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 = y2 – x2, x $ y = x + y2, 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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Question : If x6 – 512y6 = (x2 + Ay2) (x4 – Bx2 y2 + Cy4), then what is the value of (A + B – C)?
Option 1: –80
Option 2: –72
Option 3: 72
Option 4: 48
Question : If x + y + z = 8, and x2 + y2 + z2 = 20, then the value of x3 + y3 + z3 – 3xyz is _______.
Option 1: 16
Option 2: 10
Option 3: 15
Option 4: –16
Question : If $x + y = 10$, $2xy = 48$ and $x > y$, then find $2x - y$.
Option 1: 6
Option 2: 8
Option 3: 4
Option 4: 3
Question : If a + b + c = 6 and a2 + b2 + c2 = 38, then what is the value of a(b2 + c2) + b(c2 + a2) + c(a2 + b2) + 3abc?
Option 1: 3
Option 2: 6
Option 3: –6
Option 4: –3
Question : If $\left(5 \sqrt{5} x^3-3 \sqrt{3} y^3\right) \div(\sqrt{5} x-\sqrt{3} y)=\left(A x^2+B y^2+C x y\right)$, then what is the value of $(3 A-B-\sqrt{15} C)$?
Option 1: –3
Option 2: –5
Option 3: 8
Option 4: 12
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