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Calculation:

To find the greatest number of 5 digits which is completely divisible by 139, we need to perform the following steps:

 Find the largest 5-digit number, which is 99999.

Divide 99999 by 139 and get the integer part of the quotient.

 Multiply the integer quotient by 139 to get the largest number divisible by 139.

Let's perform these calculations step-by-step:

1. Largest 5-digit number: 99999

2. Divide 99999 by 139: 99999 / 139 = 719.4245 

The integer part of the quotient is 719.

3. Multiply 719 by 139: 719 × 139 = 99941

So, the greatest 5-digit numb er that is completely divisible by 139 is 99941.

∴  The correct answer is option 3) 99941.

Given:

Digits: 3, 0, 7, 9, 6

Concept Used:

The largest number is formed by arranging the digits in descending order.

The smallest number is formed by arranging the digits in ascending order with the condition that 0 cannot be the leading digit (to ensure it remains a 5-digit number).

Calculation:

1. Form the Largest Number:

Arrange the digits in descending order: 97630.

2. Form the Smallest Number:

Arrange the digits in ascending order ensuring 0 is not at the front:

• The smallest digit (excluding 0) is 3, so it should lead. The remaining digits should follow in ascending order: 30679.

3. Calculate the Difference:

Largest number=97630Largest number=97630Largest number=97630 $\text{Largest number} = 97630$

 Smallest number = 30679

$\text{Difference} = 97630 - 30679$

Difference = 97630 − 30679 = 66951

The difference between the largest and the smallest 5-digit numbers formed by the digits 3, 0, 7, 9, 6 is 66951.

The correct answer is Option 3) 66951.

Calculation:

The denominators are:

6, 12, 20, 30, ...

Let's examine the differences between consecutive terms:

12 - 6 = 6 

20 - 12 = 8 

30 - 20 = 10 

The differences between the denominators are increasing by 2 each time:

6, 8, 10, ...

Following this pattern, the next difference should be 12:

30 + 12 = 42 

After 42, the next difference should be 14:

42 + 14 = 56

So, the next two terms in the pattern will have the denominators 42 and 56.

Thus, the next two terms in the sequence are 1 /42 and 1/56.

Hence, the correct answer is: 1/42, 1/56

Given:

The equation for the multiplication is:

(234) × (3*5) = 80730

Calculation:

To find the digit that fits in the place of *, denote the missing digit as x.

(234) × (305 + 10x) = 80730

Calculate:

234 × 305 + 2340x = 80730

71370 + 2340x = 80730

2340x = 80730 - 71370

2340x = 9360

x = 9360 / 2340

x = 4

∴ The digit that replaces * to make the equation correct is 4.

Given:

A cuboid where one of the side faces is a square with an area of 36 cm², and the longer edge of each of the four rectangular faces is 12 cm.

Calculation:

As one side face is a square with each side measuring  \(\sqrt{36}\) = 6 cm, two dimensions of the cuboid are 6 cm.

The dimensions of the cuboid are therefore 6 cm (width), 12 cm (length), and 6 cm (height).

The rectangular faces are thus 6 cm x 12 cm.

The area of each rectangular face is:

6 cm × 12 cm = 72 cm²

∴ The area of each of the rectangular faces is 72 cm².

Solution:

The figure is a flower with six petals. To determine the number of lines of symmetry

each line of symmetry will pass through the center of the flower and split the figure into two identical halves.

Since the flower has six petals, it has six lines of symmetry.

Each line of symmetry passes through the center of the flower and one petal, bisecting the figure perfectly.

∴ The figure has 6 lines of symmetry.

Given :

Joseph runs 1 km in one round of the park, the perimeter of the square is 4 times the length of one side.

Concept use:

Perimeter = 4 ×  Side

Area = Side2

Calculations:

Joseph runs 1 km in one round, the perimeter is also equal to 1 km.

So, 4 ×  Side = 1

Dividing both sides by 4, we get:

Side = 1/4 km

Now,

Area = Side²

= (1/4)²

= 1/16 sq km

So, the correct answer is option 4) 0.0625 sq km.

Given:

When the side of a square is doubled, the new side becomes twice the original side length.

Calculation:

Let's denote the original side length as ssss s

.

When doubled, the new side length becomes 2s2s2s2s 2s

.

Original area = s×s=s2s×s=s2s×s=s2s×s=s2 s $\times s = s^2$

New area = (2s) × (2s) = 4s²

Comparing the new area to the original area:

New area = 4s²

Original area = s²

The new area is

444 4

4 times the original area.

So, the correct answer is option 3.

Given:

Capacity of the refrigerator = 270 liters

Height of the refrigerator = 1 meter = 100 centimeters

Width of the refrigerator = 0.5 meters = 50 centimeters

We know that the volume of a rectangular solid is given by the formula: Volume = Length × Width × Height

Now,

Convert the capacity from liters to cubic centimeters.

1 liter = 1000 cubic centimeters

270 liters = 270 × 1000 = 270,000 cubic centimeters

 Volume = Length × Width × Height

270,000 = Length × 50 × 100 Length = 270,000 / (50 × 100)

Length = 54 centimeters

Hence, the correct answer is option 4) 54.

Calculation:

Determine the number of days from January 9, 2023, to April 12, 2023.

Number of days in January after January 9 = 31 - 9  = 22 days

Number of days in February = 28 days

Number of days in March = 31 days

Number of days in April up to April 12 = 12 days

Total number of days = 22 + 28 + 31 + 12 = 93 days

Divide the total number of days by 7 to find the number of weeks and the remainder.

93 days ÷ 7 = 13 weeks with a remainder of 2 days

 Since January 9, 2023, was a Monday,

we need to add the remainder of 2 days to Monday to find the day of the week for April 12, 2023. Monday + 2 days = Wednesday

Hence, April 12, 2023, is a Wednesday.