Sainik School Entrance Book Class 6 Mathematics (Paper-1) Mock Test

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Mathematics (Paper-1) Mock Test - 5

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Weekly Quiz Competition

Question 1
3 / -0

What is the smallest six-digit number that can be formed using all the digits 2, 3, 1, 2, 4, 1?

A
231241

B
123241

C
112234

D
112324

Solution

The smallest six-digit number that can be formed using all the digits 2, 3, 1, 2, 4 and 1 is 112234.
Question 2
3 / -0

What is the largest even number that can be formed using all the digits 2, 5, 6, 1, 4, 9 and 8?

A
9865412

B
9865214

C
6598214

D
9854126

Solution

9865412 is the largest even number that can be formed using the given digits. In it, the digits are arranged in order from largest to smallest, and 2 lies at the end for it to make even.
Question 3
3 / -0

Choose the option that correctly arranges the following numbers in descending order:

68129, 61892, 68291, 69812, 61982

A
69812, 68129, 68291, 61982, 61892

B
61892, 61982, 68129, 68291, 69812

C
69812, 68291, 68129, 61982, 61892

D
68129, 68291, 61892, 61982, 69812

Solution

Following is the correct descending order:

69812 > 68291 > 68129 > 61982 > 61892
Question 4
3 / -0

The sum of two numbers is 523582 and one of them is 9729. What is the second number?

A
513853

B
513854

C
513851

D
513852

Solution

One number is 9729.
Let the other number be x.
We have:
x + 9729 = 523582
x = 523582 - 9729 = 513853
Question 5
3 / -0

How many weeks are there in 1 leap year and 26 days?

A
56

B
54

C
53

D
52

Solution

Number of days in a leap year = 366
Here, total number of days = 1 leap year + 26 days = 366 + 26 = 392
Number of weeks = 392 ÷ 7 = 56
Question 6
3 / -0

Write 450 in Roman numerals.

A
IXL

B
CDL

C
DCL

D
CCXXD

Solution

450 = 400 + 50 = (500 - 100) + 50 = CDL
Question 7
3 / -0

Find the value of x from the following equation:

18 ÷ x + 18 × 18 - 18 = 307

A
9

B
16

C
18

D
4

Solution

18 ÷ x + 18 × 18 - 18 = 307
(18 ÷ x) + (18 × 18) - 18 = 307
18/x + 324 - 18 = 307
18/x + 306 = 307
18/x = 307 - 306
18 = 1 × x
Question 8
3 / -0

Arjun slept at 09:15 PM one night and woke up next morning at 06:45 AM. Find the duration of his sleep.

A
8 hours and 45 minutes

B
9 hours and 15 minutes

C
9 hours and 30 minutes

D
9 hours and 45 minutes

Solution

From 09:15 PM to 12:00 midnight, we have 2 hours and 45 minutes.
From 12:00 midnight to 6:45 AM, we have another 6 hours and 45 minutes.
Total duration of sleep = 2 hours and 45 minutes + 6 hours and 45 minutes
= 8 hours and 90 minutes
= 9 hours and 30 minutes
Question 9
3 / -0

Which of the following fractions is the greatest?

A
4/5

B
3/4

C
2/5

D
2/4

Solution

4/5 = 0.80
3/4 = 0.75
2/5 = 0.40
2/4 = 0.50
0.80 is the greatest of all.
So,4/5 is the greatest fraction out of the given options.
Question 10
3 / -0

Find the value of 15 × 71 + 72 × 8 + 7 - 72 × 7.

A
1117

B
1144

C
1163

D
None of these

Solution

15 × 71 + 72× 8 + 7 - 72 × 7

= 1065 + 576 + 7 - 504 = 1144
Question 11
3 / -0

The number that must be added to 145231 to make it equal to the difference between 564982 and 267661 is

A
151090

B
152090

C
150290

D
151300

Solution

First, let us calculate the difference between 564982 and 267661 = 564982 - 267661 = 297321
Now, 297321 - 145231 = 152090
Hence, the required number is 152090.
Question 12
3 / -0

What is the value of 2 + 10/5 + 1/1000 + 1?

