Fields and Field Extensions - Algebra - Mathematics Previous Year Questions

1

2008 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2008

For two random variables \(X\) and \(Y\), the regression lines are given by \(Y = 5X - 15\) and \(Y = 10X - 35\). Then the regression coefficient of \(X\) on \(Y\) is

A

0.1

B

0.2

C

5

D

10

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2

2009 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2009

\(\mathbb{Z}_2[x] / \langle x^3 + x^2 + 1 \rangle\) is

A

a field having 8 elements

B

a field having 9 elements

C

an infinite field

D

NOT a field

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3

2009 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2009

The value of \( k \) is

A

\(2 \)

B

\(4 \)

C

\(1 \)

D

\(-2 \)

Check answer

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4

2010 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2010

Let \( E \) and \( F \) be any two events with \( P(E \cup F) = 0.8, P(E) = 0.4 \) and \( P(E|F) = 0.3 \). Then \( P(F) \) is

A

\(\frac{3}{7} \)

B

\(\frac{4}{7} \)

C

\(\frac{1}{5} \)

D

\(\frac{2}{5} \)

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5

2010 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2010

Consider the algebraic extension \( E = \mathbb{Q}(\sqrt{2}, \sqrt{3}, \sqrt{5}) \) of the field \( \mathbb{Q} \) of rational numbers. Then \( [E : \mathbb{Q}] \), the degree of \( E \) over \( \mathbb{Q} \), is

A

3

B

4

C

7

D

8

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6

2010 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2010

The value of \( a \) is

A

4

B

2

C

1

D

0.5

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7

2010 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2010

Which of the following options is the closest in meaning to the word below:
Circuitous

A

cyclic

B

indirect

C

confusing

D

crooked

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8

2010 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2010

The question below consists of a pair of related words followed by four pairs of words. Select the pair that best expresses the relation in the original pair. Unemployed : Worker

A

fallow : land

B

unaware : sleeper

C

wit : jester

D

renovated : house

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9

2010 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2010

Choose the most appropriate word from the options given below to complete the following sentence:
If we manage to ____________ our natural resources, we would leave a better planet for our children.

A

uphold

B

restrain

C

cherish

D

conserve

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10

2010 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2010

Choose the most appropriate word from the options given below to complete the following sentence:
His rather casual remarks on politics ____________ his lack of seriousness about the subject.

A

masked

B

belied

C

betrayed

D

suppressed

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11

2010 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2010

Modern warfare has changed from large scale clashes of armies to suppression of civilian populations. Chemical agents that do their work silently appear to be suited to such warfare; and regrettably, there exist people in military establishments who think that chemical agents are useful tools for their cause.
Which of the following statements best sums up the meaning of the above passage:

A

Modern warfare has resulted in civil strife.

B

Chemical agents are useful in modern warfare.

C

Use of chemical agents in warfare would be undesirable.

D

People in military establishments like to use chemical agents in war.

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12

2011 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2011

The number of irreducible quadratic polynomials over the field of two elements \( \mathbf{F}_2 \) is

A

0

B

1

C

2

D

3

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13

2011 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2011

Choose the most appropriate word from the options given below to complete the following sentence:
It was his view that the country’s problems had been __________________ by foreign technocrats, so that to invite them to come back would be counter-productive.

A

identified

B

ascertained

C

exacerbated

D

analysed

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14

2011 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2011

The question below consists of a pair of related words followed by four pairs of words. Select the pair that best expresses the relation in the original pair:
Gladiator : Arena

A

dancer : stage

B

commuter : train

C

teacher : classroom

D

lawyer : courtroom

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15

2011 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2011

Choose the most appropriate word from the options given below to complete the following sentence:
Under ethical guidelines recently adopted by the Indian Medical Association, human genes are to be manipulated only to correct diseases for which __________________ treatments are unsatisfactory.

A

similar

B

most

C

uncommon

D

available

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16

2011 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2011

Choose the word from the options given below that is most nearly opposite in meaning to the given word:
Frequency

A

periodicity

B

rarity

C

gradualness

D

persistency

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17

2011 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2011

The horse has played a little known but very important role in the field of medicine. Horses were injected with toxins of diseases until their blood built up immunities. Then a serum was made from their blood. Serums to fight with diphtheria and tetanus were developed this way.
It can be inferred from the passage, that horses were

A

given immunity to diseases

B

generally quite immune to diseases

C

given medicines to fight toxins

D

given diphtheria and tetanus serums

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18

2012 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2012

Choose the most appropriate word from the options given below to complete the following sentence:
Given the seriousness of the situation that he had to face, his __ was impressive.

A

beggary

B

nomenclature

C

jealousy

D

nonchalance

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19

2012 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2012

Which one of the following options is the closest in meaning to the word given below?
Latitude

A

Eligibility

B

Freedom

C

Coercion

D

Meticulousness

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20

2013 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2013

A number is as much greater than 75 as it is smaller than 117. The number is:

A

91

B

93

C

89

D

96

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