Geometry Exercises Question Bank

Abhishek Jain

1. 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 2. The area of a circle is 154cm, 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 3. Find the supplement of angle 75. (a) 105 (b) 90 (c) 15 (d) 125 4. Find the angle whose supplement & thrice its complement are in the ratio of 5:6. (a)60 (b) 30 (c) 90 (d) 120 5. Find the larger angle made by the hands of the clock at 8:00. (a) 120 (b) 180 (c) 240 (d) 200 6. 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) 2524m (b) 3200m (c) 2400m (d) 2800m 7. Find the diagonal of a square whose side is of 8m . (a) 82m (b) 16m (c) 8m (d) 182m 8. A solid metal cylinder having a radius of 5cm and height of 18 cm is melted down and recast as a cone having radius of 3cm. Find the height of the cone. (a) 150cm (b) 100cm (c) 120cm (d) 125cm 9. 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 relationship cannot be determined. 10. Calculate the area of the square having perimeter equal to the area of a rectangle as 44cm. (a) 120cm (b) 142cm (c) 121cm (d) 144cm 11. Calculate the area of a rectangle with length as (1-a) and breadth as (1+a). (a) a (b) 1/a (c) 1+a (d) 1-a 12. Calculate both sides of a rectangle, given the perimeter and area of the rectangle as 24m and 36mrespecively. (a) 10m,2m (b) 12m,3m (c) 6m,6m (d) 18m,2m 13. 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 14. An isosceles right triangle has hypotenuse of 16 inches. Find the length of other side. (a) 6 inches (b) 82 inches (c) 72 inches (d) 62 inches 15. 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 16. If the radius of the circle is tripled, the area is multiplied by: (a) 8 (b) 2 (c) 4 (d) remains unchanged 17. 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) 24 m (b) 25 m (c) 32 m (d) 33 m 18. 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 19. 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) 100m (b) 108m (c) 200m (d) 234m 20. A line segment AB is 32 m 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 21. 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 22. 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) 2ab units (d) Cannot be determined 23. The perimeter of the rectangle is 28 cm and the breadth is 6 times the length. Find the area of rectangle. (a) 20cm (b) 28cm (c) 14cm (d) 24cm 24. 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 25. 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 26. 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 27. 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 616m area only? (a) 10m (b) 12m (c) 14m (d) 15m 28. Calculate the total surface area of a cuboid whose dimensions are 12m, 10m and 5m. (a) 400m (b) 460m (c) 360m (d) 480m

29. Find the total surface area of a cone with height as 21cm and radius of its base being 28 cm. (a) 5042cm (b) 5544cm (c) 5142cm (d) 5000cm 30. Find the in radius of the triangle with sides 5,12 &13cm? (a)12 (b) 11.5 (c) 2 (d) 12.5 31. 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 32. Find the circum radius of the triangle with sides 5,12 &13cm? (a)12 (b) 11.5 (c) 3 (d) 6.5 33. 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) 262 mts (b) 25 mts (c) 24mts (d) 252 mts 34. 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 35. 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 cm (b) 66 cm (c) 124 cm (d) 98 cm 36. An angle is equal to one-fourth of its supplement. The angle is : (a) 42 (b) 37 (c) 57 (d) 36 37. A wire was in the shape of rectangle, with length as 14cm and breadth as 11cm.The wire is then molded into a circle. Find the circumference of the circle. (a) 44 cm (b) 54 cm (c) 50 cm (d) 40 cm 38. 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 39. Find the area of a triangle having sides 7m, 8m, and 9m. (a) 125 m (b) 30m (c) 123 m (d) 85 m

40. Find the circum radius of the triangle with sides 3, 4 &5cm? (a) 2.5 (b) 2 (c) 3 (d) 12.5 41. 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 relationship cannot be determined. 42. A plot of land is in the shape of a trapezium whose dimensions are given in the figure below : Hence the perimeter of the field is (a) 50 m (b) 64 m (c) 72 m (d) None of the above 43. Find the area of the sector covered by the hour hand after it has moved through 3 hours and the length of the hour hand is 7cm. (a) 77 sq cm (b) 38.5 sq. cm (c) 35 sq. cm (d) 70 sq. cm 44. What is the measure of the circum radius of a triangle whose sides are 9, 40 and 41? (a) 6 cm (b) 4 cm (c) 24.5 cm (d) 20.5 cm Q45. If the sum of the interior angles of a regular polygon measures up to 1440 degrees, how many sides does the polygon have? (a) 10 (b) 8 (c) 12 (d) 9 Q46. What is the measure of in radius of the triangle whose sides are 24, 7 and 25? (a) 12.5 (b) 3 (c) 6 (d) none of these Q47. What is the circum radius of a triangle whose sides are 7, 24 and 25 respectively? (a) 18 (b) 12.5 (c) 12 (d) 14 Q48. ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all equal. What is the perimeter of the parallelogram? (a) 9 (b) 10 (c) 11 (d) none of these

49. PQRS is a parallelogram and ST = TR. What is the ratio of the area of triangle QST to the area of the parallelogram? (a) 1:2 (b) 2:3 (c) 5:6 (d) none of these 50. Two equal circles are cut out of a rectangle of card of dimensions 16 by 8. The circles have the maximum diameter possible. What is the approximate area of the paper remaining after the circles have been cut out? (a) 21 (b) 23 (c) 25 (d) none of these 51. ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS = 6. What is the length of the arc AQB? (a) 5pi (b) 6pi (c) 7pi (d) none of these 52. Radius of circle center O is 3 times the radius of circle center C. C = O .If the shaded area of circle C is 2 then what is the area of the shaded part of circle O ? (a) 6 (b) 12 (c) 18 (d) none of these 53. In triangle ABC, AD = DB , DE is parallel to BC, and the area of triangle ABC is 40. What is the area of triangle ADE ? (a) 10 (b) 15 (c) 20 (d)30 54. Rectangle ABCD has a perimeter of 26. The half circle with diameter AD has an area of 8. What is the perimeter of the part of the figure that is not shaded? (a) 26 + 4 (b) 18 + 8 (c) 18 + 4 (d) none of these 55. Find the number of triangles in an octagon. (a) 326 (b) 120 (c) 56 (d) cannot be determined 56: Find the area of the sector covered by the hour hand after it has moved through 3 hours and the length of the hour hand is 7cm. (a) 77 (b) 38.5 (c) 35 (d)70 57. If median AD of an equilateral triangle ABC is 9cm and G is centroid . Find AG? (a) 3 (b) 6 (c) 12 (d)11 58. The ratio of the side & height of an equilateral triangle is (a) 1:1 (b) 2:3 (c) 3 : 2 (d) 2:1

