Question : Simplify: $\frac{(612+388)^2+(612-388)^2}{(612 \times 612)+(388 \times 388)}=?$
Option 1: 1
Option 2: 4
Option 3: 2
Option 4: 3
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Correct Answer: 2
Solution : Given: $\frac{(612+388)^2+(612-388)^2}{(612 \times 612)+(388 \times 388)}$ $= \frac{(612)^2 + (388)^2 +2 \times 612 \times 388 + (612)^2 + (388)^2 -2 \times 612 \times 388}{(612)^2 + (388)^2 }$ $= \frac{2[(612)^2 + (388)^2 ]}{(612)^2 + (388)^2 }$ $= 2$ Hence, the correct answer is 2.
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Question : Simplify the expression: $\frac{143 \times 143+143 \times 139+139 \times 139}{143 \times 143 \times 143-139 \times 139 \times 139}$
Option 1: $\frac{1}{2}$
Option 2: $282$
Option 3: $\frac{1}{4}$
Option 4: $4$
Question : Simplify: $\sqrt{\frac{4\frac{1}{7}-2\frac{1}{4}}{3\frac{1}{2}+1\frac{1}{7}}+\frac{2}{2+\frac{1}{2+\frac{1}{5-\frac{1}{5}}}}}$
Option 1: $1$
Option 2: $4$
Option 3: $\sqrt{\frac{159}{130}}$
Option 4: $2$
Question : Find the value of the given expression: $\frac{(4\frac{1}{3}+3\frac{1}{3}\times 1\frac{4}{5}\div 3\frac{3}{4}\times (1\frac{1}{2}+1\frac{1}{3}))}{(\frac{2}{3}\div \frac{5}{6}\times \frac{2}{3})}$
Option 1: $11 \frac{3}{8}$
Option 2: $10\frac{1}{8}$
Option 3: $14\frac{3}{8}$
Option 4: $16\frac{5}{8}$
Question : Simplify the following expression. $\frac{(0.96 \times 0.96 \times 0.96+0.04 \times 0.04 \times 0.04)}{(0.96 \times 0.96-0.96 \times 0.04+0.04 \times 0.04)}$
Option 1: 0
Option 2: 0.82
Option 4: 1
Question : Simplify: $\frac{(379+276)^2+(379-276)^2}{379 \times 379+276 \times 276}$
Option 1: 2
Option 2: 655
Option 3: 103
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