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

Result

Mathematics (Paper-1) Mock Test - 1

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
4 / -0

If z denotes a digit in the given number 789z45, such that the number is divisible by 3, then what can be the value of z?

A
0

B
1

C
2

D
5

Solution

Given that 789z45 is a multiple of 3.
So, (7 + 8 + 9 + z + 4 + 5) is a multiple of 3, or (z + 33) is a multiple of 3.
So, z could be 0, 3 , 6 and 9.
From the options we can say z can be 0.
Question 2
4 / -0

(2³ + 6) : 4²is same as

A
7 : 6

B
6 : 7

C
7 : 8

D
8 : 7

Solution

2³ + 6 : 4²
= (8 + 6) : 4²
= 14 : 16
= 7 : 8
Question 3
4 / -0

Find the simplified form of (x² – 3)(x + 3) + 9.

A
– x(x² + 3x + 3)

B
– x(x² + 3x – 3)

C
x(x² + 3x – 3)

D
x(x² + 3x + 3)

Solution

(x² – 3) (x + 3) + 9
= x³ + 3x² – 3x – 9 + 9
= x³ + 3x² – 3x
= x(x² + 3x – 3)
Question 4
4 / -0

The mean consumption of petrol of a group of 20 cars is 65 litres. 2 other cars with consumption as 89 litres and 85 litres, respectively were added to the group. What is the new mean consumption for the group of cars?

A
68

B
67

C
69

D
70

Solution

Total consumption of petrol = Mean × Number of cars

Total consumption of petrol of the original group = 65 × 20 = 1300

Total consumption of petrol of the new group = Total consumption of petrol of the original group + Consumption of petrol of the 2 new cars
= 1300 + 89 + 85 = 1474

Number of cars in the new group = Number of cars in the original group + Number of cars from the new data
= 20 + 2 = 22
New average consumption = 1474 / 22= 67 litres
Question 5
4 / -0

A dice is rolled and a coin is tossed. What is the probability of getting heads and an even number?

A
1/6

B
1/2

C
1/4

D
3/4

Solution

Possible outcomes are {(1, H), (2, H), (3, H), (4, H), (5, H), (6, H), (1, T), (2, T), (3, T), (4, T), (5, T), (6, T)}
Favourable outcomes = {(2, H), (4, H), (6, H)}
Hence, required probability = Number of favourable outcomes/Total number of outcomes
Required Probability = 3/12 = 1/4
Question 6
4 / -0

What will be the value of 56² - 14²?

A
2940

B
2940

C
3670

D
4520

Solution

We know
a² - b² = (a + b) (a - b)
Here, a = 56 and b = 14
So, 56² - 14²
= (56 + 14)(56 - 14)
= (70) × (42) = 2940
Question 7
4 / -0

Which of the following is a perfect cube?

A
216000

B
625000

C
2000

D
172800

Solution

216000 is a perfect cube because 216000 = 6 x 6 x 6 x 10 x 10 x 10, which means 216000 is a cube of 60.
Question 8
4 / -0

A batch of troopers was in a camp for 1 month and 20 days from 1^st June. There was enough food for 70 troopers, but 10 of them left after 20^th day. How long will the food last, if they consume food at the same rate?

A
50 days

B
55 days

C
65 days

D
75 days

Solution

1 month and 20 days = 50 days
Number of troopers after 20^th day = (70 - 10) = 60

70 troopers and food for 50 days.
One trooper had food for (70 × 50) days.

So, we have 70 × 50 = 70 × 20 + 60 × x
70 × 30 = 60 × x
x = 35

Total number of days food will last = 20 + 35 = 55 days
Question 9
4 / -0

Mohak is travelling from one part of Toronto to another, which is 30 km away. He began his journey in a metro at the speed of 50 km/h and covered half of the distance. Then, he covered the rest of the distance in a local bus at a speed of 20 km/h. How much time did he take to reach from one part of Toronto to another?

A
0.45 hours

B
0.75 hours

C
1.05 hour

D
1.20 hours

Solution

As you know, time = Distance / Speed
Total time = Time in metro + Time in local bus
By substituting the values in the formula, we get (15 / 50) + (15 / 20)
or, 0.30 + 0.75 = 1.05
Mohak took 1.05 hours to finish his journey.
Question 10
4 / -0

How many 2-digit numbers are possible such that the sum of their digits is equal to twice the difference between the digits?

A
2

B
3

C
6

D
11

Solution

Let xy be the number.
x + y = 2(x - y) or x + y = 2(y - x)
⇒ x = 3y or y = 3x
So, different numbers are 31, 62, 93, 13, 26 and 39.
Therefore, 6 different numbers are possible.
Question 11
4 / -0

If 0.48 + 1(8a + 3) = 0.96(0.5 + 9a), then a is equal to

A
-0.46875

B
4.6875

C
-0.046875

D
0.46875

Solution

0.48 + 1(8a + 3) = 0.96(0.5 + 9a)

0.48 + 8a + 3 = 0.48 + 8.64a

8a - 8.64a = - 3

-0.64a = -3

a = 4.6875
Question 12
4 / -0

A person has a rope and he wants to make a square from that rope. The square that he makes using the rope has an area of 225 m². Find the length of the rope.