59. In a right angle triangle PQR, right angle at Q , PS = SQ = SR and angle SPQ =540. Find angle RSQ? (a) 720 (b) 1080 (c) 360 (d) 540 60. The area of a triangle with base x units is equal to area of a square with side x units. Then the altitude of the triangle is: (a) x (b) 2x (c) 3x (d) 4x 61. The ratio between length & perimeter of a rectangle plot is 1:3. What is the ratio between length & breadth of the plot? (a) 2:1 (b) 3:2 (c) data inadequate (d) 1:2 62. The diagonal of a square A is (x+ y). The diagonal of a square B with twice the area of A is: (a) 2 (x+ y) (b) 2(x+ y) (c) 2x+ 4y (d) 4x+ 2y 63. The area of a right angled triangle is 20 sq. cm. and one of the sides containing right angle is 4 cm. the altitude on the hypotenuse is (a) 20/29 (b) 8cm (c) 10 (d) (40/41) 64. The whole surface of a cube is 216 cm2. The volume in cm3of cube is : (a) 108 (b) 54 (c) 432 (d) 216 65. The radius of base of a right circular cone is R & is height is 2H, then its volume is : (a) 2/3 R^2 H (b) R^2 H (c) 2 R^2 H (d) 1/3 R^2 H 66. If the curved surface of a cylinder be double the area of the ends then the ratio of its height and radius is : (a) 2:3 (b) 1:1 (c) 2:1 (d) 1:2 67. The radius of the base of a cylinder is 2 cm & its height 7 cm, then its curved surface in cm2is : (a) 44 (b) 22 (c) 88 (d) 56 68. Each edge of a cube is increased by 50%. The percent of increase in the surface area of the cube is : (a) 50 (b) 100 (c) 120 (d) 125

69. The sides of a triangle are 3 cm, 4 cm & 5 cm. Its area in cm2 is (a) 12 (b) 15 (c) 20 (d) 6 70. The radius of a circle is diminished by 10%, the area is diminished by: (a) 10% (b) 21% (c) 19% (d) 20% 71. If the cost of white washing the four walls of a rectangular room is Rs. 25, then the cost of white washing a room twice the length , breadth and the height will be Rs. : (a) 50 (b) 100 (c) 150 (d) 200 72. The difference between the length & breadth of a rectangle is 23m. If the perimeter of the rectangle is 206 m, find its area in sq. cm (a) 2420 (b) 2480 (c) 2520 (d) 1520 73. The length & breadth of a rectangle is in ratio 3:2. If cost of fencing it @ Rs. 12. 5 per meter is Rs. 2000. By how much its length exceed its breadth in meters? (a) 16 (b) 32 (c) 80 (d) 160 74. The volume of a cube is 216 cm3, its side is : (a) 16 (b) 6 (c) 26 (d) 32 75. When recast, the radius of an iron rod is made one- fourth. If its volume remains constant, then the new length will become (a) times of original (b) 1/16 times of the original (c) 16 times of original (d) 4 times of original 76. A right circular cone & a right circular cylinder have equal base & equal height. If the radius of the base & the height are in the ratio 5:12, then ratio of total surface area of the cylinder to that of the cone is (a) 3:1 (b) 13:9 (c) 17:9 (d) 34:9 77. Each edge of a cube is increased by 20%. The percent of increase in the surface area of the cube is : (a) 43 (b) 45 (c) 41 (d) 44 78. The sides of a triangle are 9 cm, 12 cm & 15 cm. Its area in cm2 is

(a) 12 (b) 15 (c) 50 (d) 54 79. The radius of a circle is diminished by 20%, the area is diminished by: (a) 40% (b) 44% (c) 36% (d) 20% 80. If the cost of white washing the four walls of a rectangular room is Rs. 50, then the cost of white washing a room twice the length , breadth and the height will be Rs. : (a) 50 (b) 100 (c) 150 (d) 200 81. A solid metallic cone is melted & recast into a solid cylinder of the same base as that of the cone. If the height of cylinder is 7 cm, the height of the cone was (a) 20 cm (b) 21 cm (c) 28 cm (d) 24 cm 82. The measures (in cm) of sides of a right angled triangle are given by consecutive integers. Its area (in cm2) is given by (a) 8 (b) 9 (c) 5 (d) 6 83. If a triangle with same base 8 cm has the same area as a circle with radius 8 cm, the corresponding altitude (in cm) of the triangle is (a) 12 (b) 20 (c) 16 (d) 32 84. The radius of the base & height of a right circular cone are in ratio 5:12. If the volume of the cone is 314 cm3, the slant height in cm is (take =3.14) : (a)12 (b) 13 (c) 15 (d) 17 85. The area (in m2) of the square which has the same perimeter as a rectangle whose lengths is 48m & is 3 times its breadth is : (a) 1000 (b) 1024 (c) 1600 (d) 1025 86. The area of an equilateral triangle is 400 3 sq m. Its perimeter is (a) 120 (b) 150 (c) 90 (d) 135 87. Diameter of a wheel is 3 m. The wheel revolves 28 times in a minute. To cover 5.280 km distance, the wheel will take (a) 10min (b) 20 min (c) 30 min (d) 40 min

88. The perimeter of a rhombus is 40 m & its height 5m. Its area in sq. m is : (a) 60 (b) 50 (c) 45 (d) 55 89.The area of the biggest circle in sq.cm., which can be drawn inside a square of side 21 cm is (a) 344.5 (b) 364.5 (c) 346.5 (d) 366.5 90. The area of rhombus is 150 cm2. The length of one of its diagonal is 10 cm. The length of the other diagonal in cm is (a) 25 (b) 30 (c) 35 (d) 36 91. A circular wire of the radius 42 cm is bent in the form of a rectangle whose sides are in 6:5. The smallest side of the rectangle is (a) 60 (b) 30 (c) 25 (d) 36 92. If radius of the base of a cone be doubled & height left unchanged then the ratio of the volume of the new cone to that of one original cone will be: (a) 1:4 (b) 2:1 (c) 1:2 (d) 4:1 93. The area of the in circle of an equilateral triangle of side 42 cm is (a) 231 (b) 462 (c) 223 (d) 924 94. The diagonals of the rhombus are 32cm & 24 cm respectively. The perimeter of the rhombus in cm is (a) 80 (b) 72 (c) 68 (d) 64 95. A rectangular water tank is 2.1 m long & 1.5 m broad. If 630 litres of water are poured into tank, how much will the water level rise? (a) 0.2m (b) 2m (c) 0.63 m (d) 1.5 m 96. How many sides does a regular polygon have whose interior and exterior angles are in the ratio 2 : 1 ? (a) 3 (b) 5 (c) 6 (d) 12 97. ABC is a triangle with base AB. D is a point on AB such that AB =5 and DB = 3. What is the ratio of the area of ADC To the area of ABC? a. 3/2 b. 2/3 c. 3/5 d. 4/25