A
5.001

B
5.01

C
4.001

D
3.0001

Solution

2 + 10/5 + 1/1000 + 1
Simplifying the above expression, we get:
2 + 2 + 0.001 + 1 = 5.001
Question 13
3 / -0

Which of the following pairs of angles contains complementary angles?

A
38° and 58°

B
64° and 26°

C
98° and 82°

D
95° and 35°

Solution

The angles 64° and 26° are complementary angles because they add up to 90°.
Question 14
3 / -0

The area of a square and a rectangle is the same. If the side of the square is 15 cm and the length of the rectangle is 25 cm, then find the perimeter of the rectangle.

A
60 cm

B
68 cm

C
70 cm

D
72 cm

Solution

Area of square = 15 × 15 = 225 cm²
Area of rectangle = 225 cm²
L × B = 225
25 × B = 225
B = 9 cm
Perimeter of rectangle = 2(25 + 9) = 68 cm
Question 15
3 / -0

How many cubes can be cut out of 20 cm from a cube of side 20 m?

A
1

B
10,00,000

C
225

D
1000

Solution

Side of bigger cube = 20 m
Side of smaller cubes = 20 cm = 0.2 m
Then, number of cubes = Volume of big cube/Volume of small cubes = (20 × 20 × 20)/(0.2 × 0.2 × 0.2) = 10,00,000 cubes
Question 16
3 / -0

Find the sum of the number 94867 and the number obtained by interchanging places of 4 and 6?

A
189915

B
191714

C
191522

D
201255

Solution

The number we get after interchanging places of 4 and 6 is 96847,
Then, 94867 + 96847 = 191714
Question 17
3 / -0

Mrinal leaves home at 3:45 PM one day and reaches his friend's home at 9:15 PM. The next day, he leaves his friend's home at 1:00 PM and reaches his home at 5:00 PM. Calculate the total time taken by him to go to and come back from his friend's home.

A
8 hrs and 30 min

B
9 hrs and 30 min

C
10 hrs

D
10 hrs and 30 min

Solution

3:45 PM to 9:15 PM = 5 hrs and 30 min

1:00 PM to 5:00 PM = 4 hrs

Total duration = 5 hrs and 30 min + 4 hrs = 9 hrs and 30 min
Question 18
3 / -0

A dragonfly flies at the speed of 11 cm/sec. It travels a distance of 121 cm before it is caught in a jar. Find the time for which it flies before getting caught.

A
11 sec

B
12 sec

C
13 sec

D
17 sec

Solution

Speed = 11 cm/sec
Distance = 121 cm
Time = ?
Using formula triangle,
So, Time = Distance / Speed
Plug-in the values,
Time = 121/11
Time = 11 sec
Question 19
3 / -0

If side of a square is doubled, then the area of the square becomes ____________ times the original area.

A
2

B
1/2

C
4

D
7

Solution

Let side of square be x.

Area = x²

If side is doubled = 2x

New area = (2x)² = 4x²

Therefore, the new area is 4 times the original area.
Question 20
3 / -0

Find the number of tiles needed to cover a plot with length and breadth as 4.45 m and 3.20 m, respectively, if the size of one tile is 20 cm by 20 cm.

A
335

B
356

C
377

D
401

Solution

Area of plot = 4.45 × 3.20 m²
or 445 × 320 cm²= 1,42,400 cm²
Area of tile = 20 × 20 = 400 cm²
Number of tiles = 142400 ÷ 400 = 356
Question 21
3 / -0

Deny wants to put a fence around his garden of length 12 m and breadth 15 m. Find the total cost of fencing at the rate of Rs. 20 per metre.

