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

#### List of areas related to circles Questions

Question No | Questions | Class |
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1 | A wire is bent in the form of a rectangle having length twice the breadth. The same wire is bent in the form of a circle. It was found that the area of the circle is greater than that of the rectangle by ( 104.5 mathrm{cm}^{2} . ) Find the length of the wire. |
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2 | sent in the ses an area rire is bent (3) 4010 55. A metal wire when bent in form of a square encloses an 484 cm. If the same wire is b in the form of a circle, then ſt ing n = 2) its area is (1) 308 cm (2) 506 cm2 (3) 600 cm (4) 616 cm |
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3 | The long and short hands of a clock are ( 6 mathrm{cm} ) and ( 4 mathrm{cm} ) long respectively. Find the sum of distances travelled by their tips in 24 hrs. ( (U s e pi=3.14) ) |
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4 | The length and breadth of a rectangle are in the ratio ( 2: 1 . ) If the area of the field is 72 sq.m, find the cost of fencing the field with barbed wire at the ratio of Rs 15 per metre. |
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5 | A circular disc of radius ( 7 mathrm{cm} ) has a sector of angle 45 degrees cut out. The area of the remaining part of the disc is A ( cdot ) 134.75 ( c m^{2} ) B . ( 144.75 mathrm{cm}^{2} ) c. ( 269.5 mathrm{cm}^{2} ) D. None of these |
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6 | The area of a circle whose radius is 6 ( mathrm{cm} ) is trisected by two concentric circles. The radius of the smallest circle is A ( cdot 2 sqrt{3} mathrm{cm} ) B . ( 2 sqrt{6} mathrm{cm} ) ( c cdot 2 mathrm{cm} ) D. ( 3 mathrm{cm} ) |
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7 | 58. If the radius of a circle is in- creased by 6%, then its area is increased by (1) 15% (2) 18.46% (3) 12.36% (4) 20% |
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8 | Given : Area of sector ( =15 pi ) sq.cm radius ( =mathbf{6} c boldsymbol{m} ) To find : Length of the arc corresponding to the sector |
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9 | The radius of a circle with centre 0 is 5 ( mathrm{cm} ) (given figure). Two radii OA and ( mathrm{OB} ) are drawn at right angles to each other. Find the areas of the segment made by the chord ( A B text { (Take } pi=3.14) ) |
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10 | Find the diameter of a circle whose circumference is equal to the sum of the circumference of the two circles of diameters ( 36 mathrm{m} ) and ( 20 mathrm{m} ) |
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11 | A wheel has diameters ( 84 mathrm{km} ). Find how many complete revolution must it take to cover 792 meters |
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12 | Four equal circles are described about four corners of a square so that each touches two of the others as shown in the fig. Find the area of the shaded portion, each side of the square measuring ( 28 mathrm{cm} ) |
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13 | A rectangular plot is ( 112 mathrm{m} ) long and ( 6 mathrm{m} ) broad. It has ( 2 mathrm{m} ) path all around it on the inside.Find the area of the path and the cost of constructing it at the rate of Rs 60 per sq ( m ) |
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14 | A swimming pool is ( 20 m ) in length, ( 15 m ) in breadth, and ( 4 m ) in depth. Find the cost of corner its floor and walls at the rate of ( R s .12 ) per square meter |
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15 | The difference between the circumference and the radius of a circle is ( 74 mathrm{cm}, ) find the area of the circle. |
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16 | A sphere with diameter ( 50 mathrm{cm} ) intersects a plane ( 14 mathrm{cm} ) from the center of the sphere. What is the number of square centimeters in the area of the circle formed? A . ( 49 pi ) в. ( 196 pi ) c. ( 429 pi ) D. ( 576 pi ) E . ( 2304 pi ) |
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17 | A circle and a squre have the same perimeter. Then: A. there areas are equal B. the area of the circle is the greater C. the area of the square is the greater D. the area of the circle is ( x ) times the area of the square E. none of these |
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18 | n figure, circle ( O ) has diameter ( overline{A B} ) of the length ( 8 . ) If smaller circle ( P ) is ( operatorname{tangent} ) to diameter ( overline{A B} ) at point ( O ) and is also tangent to circle ( O ), calculate the approximate area of the shaded region. A . 3.14 B. 6.28 ( c .9 .42 ) D. 12.57 E . 25.13 |
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19 | How to find area of circle? | 10 |

20 | The radius of a semi-circular plot is 21 m. Find its area and perimeter. |
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21 | Find the area of both the segments of a Circle of radius ( 43 mathrm{cm} ) with central angle ( 120^{circ} .left[text { Given, } sin 120^{circ}=frac{sqrt{3}}{2} a n d sqrt{3}=right. ) 1.73] |
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22 | In the given figure the diameter of the biggest semi circle is ( 56 mathrm{cm} ) and the radius of the smallest circle is ( 7 mathrm{cms} ) The area of the shaded portion is A ( cdot 482 mathrm{cm}^{2} ) B. ( 462 mathrm{cm}^{2} ) ( mathbf{c} cdot 654 mathrm{cm}^{2} ) D. ( 804 mathrm{cm}^{2} ) |
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23 | Find the sum of the perimeters of the figures given below A. ( 350 mathrm{cm} ) B. 360 cm c. ( 370 mathrm{cm} ) D. ( 380 mathrm{cm} ) |
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24 | The area of a circle is the measurement of the region enclosed by its A . radius B. centre c. circumference D. area |
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25 | Area of square is 10,000 sq m Then its side measures(in ( mathrm{m}) ) | 10 |

26 | A circle is inscribed in a square and then a smaller square is inscribed in the circle. The ratio of the area of the smaller square to that of the larger square is A . 1: 4 B. ( sqrt{2}: 2 ) ( c cdot 1: 2 ) D. ( 1: sqrt{2} ) E . 2: 3 |
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27 | In Figure ( 5, ) rectangle ( A B C D ) is inscribed in a circle. If the radius of the circle is 1 and ( A B=1 ), find the area of the shaded region. ( mathbf{A} cdot 0.091 ) B. 0.285 c. 0.614 D. 0.705 E . 0.732 |
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28 | If the radius of a circle is tripled, the ares becomes. A. 9 times B. 3 times c. 6 times D. 30 times |
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29 | Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius ( 5 mathrm{m} ) drawn in a park. Reshma throws a ball to Salma. Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is ( 6 mathrm{m} ) each, what is the distance between Reshma and Mandip? ( mathbf{A} cdot 4.8 mathrm{m} ) B. ( 9.6 mathrm{m} ) ( c cdot 2.4 m ) D. ( 7.2 mathrm{m} ) |
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30 | Find the area of a sector in radians whose central angle is ( 45^{circ} ) and radius is 2 A ( cdot frac{pi}{3} ) в. ( c cdot frac{pi}{2} ) D. |
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31 | In the figure 7.31 , radius of the circle is ( mathbf{7} boldsymbol{c m} ) and ( boldsymbol{m}(boldsymbol{a} boldsymbol{r} boldsymbol{c} boldsymbol{M} boldsymbol{B} boldsymbol{N})=boldsymbol{6} boldsymbol{0}^{o} ) find Area of the circle. A . 45 B . 42.96 c. 43.96 D. 44 |
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32 | If an area enclosed by a circle or a square or an equilateral triangle is the same, then the maximum perimeter is possessed by: A. the circle B. the square c. the equilateral triangle D. the triangle and square have equal perimeters greater than that of circle |