A
40 cm

B
25 cm

C
20 cm

D
60 cm

Solution

Area = side²
225 = side²
Side = (225)^1/2
= 15 m
Length of rope = Perimeter of square
Perimeter = 4 × Side
= 4 × 15
= 60 cm
Question 13
4 / -0

The perpendicular distance between the parallel sides of a trapezium is 15 cm. If the area of the trapezium is 495 cm², then find the length of the larger of parallel sides, if they are in ratio of 6 : 5.

A
18 cm

B
24 cm

C
48 cm

D
36 cm

Solution

Let us say length of parallel sides is 5x and 6x.
So, sum of length of parallel sides = 5x + 6x = 11x cm
Perpendicular distance between two sides = 15 cm
Area (A) = 495 cm²
Area of trapezium = (1/2) × (Sum of lengths of parallel sides) × (Perpendicular distance between parallel sides)
So, 495 = (1/2) × (11x) × 15
165x = 990
x = 6
So, parallel sides = 5x = 5 × 6 = 30 cm
6x = 6 × 6 = 36 cm
Larger side = 36 cm
Question 14
4 / -0

Which of the following least numbers must be added to 621 to make it a perfect square?

A
1

B
4

C
5

D
3

Solution

Perfect square closer to 621 = 625
Given number = 621
Therefore, least number must be added = 625 – 621 = 4
Question 15
4 / -0

A person is filling fuel in the car. The tank of the car is in the form of a cylinder. If height of tank is 80 cm and diameter is 84 cm, then calculate the fuel that a person can fill in that car.

A
44.12 litres

B
443.52 litres

C
4435.20 litres

D
444.52 litres

Solution

To find the capacity of the cylindrical tank, we would find its volume.
Volume of the cylinder = πr²h (where r = Radius of cylinder and h = Height of cylinder)
Given diameter = 84, radius (r) = (84/2) = 42 cm
Volume = (22/7) × 42²× 80 = 4,43,520 cm³= 0.443520 m³
Now, 1 m³ = 1000 L
Thus, 0.443520 m³ = 0.443520 × 1000 = 443.52 litres
Question 16
4 / -0

By what least number should 13718 be divided to get a perfect cube?

A
3

B
19

C
5

D
2

Solution

Given number is 13718.
13718 = 2 × 19 × 19 × 19
Least number that should be divided from 13718 to get a perfect cube = 2
Question 17
4 / -0

A sold a watch to B at a gain of 5% and B sold it to C at a gain of 4%. If C paid Rs. 1,092 for it, the price paid by A is

A
Rs. 993.72

B
Rs. 996

C
Rs. 1,000

D
Rs. 995.90

Solution

Given: C paid Rs. 1,092.
Let the sum paid by A be Rs. X.
Then, amount paid by B to A = Rs. 1.05X
Amount paid by C to B = 1.04 × 1.05X = Rs. 1,092
⇒X = Rs. 1,000
Short Cut method:
From options:
Suppose A paid Rs. 1,000.
Then, B paid to A = 1,000 × 5/100 + 1,000 = Rs. 1,050
Moreover, C paid to B = 1,050 + (1050 × 4/100) = Rs. 1092
It satisfies the given condition.
Question 18
4 / -0

Adolf can do a task in 15 days, but Beggie can do the same task in 25 days. Both started working together, but after 6 days, Adolf left. In how many days will Beggie complete the remaining task?

A
27

B
9

C
17

D
25

Solution

Adolf does 1/15 of work in a day.
Beggie does 1/25 of work in a day.
When they work together, total work will be done in a day
= 1/15 + 1/25 = 8/75
So, in 6 days, total work will be done by them = 8 / 75 × 6 = 48 / 75
Let the amount of work done left be 'x'.
48/75 + x = 1
x = 1 - 48/75
x = (75 - 48) / 75 = 27 / 75
x = 9/25
So, the remaining task will be completed by Beggie in 25 × (9/25) = 9 days.
Question 19
4 / -0

There are 96 square tiles which make up the floor of the hall in a wedding palace. If the perimeter of each tile is 8 m, what is the area of the floor of the hall?

A
356 m²

B
372 m²

C
384 m²

D
392 m²

Solution

Perimeter of each square tile = side x number of sides
8 = side x 4
8 ÷ 4 = side
side = 2 m
Area of each tile = side²
= 2²
= 4 m²
Area of 96 tiles on the floor = 4 x 96
= 384 m²
Question 20
4 / -0

Find the number of small cubes of 100 cm edge that can be cut out from a cube of 5 m edge.

