Practice Test

Q1) Four solid metal spheres with same radii are melted and recast into a hemisphere without losing any metal. What is the percentage change in the total surface area of the solid? Show Answer

Q2) A solid metal right circular cylinder is melted and recast into a right cone of the sane base radius. What is the percentage increase in the height of the solid?

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Q3) Find the total surface area of a hemisphere with radius 28 cm. Show Answer

Q4) A spherical ball whose radius is 21 cm and is dropped in a vessel filled with water up to the brim. Find the volume of water displaced by the ball.

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Q5) The length, breadth and height of a rectangular room are 15ft, 10 ft and 12 ft. It has one door which measures 6 ft x 4 ft and two windows which measures 5 ft x 5 ft. What will be the expenditure incurred to paint the inner walls of the room (excluding the door, windows, the roof and the floor) at the rate of Rs.14 per sq. ft? Show Answer

Q6) A rectangular tank 11m in length, 4m in width and 4m in height is filled with water. How much time (in seconds) is required by a circular pipe which has a radius 20cm to fill the remaining portion of the tank, if water flows into the tank at a rate of 7m/s? Show Answer

Q7) Geeta wants to build a rectangular well 30m wide, 40m long and 20m deep with its open surface on the ground. She also wants to build a wall of uniform width 1 m and height 0.5m around the well using the earth removed from the well. How much extra earth is left after building the wall?

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Q8) A right angled triangle has its area equal to that of a square whose side is 6 cm. What is the altitude of the triangle, if it is twice its base? Show Answer

Q9) Find the area of the circular path of the external radius of the circular plot is 25m and the width of the path is 4m? Show Answer

Q10) If the length of diagonals of a rhombus is 6m and 15m, then what is the area of the rhombus? Show Answer

Q11) If the side of the square increases by 20% then what is the increase in its area and perimeter respectively?

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Q12) Which of the following is a reflex angle? Show Answer

Q13) A line X cuts three parallel line segments AB, CD, and EF at points P, Q and R respectively and another line Y cuts (AB, CD and EF) at points S,T and U respectively. If 2 x PQ = QR and the length of the segment ST is 4 cm, then what is the length of the segment TU? Show Answer

Q14) Which of these is a reflex angle? Show Answer

Q15) A house made of cardboard has 4 walls, a base and a roof top each of dimension 6m. A metal rod is to be placed inside the house for its stability such that the rod should touch of two farthest vertices. Find the length of the rod Show Answer

Q16) How many liters of milk can be filled in a spherical tank of outer diameter of 10 m, with the thickness if the tank being 2 m? Show Answer

Q17) A cylindrical vessel of radius 21m and height 5 m is 60% filled with water. How many pebbles of diameter 2 m are approximately required to fill the vessel? Show Answer

Q18) Find the percentage change in the volume of a cuboid if two of its dimension change by 20% and third dimension changes by 25% Show Answer

Q19) A distemper used in painting a cylindrical box of radius and height of 2cm and having a top and base is now used to paint a spherical ball of the same radius. What percentage of the spherical ball would be painted if the same amount of distemper is used? Show Answer

Q20) A rectangular cuboid has length , breadth and height in the ratio 1: 2: 4. A rod of length 28m equivalent to the body diagonal is placed inside the cuboid. If due to decay, the length of the body diagonal reduces by 25%, how much does it becomes if the dimension are in the same ratio as before? Show Answer

Q21) A gold solid cylinder of radius 7 cm and 4cm and a gold spherical ball of radius 7 cm is melted. An aluminium sheet of length 31 cm and breadth 11 cm is plated with the liquid gold. Find the height of the gold plated with the liquid gold. Find the height of the gold plated on the aluminium sheet? Show Answer

Q22) Two circles with centres P and Q cut each other at two distinct points A and B. The circles have the same radii and neither P nor Q falls within the intersection of the circles. What is the smallest range that includes all possible values of the angle AQP in degrees ? Show Answer

Q23) An equilateral triangle BPC is drawn inside a square ABCD. What is the value of the angle APD in degrees? Show Answer

Q24) An equilateral triangle BPC is drawn inside a square ABCD. What is the value of the value of the angle APD in degrees? Show Answer

Q25) What is the distance (in cm) between two parallel chords of length 32cm and 24cm in a circle of radius 20 cm ? Show Answer

Q26) Four points A,B,C and D lie on a straight line in the X-Y plane, such that AB=BC=CD and the length of AB is 1 m. An ant at A wants to reach a sugar particles at D. But there are insect repellents kept at points B and C. The ant would not go within one metre of any insect repellent. The minimum distance in metres the ant must traverse to reach the sugar particle is
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Q27) What is the ratio of the length of PQ to that of QO? Show Answer

