Comprehension

Direction : Consider the following for the items that follow :  

Let (8 + 3√7) 20  = U + V and (8 - 3√7) 20  = W, where U is an integer and 0 < V < 1.

What is V + W equal to? 

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. 8
  2. 4
  3. 2
  4. 1

Answer (Detailed Solution Below)

Option 4 : 1
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Detailed Solution

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Explanation:

Given:

(8 + 3√7) 20  = U + V...(i)

(8 - 3√7) 20  = W...(ii)

Here, 0 < W < 1 

Now, adding Eqs. (i) and (ii), we get

U + V +W = (8 + 3√7) 20 + (8 - 3√7) 20

= 2[20C0820+ 20C2818. (3√7 )2+........+(3√7)20

⇒ It is an even number.

Also, 0 < V < 1, 0 < W < 1 and U is an integer

Thus,  V + W is an integer

V + W = 1

∴ Option (d) is correct.

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