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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
62Questions
1Topics

Group Theory question pattern

Every graph below is calculated only from this selection.

Questions by year

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

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 32 51.6%
Easy 26 41.9%
Hard 4 6.5%

Question type distribution

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

MCQ 39 62.9%
Numerical Answer Type (NAT) 17 27.4%
MSQ 3 4.8%
Fill in the blanks 3 4.8%

Subject weightage

Top subjects by unique question coverage.

Mathematics
62 Qs

Most asked topics

Top topics across the included previous year papers.

Algebra
62 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Group Theory
62 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
2 Qs
Mathematics (MA) 2017
2 Qs
Mathematics (MA) 2016
2 Qs
Mathematics (MA) 2015
1 Qs
Mathematics (MA) 2014
2 Qs
Mathematics (MA) 2013
7 Qs
Mathematics (MA) 2012
5 Qs
Mathematics (MA) 2011
3 Qs
Mathematics (MA) 2010
9 Qs
Mathematics (MA) 2009
2 Qs
Mathematics (MA) 2008
3 Qs
Mathematics (MA) 2007
3 Qs

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
Mathematics (MA) 202620262View paper
Mathematics (MA) 202520251View paper
Mathematics (MA) 202420246View paper
Mathematics (MA) 202320233View paper
Mathematics (MA) 202220222View paper
Mathematics (MA) 202120212View paper
Mathematics (MA) 202020203View paper
Mathematics (MA) 201920192View paper
Mathematics (MA) 201820182View paper
Mathematics (MA) 201720172View paper
Mathematics (MA) 201620162View paper
Mathematics (MA) 201520151View paper
Mathematics (MA) 201420142View paper
Mathematics (MA) 201320137View paper
Mathematics (MA) 201220125View paper
Mathematics (MA) 201120113View paper
Mathematics (MA) 201020109View paper
Mathematics (MA) 200920092View paper
Mathematics (MA) 200820083View paper
Mathematics (MA) 200720073View paper

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
Let \( X \) have a binomial distribution with parameters \( n \) and \( p \), where \( n \) is an integer greater than 1 and \( 0 < p < 1 \). If \( P(X = 0) = P(X = 1) \), then the value of \( p \) is
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7
2010 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2010

Which one of the following groups is simple?

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8
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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9
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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10
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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11
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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12
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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13
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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14
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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15
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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16
2011 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2011
Choose the word from the options given below that is most nearly opposite in meaning to the given word:
Frequency
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17
2011 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2011
The horse has played a little known but very important role in the field of medicine. Horses were injected with toxins of diseases until their blood built up immunities. Then a serum was made from their blood. Serums to fight with diphtheria and tetanus were developed this way.
It can be inferred from the passage, that horses were
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18
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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19
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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20
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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Showing 20 of 62 questions