Sainik School Entrance Book Class 9 Mathematics (Paper-1) Mock Test

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Mathematics (Paper-1) Mock Test - 4

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Weekly Quiz Competition

Question 1
4 / -0

Which of the following numbers is divisible by 12?

A
50978

B
4284

C
101954

D
101956

Solution

4284 - On adding the digits, we get 4 + 2 + 8 + 4 = 18 (divisible by 3).
As 4284 is divisible by both 4 and 3, so it is divisible by 12.
Question 2
4 / -0

A, B and C brought mangoes in the ratio 5 : 3 : 2. If the difference between number of mangoes with A and C is 60, then find the difference between the number of mangoes with B and C.

A
20

B
30

C
40

D
50

Solution

Let the respective number of mangoes brought by A, B and C be 5x, 3x and 2x.
Now, 5x - 2x = 60
⇒ x = 20
Now, share of B = 60 and share of C = 40
Therefore, the required difference = 60 - 40 = 20
Question 3
4 / -0

A positive integer, when multiplied by 12 gives a number, which is 1 less than the square of 7. Find the value of that positive integer.

A
2

B
4

C
6

D
8

Solution

First of all, square of 7
= 7²
= 49
According to the question,
⇒49 - 1 = 48
Le thr required number be x.
x × 12 = 48
x = 48/12 = 4
Positive integer = 4
Question 4
4 / -0

100^2.5 : 16² is the same as

A
3125 : 32

B
625 : 16

C
625 : 8

D
3125 : 8

Solution

100^2.5: 16²

= (10)²^×^2.5 : 2⁸

= 10⁵ : 2⁸

= 5⁵ : 2³

= 3125 : 8
Question 5
4 / -0

The diagonal of a square is equal to the side of an equilateral triangle. If the area of the square is 15√3 sq. cm, then what is the area of the equilateral triangle?

A
45/√2 sq. cm

B
45√2 sq. cm

C
45 sq. cm

D
45/2 sq. cm

Solution

Let side of square = a cm
Diagonal of square = a√2 cm
Area of square = a²sq. cm
A.T.Q.,
a² = 15√3
Also, side of equilateral triangle = a√2 cm
Area of equilateral triangle = (√3/4)(Side)²sq. cm
= (√3/4)(a√2)² sq. cm
= (√3/2)a²sq. cm
= (√3/2)15√3 sq. cm
= 45/2 sq. cm
Question 6
4 / -0

In a box, there are 5 red, 9 green and 6 black balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

A
1/4

B
3/7

C
7/10

D
3/10

Solution

Total number of balls = 5 + 9 + 6 = 20
E = event that the ball drawn is neither red nor green = event that the ball drawn is black = 6
Therefore, P(E) = 6/20 = 3/10
Question 7
4 / -0

What is the smallest number which when multiplied by 1944 will make it a perfect square?

A
2

B
3

C
6

D
8

Solution

1944 = 2³ × 3⁵
So, to make it a perfect square, we have to multiply it with 2 × 3 = 6.
Question 8
4 / -0

Which of the following will be the smallest number to be multiplied with 134456 to make it a perfect cube?

A
7

B
8

C
4

D
17

Solution

134456 = 2 x 2 x 2 x 7 x 7 x 7 x 7 x 7
So, we will multiply it by 7 to make a perfect cube.
Question 9
4 / -0

A person buys several fruits at the rate of 16 for Rs. 24 and sells them at the rate of 8 for Rs. 18. What is his gain percent?

A
50%

B
60%

C
40%

D
25%

Solution

Cost price of 16 fruits = Rs. 24 … (i)
Sale price of 8 fruits = Rs. 18 … (ii)
∴ Sale price of 16 fruits = Rs. 36 … (iii)
Thus, required gain percent = 36 – 24 / 24× 100% = 50%
Question 10
4 / -0

A watch was sold at a loss of 10 percent. If it was sold for $70 more, there would have been a gain of 4 percent. What was the CP of the watch?

A
$475

B
$500

C
$550

D
$600

Solution

Let the cost price of the watch is $x.
Selling Price = 0.9x$
New Selling Price = 0.9x + 70
New gain = 4% of x = 0.04x
According to the question,
0.9x + 70 - x = 0.04x
0.14x = 70
x = $500
Question 11
4 / -0

Ten men can clean 2 acres of a field in 12 days. How many men can clean 3 acres of the field in 6 days?

