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
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Correct Answer: 40
Solution : Given, $\frac{4\left[(17)^3-(7)^3\right]}{(17)^2+(7)^2+119}$ = $\frac{4(17-7)((17)^2+(7)^2+(17)(7))}{(17)^2+(7)^2+(17)(7)}$ = $4×10$ = $40$ Hence, the correct answer is 40.
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Question : Simplify the given expression. $40 \times 7-2 \times\left(11^3 \div 11\right) \div 22+30$
Option 1: 297
Option 2: 298
Option 3: 300
Option 4: 299
Question : The value of $2 \frac{3}{5} \div\left[2 \frac{1}{3} \div\left\{4 \frac{1}{3}-\left(2 \frac{1}{2}+\frac{2}{3}\right)\right\}\right]$ is equal to:
Option 1: $1 \frac{3}{10}$
Option 2: $2 \frac{7}{10}$
Option 3: $2 \frac{3}{7}$
Option 4: $1 \frac{3}{7}$
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
Question : Simplify the given expression $\frac{3\left(\sin ^4 z-\cos ^4 z+1\right)}{\sin ^2 z}$
Option 1: 9
Option 2: 2
Option 3: 4
Option 4: 6
Question : Find the value of the given expression. $\left(2 \frac{1}{2}÷ 1 \frac{7}{8}\right) ÷\left(9 \frac{3}{8}÷ 11 \frac{2}{3} \text { of } \frac{1}{8}\right)$
Option 1: $\frac{33}{135}$
Option 2: $\frac{11}{135}$
Option 3: $\frac{28}{135}$
Option 4: $\frac{57}{135}$
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