Simplication MCQs

Find the value of $$a$$ in the following equation. (Given: $$a$$ < 10.)
$$\frac{{\left( {187 \div 17 \times a - 3 \times 3} \right)}}{{\left( {{8^2} - 9 \times 7 + {a^2}} \right)}} = 1$$

What is the simplified value of the following?
$$\frac{{9 \div \frac{3}{7}{\text{ of }}\left( {9 + 6 \times \overline {4 - 2} } \right) + \left[ {\frac{1}{5} \div \frac{7}{{25}} - \left\{ {\frac{5}{8} + \frac{6}{{16}}} \right\}} \right]}}{{24 \div \overline {16 - 10} + 36 \div \left( {5 + 20 \div 4 - 1} \right)}}$$

If a - b = 3 and a² + b² = 29, find the value of ab.

If x + y = 2a, then the value of $$\frac{a}{{x - a}} + \frac{a}{{y - a}}\,{\text{is = ?}}$$

$${\text{If }}\left[ {4 - \frac{5}{{1 + \frac{1}{{3 + \frac{1}{{2 + \frac{1}{4}}}}}}}} \right]$$    part of a journey takes ten minutes, then to complete $$\frac{3}{5}$$th of that journey, it will take = ?

If 1² + 2² + 3² + . . . . . + p² = $$\left[ {\frac{{{\text{p}}\left( {{\text{p}} + 1} \right)\left( {2{\text{p}} + 1} \right)}}{6}} \right]{\text{,}}$$     then 1² + 3² + 5² + . . . . . + 17² is = ?

Given that ( 1² + 2² + 3² + .......... + 10² ) = 385, then the value of ( 2² + 4² + 6² + .......... + 20² ) is equal to = ?

Supply the two missing figures in order indicated by x and y in the given equation, the fractions being in their lowest terms. $${\text{5}}\frac{1}{x} \times y\frac{3}{4} = 20$$

Which of the following values of x and y satisfy the following equations i and ii?
i. 3x + y = 19
ii. x - y = 9