Glass buildings can be strengthened using iron frames. A glass structure and its iron frame are shown below. The frame consists of equal triangles. The dimensions of a triangle are shown below. 1. How much area is enclosed by one triangle? 2. What is the area of part 1 of the frame? A. 84 m² B. 1680 m² C. 3360 m² D. 3696 m² 3. Is the area of part 1 equal to the area of part 2? Why? 4. Maintenance of the building’s exterior is done by a company. The company charges Rs 750 per square meter per month. Which of the following calculations represents the monthly maintenance charges? A. 24 × 12 B. 750 × 24 C. 3024 × 750 D. 6720 × 750

1. 24 m² 2. D. 3696 m² 3. No, with valid reasoning ● No, the area reserved under part 1 is not equal to the area reserved under part 2. Area under part 1 is 3696 m² whereas the area under part 2 is 3024 m² 4. D. 6720×750

Glass buildings can be strengthened using iron frames. A glass st…

In the quadrilateral ABCD given below, ∠DAC = 90° and AB = AC = AD = DE = EB.

8. What is the value of ∠EAC?
A. 15°
B. 30°
C. 45°
D. 90°
9. Which type of quadrilateral is ABCE?
A. Rhombus
B. Kite
C. Trapezium
D. Parallelogram
10. What is the value of ∠ABE?
A. 20°
B. 30°
C. 45°
D. 60°

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Raju designs a hut for homeless people. The hut is a combination of a cuboid and a right cone. The top of the hut is a cone with radius 4 m and height 1 m. It is made of economical material. The loor of the tent is covered with rugs.
The total height of the tent is 4.5 m. The cuboidal part of the tent is 6 m long and 5 m wide.
1. What is the outer surface area (in m²) of the hut?
A. 77
B. 77+4π√17
C. 137+4π√17
D. 137+4π(4+√17)
2. The length and width of a rug used for the loor are 2.6 m and 2 m respectively.
What is the minimum number of rugs required to cover the loor of the tent house?

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Draws a graphical representation of the points scored by team B.
His graphical representation is given below.

10. Suman says, “Arun’s graphical representation is not appropriate.”
Do you agree with Suman? Mention YES or NO. Give reason to justify your choice.

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This is the picture of a gas balloon illed with helium gas.

This balloon has 18 faces that are square in shape and 8 equilateral faces that are triangular.
3. Which of the following is the net of the balloon?

4. The side length of the square is 20 cm. What is the total surface area of the balloon?

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Given below is the igure of a circle with centre O.
The measure of ∠BOC = 88°.

9. What is the measure of ∠BAC?
A. 44°
B. 60°
C. 88°
D. 176°
10. Priya claims, “The length of OB is equal to the length of OC.”
Siya and Aditi provide different justiications for Priya’s claim.
Siya says, “OB and OC are radii of the same circle.”
Aditi says, “OC is the base of ∠BOC.”
Who has given the correct justiication for Priya’s claim?

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Hard plastic square shaped sheets are available in the.
The side length of sheets is as per requirement.
The price of a sheet is z per square meter.
Anuj requires two sheets – a smaller sheet with side length x m and a larger sheet with side length ym. He has two choices:
Choice 1 – buy two separate sheets of side lengths x m and y m
Choice 2 – buy a single sheet with side length (x+ y) m
4. What is the height of each container?
5. What is the difference in price between the two choices?
6. The area of a rectangle is $\left(3 x^2+x-2\right)$ square units. Its width is $(1+x)$ units. What is the length of the rectangle?
7. A polynomial is expressed as $x^3+b x^2+c x+d=0$. The same polynomial can be written in factor form as $x+p x+q x+r=0$.
How is the constant term in the polynomial related to its factors p, q, and r?
A. $d=p+q+r$
B. $d=(p+q) \times r$
C. $d=p \times q \times r$
D. $d=p q+q r+p r$
8. A polynomial is divided by $(x-1)$. The quotient obtained is $3 x^3-x^2-x-4$, and the remainder is -5 . Which polynomial meets these conditions?
A. $3 x^3-x^2-x-9$
B. $3 x^3-x^2-x-4$
C. $3 x^4-4 x^3-3 x+4$
D. $3 x^4-4 x^2-3 x-1$
9. What is the common factor of $x^3-x^2$ and $-22 x^2+142 x-120 ?$
A. x
B. (x – 1)
C. $x^2$
D. 1
10. A polynomial is expressed as: $p (x)=x^3+x^2-x-1$
At what values of $x$ is the polynomial $p (x)=0$ ?

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Read the Source/ Text given below and answer any four questions:
Veena planned to make a jewellery box to gift her friend Reeta on her marriage. She made the jewellery box of wood in the shape of a cuboid. The jewellery box has the dimensions as shown in the figure below. The rate of painting the exterior of the box is $Rs. 2$ per $\ cm^2$. After making the box she took help from his friends to decorate the box.
The blue colour was painted by Deepak, Black by Suresh, green by Harsh and the yellow was painted by Naresh.

What is the volume of the box?

$24000\ cm^3$
$1200\ cm^3$
$800\ cm^3$
$600\ cm^3$

How much area did Suresh paint?

$24000\ cm^2$
$1200\ cm^2$
$800\ cm^2$
$600\ cm^2$

How much area did Deepak paint?

$24000\ cm^2$
$600\ cm^2$
$800\ cm^2$
$1200\ cm^2$

What amount did Harsh charge?

$Rs. 800$
$Rs. 1200$
$Rs. 1600$
$Rs. 2000$

What amount did Veena pay for painting:

$Rs. 2600$
$Rs. 5200$
$Rs. 5000$
$Rs. 6000$

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Read the passage given below and answer any four questions:
Sohan's house has one bedroom hall with kitchen. His son needed a separate room for study. Thus Sohan planned to construct a new room with length $4\ m$, width $2\ m$ and the height 3m as shown in the following figure.
The room was separate at the roof of the house. The dimensions of the bricks used are: $25\ cm \times 10\ cm \times 5\ cm.$

Total how many bricks will be required? $(1m^3 =1000000\ cm^3):$

$30000$
$40000$
$28800$
$27000$

How many bricks will be used on both walls along the length $($length $= 4\ m)$?

$19200$
$20200$
$18800$
$17000$

How many bricks will be used on both walls along the width $($width $= 3\ m)$?

$19200$
$9600$
$10000$
$15000$

What is the volume of the room?

$24m^3$
$12m^3$
$20m^3$
$15m^3$

What is the area of the floor?

$10m^2$
$12m^2$
$8m^2$
$8m^3$

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Read the passage given below and answer these questions:
Once four friends Rahul, Arun, Ajay and Vijay went for a picnic at a hill station. Due to peak season, they did not get a proper hotel in the city. The weather was fine so they decided to make a conical tent at a park. They were carrying $300\ m^2$ cloth with them. As shown in the figure they made the tent with height $10\ m$ and diameter $14\ m.$ The remaining cloth was used for the floor.

How much Cloth was used for the floor?

$31.6\ m^2$
$16\ m^2$
$10\ m^2$
$20\ m^2$

What was the volume of the tent?

$300\ m^3$
$160\ m^3$
$513.3\ m^3$
$500\ m^3$

What was the area of the floor?

$50\ m^2$
$100\ m^2$
$150\ m^2$
$154\ m^2$

What was the total surface area of the tent?

$400\ m^2$
$422.4\ m^2$
$300\ m^2$
$400\ m^2$

What was the latent height of the tent?

$12\ m$
$12.2\ m$
$15\ m$
$17\ m$

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