We provide perimeter and area practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on perimeter and area skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of perimeter and area Questions

Question No | Questions | Class |
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1 | A horse is tied to a vertex of a field having the shape of an equilatera triangle with a rope, the length of which is half of the length of a side of the triangle. The percentage of the total area of the field over which the horse can graze is approximately A . 20 to 22% B. 25 to 27% c. 30 to 32% D. 48 to 50% |
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2 | Find the area of a quadrant of a circle whose radius is ( 7 mathrm{cm} ) |
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3 | A circular garden has an area of ( 314 m^{2} ) A sprinkle at the centre of garden can cover an area that has a radius of ( 12 mathrm{m} ) Will the sprinkle water the entire garden? |
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4 | A postage stamp is ( 12 mathrm{mm} ) in breadth and ( 20 mathrm{mm} ) in length. Find the area of ( operatorname{stamp} operatorname{in} c m^{2} ) A . 0.24 в. 240 c. 24 D. 2.4 |
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5 | If the radius of a circle is increased by ( 10 %, ) then the corresponding area of the new circle will be ( ldots(pi=3.14) ) A. ( 121 pi r^{2} ) 2 В. ( 12.1 pi r^{2} ) c. ( 1.21 pi^{2} ) D. None of the given three |
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6 | n figure OPQR is a rhombus, three of whose vertices lie on the circle with centre ( 0 . ) If the area of rhombus is 32 ( sqrt{3} mathrm{cm}^{2}, ) find the radius of the circle. ( 4.6 mathrm{cm} ) B. 2 cm ( c .4 mathrm{cm} ) ( D ) |
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7 | The length, breadth and height of a room are ( 850 mathrm{cm}, 625 mathrm{cm} ) and ( 475 mathrm{cm} ) Find the length of the longest rod that cam measure the dimensions of the room exactly. |
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8 | The girth of the roller is ( 75 mathrm{cm} ) and its width is 2 metres. How many revolutions must it make to roll a field whose area is 3 hectare? A . 2000 B. 20000 ( c cdot 200 ) D. NONE OF THESE |
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9 | Is it true to say that area of a segment of a circle is less than the area of its corresponding sector? Why? A. yes, it is true for minor segment since ar.minor segment = ar.sector-triangle made by the radii and the chord of the segment. B. Yes, it is only true for major segment since ar.minor segment = – ar.sector-triangle made by the radii and the chord of the segment C. No, it is only true for major segment since ar.minor segment =ar.sector-triangle made by the radii and the chord of the segment. D. No, it is only true for minor segment since ar.minor segment =ar.sector-triangle made by the radii and the chord of the segment. |
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10 | If the perimeter is half of the area of the circle numerically then find the radius of the circle. |
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11 | A circle of radius ( 4 mathrm{cm} ) is cut into 6 equal pieces find area of each part |
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12 | n given figure, ABCD is a rectangle, having ( A B=20 mathrm{cm} ) and ( B C=14 mathrm{cm} ) Two sectors of ( 180^{circ} ) have been cut-off. Calculate the area of the shaded region. |
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13 | The other end of the diameter through the point (-1,1) on the circle ( x^{2}+ ) ( y^{2}-6 x+4 y-12=0 ) is : ( mathbf{A} cdot(-7,5) ) B. (-7,-5) c. (7,-5) D. (7,5) |
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14 | A pond ( 100 m ) in diameter is surrounded by a circular grass walk ( 2 m ) wide. How many square meters of grass is there on the walk? ( mathbf{A} cdot 98 pi ) в. ( 100 pi ) ( c .204 pi ) D. 202pi |
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15 | A path ( 5 mathrm{cm} ) wide runs along inside a square park of side ( 100 mathrm{cm} ). Find the area of the path. Also find the cost of cementing at the the rate of Rs 250 per 10 sq.cm. |
