
question_answer1) The area of a rhombus is \[28\text{ }c{{m}^{2}}\] and one of its diagonals is 4 cm. Find its perimeter.
A) \[4\sqrt{53}\,\,cm\]
B) \[36\,cm\]
C) \[2\sqrt{53}\,cm\]
D) \[44\,cm\]
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question_answer2) The area of a trapezium is \[28\text{ }c{{m}^{2}}\]and one of its parallel sides is\[6\text{ }cm\]. If its altitude is \[4\text{ }cm,\] find its other parallel side.
A) \[4\text{ }cm\]
B) \[\text{8 }cm\]
C) \[\text{6 }cm\]
D) \[\text{10 }cm\]
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question_answer3) The perimeter of a trapezium is \[\text{52 }cm\] and its nonparallel sides are each equal to \[10\text{ }cm\]. If its altitude is 8 cm, what is its area?
A) \[128\,\,c{{m}^{2}}\]
B) \[112\,\,c{{m}^{2}}\]
C) \[118\,\,c{{m}^{2}}\]
D) \[124\,\,c{{m}^{2}}\]
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question_answer4) A man bought a rectangular field of length \[144\text{ }m\] and width \[64\text{ }m\]. In exchange for this field he wanted to buy a square field of the same area. What would the side of the square field be?
A) \[104\text{ }m\]
B) \[208\text{ }m\]
C) \[96\,m\]
D) \[416\,m\]
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question_answer5) The area of a parallelogram is \[120\text{ }c{{m}^{2}}\]and its altitude is 10 cm. Find the length of the base.
A) \[24\,cm\]
B) \[12\,cm\]
C) \[8\,cm\]
D) \[4\,cm\]
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question_answer6) What is the area of an isosceles triangle having base 'Y' cm and one side 'Y' cm?
A) \[\frac{x}{2}\sqrt{{{y}^{2}}+\frac{{{x}^{2}}}{4}}c{{m}^{2}}\]
B) \[\frac{x}{2}\sqrt{\frac{4{{y}^{2}}{{x}^{2}}}{4}}c{{m}^{2}}\]
C) \[\frac{{{x}^{2}}{{y}^{2}}}{4}c{{m}^{2}}\]
D) \[\frac{{{x}^{2}}+{{y}^{2}}}{4}c{{m}^{2}}\]
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question_answer7) What is the length of the diagonal of a square whose area is\[16900\text{ }{{m}^{2}}\]?
A) \[130\,m\]
B) \[130\sqrt{2}\,m\]
C) \[169\,m\]
D) \[144\,m\]
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question_answer8) The sides of a triangle are \[3\text{ }cm,\text{ }5\text{ }cm\] and \[\text{4 }cm\]. What is its area?
A) \[6\,\,c{{m}^{2}}\]
B) \[75\,\,c{{m}^{2}}\]
C) \[5\sqrt{2}\,\,c{{m}^{2}}\]
D) \[10\,\,c{{m}^{2}}\]
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question_answer9) The Lase of an isosceles right triangle is\[30\text{ }cm\] Find its area.
A) \[225\,c{{m}^{2}}\]
B) \[225\sqrt{3}\,c{{m}^{2}}\]
C) \[5\sqrt{2}\,c{{m}^{2}}\]
D) \[6\sqrt{3}\,c{{m}^{2}}\]
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question_answer10) The sides of a triangle are \[16\text{ }cm,\] \[30\text{ }cm\] and\[34\text{ }cm\]. What is its area?
A) \[120\,c{{m}^{2}}\]
B) \[260\,c{{m}^{2}}\]
C) \[240\,c{{m}^{2}}\]
D) \[272\,c{{m}^{2}}\]
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question_answer11) The adjacent sides of a parallelogram are \[8\text{ }cm\] and\[9\text{ }cm\]. The diagonahnining the ends of these sides is\[13\text{ }cm\]. Calculate the area of the parallelogram.
