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Previous year question hub

Group Theory - Algebra - Mathematics Previous Year Questions

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

20Papers
20Years
63Questions
1Topics

Group Theory question pattern

Every graph below is calculated only from this selection.

Questions by year

Compare question counts across years.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 35 55.6%
Easy 24 38.1%
Hard 4 6.3%

Question type distribution

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

MCQ 40 63.5%
Numerical Answer Type (NAT) 17 27%
MSQ 3 4.8%
Fill in the blanks 3 4.8%

Subject weightage

Top subjects by unique question coverage.

Mathematics
63 Qs

Most asked topics

Top topics across the included previous year papers.

Algebra
63 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Group Theory
63 Qs

Paper coverage

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

Mathematics (MA) 2026
2 Qs
Mathematics (MA) 2025
1 Qs
Mathematics (MA) 2024
6 Qs
Mathematics (MA) 2023
3 Qs
Mathematics (MA) 2022
2 Qs
Mathematics (MA) 2021
2 Qs
Mathematics (MA) 2020
3 Qs
Mathematics (MA) 2019
2 Qs
Mathematics (MA) 2018
3 Qs
Mathematics (MA) 2017
2 Qs
Mathematics (MA) 2016
2 Qs
Mathematics (MA) 2015
1 Qs
Mathematics (MA) 2014
2 Qs
Mathematics (MA) 2013
8 Qs
Mathematics (MA) 2012
6 Qs
Mathematics (MA) 2011
1 Qs
Mathematics (MA) 2010
8 Qs
Mathematics (MA) 2009
2 Qs
Mathematics (MA) 2008
3 Qs
Mathematics (MA) 2007
4 Qs

Included previous year papers

Newest papers appear first. Search these papers or sort by year and name.

Paper nameYearPDFAttempt
Mathematics (MA) 20262026
2 questions in this view		2026
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Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Mathematics (MA) 20252025
1 questions in this view		2025
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ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Mathematics (MA) 20242024
6 questions in this view		2024
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ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Mathematics (MA) 20232023
3 questions in this view		2023
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Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Mathematics (MA) 20222022
2 questions in this view		2022
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Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Mathematics (MA) 20212021
2 questions in this view		2021
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Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Mathematics (MA) 20202020
3 questions in this view		2020
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Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20192019
2 questions in this view		2019
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Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20182018
3 questions in this view		2018
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ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20172017
2 questions in this view		2017
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Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20162016
2 questions in this view		2016
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Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20152015
1 questions in this view		2015
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Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20142014
2 questions in this view		2014
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Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20132013
8 questions in this view		2013
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ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20122012
6 questions in this view		2012
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20112011
1 questions in this view		2011
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20102010
8 questions in this view		2010
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20092009
2 questions in this view		2009
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20082008
3 questions in this view		2008
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20072007
4 questions in this view		2007
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download

All Group Theory previous year questions

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

1
2008 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2008
Let \(G = \mathbb{R} \setminus \{0\}\) and \(H = \{-1, 1\}\) be groups under multiplication. Then the map \(\varphi : G \to H\) defined by \(\varphi(x) = \frac{x}{|x|}\) is
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2
2008 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2008
Let \(G\) be a group of order 45. Let \(H\) be a 3-Sylow subgroup of \(G\) and \(K\) be a 5-Sylow subgroup of \(G\). Then
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3
2008 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2008
Consider the action of \(S_4\), the symmetric group of order 4, on \(\mathbb{Z}[x_1, x_2, x_3, x_4]\) given by \[ \sigma \cdot p(x_1, x_2, x_3, x_4) = p(x_{\sigma(1)}, x_{\sigma(2)}, x_{\sigma(3)}, x_{\sigma(4)}) \text{ for } \sigma \in S_4. \] Let \(H \subseteq S_4\) denote the cyclic subgroup generated by (1 4 2 3). Then the cardinality of the orbit \(O_H(x_1x_2 + x_3x_4)\) of \(H\) on the polynomial \(x_1x_2 + x_3x_4\) is
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4
2009 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2009
If \( Z(G) \) denotes the centre of a group \( G \), then the order of the quotient group \( G/Z(G) \) cannot be
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5
2009 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2009
Let \( Aut(G) \) denote the group of automorphisms of a group \( G \). Which one of the following is NOT a cyclic group ?
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6
2010 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2010

Which one of the following groups is simple?