98. In two triangles, the ratio of the area is 4 : 3 and ratio of their heights is 3 : 4. Find the ratio of their bases? a. 16: 9 b. 9 : 16 c. 9 : 12 d. 16: 12 99. The circum radius of an equilateral triangle is 8 cm. the in radius of the triangle is? a. 3.25cm b. 3.50cm c. 4cm d. 4.25 cm 100. Four equal circles each of radius A units touch one another. The area enclosed between them ( = 22/7) in square units, is? a. 3 A2 b. 6 A2 / 7 c. 41A2 /7 d. A2 /7 101. The lengths of the perpendiculars drawn from any point in the interior of an equilateral triangle to the respective sides are A, B and C. the length of each side of the triangle is? a. 2/3 (A + B+ C) b. 1/3 (A+B+C) c. 1/3 (A+B+C) d. 4/3 (A+B+C) 102. The area of a regular hexagon of side 23 cm is? a. 183 b. 123 c. 363 d. 273 103. The diagonals of a rhombus are 24m & 10 m, its slant height is (a) 60/13 (b) 120/13 (c) 45 (d) 55 104. The perimeter of a rhombus is 80 m & its height 5m. Its area in sq. m is : (a) 60 (b) 100 (c) 45 (d) 55 105. The chord of length 16 cm is at a distance of 15cm from the centre of the circle then the length of the chord of the same circle which is at the distance of 8 cm from the centre is Equal to? a. 10cm b. 20cm c. 30cm d. 40cm 106. The ratio of the areas of two isosceles triangles having the same vertical angle (angle between equal sides) is 1:4, the ratio of their heights is? a. 1:4 b. 2:5 c. 1:2 d. 3:4 107. Three circles of diameter 10 cm each, are bound together by a rubber band, in cm if it is stretched as shown, is?

a. 30 b. 30+ 10 c. 10 d. 60+ 20 108. The length of the each side of an equilateral triangle is 143. The area of the in- circle, in cm 2 is a. 450 b. 308 c.154 d. 77 109. Each interior angle of a regular polygon is 18 more than eight times an exterior angle. The number of sides of the polygon is? a. 10 b. 15 c. 20 d. 25 110. If the sum of three dimensions and the total surface area of a rectangular box are 12cm and 94cm2 respectively, than the maximum length of a stick that can be placed inside the box is? a. 52 cm b. 5 cm c. 6cm d.25cmg 111. The diagonal of a cube is 153 cm. find the side of cube ? a. 120 b.14 c. 15 d. 12 112. The total surface area of a solid right circular cylinder is twice that of a solid sphere. If they have the same radii, the ratio of the volume of the cylinder to that of the sphere is given by ? a. 9:4 b. 2:1 c. 3:1 d. 4:9 113. The radius of the in circle of a triangle is 2 cm. if the area of the triangle is 6 cm2, then its perimeter is? a. 2cm b. 3 cm c. 6cm d. 9 cm 114. The diagonal of a cube is 153 cm. find the ratio of its total surface area and volume? a. 2:5 b. 5:2 c. 3:5 d. 5:3 115. Water is flowing at the rate of 3 km/hr through a circular pipe of 20 cm internal diameter into a circular cistern of diameter 10m and depth 2m. in how much time will the cistern be filled? a. 1hr b. 1hr, 40min c. 1hr, 20 min d. 2hr, 40 min 116. If the side of a square is increased by 50%, its area is increased by? a. 125% b. 100% c. 75% d. 50%

117. If a wire is bent into the shape of a square. Then the area of the square so formed is 81cm2. When the wire is bent into a semicircular shape. Then the area, (in cm2) of the semicircle will be? a. 22 b. 44 c. 77 d. 154 118. If the radius of a circle is increased by 50%, its area is increased by? a. 125% b. 100% c. 75% d. 50% 119. A bicycle wheel makes 5000 revolutions in moving 11km. then the radius of the wheel is ( in cm)? a. 70 b. 35 c. 17.5 d. 140 120. A river 3m deep and 40m wide is flowing at the rate of 2km.hr. How much water (in liters) will fall into the sea in a minute? a. 4, 00,000 b. 40, 00,000 c. 40,000 d. 4,000 121. The perimeter of a triangle is 40 cm and its area is 60 cm2. If the largest side measures 17cm, then the length (in cm) of the smallest side of the triangle is? a. 4 b. 6 c. 8 d. 15 122. The volume (in m3) of the rain water that can be collected from 1.5 hectares of ground in a rainfall of 5 cm is? a. 75 b. 750 c. 7500 d. 75000 123. The area of thee consecutive faces of a cuboid are 12 cm2, 20 cm2 and 15 cm2, then the volume of the cuboid is? a. 3600 b. 100 c. 80 d. 60 124. Water is flowing at the rate of 5 km/hr through a pipe of diameter 14 cm into a Rectangular tank which is 50 m long, 44m wide. The taken, in hours, for the rise in the level of water in the tank to be 7 cm is? a. 2 b. 3/2 c. 3 d. 5/2 125. The sides of a triangle are in the ratio 2:3:4, the perimeter of the triangle is 18 cm. The area (in cm2) of the triangle is? a. 9 b. 36 c.42 d. 315

126. A copper wire is bent in the form of an equilateral triangle and has area 1213 cm2. If the same wire is bent into the form of a circle, the area is (in cm2) enclosed by the wire is? a. 364.5 b. 693.5 c. 346.5 d. 639.5 127. Meeting point of all perpendicular bisectors is called as a. centroid b. orthocenter c. circumcenter d. incenter 128. Water flows into a tank which is 200m long and 150 m wide, through a pipe of cross- section 0.3m0.2m at 20 km/hr. then the time ( in hr) for the water level in the tank to reach 8m is ? a. 50 b. 120 c. 150 d. 200 129. In an equilateral triangle ABC of side 10 cm, the side BC is trisected at D. The length (in cm) of AD is? a. 37 b. 73 c. 107 /3 d. 710/ 3 130. The floor of a room is of size 4m 3m and its height is 3m. The walls and ceiling of the room require painting. The area to be painted is? a. 66m2 b. 54m2 c. 43m2 d. 33m2 131. What is the ratio of circumradius & inradius of an equilateral triangle? a. 2:1 b. 1:2 c. 1:1 d. 2:3 132. The length (in cm) of a chord of a circle of radius 13cm at a distance of 12 cm form its centre is? a. 5 b. 8 c. 10 d. 12 133. The radius of base and slant height of a cone are in the ratio 4:7 . if its curved surface area is 792cm2 ,then the radius (in cm) of its base is ? a. 8 b. 12 c. 14 d. 16 134.The perimeter of a rhombus is 146 cm and one of its diagonal is 55 cm. The other diagonal is? a. 92 cm b. 73 cm c. 48 cm d. 72 cm 135. The ratio of the areas of two isosceles triangles having equal vertical angles is 1:4. The ratio of their heights will be? a. 1:2 b. 3:4 c. 2:3 d. 6:7

