Question : Simplify the given expression. $\frac{120 \times 120 \times 120-100 \times 100 \times 100}{120 \times 120+120 \times 100+100 \times 100}$
Option 1: 20
Option 2: 25
Option 3: 10
Option 4: 15
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Correct Answer: 20
Solution : Use identity: a3 – b3 = (a – b)(a2 + ab + b2) $\frac{120 \times 120 \times 120-100 \times 100 \times 100}{120 \times 120+120 \times 100+100 \times 100}$ = $\frac{(120 -100) (120 \times 120+120 \times 100+100 \times 100)}{120 \times 120+120 \times 100+100 \times 100}$ = $20$ Hence, the correct answer is 20.
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Question : Simplify the given expression. $18 \div 3$ of $2 \times 5+72 \div 18$ of $2 \times 3-4 \div 8 \times 2$
Option 1: $20$
Option 2: $\frac{20}{3}$
Option 3: $\frac{25}{3}$
Option 4: $25$
Question : Simplify the following expression. 120 ÷ 15 of 4 + [11 × 4 ÷ 4 of {4 × 2 – (8 – 11)}]
Option 1: $\frac{120}{61}$
Option 2: $\frac{61}{120}$
Option 3: $3$
Option 4: $-3$
Question : Simplify the following. $\frac{0.01 \times 0.01 \times 0.01+0.003 \times 0.003 \times 0.003}{0.05 \times 0.05 – 0.015 \times 0.05 + 0.015 \times 0.015}$
Option 1: $\frac{13}{25} \times 10^3$
Option 2: $\frac{13}{15} \times 10^{–3}$
Option 3: $\frac{13}{15} \times 10^3$
Option 4: $\frac{13}{25} \times 10^{–3}$
Question : Simplify the given expression. $ \frac{432 \times 432+247 \times 247-432 \times 247}{432 \times 432 \times 432+247 \times 247 \times 247} $
Option 1: $\frac{1}{259}$
Option 2: $\frac{1}{185}$
Option 3: $\frac{1}{679}$
Option 4: $\frac{1}{450}$
Question : Simplify the given expression. $\frac{(326+222)^2-(326-222)^2}{(326 \times 222)}$
Option 1: 1
Option 2: 4
Option 3: 3
Option 4: 2
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