R.K. Singh Solutions for Chapter: Algebra, Exercise 1: Model Questions

If point $\mathrm{A}$ is in third quadrant and $3 \tan \mathrm{A}-4=0$ then the value of $5 \sin 2 \mathrm{A}+3 \sin \mathrm{A}+4 \cos \mathrm{A}=?$

$\left[{\mathrm{a}}^{\frac{1}{8}}+{\mathrm{a}}^{-\frac{1}{8}}\right]\left[{\mathrm{a}}^{\frac{1}{8}}-{\mathrm{a}}^{-\frac{1}{8}}\right]\left[{\mathrm{a}}^{\frac{1}{4}}+{\mathrm{a}}^{{}^{-\frac{1}{4}}}\right]\left[{\mathrm{a}}^{\frac{1}{2}}+{\mathrm{a}}^{-\frac{1}{2}}\right]=?$

The value of expression $\frac{{\left({\mathrm{x}}^2-{\mathrm{y}}^2\right)}^3+{\left({\mathrm{y}}^2-{\mathrm{z}}^2\right)}^3+{\left({\mathrm{z}}^2-{\mathrm{x}}^2\right)}^3}{(\mathrm{x}-\mathrm{y}{)}^3+(\mathrm{y}-\mathrm{z}{)}^3+(\mathrm{z}-\mathrm{x}{)}^3}$ is:

If $\mathrm{x}={\mathrm{a}}^{\frac{2}{3}}-{\mathrm{a}}^{-\frac{2}{3}}$ then the value of ${\mathrm{x}}^3+3\mathrm{x}$ is:

If $\mathrm{a}+\mathrm{b}+\mathrm{c}=0$ then the value of $\frac{1}{{\mathrm{a}}^2+{\mathrm{b}}^2-{\mathrm{c}}^2}+\frac{1}{{\mathrm{b}}^2+{\mathrm{c}}^2-{\mathrm{a}}^2}+\frac{1}{{\mathrm{a}}^2+{\mathrm{c}}^2-{\mathrm{b}}^2}=?$

If $\mathrm{y}+\frac{1}{\mathrm{z}}=1$ and $\mathrm{x}+\frac{1}{\mathrm{y}}=1$, then the value of $\mathrm{xyz}$ is:

In the solution of equation $\frac{\mathrm{x}}{4}+\frac{\mathrm{y}}{3}=\frac{5}{12}$ and $\frac{\mathrm{x}}{2}+\mathrm{y}=1$ the value of $(\mathrm{x}+\mathrm{y})$ is:

If $\mathrm{\alpha }$ and $\mathrm{\beta }$ are the root of equation ${\mathrm{x}}^2+\mathrm{px}+\mathrm{q}=0$ then the value of $\frac{\mathrm{\alpha }}{\mathrm{\beta }}+\frac{\mathrm{\beta }}{\mathrm{\alpha }}$ is: