Question : What is the value of the given expression? $\frac{4^{a + 4}- 5 \times 4^{a + 2}}{15 \times 4^a - 2^2 \times 4^a}$
Option 1: 16
Option 2: 64
Option 3: 20
Option 4: 24
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Correct Answer: 16
Solution : $\frac{4^{a+ 2}(4^{2} - 5 \times 1)}{4^{a}(15 - 4)}$ $=\frac{4^{a + 2}(11)}{4^{a}(11)}$ $=\frac{4^{a}\times4^{2}(11)}{4^{a}(11)}$ $=4^2$ $=16$ Hence, the correct answer is 16.
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Question : Find the simplified value of the given expression. $4 \frac{4}{5} ÷ \frac{3}{5} \text { of } 5+\frac{4}{5} \times \frac{3}{10}-\frac{1}{5}$
Question : Simplify the given expression. $18 \div 3$ of $2 \times 5+72 \div 18$ of $2 \times 3-4 \div 8 \times 2$
Question : What is the value of S $=\frac{1}{1×3×5}+\frac{1}{1×4}+\frac{1}{3×5×7}+\frac{1}{4×7}+\frac{1}{5×7×9}+\frac{1}{7×10}+....$ Up to 20 terms, then what is the value of S?
Question : The value of $15 \div 8-\frac{5}{4}$ of $\left(\frac{8}{3} \times \frac{9}{16}\right)+\left(\frac{9}{8} \times \frac{3}{4}\right)-\left(\frac{5}{32} \div \frac{5}{7}\right)+\frac{3}{8}$ is:
Question : Let $x=\frac{5 \frac{3}{4}-\frac{3}{7} \times 15 \frac{3}{4}+2 \frac{2}{35} \div 1 \frac{11}{25}}{\frac{3}{4} \div 5 \frac{1}{4}+5 \frac{3}{5} \div 3 \frac{4}{15}}$. When $y$ is added to $x$, the result is $\frac{7}{13}$. What is the value of $y$?
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