Testbook Logo
Exams SuperCoaching Test Series Skill Academy
More
English
Hindi

Question

Download Solution PDF

In any group, the number of improper subgroups is 

This question was previously asked in
UP TGT Mathematics 2016 Official Paper
Download PDF Attempt Online
View all UP TGT Papers >
  1. 2
  2. 3
  3. depends on the group
  4. 1

Answer (Detailed Solution Below)

Option 1 : 2
Free Tests
View all Free tests >
Free
UP TGT Arts Full Test 1
7.2 K Users
125 Questions 500 Marks 120 Mins
Start Now

Detailed Solution

Download Solution PDF

Concept:

If G is a group, then the subgroup consisting of G itself is the improper subgroup of G. All other subgroups are proper subgroups

In any group, the number of improper subgroups is 2

Download Solution PDF
Latest UP TGT Updates

Last updated on Jul 12, 2025

-> The UP TGT Admit Card (2022 cycle) will be released on 12th July 2025

-> The UP TGT Exam for Advt. No. 01/2022 will be held on 21st & 22nd July 2025.

-> The UP TGT Notification (2022) was released for 3539 vacancies.

-> The UP TGT 2025 Notification is expected to be released soon. Over 38000 vacancies are expected to be announced for the recruitment of Teachers in Uttar Pradesh. 

-> Prepare for the exam using UP TGT Previous Year Papers.

More Groups Questions

Q1.Let (G) be a cyclic group of n roots of unity under multiplication, then its generator is :
Q2.Let H1 = {0, ±2, ±4, ±6, ....} H2 = {0, ±3, ±6, ±9, ....} and Z = {0, ±1, ±2, ±3, ....}, then the true statement is
Q3.Which of the following statements is/are TRUE for a group G ?
Q4.The number of generators of the cyclic group G of order 8 is
Q5.The number of generators of a cyclic group of order 10 is
Q6.Consider the set S = {1, ω, ω2}, where ω and ω2 are cube roots of unity. If * denotes the multiplication operation, the structure (S, *) forms 
Q7.Any group of order 3 is
Q8.If G is a cyclic group of order 24 and \({a^{2002}} = {a^n}\) where a ϵ G and 0 < n < 24. Then the value of n is
Q9.Consider the group Z495 under addition modulo 495. (i) {0, 99, 198, 307, 406} is the unique subgroup of Z495 of order 5. (ii) {0, 55, 110, 165, 220, 275, 330, 385, 440} is the unique subgroup of Z495 of order 9. Then,

More Set Theory & Algebra Questions

Q1.If L = {1, 2, 3, 4, 6, 9, 36} is the lattice find the number of complements 9 is having in the below given Hasse diagram?
Q2.A flip-flop is used to store the ____________.
Q3.Match List-I with List-II List I Propositions List II Disjunctive Normal Form (DNF) A. P ∧ (P → Q) I. P ∨ Q B. ¬ (P ∨ Q) → (P ∧ Q) II. (P ∧ ¬ P) ∨ (P ∧ Q) C. P → Q III. (¬ P) ∨ Q D. P ∨ (Q ∧ R) IV. (P ∧ P) ∨ (P ∧ Q) ∨ (P ∧ R) ∨ (Q ∧ R) Choose the correct answer from the options given below :
Q4.If N2 = N × N, N is set of natural numbers and R is relation on N2, s.t. RC N2 × N2 i.e. <x,y> R<u,v> ↔ xv = yu, then which of the followings are TRUE? (A) Reflexive (B) Symmetric (C) Transitive (D) Assymmetric Choose the correct answer from the options given below:
Q5.Match List-I with List-II List I List II A. ϕ ∩ {ϕ} = I. ϕ  B. {ϕ} ∩ {ϕ} = II. {ϕ} C. {ϕ, {ϕ}} - ϕ = III. {{ϕ}} D. ϕ ∪ {{ϕ}} = IV. {ϕ, {ϕ}} Choose the correct answer from the options given below :
Q6.Consider universe positive integer X= {1 ≤ n ≤ 8}, proposition P= "n is an even integers", Q = "(3 ≤ n ≤ 7) ^ (n ≠ 6)". Then truth set of P ↔ Q is 
Q7.Let (Z, +) denote the group of all integers under addition. Then the number of all automorphisms of (Z, +) is
Q8.If A = {4n + 2 | n is a natural number} and B = {3n | n is a natural number}. Which of the following is correct for A ⋂ B?
Q9.Consider the following statements. A. The identity is unique in any monoid. B. A monoid is a group if there exists inverse of each element of monoid. C. Semi group has closure, associative and identity properties. D. Quasi group has closure property. Choose the correct answer from the options given below: 
Q10.Let N denote the set of all natural numbers and R be the relation on NXN defined by (a, b) R(c, d), if ad(b + c) = bc(a + d). Then R is 
Crack Super Pass Live with
India's Super Teachers
Explore Supercoaching For FREE
Suggested Test Series
View All >
Pedagogy for All Teaching Exams (Paper 1 & 2) - Let's Crack TET!
345 Total Tests with 3 Free Tests
Start Free Test
UP TGT Mock Test Series 2025
444 Total Tests with   3 Free Tests
Start Free Test
Suggested Exams
Exam-Logo
UP TGT

UP TGT Important Links

More Engineering Mathematics Questions

Q1.If L = {1, 2, 3, 4, 6, 9, 36} is the lattice find the number of complements 9 is having in the below given Hasse diagram?
Q2.Which of the following statements is/are TRUE for undirected graphs?
Q3.A flip-flop is used to store the ____________.
Q4.Let \(\rm \begin{pmatrix}2&a\\\ b&c\end{pmatrix}\) be a 2 x 2 real matrix for which 6 is an eigenvalue. Which of the following statements is necessarily true?
Q5.If the value of the approximate solution of the initial value problem   \(\rm \left\{\begin{matrix}y'(x)=x(y(x)+1), &x\in R\\\ y(0)=β \end{matrix}\right.\) at x = 0.2 using the forward Euler method with step size 0.1 is 1.02, then the value of β is 
Q6.The system of linear equations 3x – 2y – kz = 10 2x – 4y – 2z = 6 x + 2y – z = 5m is inconsistent if :
Q7.The statement among the following that is a tautology is:
Q8.The logical statement (p ⇒ q) ∧ (q ⇒∼ p) is equivalent to
Q9.An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value k when k consecutive heads are obtained for k = 3, 4, 5, otherwise 𝑋 takes the value -1. The expected value of X, is
Q10.For the statements p and q, consider the following compound statements: (a) (~q∧(p → q)) → ~p (b) ((p∨q))∧~p) → q Then which of the following statements is correct?
Important Exams
Super Coaching
Exams
Test Series
Previous Year Papers
Objective Questions
Testbook USA SAT Exam
Testbook USA ACT Exam
US College Admissions Guide
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
[email protected]
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Our Apps
Follow us on
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Get Free Access Now
Hot Links： teen patti master apk download teen patti master official teen patti joy official