Algebra MCQs

$${\text{If }}\,\sqrt {1 + \frac{x}{9}} = \frac{{13}}{3}{\text{,}}$$    then the value of x is?

If x : y = 4 : 15 then the value of $$\left( {\frac{{x - y}}{{x + y}}} \right)$$   is?

If $${x^2} + \frac{1}{{{x^2}}} = 66{\text{,}}$$    then the value of $$\frac{{{x^2} - 1 + 2x}}{x}$$   = ?

If $$\frac{1}{p} + \frac{1}{q}$$  = $$\frac{1}{{p + q}}{\text{,}}$$   then the value of p³ - q³ is?

If $$\frac{{22\sqrt 2 }}{{4\sqrt 2 - \sqrt {3 + \sqrt 5 } }} = a + \sqrt 5 b$$      with a, b > 0, then what is the value of (ab) : (a + b)?

If (x - 4)(x² + 4x + 16) = x³ - p, then p is equal to?

The simplest form of the expression $$\frac{{{p^2} - p}}{{2{p^3} + {p^2}}}$$   + $$\frac{{{p^2} - 1}}{{{p^2} + 3p}}$$   + $$\frac{{{p^2}}}{{p + 1}}$$   = ?

If a² + b² + c² = ab + bc + ca, then the value of $$\frac{{a + c}}{b}$$  is?

If a + b + c + d = 4, then find the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)\left( {1 - c} \right)}}$$     + $$\frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)\left( {1 - d} \right)}}$$     + $$\frac{1}{{\left( {1 - c} \right)\left( {1 - d} \right)\left( {1 - a} \right)}}$$     + $$\frac{1}{{\left( {1 - d} \right)\left( {1 - a} \right)\left( {1 - b} \right)}}$$     is?