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33 | The perimeter of the table. A ( .402 .60 mathrm{cm} ) B. ( 522.60 mathrm{cm} ) c. ( 342.60 mathrm{cm} ) D. None of these |
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34 | A piece of land is 100 metres ( times 21 ) metres. A semi-circular plot has been added on one side of its breadth. How long will it take a man to walk round it at the rate of 3.6 kilometres per hour? |
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35 | A chord ( A B ) of a circle, of radius ( 14 mathrm{cm} ) makes an angle of ( 60^{circ} ) at the centre of the circle. Find the area of the minor segments of the circle. |
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36 | The radius of a wheel is 0.25 m. How many rounds will it take to complete the distance of ( 11 k m ? ) A. 7000 в. 8000 c. 9000 D. 6000 |
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37 | A chord of a circle radius ( 14 mathrm{cm} ) makes a right angle at the centre. Find the areas of the minor and major segments of the circle |
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38 | The area of a square is numerically equal to the perimeter of the square, then the side of square is A . 2 units B. 3 units c. 4 units D. 5 units |
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39 | What is the area of the circle whose equation is ( (x-3)^{2}+(y+5)^{2}=18 ? ) ( mathbf{A} cdot 9 pi ) B. ( 18 pi ) c. ( 72 pi ) D. ( 81 pi ) E . ( 324 pi ) |
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40 | How many times a wheel of radius 28 cm must rotate to go 352 m?(Take ( pi= ) ( frac{22}{7} ) |
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41 | Abhay made a straight cut through a circular rubber band and then laid the rubber band flat, as shown in the figure. Which measure corresponds to the length of the cut rubber band? A. Chord B. Circumference c. Diameter D. Radius |
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42 | If ( A C ) passes through the centre of the circle, then the area of the shaded region in the given figure is A ( cdot frac{a^{2}}{2}(3-pi) ) B ( cdot a^{2}left(frac{pi}{2}-1right) ) ( mathbf{c} cdot 2 a^{2}(pi-1) ) ( ^{mathrm{D}} cdot frac{a^{2}}{2}left(frac{pi}{2}-1right) ) |
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43 | The perimeters of a circular field and a square field are equal. If the area of the square field is ( 12100 m^{2} ), then the area of the circular field will be A. ( 15500 m^{2} ) В. ( 15400 m^{2} ) c. ( 15200 m^{2} ) D. ( 15300 m^{2} ) |
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44 | In Figure ( 5, ) rectangle ( A B C D ) is inscribed in a circle. If the radius of the circle is 2 and ( overline{C D}=2, ) find the area of the shaded region. A. 0.36 3. 0.47 7 ( c .0 .57 ) D. 0.707 ( =0.86 ) |
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45 | If the circumference (in ( c m ) ) and the ( operatorname{area}left(operatorname{in} c m^{2}right) ) of a circle are equal then find the radius of the circle A . ( 1 c m ) в. 2 ст ( c .3 c m ) D. ( 4 c m ) |
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46 | Let ( C ) and ( A ) be the circumference and the area of a circle respectively. If ( x C ) is the circumference of another circle whose area is ( 2 A ), then ( x ) equals begin{tabular}{l} A ( cdot 2 sqrt{2} ) \ hline end{tabular} B. 2 ( c cdot sqrt{2} ) D. ( frac{1}{2} ) |
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47 | The moon is about ( 384000 mathrm{km} ) from the earth and its path around the earth is nearly circular. Find circumference of the path travelled by the moon every month. |
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48 | The area of the part of the square filed in which a horse tied to a fixed pole at one comer by means of a 10 m rope, can graze is A . ( 25 pi s q . m ). в. ( 100 pi s q . m ) c. ( 50 pi s q . m ) D. ( 5 pi s q . m . ) |
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49 | The diameter of a circle is ( 10 mathrm{cm} . ) Find the length of the arc, in cm, (nearest integral value), when the corresponding central angle is ( 45^{circ} ) |
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50 | Calculate the area of the rectangle whose length ( 20 m ) and breadth ( 11 m ) | 10 |

51 | A chord ( A B ) of circle of radius ( 14 c m ) makes an angle of ( 60^{circ} ) at the centre of the circle .The area of the minor segment of the circle is ( left(text { Use } pi=frac{22}{7}right) ) A ( cdot frac{308}{3} c m^{2} ) в. ( frac{208}{3} mathrm{cm}^{2} ) c. ( frac{108}{3} mathrm{cm}^{2} ) D. ( frac{408}{3} mathrm{cm}^{2} ) |
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52 | If the difference between the circumference and radius of a circle is ( 37 mathrm{cm}, ) then the area of the circle is ( A cdot 111 mathrm{cm}^{2} ) B. ( 148 mathrm{cm}^{2} ) ( c cdot 259 mathrm{cm}^{2} ) D. ( 154 mathrm{cm}^{2} ) |
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53 | A chord of a circle of radius ( 6 mathrm{cm} ) subtends an angle of ( 60^{circ} ) at the centre of the circle. The area of the minor segment is (use ( pi=3.14) ) A ( cdot 6.54 mathrm{cm}^{2} ) в. ( 0.327 mathrm{cm}^{2} ) c. ( 7.25 mathrm{cm}^{2} ) D. 3.27 ( c m^{2} ) |
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54 | A sector of a circle of radius ( 8 mathrm{cm} ) contains an angle of ( 135^{circ} . ) Find the area of the sector. |
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55 | Which of the following is/are correct? This question has multiple correct options A. Area of a circle with radius ( 6 mathrm{cm} ), if angle of sector is ( 60^{circ}, ) is ( frac{132}{14} mathrm{cm}^{2} ) B. If a chord of circle of radius ( 14 mathrm{cm} ) makes an angle of ( 60^{circ} ) at the centre of the circle, then area of major sector is ( 512.87 mathrm{cm}^{2} ) C. The ratio between the circumference and area of a circle of radius ( 5 mathrm{cm} ) is 2: 5 D. Area of a circle whose radius is ( 6 mathrm{cm} ), when the length of a arc is ( 22 mathrm{cm}, ) is ( 66 mathrm{cm}^{2} ) |
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56 | Find the area of shaded region? | 10 |

57 | In the given figure two concentric circle with centre ( O ) have radii ( 21 c m ) and ( 42 c m . ) If ( A O B=60 ) Find the area of the shaded region (Use ( left.pi=frac{22}{7}right) ) |
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58 | 58. The diameters of two circles are the side of a square and the di- agonal of the square. The ratio of the areas of the smaller circle and the larger circle is (1) 1 : 2 (2) 1:4 (3) V: V3 (4) 1 : 72 |
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59 | An equilateral triangle and a square have equal perimeters. If side of the triangle is ( 9.6 mathrm{cm} ; ) what is the length of the side of the square? ( mathbf{A} cdot 6.2 mathrm{cm} ) B. ( 3.2 mathrm{cm} ) ( c .5 .2 mathrm{cm} ) D. ( 7.2 mathrm{cm} ) |
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60 | ( mathbf{n} ) fig., ( A B ) and ( C D ) are two diameters of ( a ) circle (with centre 0) perpendicular to each other and 0 D is the diameter of the smaller circle. If ( boldsymbol{O} boldsymbol{A}=mathbf{1 4} boldsymbol{c m}, ) find the area of the shaded region |
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61 | ( A, B, ) and ( C ) are three points on a circle with centre ( boldsymbol{O} ) such that ( boldsymbol{B O C}=mathbf{3 0}^{mathbf{o}} ) and ( angle A O B=60^{circ} . ) If ( D ) is a point on the circle other than the arc ( A B C ), find ( angle A D C ) ( A cdot 45 ) В. 60 ( c cdot 22.5^{circ} ) 0.30 |
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62 | In a circle of radius ( 21 mathrm{cm}, ) an arc subtends an angle of ( 60^{circ} ) at the centre. The area of the segment formed by the corresponding chord of the arc is : A ( .42 mathrm{cm}^{2} ) В. 421.73 ( c m^{2} ) c. ( 429.43 mathrm{cm}^{2} ) D. ( 40 mathrm{cm}^{2} ) |
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63 | Find the angle subtended at the centre of the circle by an are whose length is ( 15 mathrm{cm} ) if the radius of the circle is ( mathbf{2 5} mathrm{cm} ) |
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64 | A circle is inscribed in a triangle whose sides are 40,40 and ( 48 mathrm{cm} ) respectively. A smaller circle touching two equal sides of the triangle and to the first circles, then the area of smaller circle is |
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65 | The area of the circle whose centre is (1,2) and which passes through the point (4,6) is A ( .25 pi ) в. ( 100 pi ) c. ( 92 pi ) D. None of these |
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66 | The area of the shaded region in the following figure is A ( .51 .33 mathrm{cm}^{2} ) В. ( 102.67 mathrm{cm}^{2} ) c. ( 205.34 mathrm{cm}^{2} ) D. can not be determined |
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67 | The diameter of the wheel of a car is ( mathbf{5 6} ) cm. Calculate : The number of times the wheel will rotate in travelling through a distance of ( 1.056 k m ) |
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68 | What will be the area of the field ( A B G F E A ? ) ( mathbf{A} cdot 7225 m^{2} ) B. ( 8225 mathrm{m}^{2} ) ( c cdot 6225 m^{2} ) D. ( 6725 m^{2} ) |
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69 | The perimeter of a square field is ( 40 mathrm{m} ) more than another square field. Three times the area of the smaller field is 50 ( m^{2} ) more than the area of the larger field. Find the sides of both the fields. |
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70 | A horse is placed for grazing inside a rectangular field ( 70 m ) by ( 52 mathrm{m} ) and is tethered to one corner by a rope ( 21 mathrm{m} ) long. On how much area can it graze? A ( .346 .5 mathrm{cm}^{2} ) В. ( 360 mathrm{cm}^{2} ) c. ( 350.5 mathrm{cm}^{2} ) D. ( 380 c m^{2} ) |
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71 | Parveen wanted to make a temporary shelter for her car, by making box-like structure with tarpoulin that covers all the four sides and the top of the car (With the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height ( 2.5 m ), with base dimensions ( 4 m times 3 m ? ) |
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72 | The area of a circle is ( (14+6 sqrt{5}) pi ) units, Find its radius. |
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73 | If ( A, B, C, D ) are four points such that ( angle B A C=30^{circ} ) and ( angle B D C=60^{circ} ) then prove that D is the centre of the circle through ( A, B ) and ( mathrm{C} ) |
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74 | Find the area of the segment AYB shown in figure, if radius of the circle is ( 21 mathrm{cm} ) and ( <A O B=120^{circ} .left(U s e pi=frac{22}{7}right) ) |
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75 | Find the area of the circle whose centre is (-3,2) and (2,5) is a point on the circle. |
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76 | If the length of a rectangle is two times its breadth and area is ( 228 mathrm{cm}^{2} ), then length and breadth are respectively A ( .20 mathrm{cm}, 10 mathrm{cm} ) в. ( 12 mathrm{cm}, 24 mathrm{cm} ) c. ( 24 c m, 12 c m ) D. ( 16 mathrm{cm}, 18 mathrm{cm} ) |
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77 | Calculate the arc length for the given diagram. A . 1.23 in B . 2.23 in c. 4.23 in D. 5.23 in |
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78 | A table-top measures ( 2 m 25 mathrm{cm} ) by 1 ( m 50 mathrm{cm} . ) What is the perimeter of the table-top? |
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79 | Find the radius of the incircle of a triangle whose sides are 18,24 and 30 |
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80 | A square park has each side of ( 100 m ) At each corner of the park, there is a flower bed in the form of a quadrant of radius ( 14 m ) as shown in figure. Find the area of the remaining part of the park. ( left[text { Use } boldsymbol{pi}=frac{mathbf{2 2}}{mathbf{7}}right] ) A ( cdot 12843 m^{2} ) B. ( 11284 m^{2} ) ( mathrm{c} cdot 9384 m^{2} ) D. ( 7382 m^{2} ) |
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81 | Taking ( boldsymbol{pi}=mathbf{3 . 1 4}, ) find the circumference of a circle whose radius is ( 8 mathrm{cm} ) |
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82 | A chord of a circle of radius ( 10 mathrm{cm} ) subtends a right angle at the centre. Find the area of the corresponding ( (i) ) Minor segment, (ii) Major segment. (use ( boldsymbol{pi}=mathbf{3 . 1 4}) ) |
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83 | Find the area of each of the following figures. |
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84 | Find the area of the circular park of Janakpuri whose circumference is ( 77 m 77 m ) A ( .671 .87 m^{2} ) B. ( 331.62 m^{2} ) ( mathbf{c} cdot 471.62 m^{2} ) D ( .401 .62 m^{2} ) |
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85 | In case of a right circular cylinder the radius of base and height are in the ratio ( 2: 3 . ) Therefore, the ratio of lateral surface area to the total surface area is A .5: 3 B. 3: 5 c. 2: 5 D. 2: 3 |
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86 | A eighth part of a full circle i.e. a octant subtends an angle of ( ldots ) at the centre. A ( cdot 60^{circ} ) B . ( 45^{circ} ) ( c .90^{circ} ) D. None of these |
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87 | A chord of a circle of radius ( 10 mathrm{cm} ) subtends a right angle at the centre. Find the area of corresponding minor segment ( (boldsymbol{pi}=mathbf{3 . 1 4}) ) |
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88 | A square park has each side ( 100 m ). At each corner of the park there is a flower bed in the form of a quadrant of radius ( 14 m, ) as shown in the figure. The area of the remaining part of the park is: |
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89 | Find the area of the shaded region ( (boldsymbol{pi}=mathbf{3 . 1 4}, sqrt{mathbf{3}}=mathbf{1 . 7 3}) ) |
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90 | n Fig 10.3 if ( mathrm{OA}=5 mathrm{cm}, mathrm{AB}=8 mathrm{cm} ) and OD is perpendicular to AB then CD is equal to ( A cdot 2 mathrm{cm} ) B. 3 ( mathrm{cm} ) ( c cdot 4 mathrm{cm} ) D |
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91 | A chord of a circle of radius ( 7 mathrm{cm} ) subtends an angle of ( 90^{circ} ) at its centre. The ratio of areas of smaller and larger segment is A .2: 7 B. 1: 10 c. 1: 11 D. none of these |
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92 | n the given figure, ( A T ) is a tangent ( A C=B C ) and ( angle A B C=50^{circ} . ) Find the ( angle B A T ) |
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93 | A square OABC is inscribed in a quardrant OPBQ of a circle. If ( O A=21 mathrm{cm} ) find the area of the shaded region. |
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94 | divides a circle into two segments i.e major segment and minor segment. A. An arc B. A chord c. A sector D. A tangent |
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95 | If the wheel of the bus is ( 90 mathrm{cm} ) diameter makes 210 revolutions per minute, then find the speed of the bus in ( k m / h r, ) to the nearest integer. |
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96 | Find the perimeter of (i) ( Delta mathrm{ABC} ) (ii) rectangle BCDE. ( mathbf{A} ) (i) ( -8 frac{1}{60} mathrm{cm}, ) (ii)- ( 5 mathrm{cm} ) 3 (i) ( -5 c m, ) (ii) ( -10 frac{1}{6} mathrm{cm} ) c. ( left(text { i) }-8 frac{1}{60} text { cm, (ii) }-10 frac{1}{5} ) cm right. ) . (i)- ( 8 mathrm{cm}, ) (ii) ( -23 mathrm{cm} ) |
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97 | If the diameter of a circle is increased by ( 200 % ) then its area is increased by A. ( 100 % ) B . 200% c. 300% D. 800% |
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98 | The given figure is made up of identical squares. Find the area of the shaded region. ( A cdot 50 mathrm{cm}^{2} ) B. ( 54 mathrm{cm}^{2} ) ( mathrm{c} cdot 58 mathrm{cm}^{2} ) D. ( 52 mathrm{cm}^{2} ) |
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99 | ( Delta L M N Delta L M N ) (2) Area of any one of the sectors. (3) Total area of all the three sectors. (4) Area of the shaded region. |
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100 | Find the area of the minor segment of a circle of radius ( 14 mathrm{cm}, ) when its central angle is ( 60^{circ} ). Also find the area of the corresponding major segment. ( left[boldsymbol{U s e} boldsymbol{pi}=frac{mathbf{2 2}}{mathbf{7}}right] ) |
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101 | If the difference between the circumference and the radius of a circle is ( 37 c m, ) then using ( pi=frac{22}{7}, ) the circumference (in cm) of the circle is: A . 154 B. 44 c. 14 D. |
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102 | In figure, square ( J K L M ) is inscribed in circle ( O . ) If the radius is ( 6, ) calculate the area of the shaded region, to the nearest tenth. A . 10.3 B. 18.2 c. 22.8 D. 28.3 E . 38.6 |
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103 | Find the diameter of a circle whose circumference is ( 15.7 mathrm{cm}- ) A. ( 5 mathrm{cm} ) B. ( 6 mathrm{cm} ) ( c cdot 7 mathrm{cm} ) D. 4.5 cm |
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104 | Find the area of a triangle, two sides of which are ( 8 mathrm{cm} ) and ( 11 mathrm{cm} ) and the perimeter is ( 32 mathrm{cm} ) |
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105 | The diameters of the front and the rear wheels of a tractor are ( 63 mathrm{cm} ) and 1.54 ( m ) respectively. Calculate their areas and circumference. |
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106 | An equilateral triangle has area ( A sqrt{3} ) Three circles are drawn with their centres at the vertices of the triangle. Diameter of each circle is equal to the length of each side of the triangle. The area of the triangle NOT included in any of the three circles is A ( cdot Aleft(sqrt{3}-frac{pi}{6}right) ) B . ( A(pi-sqrt{3}) ) c. ( A(3 pi-sqrt{3}) ) D. ( Aleft(sqrt{3}-frac{pi}{2}right) ) |
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107 | In the fig., ( O A B C ) is a square inscribed in a quadrant ( O P B Q . ) If ( O A=20 mathrm{cm} ) Find the area of shaded region. ( [boldsymbol{pi}=mathbf{3 . 1 4}] ) |
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108 | The perimeter of a square is ( 56 mathrm{m} ). The area of rectangle is 8 sq.m less than the area of the given square. If the length of the rectangle is ( 16 mathrm{m} ), find its breadth. |
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109 | The diameter of a circle is ( 1 . ) Calculate the area of the circle. A ( cdot frac{pi}{8} ) B. c. D. ( pi ) E . ( 2 pi ) |
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110 | A chord of a circle of radius ( 12 mathrm{cm} ) subtends an angle of ( 120^{circ} ) at the centre. Find the area of the corresponding segment of the circle. (Use ( pi=3.14 text { and } sqrt{3}=1.73) ) |
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111 | In a circle a central angle of ( 60^{circ} ) intercepts an arc of 15 inches. How many inches is the radius of the circle? A ( cdot frac{45}{pi} ) в. ( c cdot 4 ) D. ( frac{2 pi}{3} ) E. not computable from given data |
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112 | In Fig. arcs have been drawn of radius ( 21 mathrm{cm} ) each with vertices ( A, B, C ) and ( D ) of the square ( A B C D ) as centres. The area of the shaded region is ( mathbf{A} cdot 693 mathrm{cm}^{2} ) B. ( 346.5 mathrm{cm}^{2} ) ( mathbf{c} cdot 2772 mathrm{cm}^{2} ) D. ( 1386 mathrm{cm}^{2} ) |
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113 | The radii of two circle are ( 4 mathrm{cm} ) and 3 ( mathrm{cm} ) respectively, The diameter of the circle having area equal to the sum of the areas of the two circles(in cm) is A . 5 B. 7 c. 10 D. 14 |
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114 | 67. If the circumference of a circle 30 is 7 the the diameter of the circle is 15 2 (1) (3) 60 (2) 2 (4) 30 |
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115 | From a circle with radius ( 21 mathrm{cm} ) a sector is cut off for which the measure of the angle at the centre is ( 150 . ) Find the length of the arc of that sector and also find the area of the sector. |
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116 | The area of a circle is 314 sq. ( mathrm{cm} ) and area of its minor sector is 31.4 sq. cm. Find the area of its major sector. A ( .282 .6 mathrm{cm}^{2} ) в. ( 200.6 mathrm{cm}^{2} ) ( mathbf{c} cdot 180.04 mathrm{cm}^{2} ) D. 1220.09cm ( ^{2} ) |
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117 | The diagram shows two arcs, A and B. Arc A is part of the circle with centre 0 and radius OP. Arc B is part of the circle with centre ( mathrm{M} ) and radius PM, where M is the mid – point of PQ. Show that the area enclosed by the two arcs is equal to 25 ( left(sqrt{3}-frac{pi}{6}right) c m^{2} ) |
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118 | Find the perimeter and area of semicircles(Half cut rings) whose diameters are ¡) ( 2.8 mathrm{cm} ) ii) ( 56 mathrm{cm} ) iii) ( 84 mathrm{cm} ) iv) ( 112 mathrm{cm} ) |
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119 | Find the area of the given figure. | 10 |

120 | Calculate the area of the designed region in Fig. common between the two quadrants of circles of radius ( 8 mathrm{cm} ) each |
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121 | The longest rod that can be placed flat on the bottom of a box is ( 45 mathrm{cm} ). The box is ( 8 mathrm{cm} ) longer than it is wide. Find the length and breadth of the box. |
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122 | The number of marble slabs of size ( 20 mathrm{cm} times 30 mathrm{cm} ) required to pave the floor of a square room of side 3 metres is A. 100 в. 150 ( c .225 ) D. 25 |
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123 | ( A ) took 15 seconds to cross a rectangular field diagonally walking at the rate of ( 52 mathrm{m} / mathrm{min} ) and ( mathrm{B} ) took the same time to cross the same field along its sides, walking at the rate of 68 ( mathrm{m} / mathrm{min.} ) The area of the field is: A ( cdot 30 m^{2} ) в. ( 40 mathrm{m}^{2} ) ( mathbf{c} cdot 50 m^{2} ) D. ( 60 m^{2} ) |
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124 | In the given figure, ( O ) is the centre of the circle, ( angle A C B=54^{circ} ) and ( B C E ) is a straight line. Find ( boldsymbol{x} ) ( A cdot 126 ) B. 54 ( c cdot 108 ) D. 90 |
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125 | Area of a sector having radius ( 12 mathrm{cm} ) and arc length ( 21 mathrm{cm} ) is A ( cdot 126 ~ c m^{2} ) B. ( 252 mathrm{cm}^{2} ) ( mathrm{c} cdot 33 mathrm{cm}^{2} ) D. ( 45 mathrm{cm}^{2} ) |
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126 | A piece of wire ( 22 mathrm{cm} ) long is bent into the form of an arc of a circle subtending an angle of ( 60^{circ} ) at its center. Find the radius of the circle ( left[boldsymbol{U s e} boldsymbol{pi}=frac{mathbf{2 2}}{mathbf{7}}right] ) | 10 |

127 | In the given figure, ( O ) is the centre of the circle and ( angle Q P R=x^{circ} ; angle O R Q=y^{circ} ) Which statement is true about ( x^{circ} ) and ( boldsymbol{y}^{circ} ? ) A ( cdot x^{circ}+y^{circ}=120^{circ} ) В . ( x^{circ}+y^{circ}=180^{circ} ) c. ( x^{circ}+y^{circ}=90^{circ} ) D. ( x^{circ}+y^{circ}=150^{circ} ) |
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128 | If the area of a semicircle is ( 84 mathrm{cm}^{2} ) then the area of the circle is A ( cdot 144 mathrm{cm}^{2} ) B. ( 42 mathrm{cm}^{2} ) ( mathbf{c} cdot 168 mathrm{cm}^{2} ) D. ( 288 mathrm{cm}^{2} ) |
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129 | Area of a square 625 sq m Then the measure of its side is A. ( 15 mathrm{m} ) B. 25 ( c cdot 20 m ) D. 24 |
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130 | If the perimeter of a circle is ( 132 mathrm{cm} ) find its area. A. 1356 sq. ( mathrm{cm} ) B. 1386 sq. ( mathrm{cm} ) c. 1340 sq. ( mathrm{cm} ) D. 1436 sq. ( mathrm{cm} ) |
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131 | Two arcs of the same circle have their lengths in the ratio ( 4: 5 . ) Then the ratio of the areas of the corresponding sectors is 4: 5 If true then enter 1 and if false then enter 0 ( A ) |
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132 | Find the radius of the circle whose circumference is ( 44 mathrm{cm} .(pi=22 / 7) ) |
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133 | In a circular table corner of radius ( 32 mathrm{cm}, ) a design is formed leaving an equilateral triangle ( A B C ) in the middle as shown in Fig. Find the area of the design |
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134 | Find the area of the shaded segment(in sq. units) ( A cdot 88.5 ) 3,90,5 ( c .86 .5 ) 88 |
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135 | Find the area of a segment of a circle with a central angle of 135 degrees and a radius of 2. Express answer to nearest integer. A . 1 B . 2 ( c .3 ) ( D ) |
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136 | The difference between the semi perimeter and the side of a ( Delta A B C ) arre 8 ( mathrm{cm}, 7 mathrm{cm} ) and ( 5 mathrm{cm} ) respectively. Find the area of the triangle |
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137 | The area of the top of the table ( mathbf{A} cdot 8478 mathrm{cm}^{2} ) B ( .65478 mathrm{cm}^{2} ) ( c cdot 7678 c m^{2} ) D. None |
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138 | Two circles touch internally. The sum of their areas is ( 116 pi ) sq. ( mathrm{cm} ) and the distance between their centers is ( 6 mathrm{cm} ) The radii of the given circles are A. ( 8 mathrm{cm} & 20 mathrm{cm} ) B. ( 4 mathrm{cm} & 10 mathrm{cm} ) c. ( 6 mathrm{cm} ) & ( 8 mathrm{cm} ) D. ( 5 mathrm{cm} ) & ( 9 mathrm{cm} ) |
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139 | What is the area of the shaded segment? ( A cdot 1 m^{2} ) 3. ( 2 m^{2} ) ( c cdot 3 m^{2} ) D. ( 4 mathrm{m}^{2} ) |
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140 | If the circumference of a circle exceeds its diameter by ( 30 mathrm{cm}, ) find the radius of the circle. |
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141 | Calculate the area of a segment of a circle with a central angle of 165 degrees and a radius of ( 4 . ) Express answer to nearest integer. A . 10 B . 20 c. 30 D. 40 |
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142 | Fill in the Blank: Two units Area: (a) ( (b) ) |
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143 | In the figure, PR and QS are two diameters of the circle. If ( P R=28 c m ) and ( P S=14 sqrt{3} mathrm{cm} ) then find the total area of two shaded segments. ( (sqrt{3}=1.73) ) A ( cdot 249,12 mathrm{cm}^{2} ) B . ( 240.76 mathrm{cm}^{2} ) c. ( 251.12 mathrm{cm}^{2} ) D. None of these |
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144 | A circle of ‘a’ radius is divided into 6 equal sectors An equilateral triangle is drawn on the chord of each sectors to lie outside the circle. The area of the resulting figure is |
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145 | Find the area of a sector with an arc length of ( 20 c m ) and a radius of ( 6 mathrm{cm} ) ( mathbf{A} cdot 20 mathrm{cm}^{2} ) B. ( 40 mathrm{cm}^{2} ) ( c cdot 60 c m^{2} ) D. ( 80 mathrm{cm}^{2} ) |
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146 | The radii of two circles are ( 8 mathrm{cm} ) and ( 6 mathrm{cm} ) respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles |
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147 | A chord of a circle of radius ( 6 mathrm{cm} ) subtends a right angle at centre. The area of the minor segment ( (pi=3.14) ) is A ( cdot 9.82 mathrm{cm}^{2} ) B. ( 10.14 mathrm{cm}^{2} ) c. ( 10.26 mathrm{cm}^{2} ) D. ( 12.35 mathrm{cm}^{2} ) |
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148 | A man walks in a horizontal circle round the foot of a pole which is inclined to the vertical. The foot of the pole is at the centre of the circle. The greatest and least angles which the pole subtends at his eye are ( tan ^{-1}left(frac{9}{5}right) ) and ( tan ^{-1}left(frac{6}{5}right) ) respectively and when he is midway between the corresponding positions, the angle is ( theta ). If the man’s height be neglected, find the length of the pole. |
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149 | The circumference of the front wheel of a cart is ( 30 mathrm{ft} ) long and that of the back wheel is 36 ft long. What is the distance travelled by the cart when the front wheel has done five more revolutions than the rear wheel? A ( .20 f t ) B. 25 ft c. ( 750 f t ) D. ( 900 f t ) |
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150 | Sonali pounded a stake into the ground, when she attached a rope to both the stake and her dog’s collar, the dog could reach 9 feet from the stake in any direction. Find the approximate area of the lawn, in square feet, the dog could reach from the stake. ( (pi=3.14) ) A . 28 B. 57 ( c .113 ) D. 254 |
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151 | The area of an equilateral triangle of side ( 13 mathrm{cm}, ) is A. 74.079 sq.cm в. 76.719 sq.cm c. 63.917 sq.cm D. 73.179 sq.cm |
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152 | A horse is tied to a peg at one corner of a square shaped grass field of side ( 15 m ) by means of a ( 5 m ) long rope. Find (i) the area of that part of the field in which the horse can graze. (ii) The increase in the grazing area if the rope were ( 10 m ) long instead of ( 5 m ) (Use ( boldsymbol{pi}=mathbf{3 . 1 4}) ) |
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153 | A boy is running around a rectangular park, whose sides are in the ratio of 4 ( 3, ) at the rate of 10 metre per second and completes a round in 42 seconds. Calculate the area of the park. |
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154 | A square and a regular hexagon have equal perimeters. Their areas are in the ratio: A .2: 1 B. ( 2 sqrt{3}: 1 ) c. ( sqrt{3}: 2 ) D. 3: 2 |
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155 | A chord of radius ( 12 mathrm{cm} ) subtends an angle of ( 120^{circ} ) at the centre. Find the area of corresponding segment of the circle. ( (22 / 7=3.14 text { and } operatorname{root} 3=1.73) ) |
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156 | 57. The wheel of a motor car makes 1000 revolutions in moving 440 m. The diameter (in metre) of the wheel is (1) 0.44 (2) 0.14 (3) 0.24 (4) 0.34 |
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157 | The diameter of a wheel is 1.26 m. How far will it travel in 500 revolutions? ( mathbf{A} cdot 1980 m ) B. 2000m ( c .2420 m ) D. ( 1890 m ) |
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158 | A wire is in the shape of a square of side ( 10 mathrm{cm} . ) If the wire is rebent into a rectangle of length ( 12 mathrm{cm} ), find its breadth. Which figure encloses more area and by how much? |
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159 | Find the circumference of the circle whose radius is ( 28 mathrm{mm} . ) Take ( pi=frac{22}{7} ) |
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160 | In the following figure, the radius of the circle is ( 7 mathrm{cm} ) and ( m(a r c R Y S)=30^{circ} ) find find: Area of the circle |
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161 | Find the area of a circle whose circumference is ( 484 mathrm{cm} ) |
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162 | Write the formulae of area and volume of different solid shapes. Find out the variables and constants in them |
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163 | n Fig., ( A B ) and ( C D ) are two diameters of a circle with centre ( O, ) which are perpendicular to each other. ( boldsymbol{O B} ) is the diameter of the smaller circle. If ( boldsymbol{O A}= ) ( mathbf{7} mathrm{cm}, ) find the area of the shaded region. ( left[boldsymbol{U s e} boldsymbol{pi}=frac{mathbf{2 2}}{mathbf{7}}right] ) ( mathbf{A} cdot 60.5 mathrm{cm}^{2} ) B . ( 63.5 mathrm{cm}^{2} ) ( mathbf{c} cdot 66.5 mathrm{cm}^{2} ) D. ( 56.5 mathrm{cm}^{2} ) |
