Lecturer Mathematics Lecturer guide

nZ is a maximal ideal of a ring Z if and only if n is:

Every group of prime order is:

The set of all solutions to the homogeneous equation Ax = 0 when A is an m x n matrix is:

The square matrix A and its transpose have the ..............eigenvalues:

Z/2Z is a quotient group of order:

Let X and Y be vectors spaces over the field F with dim X = m and dim Y = n then the dim Hom (X,Y):

The number of conjugacy classes of symmetric group of degree 3 is:

A group G having order ................where p is prime is always abelian:

An indexed set of vectors (v₁, v₂.....,v_r) in Rn is said to be .............if the vector equation x₁v₁ + x₂v₂............+x_pv_p = 0 has only the trivial solution:

If 7 cards are dealt from an ordinary deck of 52 playing cards, what is the probability that least 1 of the m will be a queen?

Let G be a cyclic group of order 24 generated by a then order of a¹⁰ is:

H is a subgroup of index ..............then H is a normal subgroup of G:

Let T : U-----> V be a linear transformation from an n dimensional vector space U (F) to a vector space V(F) then:

intersection of any collection of normal subgroups of a group G:

The group of Quaterninons is a non abelian group of order:

All subgroups of an abelian group are ................subgroups:

If a vector space V has basis of n vectors, then every basis of V must consist of exactly ...............vectors:

The dimension of the row space or column space of a matrix is called the .............. of the matirx:

A ring R is a Boolean Ring if, for all x & R:

A. ^X2= X

B. ^X2 = -X

C. X² = 0

D. ^X2 = 1

......................... is the set of all those elements of a group G which commutes with all other:

If H is a normal subgroup of G, then Na (H) = 

The set Cn of all, nth roots of unity for a fixed positive integer n is a group under:

An n x n matrix with n distinct eigenvalues is:

Any two conjugate subgroups of a group G are: