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

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Mathematics (Paper-1) Mock Test - 3

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Weekly Quiz Competition

Question 1
4 / -0

If 81466x is divisible by 9, then find the value of x.

A
7

B
9

C
2

D
4

Solution

8 + 1 + 4 + 6 + 6 + x = 25 + x
For 81466x to be divisible by 9, the sum of all its digits should also be divisible by 9.
∴ 25 + x should be equal to 27.
⇒ x = 27 – 25 = 2
Question 2
4 / -0

16 friends went on a trip. Each one brought a chocolate for the trip. Each children ate (5/8)^thof the chocolate they had. How many chocolates were eaten in all?

A
8

B
9

C
10

D
11

Solution

Fraction of chocolate eaten by each friend =5/8
Number of friends = 16
Therefore, total number of chocolate eaten = 16 × 5/8 = 10
Question 3
4 / -0

Which of the following fractions is the smallest?

A
17/21

B
23/3

C
18/7

D
42/9

Solution

17/21 is less than 1.

23/3 is approximately 8.

18/7 is between 2 and 3.

42/9 is between 4 and 5.

So, 17/21 is the smallest.
Question 4
4 / -0

Amy is sharing his toys among three orphanage houses A, B and C. The toys are divided in a ratio 2 : 3 : 5. If C has got 150 toys, then how many total toys were there?

A
450

B
400

C
300

D
290

Solution

Let the number of toys received by A, B and C be 2x, 3x, 5x respectively.
Given that C has got 150.
Therefore, 5x = 150
or, x =150/5
or, x = 30
So, A got = 2x = Rs. 2 × 30 = 60
B got = 3x = 3 × 60 = 90
Therefore, total amount (60 + 90 + 150) = 300
Question 5
4 / -0

5/7 of x = 4/8 of y, then x : y is

A
1 : 2

B
7 : 10

C
10 : 7

D
2 : 1

Solution

5/7 x = 4/8 y
⇒ x/y = 28/40 = 7/10
Question 6
4 / -0

The sum of digits of a two-digit number is 12. If the units digit is one-half the tens digit, find the two-digit number.

A
66

B
48

C
39

D
84

Solution

Let the digit at one's place be 'x' and the digit at tens place be 'y'.

x + y = 12

ATQ,

2x = y

Therefore, x + 2x =12
3x =12
x = 4

and y = 8

So, the required number is 84.
Question 7
4 / -0

A positive number is 5 times the other number. If 21 is added to both the numbers, then greater of the two numbers becomes twice the smaller number. What are the numbers?

A
5 and 25

B
7 and 35

C
6 and 30

D
8 and 40

Solution

Let one number be x.
Other number = 5x
Adding 21 to both numbers, they become x + 21 and 5x + 21, respectively.
According to the question, we have
5x + 21 = 2(x + 21) (As 5x + 21 is greater)
5x + 21 = 2x + 42
⇒ 5x - 2x = 42 - 21
⇒ 3x = 21
⇒ x = 21/3 = 7
Numbers are 7 and 35.
Question 8
4 / -0

The mean of 20 observations is p. If each observation is multiplied by 3 and then 1 is added to it, the new mean obtained will be

A
3p + 20

B
p + 20

C
3p + 1

D
3(p + 1)

Solution

Mean of 20 observations is p.
So, sum of the observations will be 20p.
When each observation is multiplied by 3, the mean will become (3 x 20p)/20
When 1 is added to each observation, new mean will be (20 + 60p)/20
So, new mean obtained after multiplying each observation by 3 and adding 1 to it = (20 + 60p)/20 = 3p + 1.
Question 9
4 / -0

One card is drawn from a deck of 52 cards. The probability of drawing a card of club is

A
1/52

B
1/26

C
1/4

D
1/13

Solution

Total number of cases = 52
Total number of favourable cases = 13 (As there are total 13 cards of club)
Required probability = 13/52 = 1/4
Question 10
4 / -0

In a trapezium, the shortest distance between the two parallel sides is 30 m and its area is 900 sq. m. If the ratio between the lengths of the parallel sides of the trapezium is 3 : 2, then find the sum of the lengths of the parallel sides.