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164 | The area of the shaded region in the diagram below where the given triangle is isoceles with vertices of base lying on axis of the radius perpendicular to the diameters of the two small semicircles, is в. ( 16(pi-1) ) c. ( 32(pi-1) ) D. ( 32(pi+1) ) |
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165 | A steel wire when bent in the form of a square encloses an area of ( 121 mathrm{cm}^{2} . ) If the same wire is bent in the form of a circle, find the area of the circle. |
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166 | A chord of a circle of radius ( 12 mathrm{cm} ) subtends an angle of ( 60^{circ} ) at the centre. Find the area of the corresponding segment of the circle. (Use ( pi=3.14 ) and ( sqrt{mathbf{3}}=mathbf{1 . 7 3} ) A ( cdot 17.43 mathrm{cm}^{2} ) B. ( 13.08 mathrm{cm}^{2} ) ( mathbf{c} cdot 11.66 mathrm{cm}^{2} ) D. ( 9.64 c m^{2} ) |
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167 | The perimeter of a rectangle is ( 130 mathrm{cm} ) If the breadth of the rectangle is ( 30 mathrm{cm} ) find its length. Also find the area if the rectangle. |
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168 | AOBCA is a quadrant of a circle of radius ( 3.5 mathrm{cm} ) with centre ( 0 . mathrm{P} ) is adjoint on OB such that ( O P=2 c m ). The area of the shaded part is A ( cdot 12.25 mathrm{cm}^{2} ) 8. ( 6.125 mathrm{cm}^{2} ) ( c cdot 12.5 mathrm{cm}^{2} ) D. None of thes |
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169 | The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii ( 24 mathrm{cm} ) and ( 7 mathrm{cm} ) is ( mathbf{A} cdot 31 mathrm{cm} ) B. ( 25 mathrm{cm} ) ( c cdot 62 mathrm{cm} ) D. ( 50 mathrm{cm} ) |
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170 | The diameter of a wheel is ( 2.8 m . ) How far will travel in 1000 revolution? |
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171 | Radius of the circular garden is 9.1 metre. What is the ( operatorname{cost}(text { in } R s) ) of preparing lawn in it at the rate of Rs.100 per 1 sq metre? ( left(pi=frac{22}{7}right) ) |
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172 | 2. The perimeter of a sheet of pa- per in the shape of a quadrant of a circle is 75 cm. Its area would (1) 100 cm2 (3) 693 cm (2) 346.5 cm2 (4) 512.25 cm2 |
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173 | The distance between the two parallel chords of length ( 8 mathrm{cm} ) and ( 6 mathrm{cm} ) in a circle of diameter ( 10 mathrm{cm} ) if the chords lic on the same side of the centre is A. ( 1 mathrm{cm} ) B. 2 ( mathrm{cm} ) ( c cdot 3 mathrm{cm} ) D. ( 4 mathrm{cm} ) |
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174 | The radius of a circular plot is ( 56 mathrm{m} ). How much will it cost to fence the plot with 4 rounds of wire at the rate of Rs. 40 per meter ? | 10 |

175 | Find the area of the shaded region in figure ,if ( mathrm{PQ}=24 mathrm{cm}, mathrm{PR}=7 mathrm{cm} ) and ( mathrm{O} ) is the centre of the circle. A ( cdot 100.98 mathrm{cm}^{2} ) B ( cdot 161.54 mathrm{cm}^{2} ) c. ( 101.54 mathrm{cm}^{2} ) D. None of these |
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176 | Illustration 2.23 If arcs of same length in two circles subtend angles of 60° and 75° at their centers, find the ratios of their radii. |
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177 | The area of a circular field is ( 13.86 m^{2} ) Find the circumference of the field. |
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178 | Two triangular walls of a flyover have been used for advertisements from both sides. The sides of each wall are ( 120 mathrm{m} ) ( 110 mathrm{m} ) and ( 20 mathrm{m} . ) The advertisements yield an earning of R.s 100 per ( m^{2} ) per year. Find the amount of revenue earned in one year. (Take ( sqrt{7}=2.65) ) A. Rs. 3,97,500 B. Rs. 3,47,500 c. Rs. 5,73,300 D. Rs. 4,73,500 |
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179 | The diameter of the moon is approximately on fourth of the diameter of the earth. Find the ratio of their surface areas. |
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180 | Find the length of the side of a square whose area is 441 sq.m. | 10 |

181 | In a circle of radius ( 6 mathrm{cm}, ) a chord of length ( 10 mathrm{cm} ) makes an angle of ( 110^{circ} mathrm{at} ) the centre of the circle. Find the circumference of the circle. |
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182 | In fig two circular flower bds have been shown on two sides of a lawn ( A B C D ) of side ( 56 mathrm{m} ). If the centre of each circular flower bed is the point of intersection ( boldsymbol{O} ) of the diagonals of the square lawn, find the sum of the areas of the lawn and flower beds ( mathbf{A} cdot 4032 m^{2} ) B . ( 4428 mathrm{m}^{2} ) ( mathbf{c} cdot 4628 m^{2} ) D. None of these |
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183 | The sum of circumference and the radius of a circle is ( 51 mathrm{cm} ), find the radius of the circle. |
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184 | The area of a circle is equal to the area of a rectangle with sides ( 112 mathrm{m} ) and ( 88 mathrm{m} ) respectively. Find the circumference of the circle. |
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185 | The perimeter of the following shaded portion of the figure is ( A cdot 40 mathrm{m} ) В. 40.07 m ( c . ) 35.72m D. 35 |
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186 | The cost of fencing a circular field at the rate of ( R s .24 ) per meter is ( R s .5280 /- ) The field is to be ploughed at the. |
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187 | The perimeter of a rectangle having area equal to ( 144 mathrm{cm}^{2} ) and sides in the ratio 4: 9 |
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188 | A wire in the shape of an equilateral triangle encloses an area of ( s mathrm{cm}^{2} ). If the same wire is bent to form a circle, then the area of the circle will be A ( cdot frac{pi s^{2}}{pi} ) B. ( frac{3 s^{2}}{pi} ) ( c cdot frac{3 s}{pi} ) D. ( frac{3 s sqrt{3}}{pi} ) |
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189 | Find the area of the sector of a circle with radius ( 4 mathrm{cm} ) and of angle ( 30^{circ} ). The answer is ( frac{x n}{3} ) then ( x= ) |
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190 | The area of a quadrant of a circle whose circumference is ( 44 mathrm{cm} ) is A ( cdot 144 mathrm{cm}^{2} ) В. ( 175.76 mathrm{cm}^{2} ) c. ( 38.5 mathrm{cm}^{2} ) D. ( 154 mathrm{cm}^{2} ) |
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191 | In the coordinate plane, a circle has center (2,-3) and passes through the point ( (5,0), ) What is the area of the circle? ( A cdot 3 pi ) B. ( 3 sqrt{2} pi ) c. ( 3 sqrt{3} pi ) D. ( 9 pi ) E . ( 18 pi ) |
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192 | Find the difference of the areas of two segments of a circle formed by a chord of length ( 5 mathrm{cm} . ) Subtending an angle of ( 90^{circ} ) till the centre. A. 32.14 sq. ( mathrm{cm} ) в. 35.42 sq. ( mathrm{cm} ) c. 38.96 sq. ( mathrm{cm} ) D. 42.43 sq. ( mathrm{cm} ) |
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193 | A chord of a circle of radius ( 15 mathrm{cm} ) subtends an angle of ( 60^{circ} ) at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use ( pi=3.14 text { and } sqrt{3}=1.73) ) |
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194 | How many time will the wheel of a can rotation in a iorrney of ( 88 mathrm{km} ), given that the diameter of the wheel is ( 56 mathrm{cm} ) ? |
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195 | A cow is tied to a pole, fixed to the midpoint of a side of a square field of dimensions ( 40 m times 40 m ), by means of ( 14 m ) long rope. Find the area that the cow can graze. A ( .254 m^{2} ) в. ( 308 m^{2} ) c. ( 245 mathrm{m}^{2} ) D. ( 380 m^{2} ) |