A) \[72\,c{{m}^{2}}\]
B) \[12\sqrt{35}\,c{{m}^{2}}\]
C) \[24\sqrt{35}\,c{{m}^{2}}\]
D) \[150\,c{{m}^{2}}\]
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question_answer12) The sides of a triangle are \[11\text{ }cm,\text{ }15\text{ }cm\]and\[16\text{ }cm\]. What is the measure of the altitude to the largest side?
A) \[30\sqrt{7}\,cm\]
B) \[30\,cm\]
C) \[\frac{15\sqrt{7}}{4}\,cm\]
D) \[\frac{15\sqrt{7}}{2}\,cm\]
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question_answer13) The perimeter of a triangular field is \[144\text{ }m\] and the ratio of its sides is\[3:4:5\]. What is the area of the field?
A) \[864\,{{m}^{2}}\]
B) \[468\,{{m}^{2}}\]
C) \[824\,{{m}^{2}}\]
D) \[486\,{{m}^{2}}\]
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question_answer14) A rectangular field has its length and breadth in the ratio \[5:3\]. Its area is \[3.75\]hectares. Find the cost of fencing it at Rs.5 per metre.
A) \[Rs.\,400\]
B) \[Rs.\,4000\]
C) \[Rs.\,1000\]
D) \[Rs.\,500\]
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question_answer15) What is the percentage change in the area of a rectangle obtained by decreasing its length and increasing its breadth by 5%?
A) \[2.5%\]increase
B) \[0.25%\] increase
C) \[0.25%\]decrease
D) \[2.5%\] decrease
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question_answer16) Find the area of the sector of a circle, whose radius is 6 m when the angle at the centre is\[{{42}^{o}}\].
A) \[13.2\,{{m}^{2}}\]
B) \[14.2\,{{m}^{2}}\]
C) \[13.4\,{{m}^{2}}\]
D) \[14.4\,{{m}^{2}}\]
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question_answer17) lf the radius of a circle is \[\frac{7}{\sqrt{\pi }}cm,\] what is the area of the circle?
A) \[154\,c{{m}^{2}}\]
B) \[\frac{49}{\pi }\,c{{m}^{2}}\]
C) \[22\,c{{m}^{2}}\]
D) \[49\,c{{m}^{2}}\]
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question_answer18) Find the area of a segment of a circle of radius \[21\text{ }cm\] if the arc of the segment has a measure of \[{{60}^{o}}\]. (Take \[\sqrt{3}=1.73\])
A) \[45.27\,c{{m}^{2}}\]
B) \[40.8\,c{{m}^{2}}\]
C) \[40.27\,c{{m}^{2}}\]
D) \[42.07\,c{{m}^{2}}\]
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question_answer19) An aquarium is in the form of a cuboid whose external measures are\[80\text{ }cm\times 30\text{ }cm\times 40\text{ }cm\]The base, side faces and back face are to be covered with a coloured paper. Find the area of the paper needed.
A) \[2000\,c{{m}^{2}}\]
B) \[8000\,c{{m}^{2}}\]
C) \[3000\,c{{m}^{2}}\]
D) \[1000\,c{{m}^{2}}\]
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question_answer20) A rectangular piece of paper \[11\text{ }cm\times 4\,cm\] is folded without overlapping to make a cylinder of height\[4\text{ }cm\]. Find the volume of the cylinder.
A) \[38.5\,c{{m}^{3}}\]
B) \[40.5\,c{{m}^{3}}\]
C) \[41.5\,c{{m}^{3}}\]
D) \[42.5\,c{{m}^{3}}\]
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question_answer21) In a building, there are 24 cylindrical pillars. The radius of each pillar is \[28\text{ }cm\] and height is\[4\text{ }m\]. Find the total cost of painting the curved surface area of all pillars at the rate of Rs.8 per \[{{m}^{2}}\].
A) \[Rs.1352.68\]
B) \[Rs.1351.68\]
C) \[Rs.1353.68\]
D) \[Rs.1340.68\]
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question_answer22) A sector of \[{{120}^{o}}\] cut out from a circle has an area of \[9\frac{3}{7}\,sq.\,cm\]. What is the radius of the circle?
