Mix Test

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Weekly Quiz Competition

Question 1
1 / -0.25

A cone and a cylinder are of the same height. Their radii of the bases are in the ratio of 2 : 1. The ratio of their volume is :

A
4 : 3

B
1 : 2

C
2 : 1

D
3 : 4

Solution

Radius of the cone : Radius of cylinder = 2 : 1 = 2x : x
Height of the cone and cylinder are the same.
Question 2
1 / -0.25

A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm as shown in the diagram. If the photograph is enlarged 20,000 times only, what would be its enlarged length?

A
2 cm

B
6 cm

C
4 cm

D
8 cm

Solution

This is a question of direct proportion as with the decrease in magnification the length enlarged will also decrease.

In direct proportion, the value of constant is given by x/y

50000/5 = 20000/a (where a is the enlarged length)

5 × 20000 = 50000 × a

100000/50000 = a

2cm = a
Question 3
1 / -0.25

When a die is thrown, what is the probability of getting a number greater than 3?

A
1/2

B
1

C
None of these

D
0

Solution

Total number of outcomes = 1,2,3,4,5,6 i.e 6

Number greater than three = 4,5,6 i.e. 3

Probability of getting a number greater than 3 = 3/6 = 1/2
Question 4
1 / -0.25

A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of the base. How many parts of the base will be used in mixture by mixing 4 part of red pigment?

A
40

B
28

C
32

D
36

Solution

This is a question of direct proportion as with the increase in the amount of red pigment the amount of base also increases
In direct proportion, the constant value is given by x/y
So, 1/8 = 4a (where a is the parts of the base to be used)
a = 32
Question 5
1 / -0.25

The curved surface area of a cone is 3815.10 mm² and the radius of the base of the cone is 27 mm. What is its height?

A
30 mm

B
35.93 mm

C
38 mm

D
34 mm

Solution

radius = r = 27 mm
The curved surface area of a cone(CSA) = 3815.10 mm²
CSA = πrl

44.95mm = l
slant height = l = 44.95 mm and let height be ' h' mm
l² = r² + h²
(44.95)2 = (27)² + h²
2020.5025 = 729 + h²
2020.5025 - 729 = h²
1291.5025 = h²

height = 35.93 mm
Question 6
1 / -0.25

If the height of a cylinder becomes 1/4 of the original height and the radius is doubled, then which of the following will be true?

A
Curved surface area will be 1/4 of the original curved surface

B
Curved surface area of the cylinder will be halved

C
Curved surface area of the cylinder will be doubled

D
Curved surface area of the cylinder will remain unchanged

Solution

Let the new height and radius be h/4 and 2r respectively, where r and h are the original radius and original height respectively of the cylinder.

We know that, curved surface area of cylinder = 2πrh

Then, the curved surface of the new cylinder = 2π(2r) × 1/4 h = 4πr × 1/4 h = πrh

= 1/2 × 2πrh [Multiplying and dividing by 2]

= 1/2 original curved surface area

Hence, the curved surface area of the cylinder will be halved.
Question 7
1 / -0.25

A covered wooden box has the inner measures as 115 cm, 75 cm and 35 cm and thickness of wood at 2.5 cm. The volume of the wood is

A
82125 cm³

B
80000 cm³

C
84000 cm³

D
85000 cm³

Solution

Given, inner measures of a wooden box as 115 cm, 75 cm and 35 cm.

Since, thickness of the box is 2.5 cm, then outer measures will be 115 + 5,75 + 5 and 35 + 5, i.e. 120 cm, 80 cm and 40 cm.

∴ The outer volume = 120 × 80 × 40 = 384000 cm³

and he inner volume = 115 × 75 × 35 = 301875 cm³ [∵ volume of cuboid = 1 × b × h]

∴ Volume of the wood = Outer volume - Inner volume

= 384000 - 301875 = 82125 cm³
Question 8
1 / -0.25

Using identity (x - a)(x + a) = x² - a², find 6² - 5²

A
-11

B
11

C
12

D
10

Solution

here x = 6 and a = 5
Put in the identity, (x - a)(x + a) = x² - a²
6² - 5² = (6 - 5) (6 + 5) = (1) (11) = 11
Question 9
1 / -0.25

Numbers 1 to 20 are written on twenty separate slips (one number on one slip) kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of getting number 7?

A
1/20

B
1/5

C
1/10

D
None of these

Solution

Total number of outcomes = 20
Probability of getting a number 7 = 1/20.
Question 10
1 / -0.25

If the radius of the base of a right circular cone is 9r mm. and its height is equal to the radius of the base, find its volume in mm³.

A
248 πr³

B
200 πr³

C
243 πr³

D
252 πr³

Solution

radius of cone = 9r and height = radius = 9r

volume of cone = 243 πr³ mm³

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Re-Attempt Weekly Quiz Competition

Mix Test - 1

Result

Mix Test - 1

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Rank

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SHARING IS CARING

Question 1

4 : 3

1 : 2

2 : 1

3 : 4

Solution

Question 2

2 cm

6 cm

4 cm

8 cm

Solution

Question 3

1/2

1

None of these

0

Solution

Question 4

40

28

32

36

Solution

Question 5

30 mm

35.93 mm

38 mm

34 mm

Solution

Question 6

Curved surface area will be 1/4 of the original curved surface

Curved surface area of the cylinder will be halved

Curved surface area of the cylinder will be doubled

Curved surface area of the cylinder will remain unchanged

Solution

Question 7

82125 cm3

80000 cm3

84000 cm3

85000 cm3

Solution

Question 8

-11

11

12

10

Solution

Question 9

1/20

1/5

1/10

None of these

Solution

Question 10

248 πr3

200 πr3

243 πr3

252 πr3

Solution

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82125 cm³

80000 cm³

84000 cm³

85000 cm³

248 πr³

200 πr³

243 πr³

252 πr³