Question : Directions: If x % y = y2 – x2, x $ y = x + y2, x # y = 2xy, then find the value of ((13 % 5) $ 6) # 15 = ?
Option 1: 480
Option 2: 720
Option 3: –360
Option 4: –3240
Correct Answer: –3240
Solution :
Given:
x % y = y
2
– x
2
, x $ y = x + y
2
, x # y = 2xy
((13 % 5) $ 6) # 15 = ?
After replacing the coded signs, the new equation will be as follows –
(13 % 5) = ((5)
2
– (13)
2
) = 25 – 169 = –144
(13 % 5) $ 6 = (–144) + (6)
2
= –144 + 36 = –108
(13 % 5) $ 6) # 15 = (–108 # 15) = 2 × (–108) × 15 = –3240
So, –3240 is the required answer to the given equation. Hence, the fourth option is correct.
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