A) \[3\,cm\]
B) \[2.5\,cm\]
C) \[3.5\,cm\]
D) \[3.6\,cm\]
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question_answer23) Find the radius of the cylinder whose lateral surface area is \[704\text{ }c{{m}^{2}}\]and height is\[8\text{ }cm\].
A) \[6\,cm\]
B) \[4\,cm\]
C) \[8\,cm\]
D) \[14\,cm\]
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question_answer24) In the figure given, RSTV is a square inscribed in a circle with centre O and radius V. What is the total area of unshaded region?
A) \[{{r}^{2}}(\pi 2)\,sq.\,units\]
B) \[2r(2\pi )\,sq.\,units\]
C) \[\pi ({{r}^{2}}2)\,sq.\,units\]
D) \[(\pi {{r}^{2}}8r)sq.\,units\]
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question_answer25) The dimensions of a hall are \[40\text{ }m,\text{ }25\text{ }m\] and\[20\text{ }m\]. If each person requires 200 cubic metres of space, how many persons can be accommodated in the hall?
A) \[120\]
B) \[150\]
C) \[140\]
D) \[100\]
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question_answer26) Three cylinders each of height \[16\text{ }cm\] and radius of base \[\text{4 }cm\] are placed on a plane so that each cylinder touches the other two. What is the volume of the region enclosed between the three cylinders?
A) \[98\,\left( 4\sqrt{3}\pi \right)\,c{{m}^{3}}\]
B) \[98\,\left( 2\sqrt{3}\pi \right)\,c{{m}^{3}}\]
C) \[98\,\left( \sqrt{3}\pi \right)\,c{{m}^{3}}\]
D) \[128\,\left( 2\sqrt{3}\pi \right)\,c{{m}^{3}}\]
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question_answer27) From a cuboid measuring \[7\text{ }cm\] by \[8\text{ }cm\] by \[9\text{ }cm,\] a cube of side \[5\text{ }cm\] is cut. What is the volume of the remaining cuboid?
A) \[397\,c{{m}^{3}}\]
B) \[389\,c{{m}^{3}}\]
C) \[398\,c{{m}^{3}}\]
D) \[379\,c{{m}^{3}}\]
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question_answer28) A stone of volume \[36\text{ }c{{m}^{3}}\]is placed in a rectangular tank measuring \[8\text{ }cm\] by \[6\text{ }cm\] by \[\text{5 }cm\]. A student wants to fill the tank with water to a height of \[\text{4 }cm\]. What is the volume of water needed?
A) \[\text{218 }c{{m}^{3}}\]
B) \[\text{156 }c{{m}^{3}}\]
C) \[\text{228 }c{{m}^{3}}\]
D) \[\text{192 }c{{m}^{3}}\]
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question_answer29) An empty tank was \[\frac{2}{5}\] full after \[1.5\,l\] of water was poured in it. The base area of the tank was\[250\text{ }c{{m}^{2}}\]. What was the height of the tank?
A) \[15\,cm\]
B) \[5\,cm\]
C) \[4\,cm\]
D) \[8\,cm\]
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question_answer30) A cuboid measuring \[20\,cm\] by \[10\,cm\] by \[4\,cm\] is constructed using \[2\,cm\] cubes. How many cubes were needed?
A) \[200\]
B) \[300\]
C) \[100\]
D) \[150\]
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question_answer31) What is the volume of a cylindrical container with base radius \[5\text{ }cm\] and height\[20\text{ }cm\]? (Take \[n=3.14\].)
A) \[157\,l\]
B) \[1.57\,l\]
C) \[1570\,l\]
D) \[15.7\,l\]
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question_answer32) What is the height of a cuboid of volume \[216\text{ }c{{m}^{3}}\]if its length and breadth measure \[8\text{ }cm\] and \[\text{6 }cm\]?
A) \[4.5\,m\]
B) \[6\,m\]
C) \[4.8\,m\]
D) \[9\,m\]
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question_answer33) A tank with a square base has a volume of \[384\text{ }c{{m}^{3}}.\] If its height is \[6\text{ }cm,\] find the length of the side of the square base.
