3 Marks Question

Question 13 Marks

The length and breadth of a room are $3 x^2 y^3$ and $6 x^3 y^2$, respectively. Find its perimeter and area.

Answer

We have, Length of the room $=3 x^2 y^3$ and,
Breadth of the room $=6 x^3 y^2$
Now, the perimeter of the room $= 2 \times $ (Length + Breadth)
$=2 \times\left(3 x^2 y^3+6 x^3 y^2\right)$
$=2\left(3 x^2 y^3+6 x^3 y^2\right)$
Also, the area of the room = Length $\times $ Breadth,
$=3 x^2 y^3 \times 6 x^3 y^2$
$=(3 \times 6) \times\left(x^2 \times x^3\right) \times\left(y^3 \times y^2\right)$
$=18 x^5 y^5$

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Question 23 Marks

The volume of a cuboid is given by the product of its length, breadth and height. The length of a cuboid is $2x^2$ times its breadth and the height is $\frac{3}{2}\text{yx},$ times of length. Find the volume of the cuboid if its breadth is $6y^2$.

Answer

We have, Breadth of the cuboid $= 6y^2$,
Length of the cuboid $=2 x^2 \times $ Breadth $=2 x^2 \times 6 y^2=12 \times 2 y^2$ and,
Height of the cuboid $=\frac{3}{2}\text{xy}\times\text{Length}=\frac{3}{2}\text{xy}\times12\text{x}^2\text{y}^2=18\text{x}^3\text{y}^3$
Now, the volume of the cuboid = Length $\times $ Breadth $\times $ Height,
$=12 x^2 y^2 \times 6 y^2 \times 18 x^3 y^3$
$=(12 \times 6 \times 18) \times\left(x^2 \times x^3\right) \times\left(y^2 \times y^2 \times y^3\right)$
$=1296 x^5 y^7$

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Question 33 Marks

One ball pen costs $Rs. x$ and one fountain pen costs $Rs. y.$ Find the cost of $y^2$ ball pens and $x^2$ fountain pens.

Answer

As, the cost of one ball pens $= Rs. x$
So, the cost of $y^2$ ball pens $= x \times y^2= Rs. xy^2$
Also, the cost of one fountain pen $= Rs. y$
So, the cost of $x^2$ fountain pens $= y \times x^2= Rs. yx^2$
Now, the total cost $= Rs. (xy^2+ yx^2)$

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Question 43 Marks

Binny spends $Rs. a$ daily and saves $Rs. b$ per week. What is her income for two weeks?

Answer

It is given that Binny spends $Rs. a$ in one day.
$\therefore$ Money spent by him in one week $= 7 \times a = 7a$
It is further given that he saves $Rs. b$ in one week; therefore we have:
Total income in one week = Total expenditure in one week + Total saving in one week
$= 7a + b$
$\therefore$ Binny's total income in $2$ weeks $= 2 \times (7a + b) = Rs. (14a + 2b)$

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Question 53 Marks

The cost of painting a rectangular metal sheet is square of its area. If the length and breadth of the rectangle are $2xy$ and $3x^2y$, then find the cost. Given that area of a rectangle is the product of its length and breadth.

Answer

We have, Length of the rectangular metal sheet $= 2xy$ and,
Breadth of the rectangular metal sheet $= 3x^2y$
Now, the area of the rectangular sheet = Length $\times $ Breadth,
$=2 x y \times 3 x^2 y$
$=6 x^3 y^2$
So, the cost of the painting the metal sheet $=\left(6 x^3 y^2\right)^2=6 x^3 y^2 \times 6 x^3 y^2=36 x^6 y^4$.

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Question 63 Marks

Aarushi spends $Rs. x$ daily and saves $Rs. y$ per week. How much money she saves in $xy^2$ weeks?

Answer

We have,
Money spent daily $= Rs. x,$
Money saved per week $= Rs. y$ and,
Number of weeks $= xy^2$
As, the money spent per week $= 7 \times x = Rs. 7x$
$\Rightarrow $ The total money saved per week $= Rs. (y - 7x)$
So, the total money saved in $xy^2$ weeks $= xy^2× (y - 7x) = Rs. xy^2(y - 7x)$

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Question 73 Marks

Ravish covers $3x^2y$ centimetres in one step. What is the distance moved by him in $2xy^2$ minutes, if he takes $xy$ steps in one minute.

Answer

We have, The distance covered in one step $=3 x^2 y \mathrm{~cm}$,
The number of steps taken in one minute $=x y$ and
The time $=2 x y^2$ minutes,
Now, the number of steps taken in $2 x y^2$ minutes $=x y \times 2 x y^2=2 x^2 y^3$
So, the distance moved in $2 x y^2$ minutes $=2 x^2 y^3 \times 3 x^2 y=6 x^4 y^4 \mathrm{~cm}$.

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Question 83 Marks

In a large hall there are $4x^2$ rows of benches. If each row has $45x^2y^3$ benches and each bench can accomodate $xy^2$ persons, determine the total number of persons if its is full up to its capacity.

Answer

We have, The number of rows in the hall $=4 x^2$,
The number of benches in each row $=5 x^2 y^3$ and,
The number of persons that can accomodate in a bench $=x y^2$
Now, the total number of benches in the hall $=4 x^2 \times 5 x^2 y^3=20 x^4 y^3$
So, the number of persons in the hall if it is full up to its capacity $=x y^2 \times 20 x^4 y^3=20 x^5 y^5$.

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Maths 3 Marks Question

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