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16 | From a piece of cardbord, in the shape of a trapezium ( A B C D, ) and ( A B | C D ) and ( angle B C D=90^{circ}, ) quarter circle is removed. Given ( A B=B C=3.5 mathrm{cm} ) and ( D E=2 c m . ) Calculate the area of the remaining piece of the cardboard (Take to be ( left.frac{22}{7}right) ) |
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17 | Mamta knitted a circular pattern and then she put a handle around it and used it as a hand fan. Find the area of the design she has made, if outer circle radius is ( 17.5 mathrm{mm} ) and inner circle radius is ( 7.5 mathrm{mm} .left[boldsymbol{U} boldsymbol{s e} boldsymbol{pi}=frac{22}{7}right] ) |
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18 | A wheel takes ( mathrm{m} ) rotations to travel a certain distance while another whee whose diameter is four times bigger than it takes n rotations to travel the same distance. The relation between A ( cdot m=4 n ) B. ( m=2 n ) ( c cdot 2 m=n ) D. ( 4 mathrm{m}=mathrm{n} ) |
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19 | In the figure the boundary of the shaded region consists of four semicircular ( operatorname{arcs}, ) the smallest two being equal. If the diameter of the largest is ( 14 mathrm{cm} ) and of the smallest is ( 3.5 mathrm{cm}, ) find 1. The length of the boundary 2. The area of the shaded region |
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20 | In the figure, ( O ) is the center of the circle ( angle R P S=40, ) then ( angle O Q P ) is equal to A .140 в. 130 ( c .90 ) ( D ) |
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21 | Four equal circles describe the four corners of a square such that each touches two of the others. If each side of the square is ( 14 mathrm{cm} ), then the area enclosed between the circumferences of the circle is: A. 24 sq cm B. 42 sq ( mathrm{cm} ) c. 154 sq ( mathrm{cm} ) D. 196 sq ( mathrm{cm} ) |
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22 | Consider the railway platform which is in square shape having side length ( 2 k m . ) Then area of the platform is 4 A . ( m ) в. ( k m ) ( mathrm{c} cdot k m^{2} ) D. ( m^{2} ) |
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23 | 60. A copper wire is bent in the shape of a square of area 81cm2. If the same wire is bent in the form of a semicircle, the radius (in cm) of the semicircle is (Take T = 22) (1) 16 (2) 14 (3) 10 (4) 7 |
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24 | The difference between the circumference and radius of a circle is ( 30 pi . ) Find the diameter of circle. A. ( frac{30 pi}{2 pi-1} ) в. ( frac{60 pi}{2 pi-1} ) c. ( frac{2 pi-1}{60 pi} ) D. None |
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25 | n Fig. ( P Q R ) is an equilateral triangle. Arcs have been drawn with radii ( 14 mathrm{cm} ) each and with centres ( boldsymbol{P}, boldsymbol{Q} ) and ( R ). The area of the shaded region is A ( cdot 102.6 mathrm{cm}^{2} ) B ( .206 mathrm{cm}^{2} ) ( mathbf{c} cdot 308 mathrm{cm}^{2} ) D. ( 345 mathrm{cm}^{2} ) |
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26 | A path 7 meters wide surrounds a circular lawn ( 252 mathrm{m} ) in diameter. Find the area of path. |
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27 | The cost of fencing a rectangular field at ( R s 18 ) per metre is ( R s 1980 . ) If the width of the field is ( 23 m ) find its length. |
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28 | In the figure, there are shown sectors of two concentric circles of radii ( 7 mathrm{cm} ) and ( 3.5 mathrm{cm} . ) Find the area of the shaded region. ( left(boldsymbol{U} boldsymbol{s e} boldsymbol{pi}=frac{boldsymbol{2} boldsymbol{2}}{boldsymbol{7}}right) ) A. 10.425 sq. ( mathrm{cm} ) B. 10.125 sq. ( mathrm{cm} ) c. 9.625 sq. ( mathrm{cm} ) D. 9.152 sq. ( mathrm{cm} ) |
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29 | Find the area of the sheet required to make a cylindrical container which is open at one side and whose diameter is ( 28 mathrm{cm} ) and height is ( 20 mathrm{cm} ). find the approximate area of the sheet required to make a lid of height ( 2 mathrm{cm} ) for this container. |
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30 | Find the circumference and area of a circle of radius ( 8.4 mathrm{cm} ) |
