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Previous year question hub

Quadratic Equation And Inequalities - Algebra - Mathematics Previous Year Questions

Practice Quadratic Equation And Inequalities - Algebra - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

45Papers
40Years
89Questions
1Topics

Quadratic Equation And Inequalities question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Quadratic Equation And Inequalities. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 49 55.1%
Easy 32 36%
Hard 5 5.6%
Not classified 3 3.4%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

Multiple Choices 66 74.2%
Subjective 15 16.9%
Numerical Answer Type (NAT) 8 9%

Subject weightage

Top subjects by unique question coverage.

Mathematics
89 Qs

Most asked topics

Top topics across the included previous year papers.

Algebra
89 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Quadratic Equation And Inequalities
89 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

JEE ADVANCED 2025 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2024 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2022 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2021 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2019 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2017 PAPER 2 OFFLINE
2 Qs
JEE ADVANCED 2016 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2015 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2014 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2013 PAPER 2 OFFLINE
1 Qs
IIT JEE 2012 PAPER 1 OFFLINE
1 Qs
IIT JEE 2012 PAPER 2 OFFLINE
1 Qs
IIT JEE 2011 PAPER 1 OFFLINE
3 Qs
IIT JEE 2011 PAPER 2 OFFLINE
2 Qs
IIT JEE 2010 PAPER 1 OFFLINE
1 Qs
IIT JEE 2009 PAPER 2 OFFLINE
1 Qs
IIT JEE 2008 PAPER 2 OFFLINE
1 Qs
IIT JEE 2007 PAPER 1 OFFLINE
1 Qs
IIT JEE 2006
2 Qs
IIT JEE 2004 SCREENING
2 Qs
IIT JEE 2004
1 Qs
IIT JEE 2003
1 Qs
IIT JEE 2003 SCREENING
1 Qs
IIT JEE 2002 SCREENING
2 Qs
IIT JEE 2000 SCREENING
4 Qs
IIT JEE 2000
1 Qs
IIT JEE 1999
1 Qs
IIT JEE 1998
1 Qs
IIT JEE 1997
2 Qs
IIT JEE 1995
1 Qs
IIT JEE 1994
3 Qs
IIT JEE 1992
1 Qs
IIT JEE 1991
1 Qs
IIT JEE 1990
1 Qs
IIT JEE 1989
4 Qs
IIT JEE 1987
1 Qs
IIT JEE 1986
4 Qs
IIT JEE 1985
3 Qs
IIT JEE 1984
5 Qs
IIT JEE 1983
2 Qs
IIT JEE 1982
8 Qs
IIT JEE 1981
1 Qs
IIT JEE 1980
4 Qs
IIT JEE 1979
4 Qs
IIT JEE 1978
6 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
JEE ADVANCED 2025 PAPER 1 ONLINE20251View paper
JEE ADVANCED 2024 PAPER 1 ONLINE20241View paper
JEE ADVANCED 2022 PAPER 2 ONLINE20221View paper
JEE ADVANCED 2021 PAPER 1 ONLINE20211View paper
JEE ADVANCED 2019 PAPER 1 OFFLINE20191View paper
JEE ADVANCED 2017 PAPER 2 OFFLINE20172View paper
JEE ADVANCED 2016 PAPER 1 OFFLINE20161View paper
JEE ADVANCED 2015 PAPER 2 OFFLINE20151View paper
JEE ADVANCED 2014 PAPER 2 OFFLINE20141View paper
JEE ADVANCED 2013 PAPER 2 OFFLINE20131View paper
IIT JEE 2012 PAPER 1 OFFLINE20121View paper
IIT JEE 2012 PAPER 2 OFFLINE20121View paper
IIT JEE 2011 PAPER 1 OFFLINE20113View paper
IIT JEE 2011 PAPER 2 OFFLINE20112View paper
IIT JEE 2010 PAPER 1 OFFLINE20101View paper
IIT JEE 2009 PAPER 2 OFFLINE20091View paper
IIT JEE 2008 PAPER 2 OFFLINE20081View paper
IIT JEE 2007 PAPER 1 OFFLINE20071View paper
IIT JEE 200620062View paper
IIT JEE 200420041View paper
IIT JEE 2004 SCREENING20042View paper
IIT JEE 200320031View paper
IIT JEE 2003 SCREENING20031View paper
IIT JEE 2002 SCREENING20022View paper
IIT JEE 200020001View paper
IIT JEE 2000 SCREENING20004View paper
IIT JEE 199919991View paper
IIT JEE 199819981View paper
IIT JEE 199719972View paper
IIT JEE 199519951View paper
IIT JEE 199419943View paper
IIT JEE 199219921View paper
IIT JEE 199119911View paper
IIT JEE 199019901View paper
IIT JEE 198919894View paper
IIT JEE 198719871View paper
IIT JEE 198619864View paper
IIT JEE 198519853View paper
IIT JEE 198419845View paper
IIT JEE 198319832View paper
IIT JEE 198219828View paper
IIT JEE 198119811View paper
IIT JEE 198019804View paper
IIT JEE 197919794View paper
IIT JEE 197819786View paper

All Quadratic Equation And Inequalities previous year questions

Practice every matching question in batches of 20, with every available option.

