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Karnataka Post Graduate Common Entrance Test

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Question : The value of $\frac{\frac{1}{3}+[4 \frac{3}{4}–(3 \frac{1}{6}–2 \frac{1}{3})]}{(\frac{1}{5} \text { of } \frac{1}{5} \div \frac{1}{5}) \div(\frac{1}{5} \div \frac{1}{5} \times \frac{1}{5})}$ lies between:

Option 1: 10.2 and 10.8

Option 2: 4.2 and 4.4

Option 3: 8.2 and 8.8

Option 4: 0.4 and 0.9

Team Careers360 13th Jan, 2024

Correct Answer: 4.2 and 4.4


Solution : Given: $\frac{\frac{1}{3}+[4 \frac{3}{4}–(3 \frac{1}{6}–2 \frac{1}{3})]}{(\frac{1}{5} \text { of } \frac{1}{5} \div \frac{1}{5}) \div(\frac{1}{5} \div \frac{1}{5} \times \frac{1}{5})}$
$=\frac{\frac{1}{3}+[ \frac{19}{4}–(\frac{19}{6}– \frac{7}{3})]}{(\frac{1}{25} \div \frac{1}{5}) \div(\frac{1}{5} \times 5 \times \frac{1}{5})}$
$=\frac{\frac{1}{3}+[ \frac{19}{4}–(\frac{19–7\times 2}{6})]}{(\frac{1}{25} \times 5) \div(\ \frac{1}{5})}$
$=\frac{\frac{1}{3}+[ \frac{19}{4}–\frac{19–14}{6}]}{\frac{1}{5} \div\ \frac{1}{5}}$
$=\frac{\frac{1}{3}+[ \frac{19}{4}–\frac{5}{6}]}{\frac{1}{5} \times 5}$
$=\frac{\frac{1}{3}+[

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