Algebra MCQs

If $$\frac{a}{b} = \frac{1}{2},$$   find the value of the expression $$\frac{{\left( {2a - 5b} \right)}}{{\left( {5a + 3b} \right)}}$$   = ?

If xy + yz + zx = 0, then $$\left( {\frac{1}{{{x^2} - yz}} + \frac{1}{{{y^2} - zx}} + \frac{1}{{{z^2} - xy}}} \right)$$       $$\left( {x,y,z \ne 0} \right) = ?$$

If $$a + \frac{1}{a} + 1 = 0\left( {a \ne 0} \right){\text{,}}$$     then the value of $$\left( {{a^4} - a} \right)\,{\text{is?}}$$

If $$\frac{a}{{q - r}}$$  = $$\frac{b}{{r - p}}$$  = $$\frac{c}{{p - q}}{\text{,}}$$   find the value of pa + qb + rc is?

If a + b + c = 0, then the value of $$\left( {\frac{{a + b}}{c} + \frac{{b + c}}{a} + \frac{{c + a}}{b}} \right)$$    $$\left( {\frac{a}{{b + c}} + \frac{b}{{c + a}} + \frac{c}{{a + b}}} \right) = \,?$$

If $$\frac{p}{a}$$ + $$\frac{q}{b}$$ + $$\frac{r}{c}$$ = 1 and $$\frac{a}{p}$$ + $$\frac{b}{q}$$ + $$\frac{c}{r}$$ = 0 where p, q, r and a, b, c are non - zero, then value of $$\frac{{{p^2}}}{{{a^2}}}$$ + $$\frac{{{q^2}}}{{{b^2}}}$$ + $$\frac{{{r^2}}}{{{c^2}}}$$ = ?

If x * y = (x + 3)² (y - 1), then the value of 5 * 4 is?

If a * b = a + b + ab, then 3 * 4 - 2 * 3 is equal to?

If x = y = 333 and z = 334, then the value of x³ + y³ + z³ - 3xyz is?