136. If each of the radius of base and height of a right circular cone is increased by 10%, then the percentage of increase in the volume of the cone will be? a. 20 b. 33.1 c. 44.2 d. 100 137. Meeting point of all the altitudes in a triangle is called as a. centroid b. orthocenter c. circumcenter d. incenter 138. Meeting point of all angle bisectors is called as a. centroid b. orthocenter c. circumcenter d. incenter 139. An equilateral triangle of side 6 cm has its corners cut off to form a regular hexagon. Area (in cm2) of this regular hexagon will be? a. 33 b. 36 c. 63 d. 53 /2 140. The length (in meter) of the longest rod that can be put in a room of dimensions 10m 10m 5m is? a. 153 b. 15 c. 102 d. 53 141. The lateral surface area of a cylinder is 1056 cm2 and its height is 16 cm. find its volume? a. 4545 cm3 b. 4455cm3 c. 5445 cm3 d. 5544cm3 142. The largest sphere is curved out of a cube of side 7 cm . The volume of the sphere (in cm3) will be? a. 718.66 b. 543.72 c. 481.34 d. 179.67 143. The radius of circle A is twice that of circle B and the radius of the circle B is twice that of circle C . Their area will be in the ratio? a. 16:4:1 b. 4:2:1 c. 1:2:4 d.1:4:16 144. Through each vertex of a triangle, a line parallel to the opposite side is drawn. The ratio of the perimeter of the new triangle, thus formed, with that of the original triangle is? a. 3:2 b. 4:1 c. 2:1 d. 2:3

145. The radii of the bases of two cylinder A and B are in the ratio 3:2 and their heights in the ratio n:1. If the volume of cylinder A is 3 times that of cylinder B, the value of n is? a. 4/3 b. 2/3 c. d. 3/2 146. The volume of a right circular cylinder and that of a sphere are equal and their radii are also equal. If the height of the cylinder be H and the diameter of the sphere D, then which of the following relation is correct? a. H=D b. 2H = D c. 2H= 3D d. 3H= 2D 147. The circumference of a circle is 100cm. The measure of a side of the square inscribed in this circle is ? a. 25 2 b. 502 / c. 502 d. 25 2 / 148.The radii of two circle are 5cm and 3cm, the distance between their centers is 24 cm . Then the length of the transverse common tangent is? a. 16 cm b. 152 cm c. 162 cm d. 15 cm 149. Each of the radius of the base and the height of a right circular cylinder is increased by 10%. The volume of the cylinder is increased by? a. 3.31% b. 14.5% c. 33.1% d. 19.5% 150. The height of a cylinder and that of a cone are in the ratio 2:3 and the radii of their bases in the ratio 3:4. The ratio of their volumes will be? a.1:9 b. 2:9 c. 9:8 d. 3:8 151. If the length and the perimeter of a rectangle are in the ratio 5:16. Then its length and breadth will be in the ratio? a. 5:11 b. 5:8 c. 5:4 d. 5:3 152. If the perimeter of a semicircular field is 144 m, then the diameter of the field is? a. 55m b. 30m c. 28m d.56m 153. The perimeter of a right angled triangle is 30 cm. if its hypotenuse is 13 cm, and then finds the other two sides (in cm)? a. 6,11 b. 5,12 c. 7,8 d. 6,9

154. Two circle touch externally .The sum of their areas is 130 cm2 and the distance between their centers is 14cm. find the radii of the circles? a.11cm, 15cm b.11 cm, 4cm c.11cm, 6 cm d. 11cm, 3cm 155. The minute hand of a clock is 10 cm long. Find the area of the face of the clock described by the minute hand between 9 AM and 9:35 AM? a. 180.5 cm2 b. 183.3 cm2 c. 182.3cm2 d. 187.3 cm2 156. A solid metallic sphere of radius 3 decimeters is melted to form a circular sheet of 1 millimeter thickness. The diameter of the sheet so formed is ? a. 26m b. 24m c. 12m d. 6m 157. The height and the radius of the base of a right circular cone are 12cm and 6cm respectively. The radius of the circular cross-section of the cone cut by a plane parallel to its base at a distance of 3 cm from the base is? a. 4cm b. 5.5 cm c. 4.5 cm d. 3.5 cm 158. Water flows through a cylindrical pipe, whose radius is 7cm, at 5m/sec. The time, it takes to fill an empty water tank with height 1.54m and area of the base (35) m2 is? a. 6 min b. 5min c. 10 min d. 9 min 159. If the difference between areas of the circum circle and the in-circle of an equilateral triangle is 44cm2, then the area of the triangle is? a. 28 cm2 b. 73 cm2 c. 143 cm2 d. 21 cm2 160. A wire, when bent in the form of a square, encloses a region having area 121 cm2. If the same wire is bent into the form of a circle, then the area of the circle is ? a. 144 cm2 b. 180cm2 c. 154 cm2 d. 176 cm2 161. If the area of a circle inscribed in a square is 9 cm2, then the area of the square is? a. 24 cm2 b. 30cm2 c.36 cm2 d. 81 cm2

162. ABC is an equilateral triangle of side 2 cm. with A, B, C as centers and radius 1 cm three arcs are drawn. The area of the region within the triangle bounded by the three arcs is? a. (33 - /2) cm2 b. (3 - 3/2) cm2 c. (3 - /2) cm2 d. (/2 - 3) 163. What is the each interior angle of a decagon? a. 360 b.1080 c. 1120 d. 1440 164. ABC is an isosceles triangle in which AB=AC. If D and E are the mid- points of AB and AC respectively. The point B, C, D, E are? a. collinear b. non-collinear c. concyclic d. none of these 165. What is the circum radius of an equilateral triangle of side 6cm? A. 22 b. 32 c. 2(3 ) d. 42 166. If two circle are such that the centre of one lies on the circumference of the other then the ratio of the common chord of the two circles to the radius of any one of the circle is? a. 2:1 b. 3 :1 c.5 :1 d.4:1 167. If one angle of a cyclic trapezium is triple of the other, then the greater one measures? a. 90 b. 105 c.120 d. 135 168. In a cyclic quadrilateral ABCD, if B- D = 60 then the measure of the smaller of the two is ? a. 60 b. 40 c. 38 d.30 169. The number of the common tangents that can be drawn to two given circles is at the most? a. 1 b. 2 c. 3 d. 4 170. ACB is a tangent to a circle at C. CD and CE are chords such that that ACE> ACD. if ACD = BCE = 50 then ? a. CD=CE b. ED is not parallel to AB c. ED passes through the centre of the circle d. CDE is a right angled triangle

171. In a circle of radius 17 cm, two parallel chords are drawn on opposite sides of a diameter. The distance between the chords is 23 cm. if the length of one chord is 16 cm, then the length of the other is ? a. 23cm b. 30 cm c. 15 cm d. none of these 172. If angle between two sides of 3cm & 4cm of a triangle is 300.. what is the area of the triangle ? a. 6cm b. 12 cm c. 15 cm d. none of these 173. ABC is a right angled triangle AB = 3 cm, BC = 5 cm and AC = 4 cm, then the in radius of the circle? a. 1 cm b. 1.25 cm c. 1.5 cm d. none of these 174. A circle has two parallel chords of lengths 6 cm and 8 cm. if the chords are 1 cm apart and the centre is on the same side of the chords, then a diameter of the circle is of length? a. 5 cm b. 6 cm c. 8 cm d. 10 cm 175. A point which is equidistant from all vertex of a triangle is called as a. centroid b. orthocenter c. circumcenter d. incenter 176. In a circle O is the centre and AB is a chord AOB = 50 then find OAB =? a. 50 b. 60 c. 55 d. 65 177. IN a circle O is the centre, AD is the diameter and AB, BC, CD are the chord. A = 50 then O=? a. 130 b. 50 c. 100 d. 80 178. IN a circle with centre O and radius 5 cm, AB is a chord of length 8 cm. if OM is perpendicular on AB, what is the length of OM ? a. 4 cm b. 5 cm c. 3 cm d. none of these 179. An equilateral ABC is inscribed in a circle with centre O. then BOOC is equal to? a. 120 b. 75 c. 180 d. 60 180. In which of the following are the lengths of diagonals equal? a. Rhombus b. Rectangle c. Parallelogram d. Trapezium

