If  where k is a natural number, the value of k?

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NDA-I (Mathematics) Official Paper (Held On: 13 Apr, 2025)
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  1. 11
  2. 13
  3. 15
  4. 17

Answer (Detailed Solution Below)

Option 2 : 13
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Detailed Solution

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Calculation:

Given,

The inequality is: , where k is a natural number.

We need to compute

Approximating √ 2≈ 1.414 , we find:

The inequality becomes:

This implies that k > 12.07 \), so the smallest integer value of k  is:

∴ The value of k  is 13.

Hence, the correct answer is Option 2. 

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