Practice IIT JAM Mathematics Test Series for Free only On ** www.examflame.com** and take your preparation to the another level. In the Series of Tests for IIT JAM 2023 this is the test of

**topic**Fundamental of Group of the

**Chapter Group Theory.**These Questions are prepared as per the Latest Syllabus of IIT JAM Mathematics 2023 . Practicing mock tests/Test series, you will get an idea about how and which type of Question will ask in the Examination. It also boost your confidence level. Also Solve

**IIT JAM Mathematics Previous Year Question Paper**. And Don’t Forget to Share with Your Friends.

**IIT JAM Mathematics Test Series 2023 : Group Theory – Fundamental of Group**

**Q1. If x,y and z are elements of a group such that xyz =1, then**

(a) yzx = 1.

(b) yxz =l.

(c) zxy =1.

(d) zyx =1.

**Q2. Which of the following is a subgroup of (C, +).**

(a) (R, +)

(b) (G, +), where G = {πr | r ∈ Q}

(c) (G, +), where G = {ir | r ∈ R}

(d) (G, +), where G= {πn | n ∈ Z}

**Q3. The value of a for which G = {a,1,3,9,19,27} is a cyclic group under multiplication modulo 56 is**

(a) 5

(b) 15

(c) 25

(d) 35

**Q4. Let U(n) be the set of all positive integers less thann and relatively prime to n. Then U(n) is a ground under multiplication modulo n. For n = 248, the number of elements in U(n) is**

(a) 60

(b) 120

(c) 180

(d) 240

**Q5. Let Q ^{c} be the set of irrational real numbers and let G = Q^{c}U ∪{0}. Then, under the usual addition of real numbers, G is**

(a) A group, since R and Q are groups under addition

(b) A group, since the additive identity is in G

(c) Not a group, since addition on G is nota binary operation

(d) Not a group, since not all elements in G have an inverse

**Q6. Let G be a group such that a ^{2} = e for each a∈G, where e is the identity element of G .Then**

(a) G is cyclic

(b) G is finite

(c) G is abelian

(d) None of these

**Q7. In the group {1,2,…,16} under the operation of multiplication modulo 17, the order of the element 3 is**

(a) 4

(b) 8

(c) 12

(d) 16

**Q8. On Z ^{+} , define * by a*b = c, where c is at least 5 more than a + b then,**

(a) * is not a binary operation

(b) * is non-commutative binary operation

(c) * is commutative binary operation

(d) * is associative binary operation

**Q9. Let G = { a ∈ R : a > 0, a ≠ 1} , define a*b = a logb then**

(a) (G,*) is semi group but not a group

(b) (G,*) is a monoid, but not a group

(c) (G,*) is a group

(d) (G,*) is an abelian group

**Q10. The set of real numbers is a group with respect to**

(a.) Arithmetic subtraction

(b.) Arithmetic multiplication

(c.) Arithmetic division

(d.) Composition defined by a•b = a + b + 1 for all real a and b

**Q11. Let G be a group and let a ∈ G if _{o}(a) = n and k is any integer. Then which one of the following is correct ?**

(a) _{o}(a^{k}) > n only

(b) _{o}(a^{k}) ≥ n

(c) _{o}(a^{k}) < n only

(d) _{o}(a^{k}) ≤ n

**Q12. In a set R of real numbers, * be defined as a*b = a + 2b then * is **

(a) Commutative

(b) Associative

(c) Not a Binary Operation

(d) Not associative but binary operations

**Q13. Consider the following statements in respect of a finite group G:**

A. O(a) = O(a^{-1}) for all a ∈ G

B. O(a) = O(bab^{-1}) for all a, b ∈ G

Which of the statements given above is/are correct?

(a) A only

(b) B only

(c) Both A and B

(d) Neither A nor B

**Q14. In the set Q of rational numbers defined * as follows: for α, β ∈ Q, α*β = ^{(α.β)}/_{3} . If Q^{+}, Q^{–}, Q^{*} respectively denote the sets of positive, negative and non-zero ratioanls, the which one of the following pairs is an abelian group?**

(a) (Q^{+},*)

(b) (Q,*)

(c) (Q^{–},*)

(d) (Q^{*},*)

**Q15. Let M (R) be set of all matrices with real entries. The usual matrix addition +” is**

(a) Commutative binary operation

(b) Non-commutative binary operation

(c) Associative binary operation

(d) Not a binary operation

NOTE : – If you need anything else more like e-books, video lectures, syllabus etc regarding your Preparation / Examination then do 📌 mention in the Comment Section below |

Hope you like the test given above for **IIT JAM Mathematics 2023** of Topic – Fundamental of Group of the Chapter **Group Theory** . To get more Information about any exam, Previous Question Papers , Study Material, Book PDF, Notes etc for free, do share the post with your friends and Follow and Join us on other Platforms links are given below to get more interesting information, materials like this.

*Answer Key*

*Answer Key*

01. | (a), (c) | 06. | (c) | 11. | (d) |

02. | (d) | 07. | (d) | 12. | (d) |

03. | (c) | 08. | (a) | 13. | (c) |

04. | (b) | 09. | (d) | 14. | (a), (d) |

05. | (c) | 10. | (d) | 15. | (d) |

**Important Searches & Tags**

- IIT JAM Mock Test Papers download
- IIT JAM test series
- Free Mock Test mathematics Mock Test
- IIT JAM Test series mathematics
- Eduncle IIT JAM Test Series
- Free Mock Test for IIT JAM Mathematics
- IIT JAM Mathematics Mock Test 2022
- IIT JAM Mock Test
- IIT JAM free Mock Test 2022
- IIT JAM Mathematics topic wise questions PDF
- IIT JAM 2022 mock Test
- Best Test Series for IIT JAM Mathematics
- Free Online Test Series for IIT JAM Mathematics
- IIT JAM mock Test 2022
- IIT JAM free Mock Test 2022
- Unacademy IIT JAM Mathematics test series
- DIPS academy Test series
- Career Endeavour Test Series IIT-JAM
- Career Endeavour Test Series pdf