The inequality 3^{N} > N³ holds when

Correct Answer is : N is a natural number except 3

N is a natural number greater than 2

N is a natural number greater than 3

Correct Answer is : N is a natural number except 3

Test Index

UPSC CDS I 2019 Math Paper

Question : 29 of 100

Marks: +1, -0

The inequality

3^{N} > N^{3}

holds when

Solution:

Concept:

Check small natural numbers to find when

3^{N} > N^{3}

fails.

Explanation:

Evaluate the inequality for natural numbers

N

starting from 1.

For

N = 1

3^{1} = 3

1^{3} = 1

⇒

3 > 1

holds.

For

N = 2

3^{2} = 9

2^{3} = 8

⇒

9 > 8

holds.

For

N = 3

3^{3} = 27

3^{3} = 27

⇒

27 > 27

is false (equality).

For

N = 4

3^{4} = 81

4^{3} = 64

⇒

81 > 64

holds.

For

N = 5

3^{5} = 243

5^{3} = 125

⇒ holds.

The inequality holds for all natural numbers except

N = 3

Answer:

Option D:

N

is a natural number except 3.

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