## 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

A) 1

B) 2

C) 3

D) 4.

**2)** The number of subfields of (distinct from itself) is

A) 1

B) 2

C) 3

D) 4.

**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

A) 0

B) 226

C) not definite

D)

**5)** The number of roots of between the circles and are

A) 3

B) 4

C) 5

D) 6.

**6)** Let be a group of order Which of the following conditions imply that is abelian?

A)

B)

C)

D)

**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

Then

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

A)

B)

C)

D)

### Gautam Kalita

Research Scholar, Tezpur University,

NET and GATE qualified.

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## Pushpanjali singh

Posted at 23:56h, 18 MayThank you