Subject Experts Solutions for Chapter: Formulae, Exercise 2: PRACTICE QUESTIONS (COMPETITION WING)

The focal length of a mirror is given by the formula $\frac{1}{\mathrm{f}}=\frac{1}{\mathrm{u}}+\frac{1}{\mathrm{v}}$. Make $\mathrm{f}$ as the subject of the formula. If $\mathrm{u}=20 \mathrm{cm} \mathrm{and} \mathrm{v}=30 \mathrm{cm}$, then find $\mathrm{f}$.

The following steps are involved in solving the above problem. Arrange them in sequential order

(A) Given $\frac{1}{\mathrm{f}}=\frac{1}{\mathrm{u}}+\frac{1}{\mathrm{v}}$

(B) $\Rightarrow \mathrm{f}=\frac{\mathrm{uv}}{\mathrm{u}+\mathrm{v}}$

(C) $\mathrm{f}=\frac{20\times 30}{20+30}=\frac{600}{50}=12 \mathrm{cm}$

(D) $\Rightarrow \frac{1}{\mathrm{f}}=\frac{\mathrm{v}+\mathrm{u}}{\mathrm{uv}}$

The length of an arc of a circle is given by the formula $\mathrm{l}=\frac{\mathrm{x}}{360°}\times 2\mathrm{\pi r}$.  If $\mathrm{l}=4\mathrm{\pi } \mathrm{cm} \mathrm{and} \mathrm{r}=18 \mathrm{cm}$, then find $\mathrm{x}$.

Write the relation between $\mathrm{H} \mathrm{and} \mathrm{m}$ from the given table.

Simple interest on a certain sum is given by $\mathrm{I}=\frac{\mathrm{PTR}}{100}$. Make $\mathrm{T}$ as the subject of the formula. Find $\mathrm{T}$ when $\mathrm{P}=₹1000, \mathrm{R}=10\% \mathrm{p}.\mathrm{a}., \mathrm{and} \mathrm{I}=₹300$

If $\mathrm{A}={\mathrm{S}}^2$ and $\mathrm{A}=324 {\mathrm{cm}}^2$, then find the value of $\mathrm{S}$ (in $\mathrm{cm}$).

In the formula $\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180°$, if $\angle \mathrm{A}=90°$ and $\angle \mathrm{B}=55°$, then $\angle \mathrm{C}=$_____.

If $\mathrm{A}=\frac{{\mathrm{d}}_1{\mathrm{d}}_2}{2}, {\mathrm{d}}_1=6 \mathrm{cm} \mathrm{and} {\mathrm{d}}_2=8 \mathrm{cm}$, then find the value of $\mathrm{A}$ (in ${\mathrm{cm}}^2$).

The number of auxiliary formulae that can be derived from the formula $\mathrm{D}=\left[\frac{\mathrm{n}\left(\mathrm{n}-1\right)}{2}\right]-\mathrm{n}$