Mathematics - 2018 - Paper-1

Greatest number = 87655210 by using given digits
We may say the procedure of forming the greatest number is as follows:
(a) The smallest digit is placed at one's place.
(b) The next greater digit is placed at ten's place.
(c) The next greater digit is placed at hundred's place and so on.
(d) The greatest digit is placed at the highest place of the number.

In ascending order, we arrange the numbers from smallest to largest.

After arranging these numbers, 52806, 52086, 52860, 52800, 58260, we will get:

52086, 52800, 52806, 52860, 58260

The first step in solving this would be to add 234251 and 352421, which would give 586672.
The next step is to subtract this from 925564, which would give 338892.

10101 × 25 = (10000 + 100 + 1) × 25
= 250000 + 2500 + 25
= 252525

If the average age of 3 sisters is 15, then sum of ages of 3 sisters = 45 years
And sum of ages of 2 sisters = 12 + 15 = 27 years
Then, the age of 3^rd sister is equal to 45 - 27 = 18 years

A leap year has 366 days.
So ,7/6 × 366 = 427 days
Now, to find weeks, we will divide 427 days with 7.
So, we have 61 weeks.

Value of (700 ÷ 10) - {(12 × 8) ÷ (34 - 10)}
= (70) - {96 ÷ 24}
= 70 - 4
= 66

To convert a number into percent, we have to multiply by 100.
2 × 100 = 200%

Cost price = Rs. 3000
Selling price =Rs. 2700
CP > SP
So, he gets loss.
Loss = CP - SP = 3000 - 2700 = Rs. 300
Loss % = 300 / 3000 × 100 = 10%

A train leaves Hyderabad at 01:15 PM on Friday and reaches Chennai at 07:30 AM on Saturday .
The duration of the journey on Friday = 10 hours and 45 minutes
The duration of the journey on Saturday = 7 hours and 30 minutes
The total duration of the journey = 18 hours and 15 minutes

Given, Karishma bought two necklaces for Rs. 1,39,500.00.
She sold one of them for Rs. 75,000 and the other one for Rs. 80,000.
Cost price for two necklaces = Rs. 1,39,500
Selling price for two necklaces = Rs. 75,000 + Rs. 80,000 = Rs. 1,55,000
Gain = Rs. 1,55,000 - Rs. 1,39,500 = Rs. 15,500

Total number of bulbs required to decorate 1 window = 64
Total number of windows in 1 floor = 48
Therefore, total number of bulbs required to decorate windows of 1 floor = 48 × 64 = 3072
Total number of floors = 85
Therefore, total number of bulbs required to decorate 85 floors = 3072 × 85 = 261120

The smallest five-digit number = 10,000, but it is not divisible by 19.
10000 = 19 × 526 + 6
So, the smallest five-digit number divisible by 19 is 19 × 527 = 10013.

38 - 8 = 30
68 - 8 = 60
HCF(30 , 60) = 30
So, the answer is 30.

The decimal notation of 10 kg 2 dag 6 g is
1 dag = 0.01 kg
2 dag = 0.02 kg
1 g = 0.001 kg
6 g = 0.006 kg
So, 10 kg 2 dag 6 g = 10 kg + 0.02 kg + 0.006 kg = 10.026 kg

Supplementary angles are those whose sum is 180°.
113° and 67° are supplementary angles.
Their sum is equal to 180°.

Length of the rectangle = 10 cm
Breadth of the rectangle = 8 cm
Perimeter of the rectangle = 2(10 + 8) = 36 cm
We know, Perimeter of square = 4 × Side
According to question,
36 = 4 × Side
Side = 9 cm
Area of square = 9 × 9 = 81 cm²

Three angles can be those of a triangle when their sum is equal to 180°.
The three angles whose sum is 180° are 32°, 69°, 79°.