Q28) What is the radius of the circle II ? Show Answer

Q29) Let the radius of each circular park be r and the distance to be traversed by the sprinters A,B and C be a,b and c, respectively. Which of the following is true? Show Answer

Q30) Let ABCDEF be a regular hexagon. What is the ratio of the area of the triangle ACE to that of the hexagon ABCDEF ? Show Answer

Q31) The area of the triangle whose vertices are (a, a), (a+1, a+1), (a+2, a) is Show Answer

Q32) The length of the common chord of two circle of radii 15 cm and 20 cm whose centers are 25 cm apart, is (in cm). Show Answer

Q33) A ladder leans against a vertical wall. The top of the ladder is 8m above the ground. When the bottom of the ladder is moved 2 m farther away from the wall, the top of the ladder rests against the foot of the wall. What is the length of the ladder? Show Answer

Q34) ABCD is a rhombus with the diagonals AC and BD intersecting at the origin on the x-y plane. The equation of the straight line AD is x + y = 1. What is the equation of BC ? Show Answer

Q35) Which of the following statements is necessarily true ? Show Answer

Q36) The points of intersection of three lines 2X + 3Y - 5 = 0, 5X - 7Y + 2 = 0 and 9X - 5Y - 4 = 0 Show Answer

Q37) Consider the five points comprising the vertices of a square and the intersection point of its diagonals. How many triangles can be formed using these points? Show Answer

Q38) Consider obtuse-angled triangles with sides 8 cm, 15 cm and x cm, If x is an integer, then how many such triangles exist? Show Answer

Q39) The proportion of the sheet area that remains after punching is Show Answer

Q40) Find the area of the part of the circle (round punch) falling outside the square sheet. Show Answer

Q41) A semicircle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawn meeting the circumference of the semicircle at D. Given that AC = 2 cm and CD = 6 cm, the area of the semicircle (in sq cm) will be Show Answer

Q42) A jogging park has two identical circular tacks touching each other and a rectangular track enclosing the two circles. The edges of the rectangles are tangential to the circle. Two friends, A and B, start jogging simultaneously from the point where one of the circular tracks touches the smaller side of the rectangular track. A jogs along the rectangular tracks, while B jogs along the two circular tracks in a figure of eight. Approximately, how much faster than A does B have to run, so that they take the same time to return to their starting point? Show Answer

Q43) Two identical circles intersect so that their centers and the points at which they intersect, form a square of side 1 cm. The area in sq cm of the portion that is common to the two circles is Show Answer

Q44) P, Q, S and R are points on the circumference of a circle of radius r, such that PQR is an equilateral triangle and PS is a diameter of the circle. What is the perimeter of the quadrilateral PQSR? Show Answer

Q45) A rectangular sheet of paper, when halved by folding it at the mid point of its longer side, results in a rectangle, whose longer and shorter sides are in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is 2, what is the area of the smaller rectangle? Show Answer

Q46) A piece of paper is in the shape of a right triangle and is cut along a line that is parallel to the hypotenuse, leaving a smaller triangle. There was a 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 square inches before the cut, what is the area (in square inches) of the smaller triangle? Show Answer

Q47) A square tin sheet of side 12 inches is converted into a box with open top in the following steps-The sheet is placed horizontally. Then, equal sized squares, each of side x inches, are cut from the four corners of the sheet. Finally, the four resulting sides are bent vertically upwards in the shape of a box. If x is an integer, then what value of x maximizes the volume of the box? Show Answer

Q48) What is the vertical spacing in cm between two consecutive turns? Show Answer

Q49) The length of the circumference of a circle equals the perimeter of a triangle of equal sides and also the perimeter of a square. The areas covered by the circle, triangle and square are c, t and s, respectively. Then, Show Answer

Q50) Consider two different cloth-cutting processes. In the first one, n circular pieces are cut from a square cloth piece of side a in the following steps : the original square of side a is divided into n smaller squares, not necessarily of the same size; then a circle of maximum possible area is cut from each of the smaller squares. In the second process, only one circle of maximum possible area is cut from the square of side a and the process ends there. The cloth pieces remaining after cutting the circles are scrapped in both the processes. The ratio of the total area of scrap cloth generated in the former to that in the latter is Show Answer

Q51) Neeraj has agreed to mow the farm lawn, which is a 20 m by 40 m rectangle. The mover mows a 1 m wide strip. If Neeraj starts at one corner and mows around the lawn towards the center, about how many times would he go round before he has mowed half the lawn? Show Answer

