#Q1 Let 0(G)=21 ,G be a non-cyclic group. Then no. of elements of order 3 will be

#Q2 Let n=72 , then no. of Abelian group of order n up to isomorphism is

#Q3 For which of the following the group G is simple

#Q4 Let H be a Sylow p-subgroup of G , then the no. of Sylow p-subgroup of G is equal to

#Q5 No. of groups up to isomorphism of order 45 is

#Q6 The no. of 5-Sylow subgroup of S_6 is

#Q7 Let H be any subgroup of G. Then the largest subgroup of G in which H is normal is

#Q8 R= {0 ,2 ,4 ,6 ,8} ring with addition modulo 10 and multiplication modulo 10. Then unity of R is

#Q9 R= {a+ √p b ; p-prime,a &b ∈R} with ordinary addition and ordinary multiplication. Then unity of R is

#Q10 Let R=(P(N),∆ ,∪ ) be the set, then R will be

#Q1 Let R=(P(N),∆ ,∩ ) then the zero element of R will be

#Q2 R=(P(N),∆ ,∩ ) be the ring, then the unity of R is

#Q3 Unity of the zero ring for ( R ,+ ,∙ ) is

#Q4 Let R be a commutative ring and a ,b are nilpotent element of R then

#Q5 Let a be a nilpotent element of index “r” in R Then 1-a is

#Q6 Characteristic of a non-zero Boolean ring is

#Q7 '6 ' is the nilpotent element of Z_12 is of Index

#Q8 Units in ring (Z_6 ,+_6 ,×_6 ) are