Select Goal &
City
Select Goal
Explore
Question:
Which of the following statements is/are TRUE ?
Which of the following statements is/are TRUE ?
Updated On: Aug 13, 2024
- The additive group of real numbers is isomorphic to the multiplicative group of positive real numbers
- The multiplicative group of nonzero real numbers is isomorphic to the multiplicative group of nonzero complex numbers
- The additive group of real numbers is isomorphic to the multiplicative group of nonzero complex numbers
- The additive group of real numbers is isomorphic to the additive group of rational numbers
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The correct option is (A) : The additive group of real numbers is isomorphic to the multiplicative group of positive real numbers.
Was this answer helpful?
0
0
Top Questions on Groups
- Consider
\(𝐺 = \left\{𝑚 + 𝑛\sqrt2\ ∶\ 𝑚, 𝑛 ∈ \Z\right\}\)
as a subgroup of the additive group ℝ.
Which of the following statements is/are TRUE ? - The center Z(G) of a group G is defined as
z(G) = {x ∈ G ∶ xg = gx for all g ∈ G}.
Let |G| denote the order of G. Then, which of the following statements is/are TRUE for any group G ? - Which one of the following is TRUE for the symmetric group S13 ?
- From the additive group Q to which one of the following groups does there exist a non-trivial group homomorphism ?
- Consider the following statements :
I. Every infinite group has infinitely many subgroups.
II. There are only finitely many non-isomorphic groups of a given finite order.
Then
View More Questions
Questions Asked in IIT JAM MA exam
- Let L1 denote the line y = 3x + 2 and L2 denote the line y = 4x + 3. Suppose that f: ℝ → ℝ is a four times continuously differentiable function such that the line L1 intersects the curve y = f(x) at exactly three distinct points and the line L2 intersects the curve y = f(x) at exactly four distinct points. Then, which one of the following is TRUE ?
- IIT JAM MA - 2024
- Differential Equations
- For n ∈ \(\N\), let
\(a_n=\frac{1}{n^{n-1}}\sum\limits_{k=0}^n\frac{n!}{k!(n-k)!}\frac{n^k}{k+1}\)
and \(\beta=\lim\limits_{n\rightarrow \infin}a_n\). Then, the value of log 𝛽 equals ___________ (rounded off to two decimal places).- IIT JAM MA - 2024
- Sequences and Series
- For \(n\ \in \N\), let
\(a_n=\frac{1}{(3n+2)(3n+4)}\) and \(b_n=\frac{n^3+\cos(3^n)}{3n+n^3}\).
Then, which one of the following is TRUE ?- IIT JAM MA - 2024
- Sequences and Series
- Consider the 4 × 4 matrix
\(M = \begin{pmatrix} 0 & 1 & 2 & 3 \\ 1 & 0 & 1 & 2 \\ 2 & 1 & 0 & 1 \\ 3 & 2 & 1 & 0 \end{pmatrix}\)
If ai,j denotes the (i, j)th entry of M-1 , then a4,1 equals __________ (rounded off to two decimal places).- IIT JAM MA - 2024
- Matrices
- Let
S = {(x, y, z) ∈ \(\R^3\) : x2 + y2 + z2 < 1}.
Then, the value of
\(\frac{1}{\pi}\iiint_s\left((x-2y+z)^2+(2x-y-z)+(x-y+2z)^2\right)dxdydz\)
equals ________ (rounded off to two decimal places).- IIT JAM MA - 2024
- Integral Calculus
View More Questions
SUBSCRIBE TO OUR NEWS LETTER
COLLEGE NOTIFICATIONSEXAM NOTIFICATIONSNEWS UPDATES
Download the Collegedunia app on 
© 2024 Collegedunia Web Pvt. Ltd. All Rights Reserved