SPSC Lecture Mathematics Past Paper

Every subgroup of a cyclic group is?

1. Non abelian
2. Non cyclic
3. Cyclic
4. None

Let H be a subgroup of a group G, then the number of left cosets is _____ the number of right cosets of H in G.

1. Less than
2. Equal to
3. Greater than
4. None

In the group G = (-1,1,-i,i), the order of -i is?

1. -1
2. 1
3. 2
4. 4

If X has n elements, then ____ permutations can be taken on X.

1. n
2. n!
3. (n - 1)!
4. (n + 1)!

The order of a cyclic permutation of length n is?

1. n
2. n!
3. (n - 1)!
4. (n + 1)!

A cycle of length _____ is called the transposition.

1. Two
2. Three
3. Four
4. None

Every group of prime order is?

1. Cyclic group
2. Non-abelian group
3. Not cyclic
4. Abelian but not cyclic group

A subset F of a topological space X is closed if and only if F = ?

1. Int(F)
2. Cl(F)
3. Bd(F)
4. X

Ext(A) =?

1. X
2. Int(A)
3. Int(A^c)
4. None

Power set of a nonempty set X is?

1. A topology on X
2. An empty set
3. Not topology on X
4. An infinite set