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Q.01 How many conjugaccy classes in S_4  ?
A. 2
B. 3
C. 4
D. 5

Check Answer
D
View Explanation
  Number of conjugacy clases of  S_n  is the P(n) where P(n) is positive integar partition of n.

As
4=4
4=2+2
4=1+1+1+1
4=1+1+2
4=1+3
Option D is corect

Q.02 If G is abelian then G/z(G) is
A. Non cyclic
B. cyclic
C. Non abelian
D. None

Check Answer
B

Q.3 Let Z be the Ring Of integars the total number of Homomorphism From Z to Z is
A. 1
B.  3
C.   2
D.  none of these

Check Answer
C
View Explanation
The only homomorphism from Z to Z are the identity and zero mapings
Correct option is C

Q.4  Let R be the usual metric space and Z be the set of integer then the clouser of Z is
A.   Z
B.   R
C.   Q
D.   N

Check Answer
A
View Explanation
As Z ‘ =U(n,n+1) is open hence Z is closed this implies closure of Z is itself.  So Z clouser=ZUZ’= Z

Correct option is A

Q.5 If N is any Normal sub-group of V_4 then \frac{V_4}{N} is
A.  Abelien
B.  Non cyclic
C   Both a and b
D.  None of these

Check Answer
A
View Explanation
As V_4 is abelain and quitent of abelain is abelian. So, Correct option is A

Q.6 If w is the imaginary cub root of unity then (1+w-w^2)^7 is
A.   128w
B.  -128w
C.  128w²
D. -128w²

Check Answer
D
View Explanation
  

We\; know\; that\\ 1+w+w^2=0\\ And\\ 1+w=-w^2\\ Also\\ w^3=1\\ Now\\ (1+w-w^2)^7=(-w^2-w^2)^7=(-2w^2)^7=-128w^2

So, Correct option is D

Q.7 Let G be a group then factor \frac{G}{G} is
A. Cyclic
B. Normal
C Both a and b
D. None

Check Answer
C
View Explanation
We know that  \frac{G}{G} ={G} which is trivialy cyclic. Also every group is itself normal. So, Correct option is C

Q.8 if V is a vector and div V=0 then V is
A.  Irrotational
B.  Solenoid
C.  Hermition
D.  None of these

Check Answer
B
View Explanation
Let V be a vector point function. V is solenoid if divV=0

 and irrotational if curl V=0. So, Correct option is B

Q.9  Consider these two functions f(x) = x² and g(x) = 2x.  What is the area between these two functions between the x values of 0 and 1?

A.  1/3

B.   2/3

C.  3/2

D.  3/4

Check Answer
B
View Explanation

\int_{0}^{1}2xdx-\int_{0}^{1}x^2dx= x^{2}|_{0}^{1}-\frac{x^3}{3}|_{0}^{1}=1-1/3=2/3. So, Correct option is B

Q.10  The center of mass of semi-circular lamina y^2 = a^2+x^2 in the upper half lies on the
A. origin
B. x-axis
C.  y-axis
D.  non of these

Check Answer
C
View Explanation

Semi Circular Means Half Circular Lamina is Filled Curve. So for Upper Half, it lies on Y axis.

Mathematics Practice Test

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