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31 | A rectangular piece is ( 20 mathrm{m} ) long and 15 ( mathrm{m} ) wide. Form its four corners, quadrants of radii ( 3.5 mathrm{m} ) have been cut Find the area of the remaining part. |
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32 | The perimeter of a semi-circular protector is ( 72 mathrm{cm} ) then its radius is ( mathrm{cm} ) A . 36 B. 28 ( c cdot 14 ) D. 7 |
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33 | A floor is ( 5 mathrm{m} ) long and ( 4 mathrm{m} ) wide. ( mathrm{A} ) square carpet of sides ( 3 mathrm{m} ) is laid on the floor. Find the area of the floor that is not carpeted. |
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34 | The cost of levelling a square lawn at Rs.15 per square meter is ( R s .19,935 ) Find the cost of fencing the lawn at Rs.22 per meter. |
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35 | EF are a AD re- 58. If ABCD is a rectangle, E. the mid-points of BC and A spectively and G is any poin EF, then A GAB equals : v point on (1) (rectangle ABCD) (2) (rectangle ABCD) (rectangle ABCD) 5 (rectangle ABCD) |
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36 | The area of a square field is ( 30 frac{1}{4} m^{2} ) Calculate the length of the side of the square. A ( cdot_{5} frac{1}{3} m ) в. ( _{5} frac{1}{2} m ) c. ( _{5} frac{2}{5} m ) D. ( _{5} frac{1}{4} m ) |
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37 | The area of the shaded region in the given figure is ( A ) в. c. ( frac{pi}{4} ) sq.units D. ( pi^{2} ) sq.unis |
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38 | A ( 3 m ) wide path runs outside and around a rectangular park of length ( 125 m ) and breadth 65 m. Find the area of the path. |
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39 | Area of a sector of central angle ( 200^{0} ) of a circle is ( 770 mathrm{cm}^{2} ). The length of the corresponding arc of this sector is A ( cdot 73 frac{1}{3} c m ) B ( cdot 156 frac{1}{3} c m ) ( mathbf{c} cdot 7 frac{1}{3} c m ) D. ( 22 frac{1}{3} ) cm |
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40 | If the outer and inner radii of a ring are ( 10 mathrm{cm} ) and ( 8 mathrm{cm}, ) then its area is nearly A. 113.443 sq. ( mathrm{cm} ) В. 113.343 sq. ( mathrm{cm} ) c. 113.243 sq. ( mathrm{cm} ) D. 113.143 sq. ( mathrm{cm} ) |
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41 | The largest possible square is inscribed in a circle of circumference ( 2 pi ) units. The area of the square in square units is ( mathbf{A} cdot 4 pi sqrt{2} ) В. ( 2 pi sqrt{2} ) ( c cdot sqrt{2} ) ( D ) |
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42 | The minute hand of a clock is ( 10 mathrm{cm} ) long. Find the area of the face of the clock described by the minute hand between 9 A.M. and 9.35 A.M. |
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43 | Find the area of circle in sq. cms, in which the chord of length ( 18 mathrm{cm} ) is at the distance of half of the radius of circle from the centre of circle: A . ( 108 pi ) B. ( 54 pi ) c. ( 27 pi ) D. ( 81 pi ) |
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44 | In adjoining fig two semicircles are drawn on sides ( A D ) and ( B C ) of a square ( A B C D . ) If ( A B=10 mathrm{cm},(pi=3.14) ) then the total area of semicircles is : A ( .78 .50 mathrm{cm}^{2} ) B. ( 68.50 mathrm{cm}^{2} ) ( c cdot 70 mathrm{cm}^{2} ) D. ( 70.48 mathrm{cm}^{2} ) |
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45 | A circular park has a path of uniform width around it. The difference between outer and inner circumference of the circular path is ( 132 m ). Its width is: Take ( left(boldsymbol{pi}=frac{22}{7}right) ) ( A cdot 22 m ) B. ( 20 m ) ( mathbf{c} cdot 21 m ) ( mathbf{D} cdot 24 m ) |
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46 | What is the radius of a circle of area ( 616 mathrm{cm}^{2} ? ) ( mathbf{A} cdot 16 mathrm{cm} ) B. ( 12 mathrm{cm} ) ( c cdot 14 c m ) D. None of these |
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47 | In the given figure, two connectric circles with centre ( boldsymbol{O} ) have radii ( 21 mathrm{cm} ) and ( 42 mathrm{cm}, ) If ( angle A O B=60^{circ}, ) find the area of the shaded region ( left[mathbf{U} mathbf{s e} boldsymbol{pi}=frac{mathbf{2 2}}{mathbf{7}}right] ) |
