Simplify - 1-2- - 1-2-1-2-1-2-1-2-1-2- 1-2-1-2 -

The correct option is B 2/3 Given expression is 1/2+ [ 1/2×1/2÷{1/2×1/2÷1/2+1} ] =1/2+ [ 1/2×1/2÷{1/2×1/2×2/1+1} ] =1/2+ [ 1/2×1/2÷{1/2× 1+ ...

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Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

Simplify : ...

Question

Simplify : $\frac{1}{2} + [\frac{1}{2} \times \frac{1}{2} \div {\frac{1}{2} \times \frac{1}{2} \div \frac{1}{2} + (\frac{1}{2} \div \frac{1}{2})}]$ .

\frac{2}{3}

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\frac{1}{2}

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\frac{1}{4}

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\frac{1}{5}

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Solution

The correct option is B $\frac{2}{3}$
Given expression is $\frac{1}{2} + [\frac{1}{2} \times \frac{1}{2} \div {\frac{1}{2} \times \frac{1}{2} \div \frac{1}{2} + 1}]$
$= \frac{1}{2} + [\frac{1}{2} \times \frac{1}{2} \div {\frac{1}{2} \times \frac{1}{2} \times \frac{2}{1} + 1}]$
$= \frac{1}{2} + [\frac{1}{2} \times \frac{1}{2} \div {\frac{1}{2} \times 1 + 1}]$
$= \frac{1}{2} + [\frac{1}{2} \times \frac{1}{2} \div {\frac{1}{2} + 1}]$
$= \frac{1}{2} + [\frac{1}{2} \times \frac{1}{2} \div \frac{3}{2}] = \frac{1}{2} + [\frac{1}{2} \times \frac{1}{2} \times \frac{2}{3}]$
$= \frac{1}{2} + \frac{1}{6} = \frac{3 + 1}{6} = \frac{4}{6} = \frac{2}{3}$

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Simplify : 12+[12×12÷{12×12÷12+(12÷12)}].

The correct option is B 23Given expression is 12+[12×12÷{12×12÷12+1}]=12+[12×12÷{12×12×21+1}]=12+[12×12÷{12×1+1}]=12+[12×12÷{12+1}]=12+[12×12÷32]=12+[12×12×23]=12+16=3+16=46=23

Simplify : $\frac{1}{2} + [\frac{1}{2} \times \frac{1}{2} \div {\frac{1}{2} \times \frac{1}{2} \div \frac{1}{2} + (\frac{1}{2} \div \frac{1}{2})}]$ .