Mathematics Practice Test

Mathematics Practice Test consist of math mcqs test papers. Test also consist of answers and each question explanations. These mcqs were uploaded on daily basis. So visit this page on daily basis for math best preparation

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

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

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

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

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

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

D
View Explanation

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

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

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

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

B
View Explanation

$\int_{0}^{1}2xdx-\int_{0}^{1}x^2dx=&space;x^{2}|_{0}^{1}-\frac{x^3}{3}|_{0}^{1}=1-1/3=2/3$. 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