Q52) A rectangular pool 20 m wide and 60 m long is surrounded by a walkway of uniform width. If the total area of the walkway is 516 sq m, how wide, in meters, is the walkway? Show Answer

Q53) Euclid has a triangle in mind. Its longest side has length 20 and another of its sides has length 10. Its area is 80. What is the exact length of its third side? Show Answer

Q54) A certain city has a circular wall around it and this wall has four gates pointing north south, east and west. A house stands outside the city, 3 km north of the north gate and it can just be seen from a point 9 km east of the south gate. What is the diameter of the wall that surrounds the city? Show Answer

Q55) A square whose side is 2 m, has its corners cut away so as to form an octagon with all sides equal. Then, the length of each side of the octagon, in meters is Show Answer

Q56) What is the number of distinct triangles with integral valued sides and perimeter as 14? Show Answer

Q57) A farmer has decided to build a wire fence along one straight side of his property. For this, he planned to place several fence-posts at 6 m intervals, with posts fixed at both ends of the side. After he bought the posts and wire, he found that the number of posts he had bought was 51 less than required. However, he discovered that the number of posts he had bought would be just sufficient if he spaced them 8 m apart. What is the length of the side of his property and how many posts did he buy? Show Answer

Q58) What is the area that can be grazed by the cow, if the length of the rope is 8 m? Show Answer

Q59) What is the area that can be grazed by the cow, if the length of the rope is 12 m? Show Answer

Q60) In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length of longer side. What is the ratio of the shorter to the longer side? Show Answer

Q61) The value of each of a set of coins varies as the square of its diameter. If its thickness remains constant and varies as the thickness, if the diameter remain constant. If the diameter of two coins are in the ratio 4 : 3, what should be the ratio of their thicknesses be if the value of the first is four times that of the second? Show Answer

Q62) A wooden box (open at the top) of thickness 0.5 cm, length 21 cm, width 11 cm and height 6 cm is painted on the inside. The expenses of painting are Rs. 70. What is the rate of painting per square centimeter? Show Answer

Q63) From a circular sheet of paper with a radius 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of uncut to the cut portion? Show Answer

Q64) A cube of side 12 cm is painted red on all the faces and then cut into smaller cubes, each of side 3 cm. What is the total number of smaller cubes having none of their faces painted? Show Answer

Q65) A right circular cone of height h is cut by a plane parallel to the base at a distance h/3 from the base, then the volume of the resulting cone and the frustum are in the ratio Show Answer

Q66) The length of a ladder is exactly equal to the height of the wall it is leaning against. If lower end of the ladder is kept on a stool of height 3 m and the stool is kept 9 m away from the wall, the upper end of the ladder coincides with the top of the wall. Then, the height of the wall is Show Answer

Q67) The sides of a triangle are 5, 12 and 13 unit. A rectangle is constructed, which is equal in area to the triangle, has a width of 10 unit. Then, the perimeter of the rectangle is Show Answer

Q68) Four friends start from four towns, which are at the four corners of an imaginary rectangle. They meet at a point which falls inside the rectangle, after traveling the distance of 40 m, 50 m and 60 m. The maximum distance that the fourth could have traveled is approximately. Show Answer

Q69) Three identical cones with base radius r are placed on their bases so that each in touching the other two. The radius of the circle drawn through their vertices is Show Answer

Q70) The diameter of hollow cone is equal to the diameter of a spherical ball. If the ball is placed at the base of the cone, what portion of the ball will be outside the once? Show Answer

Q71) A slab of ice 8 inches in length, 11 inches in breadth and 2 inches thick was melted and resolidifed in the form of a rod of 8 inches diameter. The length of such a rod, in inches, in nearest to Show Answer

Q72) Which one of the following cannot be the ratio of angles in a right angled triangle? Show Answer

Q73) In a triangle, ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC? Show Answer

Q74) Two circles, both of radii 1 cm, intersect such that the circumference of each one passes through the center of the other. What is the area (in sq cm) of the intersecting region? Show Answer

Q75) Consider a right circular cone of base radius 4 cm and height 10 cm. A cylinder is to be placed inside the cone with one of the flat surfaces resting on the base of the cone. Find the largest possible total surface area (in sq cm) of the cylinder Show Answer

Q76) If the circumference and area of circle are numerically equal, then the diameter is equal to Show Answer

Q77) The diameter of a toy wheel is 14 cm. What is the distance traveled by it in 15 revolutions ? Show Answer

Q78) If the circumference of a circle is decreased by 50% then the percentage of decrease in its area is Show Answer

Q79) The perimeter of two squares are 40 cm and 32 cm. The perimeter of a third square whose area is the difference of the area of two squares is Show Answer