1
1978 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1978
Sketch the solution set of the following system of inequalities: \({x^2} + {y^2} - 2x \ge 0;\,\,3x - y - 12 \le 0;\,\,y - x \le 0;\,\,y \ge 0.\)
Write your response
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2
1978 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1978
Show that the square of \(\,{{\sqrt {26 - 15\sqrt 3 } } \over {5\sqrt 2 - \sqrt {38 + 5\sqrt 3 } }}\) is a rational number.
Write your response
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3
1978 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1978
Solve for \(x:{4^x} - {3^{^{x - {1 \over 2}}}}\, = {3^{^{x + {1 \over 2}}}}\, - {2^{2x - 1}}\)
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4
1978 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1978
Find all integers \(x\) for which \(\left( {5x - 1} \right) < {\left( {x + 1} \right)^2} < \left( {7x - 3} \right).\)
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5
1978 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1978
Solve for \(x:\,\sqrt {x + 1} - \sqrt {x - 1} = 1.\)
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6
1978 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1978
If \(\left( {m\,,\,n} \right) = {{\left( {1 - {x^m}} \right)\left( {1 - {x^{m - 1}}} \right).......\left( {1 - {x^{m - n + 1}}} \right)} \over {\left( {1 - x} \right)\left( {1 - {x^2}} \right).........\left( {1 - {x^n}} \right)}}\)

where \(m\) and \(n\) are positive integers \(\left( {n \le m} \right),\) show that
$$\left( {m,n + 1} \right) = \left( {m - 1,\,n + 1} \right) + {x^{m - n - 1}}\left( {m - 1,n} \right).$$

Write your response
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7
1979 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1979
If \(\ell\), m, n are real, \(\ell \ne m\), then the roots by the equation :
\((\ell - m)\,{x^2} - 5\,(\ell + m)\,x - 2\,(\ell - m) = 0\) are
A
Real and equal
B
Complex
C
Real and unequal
D
None of these.
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8
1979 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1979
Let a > 0, b > 0 and c > 0. Then the roots of the equation \(a{x^2} + bx + c = 0\)
A
are real and negative
B
have negative real parts
C
both (a) and (b)
D
none of these
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9
1979 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1979
If x, y and z are real and different and \(\,u = {x^2} + 4{y^2} + 9{z^2} - 6yz - 3zx - 2xy\), then u is always.
A
non negative
B
zero
C
non positive
D
none of these
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10
1979 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1979
The equation x + 2y + 2z = 1 and 2x + 4y + 4z = 9 have
A
only one solution
B
only two solution
C
Infinite number of solutions
D
None of these.
Open complete paper
11
1980 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1980
Both the roots of the equation (x - b) (x - c) + (x - a) (x - c) + (x - a) (x - b) = 0 are always
A
positive
B
real
C
negative
D
none of these.
Open complete paper
12
1980 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1980
If \(\,({x^2} + px + 1)\,\) is a factor of \((a{x^3} + bx + c)\), then
A
\({a^2} + {c^2} = - ab\,\)
B
\({a^2} - {c^2} = - ab\)
C
\({a^2} - {c^2} = ab\)
D
none of these
Open complete paper
13
1980 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1980
The least value of the expression \(2\,\,{\log _{10}}\,x\, - \,{\log _x}(0.01)\) for x > 1, is
A
10
B
2
C
- 0.01
D
none of these.
Open complete paper
14
1980 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1980
Given \({n^4} < {10^n}\) for a fixed positive integer \(n \ge 2,\) prove that \({\left( {n + 1} \right)^4} < {10^{n + 1}}.\)
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15
1981 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1981
For every integer n > 1, the inequality \({(n!)^{1/n}} < {{n + 1} \over 2}\) holds.
A
TRUE
B
FALSE
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16
1982 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1982
If p, q, r are any real numbers, then
A
max (p, q) < max (p, q, r )
B
min (p, q) = \({1 \over 2}\left( {p + q - \left| {p - q} \right|} \right)\)
C
max (p, q) < min (p, q, r)
D
none of these
Open complete paper
17
1982 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1982
Show that the equation \({e^{\sin x}} - {e^{ - \sin x}} - 4 = 0\) has no real solution.
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18
1982 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1982
\(mn\) squares of equal size are arranged to from a rectangle of dimension \(m\) by \(n\), where \(m\) and \(n\) are natural numbers. Two squares will be called ' neighbours ' if they have exactly one common side. A natural number is written in each square such that the number written in any square is the arithmetic mean of the numbers written in its neighbouring squares.Show that this is possible only if all the numbers used are equal.
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19
1982 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1982
If \(2 + i\sqrt 3\) is root of the equation \({x^2} + px + q = 0\), where p and q are real, then (p, q) = (..........,....................).
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20
1982 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1982
The coeffcient of \({x^{99}}\) in the polynomial (x -1) (x - 2)...(x - 100) is ..............
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Showing 20 of 89 questions