| Coverage : The GRE Practice Test - Math - Geometry has been designed to test the important concepts related to geometry. The test covers important topics like determining area of a triangle, circle, square or rectangle, evaluating perimeter, different kinds of triangles, computing angles made by two hands of clock, calculating volume of a cylinder etc.
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| 1. | Find the area of triangle ABC, where AB is the diameter of a circle. C lies on the perimeter of that circle at a distance of 5 units from A and 12 units from B. |
| a. | | 32 units |
| b. | | 35 units |
| c. | | 30 units |
| d. | | 31 units
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| 2. | The diameter of a circle is formed by the line joining points (6,-2) and (-6,3). Find the perimeter of the circle. |
| a. | | 13pi |
| b. | | 15pi |
| c. | | 9pi |
| d. | | 8pi
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| 3. | Calculate the area of the circle having center at (3,0) and the circle passes through (-1,-3). |
| a. | | 22pi |
| b. | | 20pi |
| c. | | 30pi |
| d. | | 25pi
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| 4. | What kind of triangle will emerge after you connect the points(-5,5), (5,5),(5,-4)? |
| a. | | Right Triangle |
| b. | | Isosceles Triangle |
| c. | | Equilateral Triangle |
| d. | | None of the above
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| 5. | Find the length of resulting line you get after connecting the points (-6,1) and (3,1). |
| a. | | 9 |
| b. | | 6 |
| c. | | 10 |
| d. | | 8.5
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| 6. | Find the smaller angle made by the hands of a clock at 2:30. |
| a. | | 120° |
| b. | | 90° |
| c. | | 105° |
| d. | | 115°
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| 7. | A train travels 4 miles north from the platform, then 4 miles west, then 2 miles again north and then 4 miles west. How far is the train from the platform? |
| a. | | 14 miles |
| b. | | 10 miles |
| c. | | 12 miles |
| d. | | 12.5 miles
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| 8. | An isosceles right triangle has hypotenuse of 16 inches. Find the length of other side. |
| a. | | 6 inches |
| b. | | 8v2 inches |
| c. | | 7v2 inches |
| d. | | 6v2 inches
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| 9. | Calculate the larger angle made by the hands of the clock at 5:10. |
| a. | | 190° |
| b. | | 200° |
| c. | | 220° |
| d. | | 262°
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| 10. | Find the type of triangle that emerges after connecting the points (-2,0),(2,2)and(2,-2). |
| a. | | Isosceles |
| b. | | Equilateral |
| c. | | Right |
| d. | | None of the above
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| 11. | A ladder which is 40 mts high is leaning against a wall which is 32 mts high. How far is the wall from the base of the ladder. |
| a. | | 26v2 mts |
| b. | | 25 mts |
| c. | | 24mts |
| d. | | 25v2 mts
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| 12. | The base of right angle triangle is 'b' units. If the area of the triangle is 'a' units, find the height of the triangle. |
| a. | | 2ab units |
| b. | | 2a/b units |
| c. | | v2ab units |
| d. | | Cannot be determined
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| 13. | Given A(-4,0), B(-2,0), C(-2,2). The triangle formed by joining these vertices will be: |
| a. | | A right angle triangle |
| b. | | An isosceles triangle |
| c. | | Both a and b |
| d. | | None of the above
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| 14. | Find the number of revolutions made by the wheel per kilometer, with 14 cm radius. |
| a. | | App.1000 revolutions |
| b. | | App.1245 revolutions |
| c. | | App.1136 revolutions |
| d. | | App.1263 revolutions
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| 15. | Find the number of spokes in the wheel of a cycle, given the angle between two consecutive spokes as 20°. |
| a. | | 18 |
| b. | | 20 |
| c. | | 36 |
| d. | | 9
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| 16. | Find the mid-point of the line segment with end points as (6,-4) and(2,-8). |
| a. | | (3,-4) |