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48 | One side of a square field is 92 m. Find the cost of raising a lawn on the field at the rate of ( R s .1 .50 ) per ( s q . m ) |
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49 | The radius of a circular wheel is ( 1 frac{3}{4} m ) How many revolutions will it make in traveling ( 11 k m ? ) |
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50 | The length and breadth of a rectangular field are ( 110 m ) and 85 m respectively. Find the perimeter of the field. How much will it cost to fence the field at the rate of ( R s 25 ) per metre? |
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51 | From a circular sheet of paper with radius ( 20 mathrm{cm}, 4 ) circles of radius ( 5 mathrm{cm} ) each are cut out. Find the ratio of the uncut to the cut portions. ( mathbf{A} cdot 1: 3 ) B. 4: 1 ( mathbf{c} cdot 3: 1 ) D. 4: 3 |
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52 | Between a square of perimeter ( 44 mathrm{cm} ) and a circle of circumference ( 44 mathrm{cm} ) which figure has a larger area and by how much? A. Square, ( 33 mathrm{cm}^{2} ) B . Circle, ( 33 mathrm{cm}^{2} ) c. Both have equal areas D. square, ( 95 mathrm{cm}^{2} ) |
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53 | The area of the shaded field shown in the given figure is: ( mathbf{A} cdot(4 pi+32) mathrm{cm}^{2} ) B ( cdot(2 pi+32) mathrm{cm}^{2} ) ( mathbf{c} cdot(2 pi+16) mathrm{cm}^{2} ) ( mathbf{D} cdot(4 pi+24) mathrm{cm}^{2} ) |
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54 | Find the circumference of the circles with the following radius:(Take ( pi=frac{22}{7} ) ) ( mathbf{1 4 c m} ) |
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55 | If the circumference of a circle is increased by ( 50 % ), by what percent will its area be increased? A . ( 75 % ) B. ( 100 % ) c. ( 125 % ) D. ( 150 % ) |
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56 | Find the circumference of a circle whose area is ( 301.84 mathrm{cm}^{2} ) |
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57 | Area of circle ( A ) is 121 times the area of circle B. The ratio of the circumference of circle ( A ) to that of ( B ) is A . 121: B. 1: 11 c. 11: 1 D. Cannot be determined |
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58 | 10. The length of a rectangle is 6 m less than three times its breadth. The length and breadth of the rectangle if its perimeter is 148 m, is (a) 54 m (b) 30m (c) 40m (d) 20m |
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59 | 68. If area of a parallelogram with sides p and q is R and that of a rectangle with sides p and qis S, then : (1) R>S (2) R<S (3) R=S (4) None of these |
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60 | Angle in a semicircle is A. Acute angle B. Straight angle C. Right angle D. Obtuse angle |
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61 | The shape of the top of a table in a restaurant is that of a segment of a circle with centre ( O ) and ( angle B O D=90^{circ} ) f ( B O=O D=60 mathrm{cm} . ) The perimeter of the table is (Take ( pi=mathbf{3 . 1 4} ) ) A . ( 402 mathrm{cm} ) в. ( 402.6 mathrm{cm} ) c. ( 401 mathrm{cm} ) D. ( 400 mathrm{cm} ) |
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62 | ABCD is a parallelogram, AD is produced to E so that DE = DC and ED produced meets AB produced in F. Prove that ( mathrm{BF}=mathrm{BC} ) |
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63 | In the figure, from the handkerchief from four corners, sectors ( P, Q, R ) and ( S ) each of ( 2 mathrm{cm} ) are cut, whose sum is ( boldsymbol{P}+ ) ( Q+R+S=A_{1} ) and a circle of diameter ( 4 mathrm{cm} ) from the centre is cut whose area is ( A_{2}, ) then is possible. A. ( A_{1} neq A_{2} ) B. ( A_{1}A_{2} ) D. ( A_{1}=A_{2} ) |
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64 | The area of a circular playground is ( 22176 m^{2} . ) Find the cost of fencing at the rate of ( R s .50 ) per ( m ) |
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65 | Find the circumference of the inner and the outer circles, shown in the adjoining figure. (Take ( boldsymbol{pi}=mathbf{3 . 1 4}) ) |