181. In a circle, PQ is the diameter of a circle with centre at O. OS is perpendicular to PR. Then OS is equal to? a. QR b. 1/3 QR c. QR d . QR 182. In a circle OM and ON are the perpendicular drawn on the chords PQ and Rs if OM = ON = 6 cm. then? a. PQ RS b. PQ

B in such a way that PA=9 cm and AB= 7 cm. the radius of the circle is? a. 5.5 cm b. 5 cm c. 4 cm d. 4.5 cm 191. ABCD is a cyclic quadrilateral. sides AB and DC, when produced meet at the point P and sides AD and BC, when produced meet at the point Q. if angle ADC= 85 and angle BPC= 40 then angle CQD is equal to? a. 30 b. 40 c. 55 d. 85 192. Two circle of radii 8 cm and 2cm respectively touch each other externally at the point A. PQ is the direct common tangent of those two circles of centers X and Y respectively. Then length of PQ is equal to a. 2 cm b. 3cm c, 4 cm d. 8cm 193. A, B, C are three points on a circle. The tangent at A meet BC produced at T, angle BTA = 40, angle cat =44. The angle subtended by BC at the centre of the circle is? a. 84 b. 92 c. 96 d.104 194. PQ is direct common tangent of two circles of radii R1 and R2 touching each other externally at A. then the value of PQ2 is? a. R1 R2 b. 2 R1 R2 c. 3 R1 R2 d. 4 R1 R2 195. Two circle with radii 5 cm and 8cm touch each other externally at a point A. if a straight line through the point A cuts the circles at point P and Q respectively, then AP : AQ is ? a. 8:5 b. 5: 8 c. 3:4 d. 4:5 196. AB and CD are two parallel chords drown on two opposite sides of their parallel diameter such that AB = 6 cm , CD= 8 cm . if the radius of the circle is 5 cm , the distance between the chords, in cm is? a. 2 b. 7 c. 5 d. 3 197. The radius of a circle is 6 cm. an external point is at a distance of 10 cm from the centre. Then the length of the tangent drawn to the circle from the external point up to the point of contact is? a. 8cm b. 10 cm c. 6cm d.12cm

198. Two circle of radii 4 cm and 9 cm respectively touch each other externally at a point and a common tangent touches them at the points P and Q respectively. Then the area of a square with one side PQ, is a. 81 cm2 b. 121 cm2 c. 196 cm2 d. 144 cm2 199. Two tangent are drawn from a point p to a circle at A and B . O is the centre of the circle. if angle AOP= 60, then angle APB is? a. 120 b. 90 c. 60 d. 30 200. If the length of a chord of a circle, which makes an angle 45 with the tangent drawn at one end point of the chord, is 6cm, then the radius of the circle is? a. 62 cm b. 5 cm c. 32 cm d. 6 cm 201. The radius of a circle is 13 cm and XY is a chord which is at a distance of 12 cm from the centre. The length of the chord is? a. 15 cm b. 12 cm c. 10 cm d. 20 cm 202. SR is a direct common tangent to the circles of radii 8 cm and 3cm respectively, their centers being 13cm apart. If the points of contact, than the length of SR is? a. 12cm b. 11cm c. 17 cm d. 10cm 203. The radius of two concentric circles are 9 cm and 15cm. if the chord of the greater circle be a tangent to the smaller circle, then the length of that chord is? a. 24cm b. 12cm c. 30cm d. 18 cm 204. O and C are respectively the orthocenter and the circum centre of an acute- angled triangle PQR. The point P and O are joined and produced to meet the side QR at S. if angle PQS = 60 and angle QCR = 130, then angle RPS=? a. 30 b. 35 c. 100 d. 60 205. The ratio of circum radii and the inradii of an equilateral triangle is? a. 2:1 b. 4:1 c. 8:1 d. 1:2 206. The ratio of the areas of the circum circle and the in-circle of an equilateral triangle is?

a. 2:1 b. 4:1 c. 8:1 d. 3:2 207. AB= 8cm and CD = 6cm are two parallel chords on the same side of the centre of a circle. The distance between them is 1cm. the radius of the circle is ? a. 5 cm b. 4 cm c. 3 cm d. 2 cm 208. Meeting point of all prependiculars is called as a. centroid b. orthocenter c. circumcenter d. incenter 209. TWO equal circles of radius 4 cm intersect each other such that each passes through the centre of the other. The length of the common chord is ? a.23cm b. 43cm c. 22cm d. 8cm 210.The length of each side of an equilateral triangle is 143 cm. The area of the in-circle, in cm2, is a. 450 b. 308 c. 154 d. 77 211. The circum centre of a triangle ABC is O. if angle BAC = 85 and angle= 75 , then the value of angle OAC is? a. 40 b. 60 c. 70 d.90 212. If I is the incentre of ABC and angle A =50, then the value of angle BIC is? a. 25 b. 115 c. 105 d. 80 213. If S is the circum centre of ABC and angle A =50, then the value of angle BCS is? a. 20 b. 40 c. 60 d. 80 214. If I is the in-centre of ABC and angle BIC = 135 then ABC is ? a. acute angled b. equilateral c. right angled d. obtuse angled 215. If O is the circum centre of ABC and angle OBC = 35, then the angle BAC is equal to? a.55 b. 110 c. 70 d. 35 216. Circum centre of ABC is O. if angle BAC=85 , angle BCA= 80 , then angle OAC is? a. 80 b. 30 c. 60 d. 75

