Question

For two real numbers \(a,b\) define \[ a \perp b = a+b+ab,\quad a \square b = a^2+b^2,\quad a \odot b = 3a+2b \] then \[ [(7 \square 5)\odot 6]\perp 8= \]

• A. \(19360\)
• B. \(7900\)
• C. \(2222\)
• D. \(2114\)

Hint:

In custom operation questions, solve strictly from innermost brackets outward using the given definitions.

Answer 1

The Correct Option is D

Concept: Solve the expression step by step according to the given custom operations.

Step 1: Evaluate \(7 \square 5\).
Given: \[ a \square b=a^2+b^2 \] So: \[ 7 \square 5=7^2+5^2 \] \[ =49+25 \] \[ =74 \]

Step 2: Evaluate \(74 \odot 6\).
Given: \[ a \odot b=3a+2b \] So: \[ 74 \odot 6=3(74)+2(6) \] \[ =222+12 \] \[ =234 \]

Step 3: Evaluate \(234 \perp 8\).
Given: \[ a \perp b=a+b+ab \] So: \[ 234 \perp 8=234+8+(234 \times 8) \] \[ =242+1872 \] \[ =2114 \] Thus, the required answer is: \[ \boxed{2114} \]