A
30 men

B
32 men

C
31 men

D
24 men

Solution

By using the formula M₁× D₁/W₁ = M₂ × D₂/W₂, we get
10 × 12/2 = M₂ × 6/3
⇒ M₂ = 30
Question 12
4 / -0

A boy goes to school at a speed of 3 km/hr and returns to his village at a speed of 2 km/hr. If he takes 5 hours in all, then the distance between the village and the school is

A
6 km

B
7 km

C
8 km

D
9 km

Solution

Let the distance between the village and the school be x km.
∴ Time taken to go to school = x/3 hr
Time taken to come back to village = x/2 hr
According to the question,
x/3 + x/2 = 5
2x + 3x = 30
5x = 30
x = 6 km
Question 13
4 / -0

Simplify 10.2 × 9.8.

A
88.96

B
96.96

C
99.96

D
100

Solution

10.2 × 9.8 can also be written as: (10 + 0.2)(10 - 0.2)
Using (a - b)(a + b) = a²- b², we get
10.2 × 9.8 = (10 - 0.2)(10 + 0.2) = 10² - 0.2² = 100 - 0.04 = 99.96
Question 14
4 / -0

Given 33698267 = 6859 x 4913, what is the cube root of 33698267?

A
323

B
391

C
437

D
357

Solution

33698267 = 6859 × 4913
Cube root of 33698267 = (Cube root of 6859) x (Cube root of 4913) = 19 × 17 = 323
Question 15
4 / -0

Which of the following numbers is definitely not a perfect square?

A
960400

B
23235722

C
23338561

D
1046529

Solution

If a number is a perfect square, it must end with 0, 1, 4, 9, 6 or 5.
23235722 ends with 2.
So, 23235722 can never be a perfect square.
Question 16
4 / -0

Adam and Benjamin have ratio of their ages as 3 : 4. Their father observes their growth and predicts that ratio of their ages after 20 years will become 7 : 8. What is the present age of Adam?

A
10 years

B
15 years

C
25 years

D
30 years

Solution

Assume, present age of Adam = 3p years and present age of Benjamin = 4p years
Now, according to the question,
(3p + 20)/(4p + 20) = 7/8
Or, 8(3p + 20) = 7(4p + 20)
Or, 24p + 160 = 28p + 140
Or, 4p = 20
Or, p = 5
So, present age of Adam = 3p years = 15 years
Question 17
4 / -0

What must be added to 16y²- 4y + 8 to get 6y² - 2y - 4?

A
-10y² + 2y - 12

B
-10y² + 4y - 12

C
-10y² + 4y + 4

D
10y² - 2y + 44

Solution

Let the term added be 'a'.
16y²- 4y + 8 + a = 6y²- 2y - 4
⇒ a = 6y²- 2y - 4 - (16y²- 4y + 8)
⇒ a = 6y²- 2y - 4 - 16y²+ 4y - 8
⇒ a = -10y²+ 2y - 12
Question 18
4 / -0

Find the value of 'X' in 2 × 8X + 15 – 4(2 + 3) × 8 = 63.

A
13

B
9

C
–0.48

D
-23.56

Solution

2 × 8X + 15 – 4(2 + 3) × 8 = 63
16X + 15 – 4(5) × 8 = 63
16X + 15 – 20 × 8 = 63
16X + 15 – 160 = 63
16X = 63 + 160 – 15
16X = 208
X = 13
Question 19
4 / -0

The base radius and volume of a right circular cylinder are 3 m and 198 m³, respectively. What is its height?

A
10.5 m

B
7 m

C
21 m

D
√21 m

Solution

Volume of a cylinder = πr²h …………. (1)
Where,
π = 22/7
r = base radius of the cylinder
h = height of the cylinder
Given: Volume of the cylinder = 198 m³
Radius of the cylinder = 3 m
Height of the cylinder = ?
Thus, 198= π(3)²h
198 = 22/7 × 9 × h [∵ (3)² = 3 × 3 = 9]
h = 7 m
Question 20
4 / -0

The average of five distinct numbers is 25. When five new numbers are added, the average increases by 5. What is the average of the five numbers that are added?

A
28

B
30

C
32

D
35

Solution

Sum of 5 numbers = 5 × 25 = 125
When 5 numbers are added, new sum = 30 × 10 = 300
Sum of the 5 new numbers = Total sum of 5 new numbers = 300 - 125 = 175
Average of these 5 numbers = 175/5 = 35
Question 21
4 / -0

A cuboid having sides 225 cm, 125 cm and 120 cm is melted into a cube. Find the edge of the cube.

