Discrete Mathematics
Q91.
Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is _______.Q92.
Let G be a finite group on 84 elements. The size of a largest possible proper subgroup of G is ________.Q94.
f (G,.) is a group such that (ab)^{-1}=a^{-1}b^{-1},\forall a,b \in G, then G is a/anQ95.
There are two elements x,y in a group (G,*) such that every element in the group can be written as a product of some number of x's and y's in some order. It is known that x * x = y * y = x * y *x * y = y* x * y *x = e where e is the identity element. The maximum number of elements in such a group is _______.Q96.
Let G be a group with 15 elements. Let L be a subgroup of G. It is known that L\neqG and that the size of L is at least 4. The size of L is _______.Q97.
The arithmetic mean of attendance of 49 students of class A is 40% and that of 53 students of class B is 35%. Then the percentage of arithmetic mean of attendance of class A and B isQ98.
Consider the set S = {1, \omega ,\omega ^{2}}, where \omega and \omega ^{2} are cube roots of unity. If * denotes the multiplication operation, the structure (S, *) formsQ100.
For the composition table of a cyclic group shown below Which one of the following choices is correct?