mathematics / Algebra
2017-2026
Year Range
Based on indexed question metadata
97
Last 5 Years
2022-2026
165
Last 10 Years
2017-2026
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165PYQs
MCQ77%
INTEGER23%
Difficulty Mix
#1 Medium136
#2 Easy16
#3 Hard13
97 in last 5 years165 in last 10 years
Last 10 Years Quadratic Equation and Inequalities Questions
Showing 15 of 165 filtered questions.
1Quadratic Equation And Inequalities
Let \(\alpha\) and \(\beta\) be the roots of the quadratic equation x2
sin \(\theta\) – x(sin \(\theta\) cos \(\theta\) + 1) + cos \(\theta\) = 0 (0 < \(\theta\) < 45o), and \(\alpha\) < \(\beta\). Then $$\sum\limits_{n = 0}^\inft...
sin \(\theta\) – x(sin \(\theta\) cos \(\theta\) + 1) + cos \(\theta\) = 0 (0 < \(\theta\) < 45o), and \(\alpha\) < \(\beta\). Then $$\sum\limits_{n = 0}^\inft...
MCQ+4 / -12019
2Quadratic Equation And Inequalities
Consider the quadratic equation (c – 5)x2 – 2cx + (c – 4) = 0, c \(\ne\) 5. Let S be the set of all integral values of c for which one root of the equation lies in the interval (0, 2) and its other root lies in the interval (2, 3). Then t...
MCQ+4 / -12019
3Quadratic Equation And Inequalities
The value of \(\lambda\) such that sum of the squares of the roots of the quadratic equation, x2 + (3 – \(\lambda\))x + 2 = \(\lambda\) has the least value is -
MCQ+4 / -12019
4Quadratic Equation And Inequalities
If \(\alpha\) and \(\beta\) are the roots of the quadratic equation,
x2 + x sin \(\theta\) - 2 sin \(\theta\) = 0, \(\theta \in \left( {0,{\pi \over 2}} \right)\), then
$${{{\alpha ^{12}} + {\beta ^{12}}} \over {\left( {{\alpha ^{ - ...
x2 + x sin \(\theta\) - 2 sin \(\theta\) = 0, \(\theta \in \left( {0,{\pi \over 2}} \right)\), then
$${{{\alpha ^{12}} + {\beta ^{12}}} \over {\left( {{\alpha ^{ - ...
MCQ+4 / -12019
5Quadratic Equation And Inequalities
All the pairs (x, y) that satisfy the inequality
\({2^{\sqrt {{{\sin }^2}x - 2\sin x + 5} }}.{1 \over {{4^{{{\sin }^2}y}}}} \le 1\)
also satisfy the equation
\({2^{\sqrt {{{\sin }^2}x - 2\sin x + 5} }}.{1 \over {{4^{{{\sin }^2}y}}}} \le 1\)
also satisfy the equation
MCQ+4 / -12019
6Quadratic Equation And Inequalities
The number of real roots of the equation
5 + |2x
– 1| = 2x
(2x
– 2) is
5 + |2x
– 1| = 2x
(2x
– 2) is
MCQ+4 / -12019
7Quadratic Equation And Inequalities
Let p, q and r be real numbers (p \(\ne\) q, r \(\ne\) 0), such that the roots of the equation \({1 \over {x + p}} + {1 \over {x + q}} = {1 \over r}\) are equal in magnitude but opposite in sign, then the sum of squares of these roots...
MCQ+4 / -12018
8Quadratic Equation And Inequalities
If an angle A of a \(\Delta\)ABC satiesfies 5 cosA + 3 = 0, then the roots of the quadratic equation, 9x2 + 27x + 20 = 0 are :
MCQ+4 / -12018
9Quadratic Equation And Inequalities
If \(\lambda\) \(\in\) R is such that the sum of the cubes of the roots of the equation,
x2 + (2 \(-\) \(\lambda\)) x + (10 \(-\) \(\lambda\)) = 0 is minimum, then the magnitude of the difference of the roots of this equation is :
x2 + (2 \(-\) \(\lambda\)) x + (10 \(-\) \(\lambda\)) = 0 is minimum, then the magnitude of the difference of the roots of this equation is :
MCQ+4 / -12018
10Quadratic Equation And Inequalities
If tanA and tanB are the roots of the quadratic equation, 3x2 \(-\) 10x \(-\) 25 = 0, then the value of 3 sin2(A + B) \(-\) 10 sin(A + B).cos(A + B) \(-\) 25 cos2(A + B) is :
MCQ+4 / -12018
11Quadratic Equation And Inequalities
If f(x) is a quadratic expression such that f (1) + f (2) = 0, and \(-\) 1 is a root of f (x) = 0, then the other root of f(x) = 0 is :
MCQ+4 / -12018
12Quadratic Equation And Inequalities
Let S = { \(x\) \(\in\) R : \(x\) \(\ge\) 0 and
\(2\left| {\sqrt x - 3} \right| + \sqrt x \left( {\sqrt x - 6} \right) + 6 = 0\)}. Then S
\(2\left| {\sqrt x - 3} \right| + \sqrt x \left( {\sqrt x - 6} \right) + 6 = 0\)}. Then S
MCQ+4 / -12018
13Quadratic Equation And Inequalities
The sum of all the real values of x satisfying the equation
2(x\(-\)1)(x2 + 5x \(-\) 50) = 1 is :
2(x\(-\)1)(x2 + 5x \(-\) 50) = 1 is :
MCQ+4 / -12017
14Quadratic Equation And Inequalities
Let p(x) be a quadratic polynomial such that p(0)=1. If p(x) leaves remainder 4 when divided by x\(-\) 1 and it leaves remainder 6 when divided by x + 1; then :
MCQ+4 / -12017
15Quadratic Equation And Inequalities
If for a positive integer n, the quadratic equation
\(x\left( {x + 1} \right) + \left( {x + 1} \right)\left( {x + 2} \right)\)\(+ .... + \left( {x + \overline {n - 1} } \right)\left( {x + n} \right)\)\(= 10n\)
has two consecutive integral...
\(x\left( {x + 1} \right) + \left( {x + 1} \right)\left( {x + 2} \right)\)\(+ .... + \left( {x + \overline {n - 1} } \right)\left( {x + n} \right)\)\(= 10n\)
has two consecutive integral...
MCQ+4 / -12017