28 Jul NET/GATE Questions
# Tick out the correct answers. More than one answer may be correct for a question. Tick out all.
1) The number of maximal ideals in is
2) The number of subfields of (distinct from itself) is
3) Let be a group of order 10. Then
A) is an abelian group
B) is a cyclic group
C) there is a normal proper subgroup
D) there is a subgroup of order 5 which is not normal.
4) Let be a matrix with entries in such that all its eigenvalues are distinct. Then its trace is
C) not definite
5) The number of roots of between the circles and are
6) Let be a group of order Which of the following conditions imply that is abelian?
7) Let be a non-zero homomorphism. Then
A) is always one-one
B) is always onto
C) is always a bijection
D) need be neither one-one nor onto.
8) Let be the polynomial ring and write the elements of as
Let denote the ideal generated by the element If then the quotient ring is
A) a ring but not an integral domain
B) an integral domain but not a field
C) a finite field of order 4
D) an infinite field.
9) Let be an matrix with complex entries which is not a diagonal matrix. Then is diagonalizable if
A) is idempotent
B) is nilpotent
C) is unitary
D) is any arbitrary matrix.
10) is a linear transformation with a minimal polynomial Then
A) there exists a vector such that
B) there exists a vector such that
C) must be singular
D) such a linear transformation is not possible.
11) Let be given by
A) is onto but not one-one
B) is one-one but not onto
C) is both one-one and onto
D) is neither one-one nor onto.
12) is the solution of the partial differential equation
Research Scholar, Tezpur University,
NET and GATE qualified.