All octagons are polygons because they have at least 3 sides.This is a correct statement.
ii) All hexagons are not triangles.
iii) All parallelogram are not rectangles.
iv) All rhombuses are not squares

When smaller Roman numeral comes before bigger Roman numeral, then we subtract, so we have IX = 9.
CDXLIX = 500 -100 + 50 - 10 + 10 - 1 = 400 + 40 + 9 = 449

Let the required number be x'.
We know that
x + 9999 = 11009
x = 11009 - 9999 = 1010

6 ÷ 6 + 6 × 6 - 6
=1 + 36 - 6
= 31

The sum of 20.08, 20.008, 20.088 and 20.888
= 20.08 + 20.008 + 20.088 + 20.888 = 81.064

For rounding a number to nearest hundreds, we will see the tens column in 37504.
0 is in the tens column, so we will round it down according to the rounding rule.
Therefore, rounding off 37504 to nearest hundred = 37500

Speed = 75 km//hr
= 75 km is covered in an hour
To cover a distance of 350 km, time required will be = 350 / 75 hours = (350 / 75 × 60 ) = 4 hrs 40 min

Volume of cube = a³
Edge of cube = 4 m = 400 cm
Volume of cube = (400)³ = 64000000 cm³
Area of rectangle = L × B × H
= 20 × 10 × 5 = 1000 cm³
Number of rectangular pieces required = 64000000/1000 = 64000 pieces

According to the question:
Since 1 km is 1000 m, therefore 10 km is 10000 m.
= 10/10000 × 100 = 0.1%

Area of rectangle = L × B
Length = 3.6 m = 360 cm
Breadth = 4.5 m= 450 cm
Area = 360 × 450 = 162000
Area of square = a²
=15² = 225
Number of tiles required = 162000 / 225 = 720

Smallest odd number that can be created using the digits 1, 2, 3, 4 and 5 is 12345.

Using the formula
C = 5/9(F-32),
C = 5/9 (200 –32) = 93.3°C

The number obtained by interchanging the places of 6 and 9 in 36490 is 39460.
The difference between the number 39460 and 36490 is 2970.

3.75 of 5% = 375/100 × 5/100 = 0.1875

7.25 of 10% = 725/100 × 10/100  = 0.725

3.75 of 5% + 7.25 of 10% = 0.1875 + 0.725 = 0.9125

As per the given pattern,
For the first column, the numbers are increasing in the steps of 10.
For the second column, the numbers are increasing in the steps of 30.
For the third column, the numbers are increasing in the steps of 40.
Now, for the fourth row, first number would be 48 + 10 = 58, the second number would be 144 + 30 = 174 and the third number would be 192 + 40 = 232.
Next row of numbers is 58, 174 and 232.

Alternate Solution

28 × 3 = 84 28 × 4 = 112
38 × 3 = 114 38 × 4 = 152
48 × 3 = 144 48 × 4 = 192
58 × 3 = 174 58 × 4 = 232

Length of field = 40 m
Breadth of field = 25 m
Perimeter of field = 2(length + breadth) = 2(40 + 25) = 130 m
Distance covered when he runs only 1 round of the field = 130 m
Distance covered when he runs 4 rounds of the field = 130 × 4 = 520 m

Length of the room = 15 m
Breadth of the room = 10 m
Area of the room = 15 m × 10 m = 150 m² = 15,00,000 cm²
Cost of carpeting 1 sq. cm = Rs. 2.00
Cost of carpeting 15,00,000 cm² = Rs. 15,00,000 × 2.00 = Rs. 30,00,000

Cost of a pack of 15 balls = Rs. 300
Cost of 1 ball = 300 ÷ 15 = Rs. 20
Cost of a pack of 12 shuttle cocks = Rs. 96
Cost of 1 shuttle cock = 96 ÷ 12 = Rs. 8
Total cost of 1 ball and 1 shuttle cock = Rs. 20 + Rs. 8 = Rs. 28
So, he would pay Rs. 28 to the shopkeeper.

Greatest common divisor of 624 and 936 is 312.

The relation between greatest common divisor and least common multiple of two numbers is,
Product of two numbers = Greatest common divisor × Least common multiple

624 × 936 = 312 × Least common multiple

624 × 936 / 312 = Least common multiple

1872 = Least common multiple

So, the smallest number which is divisible by 624 and 936 is 1872.

Time spent by Amar in studying Science = 3/8
Time spent by Amar to study English = 2/5 ofScience
Time spent by Amar in studying English = 2/5 × 3/8 = 6/40 = 3/20