Download CBSE Sample Paper 2024-25 for class 12th to 8th

Mix Test - 6

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Mix Test - 6

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Weekly Quiz Competition

Question 1
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Using a suitable identity find (2x + 3)².

A
16x² + 12x + 9

B
4x² + 12x + 10

C
4x² + 12x + 9

D
4x² - 12x + 12

Solution

(2x + 3 )²
= (2x )² + 2 × 2x × 3 + (3)²(using identity (a + b)² = a² + b² + 2ab)
= 4x²+ 12x + 9
Question 2
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100 persons had food provision for 24 days. If 20 persons left the place, the provision will last for

A
30 days

B
80 days

C
40 days

D
120 days

Solution

∵ 100 persons had food provision for 24 days.

∴ 1 person had food provision for 24 × 100 i.e. 2400 days.

If 20 persons left the place, then remaining persons = (100 - 20) = 80

∴ 80 persons had food provision for 2400/80 i.e. 30days
Question 3
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A
39

B
34

C
45

D
32

Solution
Question 4
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A road map with a scale of 1 cm represents 36 km. When Ravi drives on a road for 144 km, what would be the distance covered by him on the map?

A
8 cm

B
16 cm

C
4 cm

D
12 cm

Solution

This is a case of direct proportion as with the increase in actual distance on road the distance covered on the map will also increase
In direct proportion, the value of constant is given by X/Y
1/36 = a/144 (where a is the distance covered on map)
36 × a = 144
a = 144/36
a = 4 cm
Question 5
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Three equal cubes each of side 4 cm are joined end to end. The volume of the cuboid so formed is :

A
64 cm³

B
192 cm³

C
96 cm³

D
48 cm³

Solution

Length of the cuboid = 4 + 4 + 4 = 12 cm
Breadth of the cuboid = 4 cm
Height of the cuboid = 4 cm
Volume of the cuboid = l × b × h = 12 × 4 × 4 = 192cm³
Question 6
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Using Identity find 78 × 82.

A
7200

B
6396

C
6300

D
6000

Solution

Use identity (a - b) (a + b) = a² - b² . Here a = 80 , b = 2
(80 - 2) (80 + 2) = (80)² - (2)²
= 6400 - 4
= 6396
Question 7
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A rectangular piece of iron sheet is 44 m long and 20 m broad. It is rolled along its length to form a cylinder. Find the volume of the cylinder so formed.

A
1080m³

B
4080m³

C
2080m³

D
3080m³

Solution

Length of the iron sheet = 44 m
breadth = 20m
now it is rolled along its length
so the circumference of cylinder = 44m
height of the cylinder will be 20 m
circumference of cylinder = 2πr

so, volume of cylinder = 3080 m³
Question 8
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From the sum of 2y² + 3yz, -y² - yz - z² and yz + 2z², subtract the sum of 3y² - z² and -y² + yz + z².

A
-y² + 2yz + 3z²

B
-y² + 3yz + z²

C
-y² + 2yz + z²

D
None of these

Solution

{(2y² + 3yz) + (-y² - yz - z²) + (yz + 2z²)} - {(3y² - z²) + (-y² + yz + z²)}
= {2y² - y² + 3yz - yz - z² + 2z²} - {3y² - y² + yz - z² + z²}
= {(y² + 3yz + z²} - {2y² + yz)
= -y² + 2yz + z²
Question 9
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A hall is 20 m long and 16 m wide. The area of its four walls i.e., equal to the area of the floor and the ceiling together.Height of the hall is :

A
8

B
9 m

C
10 m

D
80/9

Solution

Area of the floor =20 × 16 = 320 m²

Area of the ceiling =20 × 16 = 320 m²

Area of four walls = Area of floor + Area of ceiling = 640m²

2(l + b) h = 640

2(20 + 16)h = 640

72 h = 640 ⇒ h = 640/72 = 80/9 m
Question 10
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If a box of sweets is divided among 24 children, they will get 5 sweets each. How many would each get, if the number of the children is reduced by 4?

A
6

B
4

C
8

D
None of these

Solution

This is a question of inverse proportion as with the decrease in the number of children the number of sweets each student gets will increase
In inverse proportion, the constant value is given by x × y
24 × 5 = (24 - 4) × a (where a is the number of sweets each student gets)
120 = 20a
120/20 = a
6 sweets = a