Simplication MCQs

$$\sqrt {\frac{{{{\left( {0.03} \right)}^2} + {{\left( {0.21} \right)}^2} + {{\left( {0.065} \right)}^2}}}{{{{\left( {0.003} \right)}^2} + {{\left( {0.021} \right)}^2} + {{\left( {0.0065} \right)}^2}}}} $$

What number must be added to the expression 16a² - 12a to make a perfect square ?

David gets on the elevator at the 11^th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?

If x + y + z = 0, then x³ + y³ + z³ + 3xyz is equal to = ?

$$\eqalign{ & {\text{Simplify if,}} \cr & {\text{I = }}\frac{3}{5} \div \frac{5}{6}{\text{,}} \cr & {\text{II = 3}} \div \left[ {\left( {4 \div 5} \right) \div 6} \right]{\text{,}} \cr & {\text{III = }}\left[ {3 \div \left( {4 \div 5} \right)} \right] \div 6\,, \cr & {\text{IV = 3}} \div {\text{4}}\left( {5 \div 6} \right) \cr & {\text{then }} \cr} $$

24.96² ÷ (34.11 ÷ 20.05) + 67.96 - 89.11 = ?

Find the sum : $$\frac{1}{2} + $$ $$\frac{1}{6} + $$ $$\frac{1}{{12}} + $$ $$\frac{1}{{20}} + $$ $$\frac{1}{{30}} + $$ $$\frac{1}{{42}} + $$ $$\frac{1}{{56}} + $$ $$\frac{1}{{72}} + $$ $$\frac{1}{{90}} + $$ $$\frac{1}{{110}} + $$ $$\frac{1}{{132}}$$ $$ = ?$$

If a + b + c = 2s, then the value of (s - a)² + (s - b)² + (s - c)² + s² will be-