Q80) The length (in cm) of a chord of a circle of radius 13 cm at a distance of 12 cm from its center is Show Answer

Q81) The perimeter of a rectangle is 180 m and the difference between length and breadth is 8 m then the area of rectangle is Show Answer

Q82) The area of a rectangle is equal to the area of a circle with circumstances equal to 39.6 m. What is the length of a rectangle if the breadth is 4.5 m ? Show Answer

Q83) The perimeter of a square is twice the perimeter of a rectangle. If the perimeter of the square is 72 and the length of the rectangle is 12 cm, what is the difference between the breadth of the rectangle and the side of the square ? Show Answer

Q84) The area of a rectangle is 180 sq cm. If the length of a rectangle is 3 cm more than its breadth, what is the breadth of the rectangle? Show Answer

Q85) The area of a circle is 154 sq. cm what is the circumference of a circle? Show Answer

Q86) The area of a square is 225 sq cm which is equal to the area of a rectangle. The length of the rectangle is 16 cm more than the breadth of the rectangle. What is the respective ratio between the side of the square and the breadth of the rectangle ? Show Answer

Q87) The length of a rectangle is twice its breadth. Also the length of the rectangle is equal to the diameter of a circle of area 154 sq cm what is the area of the rectangle ? Show Answer

Q88) The area of a square is equal to the area of a rectangle of length 32 cm. The perimeter of the rectangle is 80 cm. What is the side of the square? Show Answer

Q89) If the perimeter of a square is equal to the radius of a circle whose area is 39424 sq cm what is the area of the square ? Show Answer

Q90) The sum of the circumference of a circle and the perimeter of a square is equal to 272 cm. The diameter of the circle is 56 cm What is the sum of the areas of the circle and the square ? Show Answer

Q91) The circumference of two circles is 88 m and 220 m respectively. What is the difference between the area of the larger circle and that of the smaller circle? Show Answer

Q92) What would be the area of a circle whose diameter is 182 cm ? Show Answer

Q93) The area of a square is four third the area of a rectangle. If the area of the square is 1024 sq cm and the length of the rectangle is 64 cm. What is the difference between the breadth of the rectangle and the side of the square ? Show Answer

Q94) The diameter of a wheel is 98 cm. The number of revolutions in which it will have to cover a distance of 1540 m is Show Answer

Q95) The length of a rectangle is three-fifth of the side of a square. The radius of a circle equal to side of the square. the circumference of the circle is 132 cm. What is the area of the rectangle, if the breadth of the rectangle is 8 cm Show Answer

Q96) The smallest side of a right angle triangle is 8 cm less than the side of a square of perimeter 56 cm. The second largest side of the right angled triangle is 4 cm less than the length of the rectangle of area 96 sq. cm and breadth 8 cm. What is the largest side of the right angle triangle ? Show Answer

Q97) The area of a square is three-fifth the area of a rectangle. The length of the rectangle 25 cm and its breadth is 10 cm less then its length. What is the perimeter of the square ? Show Answer

Q98) The length of a rectangle is 16 cm which is 2 cm more than the diameter of a circle. What is the area of the circle? Show Answer

Q99) If the length of a rectangle is increased by 10% and its breadth is decreased by 10% then its area Show Answer

Q100) Three horses are tethered at 3 corners of a triangular plot of land having sides 20 m, 30 m and 40 m each with a rope of length 7m. The are in sq m of the region of this plot which can be grazed by the horses is Show Answer

Q101) What would be the area of a square whose diagonal measures 28 cm ? Show Answer

Q102) A man riding a bicycle completes one lap of a circular field along its circumference at the speed of 79.2 km/hr in 2 min 40 sec What is the area of the field? Show Answer

Q103) The area of a rectangle is equal to the area of a circle with circumference equal to 220 m. What is the length of the rectangle of its breadth is 50 m? Show Answer

Q104) The area of a square is 1024 sq cm. What is the file ratio of the length to the breadth of a rectangle whose length is twice the side of the square and breadth is 12 cm less than the side of this square ? Show Answer

Q105) What is the area of a circle whose radius is equal to the side of a square whose perimeter is 112 m ? Show Answer

Q106) The breadth of a rectangle is half of its length. Also the length of the rectangle is equal to the radius of a circle of area 154 sq cm. What is the perimeter of the rectangle ? Show Answer

Q107) The respective ratio of the length and breadth of a rectangular plot is 3 : 2. If the length of the plot is 40 m more than its breadth what is the perimeter of the rectangular plot ? Show Answer

Q108) If each side of a square is increased by 10% then what is the percentage of increase the area ? Show Answer