A
Rs. 900

B
Rs. 970

C
Rs. 1030

D
Rs. 1080

Solution

Perimeter of garden = 2(l + b) = 2(12 + 15) = 54 m
Cost of fencing per metre = Rs. 20
Cost of fencing 54 metres = 54 × 20 = Rs. 1080
Question 22
3 / -0

A tank contains 250 litres of oil, 176.39 litres of which was used. How much oil was left in the tank?

A
77.61 litres

B
73.61 litres

C
71.61 litres

D
70.61 litres

Solution

Initial quantity of oil = 250 litres
Quantity of oil used = 176.39 litres
Remaining quantity = 250 - 176.39 = 73.61 litres
Question 23
3 / -0

5/2 = ____%

A
250

B
0.025

C
0.75

D
125

Solution

5/2 x 100 = 250%
Question 24
3 / -0

Karan bought a motorcycle for Rs. 2,60,000 and paid extra 10% as the cost of insurance. How much in total did he spend to buy that motorcycle?

A
Rs. 2,92,000

B
Rs. 2,86,000

C
Rs. 2,56,000

D
Rs. 2,26,000

Solution

Base price = Rs. 2,60,000
Insurance cost = 10% of 2,60,000 = 10/100 × 2,60,000 = Rs. 26,000
Total money spent = Rs. 2,60,000 + Rs. 26,000 = Rs. 2,86,000
Question 25
3 / -0

Deepak purchased two bikes for a total of Rs. 2,15,000. He sold one for Rs. 97,000 and the other for Rs. 1,07,000. Find the amount of loss he incurred on the sale of the two bikes?

A
Rs. 5000

B
Rs. 6000

C
Rs. 7000

D
Rs. 11,000

Solution

Cost price of the two bikes = Rs. 2,15,000
Selling price of the two bikes = Rs. (97,000 + 1,07,000) = Rs. 2,04,000
Loss = Rs. 2,15,000 – Rs. 2,04,000 = Rs. 11,000
Question 26
3 / -0

The age of Jatin 5 years ago was (1/7) of what his age will be 25 years from now. Find the present age of Jatin.

A
40 years

B
30 years

C
20 years

D
10 years

Solution

Let the present age of Jatin be x.
According to the question:
1/7 (x + 25) = (x – 5)
x + 25 = 7(x – 5)
x + 25 = 7x – 35
x – 7x = –35 – 25
–6x = – 60
x = 10
Question 27
3 / -0

Amar sold a refrigerator for Rs. 15,000 and earned a profit of Rs. 3000. How much did Amar buy the refrigerator for?

A
Rs. 12,000

B
Rs. 15,000

C
Rs. 18,000

D
Rs. 11,000

Solution

Let CP be Rs. x.
We know:
SP - CP = Profit
15,000 - x = 3000
x = Rs. 12,000
Question 28
3 / -0

Sahiba bought 4 diamond bangle sets for Rs. 4,25,000. She sold each one of them for Rs. 1,25,000. Calculate the amount of profit she made.

A
Rs. 1,00,000

B
Rs. 70,000

C
Rs. 75,000

D
Rs. 60,000

Solution

CP of four diamond bangle sets = Rs. 4,25,000
SP of four diamond bangle sets = Rs. 1,25,000 × 4 = Rs. 5,00,000
Profit = SP - CP = 5,00,000 - 4,25,000 = Rs. 75,000
Question 29
3 / -0

A number, when added to the number 94267, gives another number which is equal to the product of 672 and 269. Find the number added to 94267.

A
83452

B
86501

C
90246

D
114501

Solution

Let the number to be added be x.
According to the question:
94267 + x = 672 × 269
94267 + x = 180768
x = 180768 - 94267
x = 86501
Question 30
3 / -0

Find the sum of 56.02, 56.253, 56.005 and 56.290.

