Two cubes of their volumes in the ratio 64 : 125. The ratio of their surface area is:

- A5 : 4
- B4 : 5
- C3 : 5
- DNone of these
**Explanation:**The ratio of their surface area is

64 : 125

4 : 5

Two cubes of thire sides ratio 2 : 3. Find its cube volumes ratio

- A27 : 7
- B27 : 8
- C8 : 27
- D8 : 25
**Explanation:**a

^{3}: b^{3}= 2^{3}: 3^{3}

= 8 : 27

Three cubes of sides 5 m, 4 m, and 3 m are melted to form a new cube. Find the surface of the new cube

- A216 Cm2
- B256 Cm3
- C216 Cm3
- DNone of these
**Explanation:**Volume of new cube = Sum of volume of three cubes

=3

^{3}+4^{3}+5^{3}=216 cm

^{3}

The diagonal of a cube is 8√3. find its volume and surface area.

- A34 Cm
^{2} - B364 Cm
^{3} - C384 Cm
^{2} - D384 Cm
^{3} **Explanation:**Let the edge of the cube be a.

so, the diagonal = 8√3

=> a=8

Surface area => 6 a2 => (6 × 8 × 8) Cm

^{2}=> 384 Cm^{2}

The surface area of a cube is 486 Cm

^{3}. Find its volume- A739 Cm
^{3} - B529 Cm
^{3} - C729 Cm
^{3} - DNone of these
**Explanation:**Surface area of cube =6X (s)

^{2}where "s" is the side of the cube

therefore,

6s

^{2}=486hence, s

^{2}=81=> s = 9 cm

theefore volume = (s)

^{3}{as all the dimensions have same length}=(9)

^{3}^{=729 cm3}

The volume of cube is equal to the surface area of that cube. Then find the distance of side of the cube

- A6 m
- B7 m
- C8 m
- D9 m
**Explanation:**Cube volume = a

^{3}cubic unitsSurface area = 6 a

^{2}sq. unitsa

^{3}= 6a^{2}a=6m

The lateral surface area of cube is 100 sq.units. find the volume of cube

- A122 m3
- B135 m3
- C125 m3
- D120 m3
**Explanation:**Lateral surface area = 4a

^{2}=100 sq.unitsSo a2 = 100/4 = 25

∴a=25 and a = root of 25 which is = 5

So 5

^{3}= 125 m^{3}

The side of a cube is 15 m, find it's surface area

- A1350 m2
- B1250 m2
- C1300 m2
- D1450 m2
**Explanation:**A=1350m²

The side of a cube is 8 m, Find the voiume

- A513 m3
- B514 m3
- C512 m3
- D502 m3
**Explanation:**V=512m³

A large field of 900 hectares is divided into two parts. The difference of the areas of the two parts is one-fifth of the average of the two areas. What is the area of the smaller part in hectares

- A395
- B385
- C415
- D405
**Explanation:**Let the areas of the two parts be x and (900-x) hectares

therefore, [x-(900-x)]=1/5[x+(900-x)/2]

=> 2x-900=90

=>x=495

Hence, area of smaller part = (900 - x) = (900 – 495) = 405 hectares.

A rectangular field has to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required

- A98
- B88
- C99
- D89
**Explanation:**Area of the field =680=680 sq. feet.

Length of the adjacent sides are

2020 feet and 68020=3468020=34 feet.

Required length of the fencing

=20+34+34=88=20+34+34=88 feet

A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, find out the area of the parking space in square feet

- A126 sq. ft.
- B128 sq. ft.
- C136 sq. ft.
- D116 sq. ft.
**Explanation:**Let l = 9 ft.

Then l + 2b = 37

=> 2b = 37 – l = 37 – 9 = 28

b = 28/2 = 14 ft.

Area = lb = 9 × 14 = 126 sq. ft.

The area of a rectangle plot is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the plot

- A20 metres
- B25 metres
- C27 metres
- D18 metres
**Explanation:**Let breadth=x meters.

Then,Length = meters

Given that,

=> x = 20

Breadth = 20

The length of a room is 6 m and width is 4.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 900 per sq. metre.

- ARs. 25660
- BRs. 25560
- CRs. 25650
- DRs. 26550
**Explanation:**l=5.5m w=3.75m

area of the floor = 6 × 4.75 sq. metre.

cost of paving = 6 × 4.75 × 900 = 6 × 4275 = Rs. 25650

A rectangular mat has an area of 120 sq.metres and perimeter of 46 m. The length of its diagonal is:

- A17 cm
- B17 m
- C17 m2
- D16 m
**Explanation:**Suppose, rectangular has lengtha and width b.

