Question : Simplify the given expression. $\frac{(381+119)^2+(381-119)^2}{(381)^2+(119)^2}$
Option 1: –1
Option 2: –2
Option 3: 1
Option 4: 2
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Correct Answer: 2
Solution : Given: $\frac{(381+119)^2+(381-119)^2}{(381)^2+(119)^2}$ Let $a=381\ and\ b= 119$ $\frac{(a+b)^2+(a-b)^2}{(a)^2+(b)^2}$ = $\frac{(a^2+b^2+2ab)+(a^2+b^2-2ab)}{a^2+b^2}$ = $\frac{a^2+b^2+a^2+b^2}{a^2+b^2}$ = $\frac{2(a^2+b^2)}{a^2+b^2}$ = $2$ Hence, the correct answer is 2.
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Question : Simplify the given expression. $\frac{(4.2)^3-0.008}{(4.2)^2+0.84+0.04}$
Option 1: 4
Option 3: 2
Option 4: –4
Question : Simplify the given expression $\frac{4\left[(17)^3-(7)^3\right]}{(17)^2+(7)^2+119}$
Option 1: 40
Option 2: 50
Option 3: 60
Option 4: 30
Question : Simplify the given expression: $\frac{4913+343}{289+49-119}$
Option 1: 24
Option 2: 26
Option 3: 22
Option 4: 20
Question : Simplify the expression: $\frac{(u–v)^{3}+(v–w)^{3}+(w–u)^{3}}{(u^{2}–v^{2})^{3}+(v^{2}–w^{2})^{3}+(w^{2}–u^{2})^{3}}$
Option 1: $\frac{1}{(u+v)(v+w)(w+u)}$
Option 2: $1$
Option 3: $\frac{3}{(u+v)(v+w)(w+u)}$
Option 4: $0$
Question : Simplify the given expression: $\frac{(0.25)^4+2×(0.25)^2+1–(0.25)^2}{(0.25)^2+0.25+1}$
Option 1: 0.6755
Option 2: 0.9025
Option 3: 0.8125
Option 4: 0.7835
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