A
220.255

B
224.568

C
220.746

D
224.482

Solution

Given numbers: 56.02, 56.253, 56.005, 56.290
Sum = 56.02 + 56.253 + 56.005 + 56.290
= 112.273 + 112.295 = 224.568
Question 31
3 / -0

An electrician is installing tube lights in a building. The building has 68 floors and each floor has 24 rooms. No less than 4 tube lights are to be installed in each room. At least how many tube lights does the electrician need for the whole building?

A
6520

B
6500

C
6528

D
7000

Solution

Number of floors in the building = 68
Number of rooms on each floor = 24
So, total number of rooms in the entire building = 68 × 24 = 1632
Minimum number of tube lights needed = 1632 × 4 = 6528
Question 32
3 / -0

How many lines can pass through two given points?

A
One

B
Two

C
Infinite

D
None of these

Solution

Only one line can pass through two given points.
Question 33
3 / -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 34
3 / -0

Round 48526 to the nearest hundred.

A
48500

B
48520

C
48526

D
49000

Solution

The given number is 48526.
We need to round it to the nearest hundred.
Here, the digit at tens place is less than 5, so the given number is rounded to 48500.
Question 35
3 / -0

The decimal representation of 175 kg and 30 g is

A
1750.3 kg

B
175.003 kg

C
175.030 kg

D
175.803 kg

Solution

175 kg = 1,75,000 g

175 kg and 30 g = (1,75,000 + 30) grams

So, it can be written as 1,75,030 g or 175.030 kg.
Question 36
3 / -0

Area of one swimming pool which is in rectangular shape is half of the area of another swimming pool which is in square shape. If the area of squared shape swimming pool is 64 m², what would be the breadth of the rectangular shaped swimming pool, provided length of the side of square pool is same as length of rectangular pool?

A
2 m

B
4 m

C
5 m

D
7 m

Solution

It is given that,
(Area of rectangular pool) = 1/2 (Area of square pool)
(Length x breadth) = 1/2 × 64 m².
Area of square pool = 64 m²
So area of rectangular pool = 32 m²
Side of square = 8 m
Also length of rectangle = length of side of square = 8 m
(8 x Breadth) = 32
Breadth = 32/8 = 4 m
Question 37
3 / -0

A car is moving at a speed of 90 km/hr on a highway. What is the speed of the car in m/s?

A
15

B
20

C
25

D
30

Solution

To convert km/hr into m/s, the speed is multiplied by 5/18.

Speed = 90 × 5/18 = 5 × 5 = 25 m/s
Question 38
3 / -0

Vinay has 3/7 of a pizza left. He divides it equally among four of his friends. What fraction of pizza does each friend get?

A
3/28

B
3/7

C
1/7

D
0

Solution

Fraction of pizza available = 3/7
It has to be further divided into 4 equal parts.
So, the fraction of pizza each friend gets = 1/4 of 3/7 = 3/28

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Re-Attempt Weekly Quiz Competition

Mathematics (Paper-1) Mock Test - 5

Result

Mathematics (Paper-1) Mock Test - 5

Score

-

Rank

-

SHARING IS CARING

Question 1

231241

123241

112234

112324

Solution

Question 2

9865412

9865214

6598214

9854126

Solution

Question 3

69812, 68129, 68291, 61982, 61892

61892, 61982, 68129, 68291, 69812

69812, 68291, 68129, 61982, 61892

68129, 68291, 61892, 61982, 69812

Solution

Question 4

513853

513854

513851

513852

Solution

Question 5

56

54

53

52

Solution

Question 6

IXL

CDL

DCL

CCXXD

Solution

Question 7

9

16

18

4

Solution

Question 8

8 hours and 45 minutes

9 hours and 15 minutes

9 hours and 30 minutes

9 hours and 45 minutes

Solution

Question 9

4/5

3/4

2/5

2/4

Solution

Question 10

1117

1144

1163

None of these

Solution

Question 11

151090

152090

150290

151300

Solution

Question 12

5.001

5.01

4.001

3.0001

Solution