Question : If $a + b = 24$ and $8ab = 256$, then what is the value of $3 a^2+3 b^2?$
Option 1: 1536
Option 2: 1024
Option 3: 512
Option 4: 1636
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Correct Answer: 1536
Solution : Given, $a + b = 24$ and $8ab = 256$ ⇒ $2ab=\frac{256}{4}=64$ We know, $(a+b)^2=a^2+b^2+2ab$ Consider $a + b = 24$ Squaring both sides, ⇒ $a^2+b^2+2ab=24^2$ ⇒ $a^2+b^2+64=576$ ⇒ $a^2+b^2=576-64$ ⇒ $a^2+b^2=512$ ⇒ $3a^2+3b^2=3\times 512$ ⇒ $3a^2+3b^2=1536$ Hence, the correct answer is 1536.
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Question : What is the value of 512 × 3 – 25 ÷ 15 × 9?
Option 1: 1521
Option 2: 1425
Option 3: 1486
Option 4: 1536
Question : What is the value of $(a+b)^2+(a-b)^2$?
Option 1: $8ab$
Option 2: $4ab$
Option 3: $4(a^2+b^2)$
Option 4: $2(a^2+b^2)$
Question : If $a-b=2$ and $ab=24$, then what is the value of $a^3-b^3$?
Option 1: 280
Option 2: 124
Option 3: 140
Option 4: 152
Question : What is the value of (22 + 1)(24+1)(28 + 1)(216 + 1) .........(2128 + 1)?
Option 1: $\frac{2^{256}-1}{2}$
Option 2: $\frac{2^{256}-1}{3}$
Option 3: $2^{256}-1$
Option 4: $\frac{2^{256}-1}{4}$
Question : Directions: If 36 @ 2 = 1296 and 4 @ 4 = 256, then 9 @ 3 = ?
Option 1: 729
Option 2: 343
Option 4: 6561
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