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7
2010 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2010
Let \( X \) have a binomial distribution with parameters \( n \) and \( p \), \( n = 3 \). For testing the hypothesis \( H_0 : p = \frac{2}{3} \) against \( H_1 : p = \frac{1}{3} \), let a test be: "Reject \( H_0 \) if \( X \ge 2 \) and accept \( H_0 \) if \( X \le 1 \)". Then the probabilities of Type I and Type II errors respectively are
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8
2010 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2010
Let \( G_1 \) be an abelian group of order 6 and \( G_2 = S_3 \). For \( j = 1, 2 \), let \( P_j \) be the statement: “\( G_j \) has a unique subgroup of order 2”. Then
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9
2010 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2010
Let \( G \) be the group of all symmetries of the square. Then the number of conjugate classes in \( G \) is
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10
2010 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2010
Four weightless rods form a rhombus \( PQRS \) with smooth hinges at the joints. Another weightless rod joins the midpoints \( E \) and \( F \) of \( PQ \) and \( PS \) respectively. The system is suspended from \( P \) and a weight \( 2W \) is attached to \( R \). If the angle between the rods \( PQ \) and \( PS \) is \( 2\theta \), then the thrust in the rod \( EF \) is
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11
2010 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2010
25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is:
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12
2010 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2010

Given digits 2, 2, 3, 3, 3, 4, 4, 4, 4 how many distinct 4 digit numbers greater than 3000 can be formed?

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13
2010 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2010
Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters). All were born on 1st January. The age difference between any two successive siblings (that is born one after another) is less than 3 years. Given the following facts:
i. Hari's age + Gita's age > Irfan's age + Saira's age.
ii. The age difference between Gita and Saira is 1 year. However, Gita is not the oldest and Saira is not the youngest.
iii. There are no twins.
In what order were they born (oldest first)?
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14
2011 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2011
The number of elements in the conjugacy class of the 3-cycle \( (2\ 3\ 4) \) in the symmetric group \( S_6 \) is
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15
2012 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2012
The order of the smallest possible non trivial group containing elements \(x\) and \(y\) such that \(x^7=y^2=e\) and \(yx=x^3y\) is
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16
2012 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2012

The number of 5-Sylow subgroup(s) in a group of order 45 is

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17
2012 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2012
Let \(\omega=\cos\frac{2\pi}{3}+i\sin\frac{2\pi}{3},\ M=\begin{pmatrix}0&i\\i&0\end{pmatrix},\ N=\begin{pmatrix}\omega&0\\0&\omega^2\end{pmatrix}\) and \(G=\langle M,N\rangle\) be the group generated by the matrices \(M\) and \(N\) under matrix multiplication. Then
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18
2012 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2012
One of the parts (A, B, C, D) in the sentence given below contains an ERROR. Which one of the following is INCORRECT?
I requested that he should be given the driving test today instead of tomorrow.
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19
2012 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2012
There are eight bags of rice looking alike, seven of which have equal weight and one is slightly heavier. The weighing balance is of unlimited capacity. Using this balance, the minimum number of weighings required to identify the heavier bag is
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20
2012 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2012
One of the legacies of the Roman legions was discipline. In the legions, military law prevailed and discipline was brutal. Discipline on the battlefield kept units obedient, intact and fighting, even when the odds and conditions were against them.

Which one of the following statements best sums up the meaning of the above passage?
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Showing 20 of 63 questions