A) \[\text{10 }cm\]
B) \[\text{8 }cm\]
C) \[\text{12 }cm\]
D) \[\text{6 }cm\]
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question_answer34) In the figure given, ABCD is a parallelogram and CDEF is a rectangle. What is the total area of the figure?
A) \[35\,c{{m}^{2}}\]
B) \[30\,c{{m}^{2}}\]
C) \[25\,c{{m}^{2}}\]
D) \[20\,c{{m}^{2}}\]
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question_answer35) What is the area of the shaded region in the following figure?
A) \[51.33\,c{{m}^{2}}\]
B) \[102.7\,c{{m}^{2}}\]
C) \[205.34\,c{{m}^{2}}\]
D) \[108.6\,c{{m}^{2}}\]
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question_answer36) If the areas of three adjacent faces of a rectangular block are in the ratio of \[2:3:4\] and its volume is \[9000\text{ }c{{m}^{3}},\] what is the length of the shortest side?
A) \[10\,cm\]
B) \[15\,cm\]
C) \[20\,cm\]
D) \[30\,cm\]
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question_answer37) Two cylinders of equal volume have their heights in the ratio \[2:1\] .What is the ratio of their radii?
A) \[2:1\]
B) \[1:2\]
C) \[\sqrt{2}:1\]
D) \[1:\sqrt{2}\]
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question_answer38) A well is to be dug \[20\text{ }m\] deep, \[2.25\text{ }m\] inside diameter, with a brick lining of \[0.35m\]thickness. What is the amount of brick work done?
A) \[14.75\,{{m}^{3}}\]
B) \[57.2\,{{m}^{3}}\]
C) \[136.75\,{{m}^{3}}\]
D) \[572\,{{m}^{3}}\]
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question_answer39) A rectangular sheet of paper, \[36\text{ }cm\times 22\text{ }cm,\]is rolled along its length to form a cylinder. Find the volume of the cylinder so formed.
A) \[2268\,c{{m}^{3}}\]
B) \[226.8\,c{{m}^{3}}\]
C) \[226\,c{{m}^{3}}\]
D) \[23.4\,c{{m}^{3}}\]
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question_answer40) A wooden box (open at the top) of thickness \[0.5\text{ }cm,\] length \[21\text{ }cm,\] width \[11\text{ }cm\] and height \[\text{6 }cm\] is painted on the inside. The expense for painting is \[Rs.\,70\]. What is the rate of painting per square centimetre?
A) \[Rs.\,0.7\]
B) \[Rs.\,0.5\]
C) \[Rs.\,0.1\]
D) \[Rs.\,0.2\]
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question_answer41) If each edge of a cube is increased by \[25%,\] what is the percentage increase in its surface area?
A) \[25%,\]
B) \[48.75%\]
C) \[50%\]
D) \[56.25%\]
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question_answer42) How many cubes of side \[4\text{ }cm\] can fill a rectangular box measuring \[60\text{ }cm\] by \[40\text{ }cm\] by\[24\text{ }cm\]?
A) \[900\]
B) \[90\]
C) \[3600\]
D) \[600\]
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question_answer43) A pit \[10\text{ }m\] long and \[2\text{ }m\] wide is filled with \[4.8\text{ }{{m}^{3}}\]of sand. What is the depth of the pit?
A) \[14\,cm\]
B) \[2.4\,cm\]
C) \[24\,cm\]
D) \[12\,cm\]
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question_answer44) The capacity of a cup is\[300\text{ }ml\]. The capacity of a jug is twice that of a cup. What is the capacity of 3 cups and 3jugs?
A) \[2.7\,l\]
B) \[2700\,l\]
C) \[27\,l\]
D) \[270\,l\]
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question_answer45) The volume of a cube is\[512\text{ }c{{m}^{3}}\]. After a smaller cube is out off from it, its volume is \[448\,c{{m}^{3}}\]. What is the length of each side of the smaller cube?
A) \[6\,cm\]
B) \[7\,cm\]
C) \[9\,cm\]
D) \[4\,cm\]
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