| b. | | (4,-6) |
| c. | | (2,2) |
| d. | | (2,-2)
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| 17. | An airjet flies 10 miles south, then 4 miles east, then 7 miles north and then 8 miles west where it finally landed. Find the shortest distance from the starting point of the journey and the point where it finally ends. |
| a. | | 7miles |
| b. | | 6 miles |
| c. | | 8 miles |
| d. | | 5 miles
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| 18. | The area of a circle is 154cm², which is equal to the area of a rectangle with one side equivalent to the radius of the circle. Find the other side of the rectangle. |
| a. | | 22/7cm |
| b. | | 11cm |
| c. | | 22cm |
| d. | | 11/7cm
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| 19. | Find the supplement of angle 75°. |
| a. | | 105° |
| b. | | 90° |
| c. | | 15° |
| d. | | 125°
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| 20. | Find the angle whose supplement divide by thrice its complement are in the ratio of 5:6. |
| a. | | 60° |
| b. | | 30° |
| c. | | 90° |
| d. | | 120°
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| 21. | Calculate the distance between points and determine:
Column A Column B
(8,7) and (9,9) (-9,0) and (-11,1) |
| a. | | The quantity in column A is greater. |
| b. | | The quantity in column B is greater. |
| c. | | Both the quantities are equal. |
| d. | | The relationship cannot be determined.
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| 22. | If the radius of the circle is trippled, the area is multiplied by: |
| a. | | 8 |
| b. | | 2 |
| c. | | 4 |
| d. | | remains unchanged
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| 23. | The perimeter of the rectangle is 28 cm and the breadth is 6 times the length. Find the area of rectangle. |
| a. | | 20cm² |
| b. | | 28cm² |
| c. | | 14cm² |
| d. | | 24cm²
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| 24. | An ice-cream cone has the height of 7cm and diameter of 6 cm. Calculate the volume of the ice-cream that will be filled in this cone. |
| a. | | 164 cm³ |
| b. | | 66 cm³ |
| c. | | 124 cm³ |
| d. | | 98 cm³
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| 25. | Find the larger angle made by the hands of the clock at 8:00. |
| a. | | 120° |
| b. | | 180° |
| c. | | 240° |
| d. | | 200°
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| 26. | The length of a wire fence around a circular garden is 44 meters. What is the area (in sq. meters) of the 2 meters concrete path laid inside the fence? |
| a. | | 24p m² |
| b. | | 25p m² |
| c. | | 32p m² |
| d. | | 33p m²
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| 27. | An angle is equal to one-fourth of its supplement. The angle is : |
| a. | | 42° |
| b. | | 37° |
| c. | | 57° |
| d. | | 36°
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| 28. | A wire was in the shape of rectangle, with length as 14cm and breadth as 11cm.The wire is then moulded into a circle. Find the circumference of the circle. |
| a. | | 44 cm |
| b. | | 54 cm |
| c. | | 50 cm |
| d. | | 40 cm
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| 29. | The perimeter of a rectangle is 220 meters, and the difference between length and breadth is 30 meters. Find the area of the rectangle. |
| a. | | 2524m² |
| b. | | 3200m² |
| c. | | 2400m² |
| d. | | 2800m²
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| 30. | Two squares have each side as 20cm and 21cm respectively. Find the side of third square whose area is equal to the sum of the areas of other two squares. |
| a. | | 28cm |
| b. | | 29cm |
| c. | | 30cm |
| d. | | 32cm
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| 31. | Find the area of a triangle having sides 7m, 8m, and 9m. |
| a. | | 12v5m² |
| b. | | 30m² |
| c. | | 12v3m² |
| d. | | 8v5m²
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| 32. | Find the diagonal of a square whose side is of 8m . |
| a. | | 8v2m |
| b. | | 16m |
| c. | | 8m |
| d. | | 18v2m
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| 33. | The area of a rhombus is 154sq.m. If one of its diagonals is 22m, find the length of the other diagonal. |
| a. | | 20m |
| b. | | 22m |
| c. | | 14m |