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66 | If perimeter of rectangle is equal to perimeter of square, then side of square is (a) 60 cm (b) 18 cm (c) 225 cm (d) 15 cm |
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67 | Assertion: The length ofrectangle exceeds its breadth by 4 cm. Iflength and breadth are each increased by 3cm, the area of the new rectangle will be 81cm- more than that of given rectangle. Length and breadth are 14 and 10 cm respectively. Reason: Area of rectangle=Length x Breadth. |
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68 | Two crossroads,each ( 2 mathrm{m} ) wide,run at right angles through the center of a rectangular park of length ( 64 mathrm{m} ) and breadth ( 38 mathrm{m} ),such that each is parallel to one of the sides of the rectangle. Find the area of the roads.also, find the area of the remaining part of the park |
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69 | In the adjoining figure, ( O A B C ) is a square of side ( 7 mathrm{cm} . O A C ) is a quadrant of a circle with ( O ) as centre. The area of the shaded region is A . ( 10.5 mathrm{cm}^{2} ) В. ( 38.5 mathrm{cm}^{2} ) ( mathbf{c} cdot 49 c m^{2} ) D. ( 11.5 mathrm{cm}^{2} ) |
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70 | A circular grass lawn of ( 35 m ) in radius has a path ( 7 m ) wide running around it on the outside. The area ofthe path is? A ( cdot 1,496 m^{2} ) B . ( 1,450 m^{2} ) c. ( 1,576 m^{2} ) D. ( 1,694 m^{2} ) |
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71 | If we join any two points on a circle through centre, we get a A. Radius B. Diameter c. chord D. None of these |
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72 | In the given figure, ( A B C D ) is a piece of cardboard in the shape of the trapezium in which ( A B | D C, angle A B C=90^{circ} ) From this piece, quarter circle ( B E F C ) is removed. Given ( D C=B C=4.2 mathrm{cm} ) and ( A E=2 mathrm{cm} . ) Calculate the area of the remaining piece of the cardboard. ( mathbf{A} cdot 7.98 mathrm{cm}^{2} ) ( mathbf{B} cdot 8 mathrm{cm}^{2} ) ( mathbf{c} cdot 9.08 mathrm{cm}^{2} ) D. ( 10.08 mathrm{cm}^{2} ) |
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73 | Find the circumference of the semicircle whose diameter is 4 cm. A. ( 3.46 mathrm{cm} ) B . ( 5.89 mathrm{cm} ) ( mathbf{c} cdot 6.28 mathrm{cm} ) D. ( 10.28 mathrm{cm} ) |
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74 | 8. The perimeter of a square is cm. Find the side of the square. |
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75 | The diameter of a wheel of a cycle is 21 cm How far will it go in 28 complete revolutions? ( A cdot 3696 mathrm{cm} ) B. 3669 cm c. ( 3966 mathrm{cm} ) D. None of these |
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76 | The number of revolutions made by a wheel of diameter ( 56 mathrm{cm} ) in covering a distance of ( 1.1 k m ) is ( left(U s e pi=frac{22}{7}right) ) ( mathbf{A} cdot 31.25 ) B. 56.25 c. 625 D. 62.5 |
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77 | 51. If the circumference of a circle 30 is , the the diameter of the T circle is (1) 15 T (3) 60 (4) 30 |
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78 | If the ratio of the areas of the two circles is ( 25: 16, ) then the ratio of their circumferences is This question has multiple correct options |
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79 | The area of a circle and a square are equal, the ratio of the sides of the square to the radius of the circle is A ( .2: sqrt{pi} ) B. ( sqrt{pi}: 1 ) c. ( sqrt{2}: 1 ) D. ( 1: sqrt{2} ) E . None of these |
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80 | 1 LUU L UPIDU 6 7. 50000 A farmer has one piece of rectangular land measuring 000 m length and 30000 m breadth. If he distributes his land 13 11 among his 5 children, how much area will each child get? 50000 |
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81 | The circumference of a circle is ( 100 mathrm{cm} ) Then the side of a square inscribed in the circle is: A ( cdot frac{100 sqrt{2}}{pi} mathrm{cm} ) B. ( frac{50 sqrt{2}}{pi} mathrm{cm} ) c. ( frac{100}{pi} mathrm{cm} ) D. ( 50 sqrt{2} mathrm{cm} ) |
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82 | Which of the following statements are true (T) and which are false (F)?
