Algebra MCQs

If $$\frac{a}{b}{\text{ = }}\frac{2}{3}$$   and $$\frac{b}{c}{\text{ = }}\frac{4}{5}{\text{,}}$$   then the ration $$\frac{{a + b}}{{b + c}}$$   equal to?

If 4pxy = (x + 2y)² - (x - 2y)², then what will be the value of p?

If ⊗ is an operation such that a ⊗ b = 2a when a > b, a + b when a < b, a² when a = b, then $$\left[ {\frac{{\left( {5 \otimes 7} \right) + \left( {4 \otimes 4} \right)}}{{3\left( {5 \otimes 5} \right) - \left( {15 \otimes 11} \right) - 3}}} \right]$$     is equal to?

If $$\frac{{4x - 3}}{x}$$   + $$\frac{{4y - 3}}{y}$$   + $$\frac{{4z - 3}}{z} = 0{\text{,}}$$   then the value of $$\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$$   is?

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

The factors of x⁴ + x² + 25 are:

If $${x^3} + \frac{3}{x}$$   = $$4\left( {{a^3} + {b^3}} \right)$$   and $$3x + \frac{1}{{{x^3}}}$$   = $$4\left( {{a^3} - {b^3}} \right){\text{,}}$$   then a² - b² is equal to?

If a + b + c = $$\frac{7}{{12}},$$ 3a - 4b + 5c = $$\frac{3}{4}$$ and 7a - 11b - 13c = $$ - \frac{7}{{12}},$$  then what is the value of a + c?

If $$x + \frac{1}{x} = 2{\text{,}}$$   then the value of $$\left( {{x^2} + \frac{1}{{{x^2}}}} \right)\left( {{x^3} + \frac{1}{{{x^3}}}} \right)$$     is?