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1. In a right angled triangle, find the hypotenuse if base and perpendicular are respectively 36015 cm and 48020 cm.

Correct Answers :

[B]

Explanation :

Let hypotenuse = x cm

Then, by Pythagoras theorem:

x^{2} = (48020)^{2} + (36015)^{2}

x fi 60025 cm

2. The perimeter of an equilateral triangle is 72 √3 cm. Find its height

Correct Answers :

[D]

Explanation :

Let one side of the D be = a

Perimeter of equilateral triangle = 3a

3. The inner circumference of a circular track is 440 cm. The track is 14 cm wide. Find the diameter of the outer circle of the track.

Correct Answers :

[B]

Explanation :

Let inner radius = A; then 2pr = 440 \ p = 70

Radius of outer circle = 70 + 14 = 84 cm

Outer diameter = 2 × Radius = 2 × 84 = 168

4. A race track is in the form of a ring whose inner and outer circumference are 352 metre and 396 metre respectively. Find the width of the track.

Correct Answers :

[A]

Explanation :

Let inner radius = r and outer radius = R

5. The outer circumference of a circular track is 220 metre. The track is 7 metre wide everywhere. Calculate the cost of levelling the track at the rate of 50 paise per square metre.

Correct Answers :

[D]

Explanation :

Let outer radius = R; then inner radius = r = R – 7

2pR = 220 fi 35m;

r = 35 – 7 = 28 m

Area of torch = p^{R2} – p^{r2} fi p^{(R2 – r2)} = 1386 m^{2}

Cost of traveling it = 1386 × 1/2 = `693

6. Find the area of a quadrant of a circle whose circumference is 44 cm

Correct Answers :

[B]

Explanation :

Circumference of circle = 2pr = 44

= r = 7 cm

Area of a quadrant = πr^{2}/4 = 38.5 cm^{2}

7. A pit 7.5 metre long, 6 metre wide and 1.5 metre deep is dug in a field. Find the volume of soil removed in cubic metres.

Correct Answers :

[D]

Explanation :

Volume of soil removed = *l × b × h*

= 7.5 × 6 × 1.5 = 67.5 m^{3}

8. Find the length of the longest pole that can be placed in an indoor stadium 24 metre long, 18 metre wide and 16 metre high.

Correct Answers :

[C]

Explanation :

The longest pole can be placed diagonally (3-dimensional)

9. The length, breadth and height of a room are in the ratio of 3 : 2 : 1. If its volume be 1296 m3, find its breadth.

Correct Answers :

[D]

Explanation :

Let the common ratio be = x

Then; length = 3x, breadth = 2x and height = x

Then; as per question 3x ◊ 2x ◊ x = 1296 fi 6x^{3} = 1296

fi x = 6 m

Breadth = 2x = 12 m

10. The volume of a cube is 216 cm^{3}. Part of this cube is then melted to form a cylinder of length 8 cm. Find the volume of the cylinder.">

Correct Answers :

[D]

Explanation :

Data is inadequate as it’s not mentioned that what part of the cube is melted to form cylinder.

11. The whole surface of a rectangular block is 8788 square cm. If length, breadth and height are in the ratio of 4 : 3 : 2, find length.

Correct Answers :

[B]

Explanation :

Let the common ratio be = x

Then, length = 4x, breadth = 3x and height = 2x

As per question;

2(4x ◊ 3x + 3x ◊ 2x + 2x ◊ 4x) = 8788

2(12x^{2} + 6x^{2} + 8x^{2}) = 8788 fi 52x^{2} = 8788

fi x = 13

Length = 4x = 52 cm

12. Three metal cubes with edges 6 cm, 8 cm and 10 cm respectively are melted together and formed into a single cube. Find the side of the resulting cube.

Correct Answers :

[B]

Explanation :

The total volume will remain the same, let the side of the resulting cube be = a. Then,

13. Find curved and total surface area of a conical flask of radius 6 cm and height 8 cm.

Correct Answers :

[A]

Explanation :

Slant length = l = = 10 cm

Then curved surface area = *prl* = p × 6 × 10 fi 60p

And total surface area = *prl* + *pr ^{2}* fi p((6 × 10) + 6

14. The volume of a right circular cone is 100p cm3 and its height is 12 cm. Find its curved surface area.

Correct Answers :

[B]

Explanation :

15. The diameters of two cones are equal. If their slant height be in the ratio 5 : 7, find the ratio of their curved surface areas.

Correct Answers :

[D]

Explanation :

Let the radius of the two cones be = *x* cm

Let slant height of 1st cone = 5 cm and

Slant height of 2nd cone = 7 cm

Then ratio of covered surface area = = 5 : 7

16. The curved surface area of a cone is 2376 square cm and its slant height is 18 cm. Find the
diameter.

Correct Answers :

[C]

Explanation :

17. The ratio of radii of a cylinder to a that of a cone is 1 : 2. If their heights are equal, find the ratio
of their volumes?

Correct Answers :

[C]

Explanation :

Let the radius of cylinder = 1(r)

Then the radius of cone be = 2(R)

18. A silver wire when bent in the form of a square, encloses an area of 484 cm^{2}. Now if the same wire is bent to form a circle, the area of enclosed by it would be

Correct Answers :

[C]

Explanation :

The perimeter would remain the same in any case.

Let one side of a square be = a cm

Then a2 = 484 fi a = 22 cm \ perimeter = 4a = 88 cm

Let the radius of the circle be = r cm

Then 2pr = 88 fi r = 14 cm

Then area = pr2 = 616 cm^{2}

19. The circumference of a circle exceeds its diameter by 16.8 cm. Find the circumference of the circle.

Correct Answers :

[D]

Explanation :

Let the radius of the circle be = p

Then 2pr – 2r = 16.8 fi r = 3.92 cm

Then 2pr = 24.6 cm

20. A bicycle wheel makes 5000 revolutions in moving 11 km. What is the radius of the wheel?

Correct Answers :

[D]

Explanation :

Let the radius of the wheel be = p

Then 5000 × 2pr = 1100000 cm fi r = 35 cm

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