217. O is the centre of a circle and arc ABC subtends an angle of 130 at O. AB is extended to P. then angle PBC is ? a. 75 b. 70 c. 65 d. 80 218. Chords AB and CD of a circle intersect externally at P. If AB = 6 cm , CD= 18 cm and PD = 40 cm , then the length of PA is? a. 5 cm b. 6 cm c. 4 cm d. 5.5 cm 219. Two circles touch each externally at point A and PQ is a direct common tangent which touches the circles at P and Q respectively. Then angle PAQ =? a. 45 b.90 c.80 d. 100 220.The length of two chords AB and AC of a circle are 8 cm and 6 cm and angle BAC = 90 , then the radius of circle is? a. 25 cm b. 20 cm c. 4 cm d. 5 cm 221. Internal bisectors of angles B and C of a triangle ABC meet at O. If angle BAC = 80 , then the value of angle BOC is ? a. 120 b. 140 c. 110 d. 130 222. The angle of a triangle are (x +5) , ( 2x - 3) and ( 3x + 4) . The value of x is? a. 30 b. 31 c. 29 d. 28 223. In a triangle ABC, in centre is O and angle 110, then the measure of angle BAC is? a. 20 b. 40 c. 55 d. 110 224. D is any point on side AC of ABC. if P, Q, x, Y, are the mid - points of AB, BC, AD, and DC respectively, then the ratio of PX and QY is? a. 1:2 b. 1:1 c. 2:1 d. 2:3 225. Let O be the in centre of a triangle ABC and D be a point on the side BC of ABC, such that OD is perpendicular on BC. If angle BOD = 15, then angle ABC=? a. 75 b. 45 c. 150 d. 90 226. In ABC, PQ is parallel to BC. If AP: PB=1:2 and AQ=3 cm, AC is equal to?

a. 6cm b. 9cm c. 12cm d. 8 cm 227.The ratio between the number of sides of two polygon is 2 :1 and the ratio between their interior angle is 4:3. The number of sides of these polygons is respectively? a. 8, 4 b. 10, 5 c.12, 6 d. 14, 7 228. O is the in centre of ABC and angle A= 30, then angle BOC is? a. 100 b. 105 c. 110 d. 90 229. In ABC, angle BAC= 90 and AB= BC. Then the measure of angle ABC is? a. 60 b. 30 c. 45 d. 15 230. A straight line parallel to the base BC of the triangle ABC intersects AB and Ac at the point D and E respectively. If the area of the ABE be 36 cm2. Then the area of the ACD is ? a. 18 cm 2 b. 36 cm2 c. 18 cm2 d. 36cm2 231. In ABC , AD is the internal bisector of angle A. meting the side BC at D . if BD = 5cm , BC= 7.5 cm . Then AB: AC is? a. 2:1 b. 1:2 c.4:5 d. 3:5 232. G is the centroid of ABC. If AG=BC, then angle BGC is ? a. 90 b. 30 c. 60 d. 120 233. In ABC, angle B = 60 , angle c= 40 . if AD bisects angle BAC and AE is perpendicular on BC , then angle EAD is? a. 10 b. 20 c. 40 d. 80 234. Consider ABD such that angle ADB= 20 and C is a point on BD such that AB=AC and CD= CA. Then the measure of angle ABC is? a. 40 b. 45 c.60 d.30 235. The 3 medians AD, BE and CF of ABC intersect at point G. if the area of ABC is 60 cm2 .then the area of the quadrilateral BDGF is? a. 10 cm2 b. 15 cm2 c. 20 cm2 d. 30 cm2 236. If G is the centroid and AD, BE, CF are three medians of ABC with area 72 cm2, , then the area of BDG is? a. 12 cm2 b. 16cm2 c. 24 cm2 d. 8 cm2

237. In ABC, AD is the median and AD = BC. If angle BAD= 30 , then measure of angle ACB is ? a. 90 b. 45 c. 30 d. 60 238. If G be the centroid of ABC and the area of GBD is 6cm2. Where D is the mid- point of side BC , then the area of ABC is ? a. 18 cm2 b. 12cm2 c. 24 cm2 d. 36cm2 239. If the ratio of areas of two similar triangles is 4:9, then the ratio of their corresponding sides is? a. 2:3 b. 4:3 c. 4:5 d. 4:3 240. Let BE and CF be the 2 medians of a ABC and G be their intersection. Also let EF cut AG at O . Then AO:OG is ? a. 1:1 b 1:2 c. 2:1 d. 3:1 241. If the ratio of areas of two similar triangles is 9:16, then the ratio of their correspond-ding sides is? a. 3:5 b. 3:4 c. 4:5 d. 4:3 242. In ABC, P and Q are the middle points of the sides AB and AC respectively. R is a point on the segment PQ such that PR: RQ= 1:2. if PR= 2cm , then BC= ? a. 4cm b. 2cm c. 12cm d. 6 cm 243. ABC is a triangle . the internal bisector of the angles A, angle B and angle C intersect the circumcircle at X, Y and Z respectively. If angle A =50, angle CZY= 30, then angle BYZ, will be? a. 45 b. 55 c.35 d. 30 244. ABC is a right - angled triangle. AD is perpendicular to the hypotenuse BC. If AC = 2 AB, then the value of BD is? a. BC/2 b. BC/3 c. BC/4 d. BC/5 245. IF G is the centroid and AD be A median with length 12 cm of ABC. Then the value of AG is ? a. 4 cm b. 8 cm c. 10 cm d. 6 cm 246. The perimeters of 2 similar triangles ABC and PQR are 36 cm and 24 cm respectively. If PQ= 10 cm, then AB is? a. 25 cm b. 10 cm c. 15 cm d. 20 cm

247. D and E are the mid- points of AB and AC of ABC, BC is produced to any point P DE , DP and EP are joined . Then? a. PED= ABC b. PED=BEC c. ADE= BEC d. BDE= BEC 248. If G is the centroid of ABC and AG= BC, then angle BGC is? a. 75 b. 45 c. 90 d.60 249. ABC and DEF are similar and their areas are respectively 64 cm2 and 121 cm2. If EF= 15.4 cm BC is? a. 12.3 cm b. 11.2 cm c. 12.1 cm d. 11.0 cm 250. What is the ratio of in- radius to the circumradius of a right angled triangle? a. 1:2 b. 1:2 c. 2:5 d. cant be determined 251. In ABC , G is the centroid ,AB =15 cm, BC= 18 cm and AC =25 cm , find GD , where D is the mid-point of BC? a.86 / 3 cm b. 286 /3 c. 8(15 ) /3 cm d. none of these 252. In ABC, AB2 + AC2 = 2500 cm2 and median AD= 25 cm , find BC? a. 25 cm b. 40 cm c. 50 cm d. 48 cm 253. Area of ABC= 30 cm2. D and E are the mid- points of BC and AB respectively. Find area of ADE? a. 10 cm2 b. 7.5 cm2 c. 15 cm2 d. none of these 254. AD is the median of a triangle ABC and O is the centroid such that AO = 10 cm. the length of OD in cm is ? a. 4 b. 5 c. 6 d. 8 255. In an equilateral triangle of side 2a, calculate the length of its altitude? a. 2a3 b. a3 c. a3/2 d. none of these 256. The internal bisectors of angle B and angle C of ABC meet at O. if angle A= 80 then angle BOC is ? a. 50 b. 160 c. 100 d. 130

