Fields and Field Extensions - Algebra - Mathematics Previous Year Questions

1

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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2

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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3

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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4

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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5

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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6

2010 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2010

The values of \( a_1 \) and \( b_1 \) respectively are

A

\(\frac{1}{2} \) and \(-\frac{1}{12} \)

B

\(-\frac{1}{12} \) and \(\frac{1}{2} \)

C

\(\frac{1}{2} \) and \(\frac{1}{12} \)

D

\(\frac{1}{12} \) and \(\frac{1}{2} \)

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7

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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8

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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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:
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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10

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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11

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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12

2011 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2011

A horizontal lever is in static equilibrium under the application of vertical forces \( F_1 \) at a distance \( l_1 \) from the fulcrum and \( F_2 \) at a distance \( l_2 \) from the fulcrum. The equilibrium for the above quantities can be obtained if

A

F_1l_1 = 2F_2l_2

B

2F_1l_1 = F_2l_2

C

F_1l_1 = F_2l_2

D

F_1l_1 < F_2l_2

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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

2012 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2012

\( Cov(X,Y) \) is

A

-0.01

B

0

C

0.01

D

0.02

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17

2012 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2012

Choose the most appropriate alternative from the options given below to complete the following sentence:
If the tired soldier wanted to lie down, he ___ the mattress out on the balcony.

A

should take

B

shall take

C

should have taken

D

will have taken

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18

2012 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2012

If \((1.001)^{1259} = 3.52\) and \((1.001)^{2062} = 7.85\), then \((1.001)^{3321} =\)

A

2.23

B

4.33

C

11.37

D

27.64

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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

2012 · Mathematics · Algebra · Fields and Field Extensions

Mathematics (MA) 2012

One of the legacies of the Roman legions was discipline. In the legions, military law prevailed and discipline was brutal. Discipline on the battlefield kept units obedient, intact and fighting, even when the odds and conditions were against them.

Which one of the following statements best sums up the meaning of the above passage?

A

Thorough regimentation was the main reason for the efficiency of the Roman legions even in adverse circumstances.

B

The legions were treated inhumanly as if the men were animals.

C

Discipline was the armies’ inheritance from their seniors.

D

The harsh discipline to which the legions were subjected to led to the odds and conditions being against them.

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