A
150

B
100

C
225

D
125

Solution

Side of bigger cube = 5 m
Side of smaller cube = 100 cm = 1 m
Then, number of small cubes = Volume of big cube/Volume of small cube = (5 × 5 × 5)/(1 × 1 × 1) = 125 cubes
Question 21
4 / -0

Ella is trying to find the volume of a cuboid whose edges are in ratio of 2 : 3 : 4. Find the volume of the cuboid, if the surface area is 1300 cm².

A
1000 cm³

B
2000 cm³

C
3000 cm³

D
6000 cm³

Solution

Ratio of edges of cuboid = 2 : 3 : 4
Let l = 4x, b = 3x and h = 2x
Surface area = 1300 cm²
2(lb + bh + hl) = 1300
2(12x² + 6x² + 8x²) = 1300
(12x² + 6x² + 8x²) = 650
26x² = 650
x² = 25
x = 5
∴ l = 20 cm, b = 15 cm and h = 10 cm
∴ Volume = lbh
= 20 × 15 × 10 = 3000 cm³
Question 22
4 / -0

A cyclist started with a speed of 30 km/hr in a race. After every lap of one hour each, he increased his speed by 5 km/h. In how many laps will he cover 450 km?

A
8

B
9

C
10

D
11

Solution

According to question, a cyclist started with a speed of 30 km/hr in a race and after every lap, he increased his speed by 5 km/h.
So, 30 + 35 + 40 + 45 + 50 + 55 + 60 + 65 + 70 = 450 km
It means there are 9 laps in which he will cover 450 km.
Question 23
4 / -0

The average of 21 results is 54. If the average of the first 11 results is 51 and that of the last 11 is 57, find the 11^th result.

A
48

B
50

C
54

D
56

Solution

Average of 21 results = 54
Total of 21 results = 54 x 21 = 1134
Average of the first 11 results = 51
Total of the first 11 results = 51 x 11 = 561
Average of the last 11 results = 57
Total of the last 11 results = 57 x 11 = 627
Therefore, 11^th result = 561 + 627 - 1134 = 1188 - 1134 = 54
Question 24
4 / -0

What will be the value of (z + 2)(z² + 2)(z - 4)?

A
z⁴ - 2z³ - 10z² - 4z - 16

B
z⁴ - 2z³ - 6z² - 4z - 18

C
z⁴ - 2z³ - 6z² - 4z - 16

D
z² + 1

Solution

(z + 2)(z²+ 2)(z - 4)

= (z(z²+ 2) + 2(z² + 2))(z - 4)

= (z³ + 2z² + 2z + 4) (z - 4)

= z(z³ + 2z² + 2z + 4) - 4(z³ + 2z² + 2z + 4)

= z⁴ + 2z³ + 2z² + 4z - 4z³ - 8z² - 8z - 16

= z⁴ - 2z³ - 6z² - 4z - 16
Question 25
4 / -0

What is the value of 9x - 52 + x²?

A
(x - 4)(x + 13)

B
(4 + x)(13 + x)

C
(4 + x)(13 - x)

D
(4 - x)(13 - x)

Solution

9x - 52 + x²
= x²+ 13x - 4x - 52
= x(x + 13) - 4(x + 13)
= (x - 4)(x + 13)
Question 26
4 / -0

If (x + y + z) = 5 and xy + yz + xz = 8, then what is the value of x²+ y²+ z²?

A
6

B
7

C
8

D
9

Solution

As we know,
(x + y + z)² = x²+ y²+ z²+ 2(xy + yz + xz)
(5)²= x²+ y²+ z²+ 2(8)
x²+ y²+ z²= 25 - 16 = 9

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Mathematics (Paper-1) Mock Test - 1

Result

Mathematics (Paper-1) Mock Test - 1

Score

-

Rank

-

SHARING IS CARING

Question 1

0

1

2

5

Solution

Question 2

7 : 6

6 : 7

7 : 8

8 : 7

Solution

Question 3

– x(x2 + 3x + 3)

– x(x2 + 3x – 3)

x(x2 + 3x – 3)

x(x2 + 3x + 3)

Solution

Question 4

68

67

69

70

Solution

Question 5

1/6

1/2

1/4

3/4

Solution

Question 6

2940

2940

3670

4520

Solution

Question 7

216000

625000

2000

172800

Solution

Question 8

50 days

55 days

65 days

75 days

Solution

Question 9

0.45 hours

0.75 hours

1.05 hour

1.20 hours

Solution

Question 10

2

3

6

11

Solution

Question 11

-0.46875

4.6875

-0.046875

0.46875

Solution

Question 12

40 cm

25 cm

20 cm

60 cm

Solution

– x(x² + 3x + 3)

– x(x² + 3x – 3)

x(x² + 3x – 3)

x(x² + 3x + 3)

356 m²

372 m²

384 m²

392 m²

1000 cm³

2000 cm³

3000 cm³

6000 cm³

z⁴ - 2z³ - 10z² - 4z - 16

z⁴ - 2z³ - 6z² - 4z - 18

z⁴ - 2z³ - 6z² - 4z - 16