A
140 cm

B
160 cm

C
150 cm

D
170 cm

Solution

Volume of the cuboid = Volume of the cube
225 × 125 × 120 = Volume of the cube = a³
3375000 = a³
a = 150 cm
Therefore, edge of the cube = 150 cm
Question 22
4 / -0

In a polygon, the measure of each interior angle is 3 times the measure of an exterior angle. How many sides does this polygon have?

A
4

B
6

C
8

D
10

Solution

Let the measure of exterior angle be x and the number of sides be n.
Measure of interior angle = 3x
x + 3x = 180°
4x = 180°
x = 180º / 4= 45°
Measure of exterior angle = 45°
Measure of interior angle = 3 x 45° = 135°
135°n = Sum
Also, sum = (n - 2) x 180°
135°n = 180°n - 360°
360° = 180°n - 135°n
Or n = 360 / 45 = 8
Question 23
4 / -0

Simplify: 24 - 16 ÷ 2 - {32 of (-2) + (6 × 5 - 4)}

A
26

B
36

C
54

D
72

Solution

First solve the brackets using BODMAS.
32 of (-2)
32 × (-2) =-64
Also, 6 × 5 - 4 =30 - 4 = 26
So, {-64 + 26} = (-38)
Now, 16 ÷ 2 = 8
∴ 24 - 8 - {-38} = 24 - 8 + 38 = 54
Question 24
4 / -0

If the number 23x4534x01 is divisible by 11, then how many values can x be substituted with?

A
1

B
4

C
9

D
10

Solution

Sum of the digits at even places = 11 + x
Sum of the digits at odd places = 11 + x
Difference is 0.
i.e. The given number is divisible by 11, irrespective of the value of x.
So, x can be anything from 0 to 9.
Thus, x can be substituted with 10 values.
Question 25
4 / -0

The area of a trapezium is 180 cm² and its height is 12 cm. If one of the parallel sides is double the other, find the length of the two parallel sides.

A
30 cm, 60 cm

B
40 cm, 80 cm

C
20 cm, 40 cm

D
10 cm, 20 cm

Solution

Area = 180 cm²
Height, h = 12 cm
Let one parallel side be a.
Other parallel side, b = 2a.
Area = 1/2 × (a + b) × h
180 = 1/2 × (3a) 1/2 ×12
3a = 30
a = 10 cm
b = 2 × 10 = 20 cm
Question 26
4 / -0

If the volume of a cube is (12)³ m³, then the total surface area of the cube is equal to

A
144 m²

B
576 m²

C
432 m²

D
864 m²

Solution

Volume of a cube = a³, where 'a' is the edge of the cube.
Given, volume of the cube = (12)³ m³
a³ = (12)³ m³
Taking cube root, we get
a = 12 m
Now, total surface area of the cube = 6a²
= 6(12)²
= 6 × 12 × 12
= 6 × 144
= 864 m²
Question 27
4 / -0

If 15 workers can build a wall in 48 hours, then how many workers will be required to build the same wall in 24 hours?

A
15

B
18

C
20

D
30

Solution

Number of workers Time taken to complete the task (in hours)

15 48

W 24

It is a case of inverse proportion.
∴ x₁y₁ = x₂y₂
15 ×48 = W × 24
Or W = 15 × 48 / 24 = 30
Question 28
4 / -0

Find the value of the integer, which when multiplied by 21 gives the product -294.

A
-11

B
-14

C
-17

D
-19

Solution

Suppose the number is y.
21 × y = -294
So, y = - 294 / 21
= -14
So, the required number is -14.

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Number of workers	Time taken to complete the task (in hours)
15	48
W	24

Mathematics (Paper-1) Mock Test - 4

Result

Mathematics (Paper-1) Mock Test - 4

Score

-

Rank

-

SHARING IS CARING

Question 1

50978

4284

101954

101956

Solution

Question 2

20

30

40

50

Solution

Question 3

2

4

6

8

Solution

Question 4

3125 : 32

625 : 16

625 : 8

3125 : 8

Solution

Question 5

45/√2 sq. cm

45√2 sq. cm

45 sq. cm

45/2 sq. cm

Solution

Question 6

1/4

3/7

7/10

3/10

Solution

Question 7

2

3

6

8

Solution

Question 8

7

8

4

17

Solution

Question 9

50%

60%

40%

25%

Solution

Question 10

$475

$500

$550

$600

Solution

Question 11

30 men

32 men

31 men

24 men

Solution

Question 12

6 km

7 km

8 km

9 km

Solution

-10y² + 2y - 12

-10y² + 4y - 12

-10y² + 4y + 4

10y² - 2y + 44