Question : Simplify the given expression.
$\frac{(3.254 \times 3.254 \times 3.254)-(0.746 \times 0.746 \times 0.746)}{(3.254 \times 3.254)+(0.746 \times 0.746)+(3.254 \times 0.746)}$
Option 1: 3.156
Option 2: 4.508
Option 3: 2.146
Option 4: 2.508
Correct Answer: 2.508
Solution : Given: $\frac{(3.254 \times 3.254 \times 3.254)-(0.746 \times 0.746 \times 0.746)}{(3.254 \times 3.254)+(0.746 \times 0.746)+(3.254 \times 0.746)}$ Let $a=3.254$ and $b=0.746$ = $\frac{a^3-b^3}{a^2+b^2+ab}$ = $\frac{(a-b)(a^2+b^2+ab)}{a^2+b^2+ab}$ = $a-b$ Putting the values, we get: = 3.254 – 0.746 = 2.508 Hence, the correct answer is 2.508.
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Question : Simplify the following expression. 25 ÷ 5 of 12 × 2 − 9 ÷ 27 of 3 × 5 − 14 ÷ 28 × 4
Option 1: $-\frac{41}{91}$
Option 2: $-\frac{31}{9}$
Option 3: 18
Option 4: $-\frac{31}{18}$
Question : Simplify: $\frac{1-\frac{3}{7} \div \frac{9}{49} \times \frac{3}{14}}{1+\frac{3}{5} \div \frac{1}{25} \times \frac{1}{30}}$
Option 1: $\frac{1}{7}$
Option 2: $\frac{1}{6}$
Option 3: $\frac{1}{3}$
Option 4: $\frac{1}{5}$
Question : The value of $\frac{\frac{5}{2}-\frac{3}{7} \times 1 \frac{4}{5} \div 3 \frac{6}{7}}{\frac{3}{2}+1 \frac{2}{5} \div 3 \frac{1}{2} \times 1 \frac{1}{4}}$ is:
Option 1: $2 \frac{3}{20}$
Option 2: $1\frac{2}{20}$
Option 3: $1 \frac{3}{20}$
Option 4: $1 \frac{7}{20}$
Question : The value of $\frac{1 \frac{1}{2} \div 3 \frac{1}{4}+\frac{1}{2} \div \frac{13}{14}+\frac{1}{5}}{\frac{1}{5} \times 3 \frac{1}{2}-\frac{1}{3} \div 1 \frac{3}{4} \times 3 \frac{1}{2}}$ is:
Option 1: 33
Option 2: 36
Option 3: 38
Option 4: 40
Question : Simplify the following. $81^{\frac{3}{4}}+[(20 \div 5 \text { of } 3 \times 6)+\{(8 \div 24 \text { of } 3) \times 4\}-10 \div 5]-\left(\frac{1}{32}\right)^{-\frac{2}{5}}$
Option 1: $24 \frac{1}{4}$
Option 2: $21 \frac{1}{9}$
Option 3: $27 \frac{4}{5}$
Option 4: $29 \frac{4}{9}$
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