If a&b = a2 + b + 1, a$b = a + b2 + 2, find (4$3) & 2.

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UP Police Constable Re-Exam 2024 Official Paper (Held On: 30 Aug, 2024 Shift 2)
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  1. 228
  2. 242 
  3. 322
  4. 286

Answer (Detailed Solution Below)

Option 1 : 228
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Detailed Solution

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Given:

a & b = a^2 + b + 1

a $ b = a + b^2 + 2

Calculation:

First, solve for 4 $ 3:

⇒ 4 $ 3 = 4 + 3^2 + 2

⇒ 4 $ 3 = 4 + 9 + 2 = 15

Now, solve for 15 & 2:

⇒ 15 & 2 = 15^2 + 2 + 1

⇒ 15 & 2 = 225 + 2 + 1 = 228

∴ (4 $ 3) & 2 = 228

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