257. One side other than the hypotenuse of right angle isosceles triangle is 6 cm. The length of the perpendicular on the hypotenuse from the opposite vertex is ? a. 6 cm b. 62 cm c. 4 cm d. 32 cm 258. The triangle is formed by joining the mid- points of the sides AB, BC and CA of ABC and the area of PQR is 6 cm2, then the area of ABC is? a. 36 cm2 b. 12cm2 c. 18cm2 d.24 cm2 259. What is the ratio of side and height of an equilateral triangle? a. 2:1 b. 1:1 c. 2:3 d. 3 :2 260. The difference between altitude and base of a right angled triangle is 17 cm and its hypotenuse is 25 cm . what is the sum of the base and altitude of the triangle? a. 24 cm b. 31 cm c. 34 cm d . cant be determined 261. In ABC, AB = 5cm , AD = 7 cm . If AD is the angle bisector of angle A . then BD : CD is ? a. 25 : 49 b. 49 : 25 c. 6 : 1 d. 5 :7 262. ABCD is a rhombus whose side AB = 4 cm and angle ABC = 120, then the length of diagonal BD is equal to? a. 1 cm b. 2 cm c. 3 cm d. 4cm 263. If an exterior angle of a cyclic quadrilateral be 50, then the interior opposite angle is? a. 130 b. 40 c. 50 d. 90 264. Measure of each interior angle of a regular polygon can never be? a. 150 b. 105 c. 108 d. 144 265. ABCD is a cyclic trapezium whose sides AD and BC are parallel to each other. if angle ABC = 72 , then the measure of the angle BCD is? a. 162 b. 18 c. 108 d. 72 266. The length of the diagonal BD of the parallelogram ABCD is 18 cm. if P and Q are the centroid of the ABC and ADC respectively then the length of the line segment PQ is?

a. 4 cm b. 6 cm c. 9 cm d. 12 cm 267. Each interior angle of a regular polygon is 18 more than eight times an exterior angle . the number of side of the polygon is? a. 10 b. 15 c. 20 d. 25 268. The side AB of A parallelogram ABCD is produced to E in such way that BE= AB . DE intersects BC at Q .The point Q divides BC in the ratio? a. 1:2 b. 1:1 c. 2:3 d. 2:1 269. If the measure of each interior angle of a regular polygon be 144, the number of sides of the polygon is? a. 10 b. 20 c. 24 d. 36 270.Each interior angle of a regular polygon is 144. The number of sides of the polygon is? a. 8 b. 9 c. 10 d. 11 271. If the length of the side PQ of the rhombus PQRS is 6 cm and angle PQR = 120, then the length of QS in cm , is ? a. 4 b. 6 c. 3 d. 5 272. If each interior angle is double of each exterior angle of a regular polygon with n sides, then the value of n is? a. 8 b. 10 c. 5 d. 6 273. If a regular polygon has each of its angles equal to 3/5 times of two right angles, then the number of sides is? a. 3 b. 5 c. 6 d. 8 274. If each interior angle of a regular polygon is 150, what is the number of sides of a polygon? a. 4 b. 8 c. 12 d. 16 275. In a quadrilateral ABCD , If AO and BO are the bisectors of angle A and angle B respectively , angle C = 70 and angle D= 30, then angle AOB=? a. 40 b. 50 c. 80 d. 100 276. How many sides does a regular polygon have whose interior and exterior angles are in the ratio 2:1 ?

a. 3 b. 5 c. 6 d. 12 277. Two parallelograms stand on equal bases and between the same parallels. The ratio of their areas is? a. 1:2 b. 2:1 c. 1:3 d.1:1 278. Any cyclic parallelogram is a? a. rhombus b. trapezium c. quadrilateral d. rectangle 279. The exterior angle of a regular polygon is one third of its interior angle, the number of sides of the polygon is? a. 2 b. 4 c. 6 d. 8 280. A polygon has 35 diagonals, the number of sides of the polygon is ? a. 4 b. 6 c. 8 d. 10 281. In a parallelogram ABCD, the bisector of angle A and angle B meet at O. then angle AOB is equal to? a. 85 b. 90 c. 110 d. none of these 282. How many diagonals are there in an octagon? a. 8 b. 16 c. 18 d. 20 283. A regular polygon is inscribed in a circle. if a side subtends an angle of 72 at the centre, then the number of sides of the polygon is? a. 5 b. 7 c. 6 d. 8 284. A regular hexagon is inscribed in a circle with centre O. then the angle subtended by each side of the square at the centre O is? a. 80 b. 90 c. 60 d. 45 285. If an angle of a parallelogram is 2/3 of its adjacent angle, the smallest angle of the parallelogram is? a. 108 b. 54 c. 72 d. 81 286. If ABCD is a parallelogram in which P and Q are the centroids of ABD and BCD, then PQ equals? a. AQ b. AP c. BP d. DQ

287. ABCD is a parallelogram and BD is a diagonal angle BAD =65 and angle DBC=45 then angle BDC is? a. 65 b. 70 c. 20 d. none of these 288. The ratio of an interior angle to the exterior angle to the exterior angle of a regular polygon is 4:1. The number of sides of polygon is? a. 10 b. 11 c. 12 d. 14 289. The difference between the interior angle and exterior angles of a regular polygon is 60. The number of sides of polygon is? a. 4 b. 5 c. 6 d.8 290. The ratio of an interior angle to the exterior angle to the exterior angle of a regular polygon is 5:1. The number of sides of polygon is? a. 10 b. 11 c. 12 d. 14 291. The exterior angle of a regular polygon is one third of its interior angle, the number of sides of polygon is? a. 2 b. 4 c. 6 d. 8 292. The area of the largest triangle that can be inscribed in a semi circle of radius x in square unit is? a. 4x2 b. x2 c. 2x2 d. 3x2 293. The exterior angle of a regular polygon is one fourth of its interior angle, the number of sides of polygon is? a. 7 b. 5 c. 10 d. 8 294. Find out the ratio of the area of the inscribed and circumscribed circle of the square? a. 2 : 1 b. 1:2 c.2 : 1 d. 1: 2 295. Area of the trapezium formed by x-axis; y-axis and the lines 3x + 4y= 12 and 6x+8y= 60 is: a. 37.5 sq. unit b. 31.5 sq. unit c. 48 sq. unit d. 36.5 sq. unit 296. The length of the side of a square is 14 cm. Find out the ratio of the radii of the inscribed and circumscribed circle of the square?

a. 2 : 1 b. 1:2 c.2 : 1 d. 2: 1 297. The perimeter of a rhombus is 146 cm and one of its diagonals is 55cm. the other diagonal is? a. 92cm b. 73 cm c. 48 cm d. 72 cm 298. If a circle with radius of 10 cm has two parallel chords 16 cm and 12 cm and they are on the same side of the centre of the circle, then the distance between the two parallel chords is? a. 2 cm b. 3 cm c. 5cm d. 8 cm 299. If the length of a chord of a circle at a distance of 12 cm from the centre is 10cm, then the diameter of the circle is? a. 13 cm b. 15 cm c. 26 cm d. 30 cm 300. Area of the in-circle of an equilateral triangle with side 6 cm is? a. /2 cm2 b. 3 cm2 c. 6 cm2 d. 3 cm2 301. If the circumradius of an equilateral triangle be 10 cm, then the measure of its in- radius is? a. 5 cm b. 10 cm c. 20 cm d. 15 cm 302. At the centres of two circles, two arcs of equal length subtend angles of 60 and 75 respectively. The ratio of the radii of the two circles is? a. 5 :2 b. 5:4 c. 3:2 d. 2:1 303. A metal wire when bent in the form of a square encloses an area 484 cm2 , if the same wire is bent in the form of a circle, then its area is? a. 308 cm2 b. 506 cm2 c. 600cm2 d. 616cm2 304. Sides of a parallelogram are in the ratio 5:4 . its area is 1000 sq. units. Altitude on the greater side is 20 units. Altitude on the smaller side is? a. 30 units b. 25 units c. 10 units d. 15 units 305. The perimeter of a rhombus is 40 cm and the measure of an angle is 60, then the area of it is? a. 1003 cm2 b. 50 (3 ) cm2 c. 160 3 cm2 d. 100 cm2