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196 | The area ( in square unit) of the circle which touches the lines ( 4 x+3 y=15 ) and ( 4 x+3 y=5 ) is ( m pi . ) Find ( m ) |
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197 | In the following figure, the radius of the circle is ( 7 mathrm{cm} ) and ( m(a r c R Y S)=30^{circ} ) find find: ( boldsymbol{A}(boldsymbol{P} boldsymbol{R} boldsymbol{X} boldsymbol{S}) ) |
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198 | A circular wire of radius ( 42 mathrm{cm} ) is cut and bent it into the form of rectangle whose sides are in the ratio of ( 6: 5 . ) The smaller side of the rectangle is ( A .30 mathrm{cm} ) B. ( 60 mathrm{cm} ) ( c .72 mathrm{cm} ) D. ( 132 mathrm{cm} ) |
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199 | Determine the area of the shaded segment A . 10 B. 11 ( c .12 ) D. 13 |
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200 | In the figure, if the ( angle A O B=60^{circ} ) and radius is ( 12 mathrm{cm} ), then find the area of the segment ( A X B .(pi=3.14, sqrt{3}=1.73) ) A . 14 B . 13.08 c. 12 D. 3.14 |
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201 | The length of minute hand of a clock is 14cm. Find the area swept by this minute hand in 10 minutes. ( left(pi=frac{22}{7}right) ) |
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202 | To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle ( 80^{circ} ) to a distance of ( 16.5 k m . ) Find the area of the sea over which the ships are warned. (Use ( pi= ) 3.14) |
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203 | The perimeter of a quadrant of a circle of radius ( frac{7}{2} mathrm{cm} ) is: ( mathbf{A} cdot 3.5 mathrm{cm} ) B. ( 5.5 mathrm{cm} ) c. ( 7.5 mathrm{cm} ) D. ( 12.5 mathrm{cm} ) |
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204 | The length of a room is ( 5 m, ) breadth is ( 3.5 m ) and height is ( 4 m . ) Find the total expenditure of whitewashing on the four walls and roof at the rate of 15 per square meter. (Answer correctly up to 1 decimal place) |
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205 | The following circular diagrams represents the yield of gram. If the yield in field-A is 400 kg, then the yield in field-B will be A. ( 600 mathrm{kg} ) в. ( 800 mathrm{kg} ) c. 900 kg D. 1200kg |
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206 | A path ( 2 m ) wide surrounds a circular pond of diameter ( 40 m ). How many cubic metres of gravel are required to grave the path to a depth of ( 20 mathrm{cm} ) ? |
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207 | Find the area of the sector of circle which substands an angle of ( 150^{circ} ) at the centre, if the radius of the circle is ( 6 mathrm{cm} ) |
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208 | A chord of a circle of radius ( 12 mathrm{cm} ) subtends an angle of ( 120^{circ} ) at the centre. Find the area of the corresponding segment of the circle. (Use ( pi=3.14 text { and } sqrt{3}=1.73) ) ( mathbf{A} cdot 88.44 ) B. 94.88 c. 43.88 D. 54.88 |
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209 | What is the length of arc AB making angle of ( 126^{0} ) at center of radius ( 8 ? ) A . ( 2.6 pi ) в. ( 5.6 pi ) c. ( 7.6 pi ) D. ( frac{1}{2} pi ) |
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210 | The radii of two circles are in the ratio ( 3: 8 . ) If the difference between their areas is ( 2695 pi mathrm{cm}^{2}, ) find the area of the smaller circle. A ( cdot 1386 mathrm{cm}^{2} ) B. ( 1280 mathrm{cm}^{2} ) ( mathbf{c} cdot 1187 mathrm{cm}^{2} ) D. ( 1546 mathrm{cm}^{2} ) |
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211 | A wire bent in the form of a circle of radius ( 42 mathrm{cm} ) is cut and again bent in the form of a square. The ratio of the regions enclosed by the circle and the square in the two cases is given by : A .11: 12 B. 21: 33 c. 22: 33 D. 14: 11 |
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212 | In the following figure, the circle centered at ( N ) has a radius of ( 4 . ) What is the area of the shaded region? ( A cdot 3 pi ) B. ( 6 pi ) ( c .9 pi ) D. ( 12 pi ) E . ( 16 pi ) |
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213 | A chord PQ of a length 12 cm subtends an angle of ( 120^{circ} ) at the center of a circle Find the area of the minor segment cut off by chord PQ. |
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214 | In given fig. of sector of circle of radius ( 10.5 mathrm{cm} . ) What is the perimeter of sector? |
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215 | In the given figure, ABCD is a trapezium of area ( 24.5 c m^{2} . ) If ( A D | ) ( boldsymbol{B C}, angle boldsymbol{D A B}=mathbf{9 0}^{0}, boldsymbol{A D}= ) ( 10 c m, B C=4 c m ) and ( A B E ) is quadrant of circle then find the area of the shaded region. |
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216 | A horse is tied to a post by a rope If the horse moves along a circular path always keep the rope tight and describes 88 metres when it has traced out ( 72^{circ} ) at the center, then the length of rope is ( A cdot 60 m ) B. ( 65 m ) ( c .70 m ) D. ( 72 m ) |
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217 | In the given figure 0 is the centre of circle of radius ( 28 mathrm{cm} . ) Find the area of the minor segment ASB |
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218 | Find the area of the segment of circle, given that the angle of the sector is ( 120^{circ} ) and the radius of the circle is ( 21 mathrm{cm} .(text { Take } pi=22 / 7) ) |
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219 | ABCD is a flower bed. If ( O A=21 c m ) and ( O C=14 m, ) find the area of the bed. [Use ( left.pi=frac{22}{7}right] ) ( A cdot 161.4 m^{2} ) в. ( 192.5 m^{2} ) c. ( 212.6 m^{2} ) D. ( 257.2 .5 m^{2} ) |
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220 | The area of a segment of a circle of radius ( 21 mathrm{cm} ) if the arc of the segment has a measure of ( 60^{circ} ) is (Take ( sqrt{mathbf{3}}=mathbf{1 . 7 3} ) ) A. 45.27 sq. ( mathrm{cm} ) B. 40.27 sq. ( mathrm{cm} ) c. 40.8 sq. ( mathrm{cm} ) D. none of these |
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221 | 68. At the centres of two circles, two arcs of equal length subtend an- gles of 60° and 75° respectively. The ratio of the radii of the two circles is (1) 5:2 (2) 5:4 (3) 3:2 (4) 2:1 |
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222 | buckel 54. If the radii of the circular en of a truncated conical bus which is 45cm high be 28 and 7 cm, then the capacity the bucket in cubic centimet is user = 2 (1) 48510 (3) 48150 (2) 45810 (4) 48051 bant : |
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223 | Find the area of the shaded region in fig., if ( boldsymbol{P} boldsymbol{Q}=mathbf{2 4 c m}, boldsymbol{P R}=mathbf{7 c m} ) and ( boldsymbol{O} ) is the centre of the circle. |
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224 | Find the radius of a circle whose circumference is ( 39.6 mathrm{cm} ) |
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225 | In the figure. ( A C=24 mathrm{cm}, B C=10 ) and ( O ) is the centre of the circle. Find the area of shaded region |
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226 | 1 70. In the figure, OED and OBA are sectors of a circle with centre O. The area of the shaded portion is 4m 45° -3m- (1) m 2 6 m m2 m2 |
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227 | In a circle with center ( 0, ) central angle ( A O B ) has a measure of ( frac{5 pi}{4} ) radians. The area of the sector formed by central angle ( A O B ) is what fraction of the area of the circle? A ( cdot frac{5}{8} ) B. ( frac{8}{5} ) c. ( frac{16}{5} ) D. ( frac{4}{5} ) |
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228 | The area of a circle is ( 24.64 . m^{2} ) What is the circumference of the circle? A . ( 14.64 m ) B. 16.36 m c. ( 17.60 m ) D. ( 18.40 m ) |
