R.K. Singh Solutions for Chapter: SSC Advanced Maths. : Previous Years Solved Papers, Exercise 16: SSC LDC/DEO Exam. : 20.10.2013

If $\mathrm{a}, \mathrm{b}$ are rationals and $\mathrm{a}\sqrt{2}+\mathrm{b}\sqrt{3}=\sqrt{98}+\sqrt{108}-\sqrt{48}-\sqrt{72}$ then the values of $\mathrm{a}, \mathrm{b}$ respectively?

Suppose $\mathrm{a}=\frac{1}{2-\sqrt{3}}+\frac{1}{3-\sqrt{8}}+\frac{1}{4-\sqrt{15}}$, then______.

If $\mathrm{x}+1+\frac{1}{\mathrm{x}+1}=1$ then ${\left(\mathrm{x}+1\right)}^5+\frac{1}{{\left(\mathrm{x}+1\right)}^5}$ will be_______.

If $\frac{1}{\mathrm{a}}-\frac{1}{\mathrm{b}}=\frac{1}{\mathrm{a}-\mathrm{b}},$ then ${\mathrm{a}}^3+{\mathrm{b}}^3$ is-

If ${\mathrm{a}}^2+{\mathrm{b}}^2+{\mathrm{c}}^2=\mathrm{ab}+\mathrm{bc}+\mathrm{ca}$ then $\frac{\mathrm{a}+\mathrm{c}}{\mathrm{b}}$ will be equal to-

If the graphs of equations $\mathrm{x}+\mathrm{y}=0$ and $5\mathrm{y}+7\mathrm{x}=24$ intersect each other at $(\mathrm{m}, \mathrm{n}).$ then the value of $(\mathrm{m}+\mathrm{n})$ will be______.

There are two circles with centres $\mathrm{P} \& \mathrm{Q}$ and radii $9 \mathrm{cm} \& 2 \mathrm{cm}$ respectively. Where $\mathrm{PQ} = 17 \mathrm{cm}$. $\mathrm{R}$ is the centre of an other circle whose radius is $\mathrm{x} \mathrm{cm}$ and it touches both the above circles externally. If $\angle \mathrm{PRQ}=90°$ then the value. of $\mathrm{x}$ will be______.

The area of a rhombus is $216{ \mathrm{cm}}^2.$ If its one diagonal is $24 \mathrm{cm}$ long then the perimeter of this rhombus is (In $\mathrm{cm}$) ______.