If all the angles of a quadrilateral are equal, it is a parallelogram. |
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83 | A roller of diameter ( 70 mathrm{cm} ) and length ( 2 mathrm{m} ) is rolling on the ground What is the area covered by the roller in 50 revolutions? A. ( 180 m^{2} ) в. ( 200 m^{2} ) c. ( 220 m^{2} ) D. ( 240 m^{2} ) |
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84 | The ratio of the outer and inner perimeters of a circular path is 23: 22 If the path is ( 5 mathrm{m} ) wide what is the diameter of the circle? Also find the area of path enclosed between the two circles. A. 3535.71 sq. ( mathrm{m} ) B . 1232.23 sq. ( mathrm{m} ) c. 2727.53 sq. ( mathrm{m} ) D. 4343.12 sq. ( mathrm{m} ) |
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85 | 71. The perimeters of five squares are 24 cm, 32 cm, 40 cm, 76 cm and 80 cm respectively. The pe- rimeter of another square equal in area to sum of the areas of these squares is (1) 31 cm (2) 62 cm (3) 124 cm (4) 961 cm |
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86 | What is the length of ( A B ? ) ( mathbf{A} cdot 8 mathrm{cm} ) B. 4.5cm C. ( 7.35 mathrm{cm} ) D. ( 7.30 mathrm{cm} ) |
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87 | The length and breadth of a rectangular piece of land are ( 500 mathrm{m} ) and ( 300 mathrm{m} ) respectively. Find the cost of the land, if ( 1 m^{2} ) of the land costs Rs. 10,000 |
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88 | Which of the following statements are true (T) and which are false (F)? In a parallelogram, the diagonals are equal. A. True B. False |
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89 | Four equal circles, each of radius ( a ) touch each other. Show that the area between then is ( frac{6}{7} a^{2} ) (Take ( left.pi=frac{22}{7}right) ) | 7 |

90 | The circumference and area of a circle of diameter ( 91 mathrm{cm} ) are, respectively A ( cdot 367 mathrm{cm}, 4986.5 mathrm{cm}^{2} ) B . ( 442 mathrm{cm}, 6166.5 mathrm{cm}^{2} ) ( mathbf{c} .286 mathrm{cm}, 6506.5 mathrm{cm}^{2} ) D. ( 456 mathrm{cm}, 5466.5 mathrm{cm}^{2} ) |
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91 | Find the radius (in ( mathrm{cm} ) ) of a circle, whose circumference is ( 22 mathrm{m} ) |
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92 | The area of a square playground is 256.6404 square metres. Find the length of one side of the playground. A. 16.04 metres B. 16.02 metres c. 16.06 metres D. 16.08 metres |
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93 | A circular grassy plot of land, ( 42 m ) in diameter, has a path ( 3.5 m ) wide running around it on the outside. Find the cost of gravelling the path at ( R s .4 ) per square metre A. ( R s .2002 ) B. Rs.2003 c. ( R s .2004 ) D. ( R s .2000 ) |
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94 | ( ln a triangle w i t h ) sides ( a, b ) and ( c, a ) semicircle touching the sides ( A C ) and ( C B ) is inscribed whose diameter lies on ( A B . ) Then, the radius of the semicircle is : A ( cdot frac{a}{2} ) в. ( frac{Delta}{s} ) c. ( frac{Delta}{a+b} ) D. ( frac{2 Delta}{a+b} ) |
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95 | If ( P Q R S ) is a square, ( A B | S Q, A ) is midpoint of ( S R ) and ( A C=C B, ) which one is true? A. ( S A=B Q ) B. ( P C ) is the bisector of ( angle S P Q ) c. ( P C ) if produced will pass through ( R ) D. All of these |
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