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229 | In the given figure, the area of the shaded portion APB is? A ( -frac{1}{4} pi r^{2} ) B. ( frac{1}{4}(pi-2) r^{2} ) c. ( frac{1}{4}(pi-1) r^{2} ) D. None of these |
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230 | 63. A circle is inscribed in a square of side 35 cm. The area of the remaining portion of the square which is not enclosed by the cir- cle is (1) 262.5 cm2 (2) 562.5 cm? (3) 962.5 cm2 (4) 762.5 cm |
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231 | Consider a circle with unit radius. There are seven adjacent sectors, ( S_{1}, S_{2}, S_{3} ldots S_{7}, ) in the circle such that their total area is ( frac{1}{8} ) of the area of the circle. Further, the area of the jth sector is twice that of the ( (j-1)^{t h} ) sector, for ( j=2, dots .7 ) Find the area of the sector ( boldsymbol{S}_{1} ) ( mathbf{A} cdot frac{3 pi}{1016} ) В. ( frac{pi}{508} ) c. ( frac{pi}{1016} ) D. ( frac{pi}{336} ) |
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232 | Given ( : A B=12 mathrm{cm}, A C=13 mathrm{cm}, mathrm{ED}=mathrm{FG}= ) ( 5 mathrm{cm}, mathrm{EF}=10 mathrm{cm} ) and ( mathrm{GD}=4 mathrm{cm} ) Find the area and the perimeter of the adjoining figure ( A cdot 88 ) sq. ( mathrm{cm} ) and ( 50 mathrm{cm} ) B. 88 sq. ( m ) and 50 cm ( c .88 ) sq. ( mathrm{cm} ) and ( 50 mathrm{m} ) D. 8.8 sq. ( mathrm{cm} ) and ( 50 mathrm{cm} ) |
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233 | 55. A metal wire when bent in the form of a square encloses an area 484 cm. If the same wire is ben in the form of a circle, then (tak ing r = 22 ) its area is (1) 308 cm2 (2) 506 cm (3) 600 cm2 (4) 616 cm |
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234 | In the figure above, ( overline{A C} ) is a diameter of the large circle and ( mathrm{B} ) lies on ( overline{boldsymbol{A C}} ) so that ( A B ) is a diameter of the small circle. If ( A B=1 ) and ( B C=2, ) Calculate the area of the shaded region. ( A cdot frac{pi}{4} ) в. ( c cdot 2 pi ) D. ( frac{9 pi}{4} ) E . ( 9 pi ) |
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235 | In the given figure find the value of ( angle A O C ) ( mathbf{A} cdot 130^{circ} ) B. ( 140^{circ} ) ( mathbf{c} cdot 150^{circ} ) D. ( 160^{circ} ) |
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236 | If the radius of the circle is increased by ( 100 % ) then the area is increased by A. ( 100 % ) B . 200% c. 300% D. 400% |
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237 | The circumference of a circular garden is ( 572 m . ) Outside the garden a road, ( 3.5 m ) wide, runs around it.Calculate the ( operatorname{cost} ) of repairing the road at the rate of Rs.375per 100.sq.m? |
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238 | The area of a square of side 16 | 10 |

239 | A design is made on a rectangular tile of dimensions ( 50 mathrm{cm} 70 mathrm{cm} ) as shown in Fig. ( 12.7 . ) The design shows 8 triangles, each of sides ( 26 mathrm{cm}, 17 mathrm{cm} ) and ( 25 mathrm{cm} ) os cut out. Find the total area of the design in ( c m^{2} ) |
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240 | If the perimeter and the area of a circle are numerically equal, then the radius of the circle is: A . 2 units B. ( pi ) units c. 4 units D. 7 units |
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241 | If the ratio of circumference of two circles is ( 4: 9, ) then what is the ratio of their areas is? A .9: 4 B. 16: 81 c. 4: 9 D. 2: 3 |
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242 | A circular pond is of diameter ( 17.5 mathrm{m} ). It is surrounded by a ( 2 mathrm{m} ) wide path. Find the cost of constructing the path at the rate of Rs. 25 per square metre (Use ( pi= ) 3.14) |
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243 | A square has the perimeter ( 40 mathrm{cm} ) What is the sum of the diagonals? | 10 |

244 | The perimeter of a sector of a circle of radius ( 5.7 m ) is ( 27.2 m . ) Find the area of the sector. |
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245 | If the area of a triangle with base ( x ) is equal to area of a square of side ( x, ) then the altitude of the triangle is A ( cdot frac{x}{2} ) B. ( x ) ( c cdot sqrt{2} x ) D. ( 2 x ) |
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246 | When a circle is cut into eighths, those sectors are called as, A. Sextants B. Quadrants c. octants D. None of these |
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247 | A wire is bent in the form of a square of side ( 16.5 mathrm{cm} . ) It is straightened and then bent into a circle. What is the radius of the circle so formed? ( left(text { Taken } pi=frac{22}{7}right) ) |
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248 | A circular flower bed is surmounted by a path ( 5 mathrm{m} ) wide as shown in fig.The diameter of the flowerbed is ( 60 mathrm{m} ). What is the area of this path? ( mathbf{A} cdot 735 pi c m^{2} ) В. ( 325 pi c m^{2} ) ( mathbf{c} cdot 635 pi c m^{2} ) D. None of these |
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249 | In the figure, an equilateral triangle of side ( 6 mathrm{cm} ) and its circumcircle is shown Find the area of shaded portion. Take ( (boldsymbol{pi}=mathbf{3 . 1 4}, sqrt{mathbf{3}}=mathbf{1 . 7 3}) ) A. ( 22.11 mathrm{cm}^{2} ) B. ( 22 mathrm{cm}^{2} ) c. ( 21.11 mathrm{cm}^{2} ) D. ( 23.11 mathrm{cm}^{2} ) |
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250 | In the given figure, ( A C ) is diameter of ( a ) circle with radius ( 5 mathrm{cm} ). if ( mathrm{AB}=mathrm{BC} ) and ( mathrm{CD}=8 mathrm{cm}, ) the area of the shaded region to the nearest whole number is- ( A cdot 28 c m^{2} ) B ( cdot 29 c m^{2} ) ( c cdot 30 c m^{2} ) ( mathbf{D} cdot 45 mathrm{cm}^{2} ) |
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251 | The perimeter of a rectangular sheet is ( 100 mathrm{cm} . ) If the length is ( 35 mathrm{cm}, ) find its breath Also find the area. | 10 |

252 | Area of region bounded by ( boldsymbol{x}=mathbf{0}, boldsymbol{y}=mathbf{0} ) ( boldsymbol{x}=mathbf{2}, boldsymbol{y}=mathbf{2}, boldsymbol{y} leq boldsymbol{e}^{x} ; boldsymbol{y} geq ln boldsymbol{x} ) is A ( .6-4 ln 2 ) B. ( 4 ln 2-2 ) c. ( 2 ln 2-4 ) D. ( 6-2 ln 2 ) |
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253 | In the figure, ( m ) ? ( P O Q=30 ) ? and radius ( O P ) ( =12 mathrm{cm}, ) then find the given area of segment PRQ (Given ( pi=3.14) ) A ( cdot 1.68 c m^{2} ) B ( cdot 2 cdot 46 c m^{2} ) ( c cdot 0.68 c m^{2} ) D. none of these |
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254 | A circle is inscribed in a square. If the area of the square is 36 sq. units, what is the area of the circle? ( mathbf{A} cdot 6 pi ) в. ( 9 pi ) c. ( 12 pi ) D. ( 18 pi ) ( E .36 pi ) |
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255 | In the above figure, ( boldsymbol{O} ) is the centre of the circle and ( angle B A C=n^{circ}, angle O C B= ) ( m^{circ} ) then A ( cdot m^{circ}+n^{circ}=90^{circ} ) B . ( m^{circ}+n^{circ}=180^{circ} ) ( mathbf{c} cdot m^{circ}+n^{circ}=120 ) D . ( m^{circ}+n^{circ}=150^{circ} ) |
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256 | f ( a r e a=900 s q . c m ) and breadth ( = ) ( 25 mathrm{cm}, ) then find length of rectangle. |
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257 | ( n ) Fig., ( A B C ) is a quadrant of a circle of radius ( 14 mathrm{cm} ) and a semicircle is drawn with ( B C ) as diameter. Find the area of the shaded region |
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258 | In a circle of radius ( 21 mathrm{cm}, ) an arc subtends and angle of ( 60^{circ} ) at the centre. Find: (i) The length of the arc (ii) Area of the sector formed by the arc (iii) Area of the segment formed by the corresponding chord |
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259 | The length of a minute hand of a wall clock is ( 8.4 mathrm{cm} . ) Find the area swept by it in half an hour. A ( cdot 100 mathrm{cm}^{2} ) В. ( 110.88 mathrm{cm}^{2} ) ( mathrm{c} cdot 120 mathrm{cm}^{2} ) D. ( 130 mathrm{cm}^{2} ) |
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