306. The adjacent side of a parallelogram are 36 cm and 27 cm in length. If the distance between the shorter sides is 12 cm . then the distance between the longer sides is ? a. 10 cm b. 12 cm c. 16 cm d. 9 cm 307. The length of a room floor exceeds its breadth by 20 m. The area of the floor remains unaltered when the length is decreased by 10 m but the breadth is increased by 5 m. the area of the floor (in m2) is? a. 280 b. 325 c. 300 d. 420 308. A right angled isosceles triangle is inscribed in a semi - circle of radius 7 cm. the area enclosed by the semi- circle but exterior to the triangle is? a. 14 cm2 b. 28 cm2 c. 44 cm2 d. 68 cm2 309. The radii of two circles are 5 cm and 3 cm, the distance between their centres is 24 cm. Then the length of the transverse common tangent is? a. 16 cm b. 152 cm c. 162 cm d. 15 cm 310. Each of the height and radius of the base of a right circular cone is increased by 100 %. The volume of the cone will be increased by? a. 700% b. 500% c. 300% d. 100% 311. The perimeter of a rhombus is 150 cm and one of its diagonals is 10cm. the other diagonal is? a. 30cm b. 60 cm c. 75 cm d. 70 cm 312. The ratio of the volume of a cube to that of a sphere , which will exactly fit inside the cube is ? a. 2: b. : 6 c. 6 : d. 8 : 313. A cube of side 1 meter is reduced 3 times in the ratio 1:2 . the area of one face of the reduced cube to that of the original cube is in the ratio? a. 1 :4 b. 1 :8 c. 1: 16 d. 1:64 314. If the radius of a sphere is increased by 2m , its surface -area is increased by 704 m2 . What was the radius of the original sphere?

a. 16m b. 15 m c. 14 m d. 12m 315. If a sphere of radius R is divided into four identical parts, then the total surface area of the four parts is ? a. 4 R2 b. 2 R2 c. 8 R2 d. 3 R2 316. Three spherical balls of radius 1cm, 2cm, and 3cm are melted to form a single spherical ball. In the process, the loss of material is 25 %. The radius of the new ball is? a. 6 cm b. 5 cm c. 3 cm d. 2 cm 317. The base of a right prism is an equilateral triangle of area 173 cm2 and the volume of the prism is 10380 cm3. The area of the lateral surface of the prism is (use 3 = 1.73) ? a. 1200cm2 b. 2400 cm2 c. 3600 cm2 d.4380 cm2 318. There is a pyramid on a base which is a regular hexagon of side 2a cm. if every slant edge of this pyramid is of length 5a/2 cm, then the volume of this pyramid is ? a. 3a3 cm3 b. 32 a3 cm3 c. 33 a3 cm3 d. 6 a3 cm3 319. The base of a right prism is an equilateral triangle of side 8 cm and height of the prism is 10 cm. Then the volume of the prism is? a. 320 3 cm3 b. 160 3 cm3 c. 150 3 cm3 d. 3003 cm3 320. The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be 1/27 of the volume of the given cone, at what height above the base, the section has been made? a. 10 cm b. 12 cm c. 16 cm d. 20 cm

1. D 2. C 3. A 4. B 5. C 6. D 7. A 8. A 9. D 10. C 11. D 12. C 13. C 14. B 15. C 16. A 17. A 18. C 19. D 20. B 21. A 22. B 23. D 24. B 25. D 26. D 27. C 28. B 29. B 30. C 31. B 32. D 33. C 34. A 35. B 36. D 37. C 38. B 39. A 40. A 41. D 42. C 43. B 44. D 45. A 46. B 47. B 48. D 49. D 50. D 51. A 52. C 53. A 54. D 55. C 56. B 57. B 58. B 59. B 60. B 61. A 62. A 63. A 64. D 65. A 66. C 67. C 68. D 69. D 70. C 71. B 72. C 73. A 74. B 75. C 76. C 77. D 78. D 79. C 80. D 81. B 82. D 83. C 84. B 85. B 86. A 87. B 88. B 89. C 90. B 91. A 92. D 93. B 94. A 95. A 96. C 97. D 98. A 99. C 100. B 101. A 102. A 103. B 104. B 105. C 106. C 107. B 108. C 109. C 110. A 111. C 112. A 113. C 114. A 115. B 116. B 117. C 118. A 119. B 120. B 121. C 122. B 123. D 124. A 125. D 126. C 127. C 128. D 129. C 130. B 131. A 132. C 133. B 134. C 135. A 136. B 137. B 138. D 139. C 140. B 141. D 142. D 143. A 144. C 145. A 146. D 147. D 148. C 149. C 150. D 151. D 152. D 153. B 154. D 155. B 156. C 157. C 158. D 159. B 160. C 161. C 162. C 163. D 164. C 165. C 166. B 167.D 168. A 169. D 170.B 171. B 172. A 173. A 174. A 175. C 176. D 177. A 178. C 179. A 180. B 181. C 182. D 183. C 184. B 185. B 186. B 187. A 188. D 189. C 190. A 191. A 192. D 193. D 194. D 195. A 196. B 197. A 198. D 199.D 200. C 201. C 202. A 203. A 204. B 205. A 206. A 207. A 208. B 209. B 210. C 211. A 212. B 213. B 214. C 215. A 216. D 217. C 218. C 219. B 220. D 221. D 222. C 223. B 224. B 225. C 226. B 227. B 228. B 229. A 230. D 231. A 232. A 233. A 234. A 235. C 236. A 237. D 238. D 239. A 240. D 241. B 242. C 243. C 244. D 245. B 246. C 247. A 248. C 249. B 250. D 251. D 252. C 253. B 254. B 255. B 256. D 257. D 258. D 259. C 260. B 261. D 262. D 263. C 264. B 265. C 266. B 267. C 268. B 269. A 270. A 271. B 272. D 273. B 274. C 275. B 276. C 277. D 278. D 279. D 280. D 281. B 282. D 283. A 284. C 285. C 286. B 287. B 288. A 289. C 290. C 291. D 292. B 293. C 294. D 295. B 296. B 297. C 298. A 299. C 300. D 301. A 302. B 303. D 304. B 305. B 306. D 307. C 308. B 309. C 310. A 311. A 312. B 313. C 314. D 315. A 316. C 317. C 318. C 319. B 320. D