A
45 m

B
60 m

C
70 m

D
85 m

Solution

Given: Area of the trapezium = 900 m2
Height = 30 m
We know,
Area of trapezium = 1/2 (sum of parallel sides) × height
Let the sum of parallel sides be 'x'.
900 = 1/2 × x × 30
x = 60 m
Question 11
4 / -0

Which among the following can definitely not be a square number?

A
9409

B
13225

C
14641

D
18747

Solution

We know that the square numbers always end with digits 0, 1, 4, 5, 6, 9.
So, from looking at the units digits in the options, we can say that 18747 can definitely not be a square number.
Question 12
4 / -0

Which of the following numbers is the same as √1225 × √625 ?

A
775

B
875

C
975

D
1000

Solution

(1225)^1/2 × (625)^1/2
(35 × 35)^1/2 × (25 × 25)^1/2
= 35 × 25
= 875
Question 13
4 / -0

Simplify 77.2² - 22.8².

A
5600

B
5555

C
5400

D
5440

Solution

Using (a - b)(a + b) = a² - b², we can do
77.2²- 22.8² = (77.2 + 22.8)(77.2 - 22.8)
77.2²- 22.8² = (100)(54.4)
= 5440
Question 14
4 / -0

The lid of a square box of side 40 cm is sealed all round with the tape. What is the length of the tape required if the lid is sealed 4 times?

A
540 cm

B
640 cm

C
160 cm

D
120 cm

Solution

Length of tape required = 4(perimeter of the lid) = 4(4 × 40) = 640 cm
Question 15
4 / -0

What is the smallest number by which 8712 must be divided, so that the quotient obtained is a perfect cube?

A
33

B
11

C
1089

D
2424

Solution

8712 = 2 × 2 × 2 × 3 × 3 × 11 × 11
3 and 11 are not grouped as triplets.
So, the smallest number is 3 × 3 × 11 × 11 = 1089.
Question 16
4 / -0

If 895768 = 1331 × 1728, what is the cube root of 895768?

A
132

B
82

C
152

D
92

Solution

We know that the cube root of 1331 = 11
And the cube root of 1728 = 12
So, the cube root of 895768 = 11 × 12 = 132
Question 17
4 / -0

A principal of Rs. 1200 amounted to Rs. 1600 in 2.5 years at a simple interest. If the rate of interest is increased by 3%, what is the new amount?

A
Rs. 1650

B
Rs. 1682

C
Rs. 1690

D
Rs. 1700

Solution

If we increase the rate of interest that means we get some extra money on the principal as simple interest.
So, now we calculate the extra SI = P × R × T/100
SI = 1200 × 3 × 2.5/100 = 90
So, the new amount = 1600 + 90 = Rs. 1690
Question 18
4 / -0

Find the number of tiles, each measuring 25 cm by 6 cm, which can cover a wall of dimensions 12 m by 8 m.

A
6400

B
9800

C
8000

D
7200

Solution

Area of a tile = 25 × 6 = 150 cm²
Area of the wall (in cm) = 1200 × 800 = 9,60,000 cm²
Number of tiles required = 9,60,000 ÷ 150
= 6400
Question 19
4 / -0

By selling a doll at $342, Mac lost 5%. At what price should he have sold it to gain 5%?

A
$378

B
$380

C
$410

D
$462

Solution

Let CP of the doll = $x
According to the question,
$342 = 0.95x, so, x = 360.
Hence, CP of the doll = $360
To gain 5%, SP = 1.05 of 360 = $378
Question 20
4 / -0

If the cost price is 130% of the selling price, what is the loss percentage?

A
30%

B
34%

C
23%

D
36%

Solution

Let SP = x
CP = 1.3x
Loss percent = [(CP - SP)/CP] × 100 = [0.3x/1.3] ×100 = 23%
Question 21
4 / -0

In a hostel of 50 girls, there are food provisions for 80 days. If 30 more girls join the hostel, how long will these provisions last?

A
128 days

B
50 days

C
55 days

D
80 days

Solution

Number of Girls Days

50 80

80 t

It is inverse proportion.
x₁y₁ = x₂y₂
50 × 80 = 80 × t
Or t = 50×80 / 80 = 50 days
Question 22
4 / -0

15 men complete a piece of work in 16 days. If 24 men are employed, then the time required to complete that work will be

A
7 days

B
8 days

C
10 days

D
12 days

Solution

Let 1 man complete 1 unit work in 1 day.
Then, the total work = 15 x 16 = 240 units
Then, the time taken by 24 men to complete the same work = 240/24 days = 10 days
Question 23
4 / -0

A man is running in a square park whose side is 25m. His speed is 3 km/hr. How much time will he take to complete 20 rounds?

