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Previous year question hub

Algebra - Mathematics Previous Year Questions

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

45Papers
36Years
128Questions
1Topics

Algebra question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Algebra. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 86 58.9%
Hard 33 22.6%
Easy 22 15.1%
Not classified 5 3.4%

Question type distribution

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

Subjective 48 32.9%
Multiple Choices 44 30.1%
Numerical Answer Type (NAT) 28 19.2%
Fill in the blanks 26 17.8%

Subject weightage

Top subjects by unique question coverage.

Mathematics
128 Qs

Most asked topics

Top topics across the included previous year papers.

Algebra
128 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Probability
25 Qs
Vector Algebra
23 Qs
Complex Numbers
20 Qs
3D Geometry
15 Qs
Quadratic Equation And Inequalities
16 Qs
Permutations And Combinations
11 Qs
Sequences And Series
10 Qs
Matrices And Determinants
5 Qs
Mathematical Induction And Binomial Theorem
2 Qs
Statistics
1 Qs

Paper coverage

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

JEE Advanced 2026 Paper 1 Online
9 Qs
JEE Advanced 2026 Paper 1 Online
9 Qs
JEE Advanced 2026 Paper 1 Online
9 Qs
JEE Advanced 2026 Paper 2 Online
6 Qs
JEE ADVANCED 2024 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2023 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2022 PAPER 2 ONLINE
2 Qs
JEE ADVANCED 2021 PAPER 1 ONLINE
2 Qs
JEE ADVANCED 2020 PAPER 2 OFFLINE
5 Qs
JEE ADVANCED 2020 PAPER 1 OFFLINE
2 Qs
JEE ADVANCED 2019 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2019 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2018 PAPER 1 OFFLINE
5 Qs
JEE ADVANCED 2018 PAPER 2 OFFLINE
4 Qs
JEE ADVANCED 2017 PAPER 2 OFFLINE
4 Qs
JEE ADVANCED 2017 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2015 PAPER 1 OFFLINE
1 Qs
IIT JEE 2011 PAPER 2 OFFLINE
1 Qs
IIT JEE 2010 PAPER 1 OFFLINE
2 Qs
IIT JEE 2010 PAPER 2 OFFLINE
1 Qs
IIT JEE 2006
2 Qs
IIT JEE 2005
3 Qs
IIT JEE 2005 MAINS
3 Qs
IIT JEE 2004
3 Qs
IIT JEE 2003
2 Qs
IIT JEE 2002
1 Qs
IIT JEE 2001
5 Qs
IIT JEE 1998
2 Qs
IIT JEE 1996
8 Qs
IIT JEE 1994
3 Qs
IIT JEE 1993
2 Qs
IIT JEE 1992
2 Qs
IIT JEE 1991
4 Qs
IIT JEE 1990
3 Qs
IIT JEE 1989
2 Qs
IIT JEE 1988
5 Qs
IIT JEE 1987
3 Qs
IIT JEE 1986
3 Qs
IIT JEE 1985
4 Qs
IIT JEE 1983
5 Qs
IIT JEE 1982
4 Qs
IIT JEE 1981
1 Qs
IIT JEE 1980
3 Qs
IIT JEE 1979
3 Qs
IIT JEE 1978
3 Qs

Browse by subtopics

Open a focused page built from the same verified paper data.

Probability

Explore previous-paper coverage, trends and focused practice for Probability.

139 questions71 papers49 years

Sequences And Series

Explore previous-paper coverage, trends and focused practice for Sequences And Series.

73 questions47 papers40 years

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
JEE Advanced 2026 Paper 1 Online20269View paper
JEE Advanced 2026 Paper 1 Online20269View paper
JEE Advanced 2026 Paper 1 Online20269View paper
JEE Advanced 2026 Paper 2 Online20266View paper
JEE ADVANCED 2024 PAPER 2 ONLINE20241View paper
JEE ADVANCED 2023 PAPER 2 ONLINE20231View paper
JEE ADVANCED 2022 PAPER 2 ONLINE20222View paper
JEE ADVANCED 2021 PAPER 1 ONLINE20212View paper
JEE ADVANCED 2020 PAPER 1 OFFLINE20202View paper
JEE ADVANCED 2020 PAPER 2 OFFLINE20205View paper
JEE ADVANCED 2019 PAPER 1 OFFLINE20191View paper
JEE ADVANCED 2019 PAPER 2 OFFLINE20191View paper
JEE ADVANCED 2018 PAPER 1 OFFLINE20185View paper
JEE ADVANCED 2018 PAPER 2 OFFLINE20184View paper
JEE ADVANCED 2017 PAPER 1 OFFLINE20171View paper
JEE ADVANCED 2017 PAPER 2 OFFLINE20174View paper
JEE ADVANCED 2015 PAPER 1 OFFLINE20151View paper
IIT JEE 2011 PAPER 2 OFFLINE20111View paper
IIT JEE 2010 PAPER 1 OFFLINE20102View paper
IIT JEE 2010 PAPER 2 OFFLINE20101View paper
IIT JEE 200620062View paper
IIT JEE 200520053View paper
IIT JEE 2005 MAINS20053View paper
IIT JEE 200420043View paper
IIT JEE 200320032View paper
IIT JEE 200220021View paper
IIT JEE 200120015View paper
IIT JEE 199819982View paper
IIT JEE 199619968View paper
IIT JEE 199419943View paper
IIT JEE 199319932View paper
IIT JEE 199219922View paper
IIT JEE 199119914View paper
IIT JEE 199019903View paper
IIT JEE 198919892View paper
IIT JEE 198819885View paper
IIT JEE 198719873View paper
IIT JEE 198619863View paper
IIT JEE 198519854View paper
IIT JEE 198319835View paper
IIT JEE 198219824View paper
IIT JEE 198119811View paper
IIT JEE 198019803View paper
IIT JEE 197919793View paper
IIT JEE 197819783View paper

Sample previous year questions

A varied preview from the papers represented in this selection, with every available option.

1
1978 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1978
Solve the following equation for \(x:\,\,2\,{\log _x}a + {\log _{ax}}a + 3\,\,{\log _{{a^2}x}}\,a = 0,a > 0\)
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2
1979 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1979
If \(\alpha ,\,\beta\) are the roots of \({x^2} + px + q = 0\) and \(\gamma ,\,\delta\) are the roots of \({x^2} + rx + s = 0,\) evaluate \(\left( {\alpha - \gamma } \right)\left( {\alpha - \delta } \right)\left( {\beta - \gamma } \right)\) \(\left( {\beta - \delta } \right)\) in terms of \(p,\,q,\,r\) and \(s\).

deduce the condition that the equations have a common root.

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3
1980 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1980
Let \(y = \sqrt {{{\left( {x + 1} \right)\left( {x - 3} \right)} \over {\left( {x - 2} \right)}}}\)

Find all the real values of \(x,\) for which \(y\) takes real values.

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4
1981 · Mathematics · Algebra · Probability
IIT JEE 1981
For a biased die the probabilities for the different faces to turn up are given below : IIT-JEE 1981 Mathematics - Probability Question 136 English

This die tossed and you are told that either face \(1\) or face \(2\) has turned up. Then the probability that it is face \(1\) is ...............

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5
1982 · Mathematics · Algebra · Sequences And Series
IIT JEE 1982
Does there exist a geometric progression containing \(27, 8\) and \(12\) as three of its terms? If it exits, how many such progressions are possible ?
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6
1983 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 1983
Find all real values of \(x\) which satisfy \({x^2} - 3x + 2 > 0\) and \({x^2} - 2x - 4 \le 0\)
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