Question
Below $u, v, w$ and $x$ represent different integers, where $u = –4$ and $\text{x}\neq1$ By using following equations, find each of the values: $u \times v = u x \times w = w u + x = w$
$a. v$
$b. w$
$c. x$
$a. v$
$b. w$
$c. x$
✓
Answer
We have, three equations $u \times v = u x \times w = w u + x = w$ and $u = -4$
$a.$ By puting the value of $u$ in $Eq.(i),$ we get $(-4) \times v = (-4)$
$\Rightarrow\text{v}=\frac{(-4)}{(-4)}=1$
$b.$ From $Eq.(ii),$ $\text{x}\times\text{w}$
$\Rightarrow\text{x}=\frac{\text{w}}{\text{w}}$
$\Rightarrow\text{x}=1$
But,
$\text{x}\neq1$
Hence, $x \times w = w, (ii)$ is possible, when $\text{w}=0(\text{x}\neq1)$
$c.$ From $Eq.(iii), u + x = w$
Put $u =$ and $w = 0$, we get
$\Rightarrow -4 + x = 0$
$\Rightarrow x = 4$
$\therefore v = 1, x = 4$ and $w = 0$
$a.$ By puting the value of $u$ in $Eq.(i),$ we get $(-4) \times v = (-4)$
$\Rightarrow\text{v}=\frac{(-4)}{(-4)}=1$
$b.$ From $Eq.(ii),$ $\text{x}\times\text{w}$
$\Rightarrow\text{x}=\frac{\text{w}}{\text{w}}$
$\Rightarrow\text{x}=1$
But,
$\text{x}\neq1$
Hence, $x \times w = w, (ii)$ is possible, when $\text{w}=0(\text{x}\neq1)$
$c.$ From $Eq.(iii), u + x = w$
Put $u =$ and $w = 0$, we get
$\Rightarrow -4 + x = 0$
$\Rightarrow x = 4$
$\therefore v = 1, x = 4$ and $w = 0$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Copy the following drawings on squared paper and complete each one of them in such a way that resulting figure has two dotted lines as two lines of symmetry:
In the following figure, $I \| m$ and a line $t$, intersects these lines at $P$ and $Q$, respectively. Find the value of $2 a+b$.
→Gold prices on $4$ consecutive Tuesdays were as under:
Draw a bar graph to show this imformation.
→| Week | First | Second | Third | Fourth |
| Rate per 10gm (in Rs.) | $8500$ | $8750$ | $9050$ | $9250$ |
Designing a Healthy Diet
When you design your healthy diet, you want to make sure that you meet the dietary requirements to help you grow into a healthy adult. As you plan your menu, follow the following guidelines.
$1.$ Calculate your ideal weight as per your height from the table given at the end of this question.
$2.$ An active child should eat around $55.11$ calories for each kilogram desired weight.
$3. \ 55\%$ of calories should come from carbohydrates. There are $4$ calories in each gram of carbohydrates.
$4. \ 15\%$ of your calories should come from proteins. There are $4$ calories in each gram of proteins.
$5. \ 30\%$ of your calories may come from fats. There are $9$ calories in each gram of fats.
Following is an example to design your own healthy diet.
Example:
$1.$ Ideal weight $= 40\ kg.$
$2.$ The number of calories needed $= 40 \times 55.11 = 2204.4$
$3.$ Calories that should come from carbohydrates
$= 2204.4 \times 0.55 = 1212.42$ calories.
Therefore, required quantity of carbohydrates
$=\frac{1212.40}{4}=303.105\text{g}=300\text{g.}$
$4.$ Calories that should come from proteins
$= 2204.4 \times 0.15 = 330.66$ calories.
Therefore, required quantity of protein
$=\frac{330.66}{4}\text{g}=82.66\text{g}.$
$5.$ Calories that may come from fat $= 2204.4 \times 0.3$
$= 661.3$ calories.
Therefore, required quantity of fat
$=\frac{661.3}{9}\text{g}=73.47\text{g.}$
$1.$ Your ideal desired weight is $.......... kg.$
$2.$ The quantity of calories you need to eat is $........g$
$3.$ The quantity of protein needed is $.........g.$
$4.$ The quantity of fat required is $.........g.$
$5.$ The quantity of carbohydrates required is $.........g.$
→When you design your healthy diet, you want to make sure that you meet the dietary requirements to help you grow into a healthy adult. As you plan your menu, follow the following guidelines.
$1.$ Calculate your ideal weight as per your height from the table given at the end of this question.
$2.$ An active child should eat around $55.11$ calories for each kilogram desired weight.
$3. \ 55\%$ of calories should come from carbohydrates. There are $4$ calories in each gram of carbohydrates.
$4. \ 15\%$ of your calories should come from proteins. There are $4$ calories in each gram of proteins.
$5. \ 30\%$ of your calories may come from fats. There are $9$ calories in each gram of fats.
Following is an example to design your own healthy diet.