A
40 hrs

B
42 hrs

C
36 hrs

D
46 hrs

Solution

Speed = 3 km/hr = 3 × (5/18) m/s = 5/6 m/s
Distance covered = (20 x (4 x 25))
= 2000 m
Time taken = Distance / Speed = 2000 × 6/5 = 2400 min = 40 hrs
Question 24
4 / -0

5(2x + 1) + 5(4x - 3) = 7(5x + 2) - 9(5x + 1) + 10x

A
2

B
1/3

C
6

D
1/2

Solution

We have,
5(2x + 1) + 5(4x - 3) = 7(5x + 2) - 9(5x + 1) + 10x
10x + 5 + 20x - 15 = 35x + 14 - 45x - 9 + 10x
10x + 20x - 35x + 45x - 10x = 14 - 9 + 15 - 5
30x = 15
x = 1/2
Question 25
4 / -0

What will be the sum of the smallest and greatest angles of the quadrilateral, if it's angles are in the ratio of 2 : 3 : 3 : 4?

A
150°

B
160°

C
170°

D
180°

Solution

Let the angles be 2x, 3x, 3x, 4x.
Sum of the angles of a quadrilateral = 360°
2x + 3x + 3x + 4x = 360°
12x = 360°
x = 30°
Required sum of angles = 2x + 4x = 6x = 6(30°) = 180°
Question 26
4 / -0

If 2/5 of a number is 15 less than the original number, then the number is

A
22

B
24

C
25

D
21

Solution

Let the original number be x.
According to the question,
x = 2/5x + 15
3x / 5 = 15
x = 25
Question 27
4 / -0

The median of set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set

A
is increased by 2

B
is decreased by 2

C
is two times the original median

D
remains the same as that of the original set

Solution

Let 9 observations arranged in ascending order be a, b, c, d, e, f, g, h and i.
Its median is e.
If the largest 4 observations is increased by 2 then, the arrangement is a, b, c, d, e, f + 2, g + 2, h + 2 and i + 2.
Now, the new median again is e.
So, the median remains the same as that of the original set.
Question 28
4 / -0

The volume of a cubical box is 59.319 cu. cm. Find the length of each side of the box.

A
3.7 cm

B
3.8 cm

C
3.9 cm

D
4.1 cm

Solution

Volume of cube = Side³
Side³= 59.319 cu.cm.

59319 is in between the 27000 and 64000
Cube root of 59319 is in between the 30 and 40.
The unit digit of 59319 is 9, It only come when cube root is also have unit digit 9.
Cube root of 59319 is 39.
And cube root of 59.319 is 3.9

Side = 3.9 cm.
Question 29
4 / -0

The volume of a cuboid is 37.5 m³_. The length of the cuboid is 10 times the breadth and its height is 30 times the breadth. Find the breadth of the cuboid.

A
5 cm

B
0.5 cm

C
50 cm

D
10 cm

Solution

Let the breadth = x m
Length = 10x m
Height = 30x m
Volume of the cuboid = 37.5 m³
x × 10x × 30x = 37.5
300x³ = 37.5
x = 5/10 m = 50 cm

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Mathematics (Paper-1) Mock Test - 3

Result

Mathematics (Paper-1) Mock Test - 3

Score

-

Rank

-

SHARING IS CARING

Question 1

7

9

2

4

Solution

Question 2

8

9

10

11

Solution

Question 3

17/21

23/3

18/7

42/9

Solution

Question 4

450

400

300

290

Solution

Question 5

1 : 2

7 : 10

10 : 7

2 : 1

Solution

Question 6

66

48

39

84

Solution

Question 7

5 and 25

7 and 35

6 and 30

8 and 40

Solution

Question 8

3p + 20

p + 20

3p + 1

3(p + 1)

Solution

Question 9

1/52

1/26

1/4

1/13

Solution

Question 10

45 m

60 m

70 m

85 m

Solution

Question 11

9409

13225

14641

18747

Solution

Question 12

775

875

975

1000

Solution