| d. | | 27m
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| 34. | A rectangular park with length and breadth of 11m and 22m, is surrounded by a path of 3m wide. Find the area of the path. |
| a. | | 100m² |
| b. | | 108m² |
| c. | | 200m² |
| d. | | 234m²
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| 35. | The sides of a triangle are in the ratio 5:6:7. If its perimeter is 36cm. Find the longest side of the triangle. |
| a. | | 10cm |
| b. | | 14cm |
| c. | | 12cm |
| d. | | 16cm
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| 36. | A solid metal cylinder having a radius of 5cm and height of 18 cm is melted down and recasted as a cone having radius of 3cm. Find the height of the cone. |
| a. | | 150cm |
| b. | | 100cm |
| c. | | 120cm |
| d. | | 125cm
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| 37. | A rectangle has an area of 36 cm and perimeter of 30 cm. Find the larger side of it. |
| a. | | 15cm |
| b. | | 18cm |
| c. | | 10cm |
| d. | | 12cm
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| 38. | A line segment AB is 32 mts long. A point C is located on AB such that AC:CB is 5:3. Find the length of CB. |
| a. | | 10m |
| b. | | 12m |
| c. | | 20m |
| d. | | 22m
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| 39. | Given: Radius of circle A is 2.5 units and radius of circle B is twice the radius of A.
Column A Column B
Area of circle A Circumference of circle B |
| a. | | The quantity in column A is greater. |
| b. | | The quantity in column B is greater. |
| c. | | Both the quantities are equal. |
| d. | | The realtionship cannot be determined.
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| 40. | Calculate the larger angle made by the hands of the clock at 23:30. |
| a. | | 192° |
| b. | | 180° |
| c. | | 220° |
| d. | | 222°
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| 41. | Calculate the area of the square having perimeter equal to the area of a rectangle as 44cm². |
| a. | | 120cm² |
| b. | | 142cm² |
| c. | | 121cm² |
| d. | | 144cm²
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| 42. | Calculate the area of a rectangle with length as (1-a) and breadth as (1+a). |
| a. | | a² |
| b. | | 1/a² |
| c. | | 1+a² |
| d. | | 1-a²
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| 43. | In a trapezium ABCD, AB+CD = 24.
Column X Column Y
Length of AB Length of CD |
| a. | | The quantity in column X is greater |
| b. | | The quantity in column Y is greater. |
| c. | | Both the quantities are equal. |
| d. | | The realtionship cannot be determined.
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| 44. | If the angles of a quadrilateral are in the ratio of 3:4:5:6. Calculate the smallest angle. |
| a. | | 60° |
| b. | | 80° |
| c. | | 100° |
| d. | | 120°
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| 45. | Calculate both sides of a rectangle, given the perimeter and area of the rectangle as 24m and 36m²respecively. |
| a. | | 10m,2m |
| b. | | 12m,3m |
| c. | | 6m,6m |
| d. | | 18m,2m
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| 46. | The areas of two circles are 4:1, find the ratio of the circumferences of the circles: |
| a. | | 4:1 |
| b. | | 1:2 |
| c. | | 1:4 |
| d. | | 2:1
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| 47. | A buffalo is tied to the ground with a rope. What should be the length of the rope, so that the buffalo can graze in 616m² area only? |
| a. | | 10m |
| b. | | 12m |
| c. | | 14m |
| d. | | 15m
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| 48. | Calculate the total surface area of a cuboid whose dimensions are 12m, 10m and 5m. |
| a. | | 400m² |
| b. | | 460m² |
| c. | | 360m² |
| d. | | 480m²
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| 49. | Find the total surface area of a cone with height as 21cm and radius of its base being 28 cm. |
| a. | | 5042cm² |
| b. | | 5544cm² |
| c. | | 5142cm² |
| d. | | 5000cm²
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| 50. | Calculate the volume of a sphere, which has a diameter of 42cm. |
| a. | | 38808cm³ |
| b. | | 38888cm³ |
| c. | | 30088cm³ |
| d. | | 38080cm³
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