Example:
$1.$ Ideal weight $= 40\ kg.$
$2.$ The number of calories needed $= 40 \times 55.11 = 2204.4$
$3.$ Calories that should come from carbohydrates
$= 2204.4 \times 0.55 = 1212.42$ calories.
Therefore, required quantity of carbohydrates
$=\frac{1212.40}{4}=303.105\text{g}=300\text{g.}$
$4.$ Calories that should come from proteins
$= 2204.4 \times 0.15 = 330.66$ calories.
Therefore, required quantity of protein
$=\frac{330.66}{4}\text{g}=82.66\text{g}.$
$5.$ Calories that may come from fat $= 2204.4 \times 0.3$
$= 661.3$ calories.
Therefore, required quantity of fat
$=\frac{661.3}{9}\text{g}=73.47\text{g.}$
$1.$ Your ideal desired weight is $.......... kg.$
$2.$ The quantity of calories you need to eat is $........g$
$3.$ The quantity of protein needed is $.........g.$
$4.$ The quantity of fat required is $.........g.$
$5.$ The quantity of carbohydrates required is $.........g.$
|
|
|
Ideal Height and Weight Proportion
|
|
|
|
|
|
Men
|
|
|
Women
|
|
|
Height
|
|
Weight
|
Height
|
|
Weight
|
|
Feet
|
$cm$
|
Kilograms
|
Feet
|
$cm$
|
Kilograms
|
|
$5’$
|
$152$
|
$48$
|
$4’7”$
|
$140$
|
$34$
|
|
$5’1”$
|
$155$
|
$51$
|
$4’8”$
|
$142$
|
$36$
|
|
$5’2”$
|
$157$
|
$54$
|
$4’9”$
|
$145$
|
$39$
|
|
$5’3”$
|
$160$
|
$56$
|
$4’1”$
|
$147$
|
$41$
|
|
$5’4”$
|
$163$
|
$59$
|
$4’11”$
|
$150$
|
$43$
|
|
$5’5”$
|
$165$
|
$62$
|
$5’$
|
$152$
|
$45$
|
|
$5’6”$
|
$168$
|
$65$
|
$5’1”$
|
$155$
|
$48$
|
|
$5’7”$
|
$170$
|
$67$
|
$5’2”$
|
$157$
|
$50$
|
|
$5’8”$
|
$173$
|
$70$
|
$5’3”$
|
$160$
|
$52$
|
|
$5’9”$
|
$175$
|
$73$
|
$5’4”$
|
$163$
|
$55$
|
|
$5’10”$
|
$178$
|
$75$
|
$5’5”$
|
$165$
|
$57$
|
|
$5’11”$
|
$180$
|
$78$
|
$5’6”$
|
$168$
|
$59$
|
|
$6’$
|
$1834$
|
$81$
|
$5’7”$
|
$170$
|
$61$
|
|
$6’1”$
|
$185$
|
$84$
|
$5’8”4$
|
$173$
|
$64$
|
|
$6’2”$
|
$188$
|
$86$
|
$5’9”$
|
$175$
|
$66$
|
|
$6’3”$
|
$191$
|
$89$
|
$5’10”$
|
$178$
|
$68$
|
|
$6’4”$
|
$193$
|
$92$
|
$5’11”$
|
$180$
|
$70$
|
A light year is the distance that light can travel in one year.
1 light year $=9460000000000 km$
(i) Express one light year in scientific notation.
(ii) The average distance between Earth and Sun is $1.496 \times 10^8 km$. Is the distance between Earth and the Sun greater than, less than or equal to one light-year?
→1 light year $=9460000000000 km$
(i) Express one light year in scientific notation.
(ii) The average distance between Earth and Sun is $1.496 \times 10^8 km$. Is the distance between Earth and the Sun greater than, less than or equal to one light-year?
Two poles, $18m$ and $13m$ high, stand upright in a playground. If their feet are $12m$ apart, find the distance between their tops.
→Find the quotient by converting the denominator into 1, 10, 100, or 1000 and verify the solution by the long division method (division by place value):
$\frac{18}{5}$
→$\frac{18}{5}$
In Fig.write all pairs of adjacent angles and all the linear pairs.
Observe the given bar graph carefully and answer the questions that follow.
$a.$ What information does the bar graph depict?
$b.$ How many motor bikes were produced in the first three months?
$c.$ Calculate the increase in production in May over the production in January.
$d.$ In which month the production was minimum and what was it?
$e.$ Calculate the average $($mean$)$ production of bikes in $6$ months.
→$a.$ What information does the bar graph depict?
$b.$ How many motor bikes were produced in the first three months?
$c.$ Calculate the increase in production in May over the production in January.
$d.$ In which month the production was minimum and what was it?
$e.$ Calculate the average $($mean$)$ production of bikes in $6$ months.
Simplify: $\frac{-11}{39}+\frac{5}{26}+\frac{2}{1}$
→