Then, an areaof rectangular equals:

(1) S = a*b =120 sq metres

and a perimeterequals:

P = 2a + 2b =46 metres

(2) a + b = P/2 =23

The length of itsdiagonal is:

l^2 = a^2 + b^2

But, a^2 + b^2 = (a + b)^2 - 2ab

Therefore:

l^2 = (P/2)^2 - 2S = 23^2 - 2*120 = 289

l = Sqrt[289] = 17 metres

Answer: The length of diagonal is 17 metres

The ratio of the areas of two squares, one having double its diagonal then the other is:

- A1:3
- B3:1
- C1:4
- D4:1
**Explanation:**

A rectangular courtyard 3.78 m lang and 5.25 m broad is to be paved exactly with square tiles, all of the same size. The minimum number of such tiles is:

- A350
- B450
- C460
- D470
**Explanation:**The length of courtyard = 3.78m = 378 cm

And, the broad of courtyard = 5.25m = 525cm

The courtyard is to be paved by square tiles of equal size.

∴ Size of square tile is the HCF of length and breadth as to cover exactly.

The HCF of 525 and 378 = 21 cm

Then, the side of each square tile = 21 cm

The number of tiles = 525×378/21×21

=450

A rectangle measures 8 Cm on length and its diagonal measures 17 Cm. What is the perimeter of the rectangle

- A46 cm
- B48 cm
- C46 m
- DNone of these
**Explanation:**Second side = √172-82

= √289-64

= 15 cm

Perimeter = 2 (l+b) = 2(8+5) Cm = 2(23) = 46 Cm

The sides of a rectangle are in the ratio of 6 : 5 and its area is 1331 sq.m. Find the perimeter of rectangle.

- A120 m
- B121 cm
- C121 m
- DNone of these
**Explanation:**Let 6x and 5x be sides of the rectangle

6x × 5x = 1331

11x2 = 1331

x2 = 1331/11 = 121 => x = 11

Length = 6x = 6 × 11 = 66

Breadth = 5x => 5 × 11 = 55

Perimeter = 2 (l+b) => 2 (66+55) = 121 m

A is a point on y-axis at a distance of 5 units from x-axis lying below x-axis. The co-ordinates of A are:

- A(5, 0)
- B(-5, 0)
- C(0, 5)
- D(0, -5)

P is a point on x-axis at a distance of 4 units from y-axis to its right. The co-ordinates of P are:

- A(4, 0)
- B(0, 4)
- C(4, 4)
- D(-4, 4)
**Explanation:**The co-ordinates of P are A(4, 0)

Find the distance of the point A(3, -3) from the origin.

- A3√2
- B3√6
- C6√2
- D7√2
**Explanation:**OA = √32+(-3)2 = √9+9 = √18 = 3√2

Find the distance of the point A(4, -4) from the origin.

- A3√2
- B2√8
- C6√2
- D8√2
**Explanation:**OA = √42+(-4)2 = √16+16 = √32 = 8√2

In which quadrant does the point(9, 0) lie

- Ax-axis
- By-axis
- C4th
- DNone of these
**Explanation:**The point (9, 0) lies in y-axis.

In which quadrant does the point(0, 9) lie

- Ax-axis
- By-axis
- C3rd
- DNone of these
**Explanation:**The point (0, 9) lies in x-axis.

In which quadrant does the point(-7, 6) lie

- A1st
- B2nd
- C3rd
- D4th
**Explanation:**The point (-7, 6) lies in 2nd quadrant.

In which quadrant does the point(9, -2) lie

- A1st
- B2nd
- C3rd
- D4th
**Explanation:**The point (9, -2) lies in 4th quadrant.

In which quadrant does the point(1, 5) lie

- A1st
- B2nd
- C3rd
- D4th
**Explanation:**The point (1, 5) lies in 1st quadrant.

In which quadrant does the point(-4, -7) lie

- A1st
- B2nd
- C3rd
- D4th

If μ

_{r}be the rth order centralmoment of a population μ_{0}, μ_{1}and μ_{2}are : (where, σ = standard deviation)- A0, 1, σ
^{2} - B 1, 0, σ
^{2} - C1, 1, σ
- D 1, 0, σ

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