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question_answer1)
O is the centre of a circle of diameter 4 cm and OABC is a square, if the shaded area is \[\frac{1}{3}\] area of the square, then the side of the square is _____.
A)
\[\pi \sqrt{3}\] done
clear
B)
\[\sqrt{3\pi }\] done
clear
C)
\[3\sqrt{\pi }\] done
clear
D)
\[3\pi \] done
clear
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question_answer2)
A steel wire when bent in the form of a square encloses an area of 121 sq. cm. If the same wire is bent into the form of a circle, find the area of the circle. [use \[\pi =\frac{22}{7}\]]
A)
\[44\text{ }c{{m}^{2}}\] done
clear
B)
\[308\text{ }c{{m}^{2}}\] done
clear
C)
\[77\text{ }c{{m}^{2}}\] done
clear
D)
\[154\text{ }c{{m}^{2}}\] done
clear
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question_answer3)
In given figure, ABC is a triangle right- angled at B, with AB = 14 cm and BC = 24 cm. With the vertices A, B and C as centres, arcs are drawn each of radius 7 cm. Find the area of the shaded region. [Use \[\pi =\frac{22}{7}\]]
A)
\[91\text{ }c{{m}^{2}}\] done
clear
B)
\[95\,c{{m}^{2}}\] done
clear
C)
\[97\,c{{m}^{2}}\] done
clear
D)
\[88\,c{{m}^{2}}~\] done
clear
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question_answer4)
If the difference between the area of a regular hexagonal plot and the area of a circular swimming tank circumscribed in it is\[26.705\text{ }{{m}^{2}}\]. Find the radius of the circular swimming tank. \[(\pi =3.143,\,\,\sqrt{3}=1.732)\]
A)
4 cm done
clear
B)
7 cm done
clear
C)
11 cm done
clear
D)
9 cm done
clear
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question_answer5)
The inner circumference of a circular track is \[24\pi \,\,m\]. The track is 2 m wide from everywhere. The quantity of wire required to surround the path completely is ___
A)
80 m done
clear
B)
81 m done
clear
C)
82 m done
clear
D)
88 m done
clear
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question_answer6)
The areas of two concentric circles are \[962.5\text{ }c{{m}^{2}}\]and \[1386\text{ }c{{m}^{2}}\]respectively. The width of the ring is _____.
A)
\[3.4\text{ }cm\] done
clear
B)
\[3.5\text{ }cm\] done
clear
C)
\[3.2\text{ }cm\] done
clear
D)
\[3.1\text{ }cm\] done
clear
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question_answer7)
A chord of a circle subtends an angle of \[{{60}^{o}}\] at the centre. If the length of the chord is 100 cm, find the area of the major segment.
A)
\[30720.5\,c{{m}^{2}}\] done
clear
B)
\[31021.42\,c{{m}^{2}}\] done
clear
C)
\[30391.7\,c{{m}^{2}}\] done
clear
D)
\[30520.61\,c{{m}^{2}}\] done
clear
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question_answer8)
A park is in the form of a rectangle\[120\text{ }m\times 100\text{ }m\]. In the centre of the park, there is a circular lawn as shown in the figure. The area of the park excluding the lawn is\[8700\text{ }{{m}^{2}}\]. Find the radius of the circular lawn. \[\left( Use\,\,\pi =\frac{22}{7} \right)\]
A)
\[32.4\text{ }m\] done
clear
B)
\[36.4\text{ }m\] done
clear
C)
\[32.6\,m\] done
clear
D)
\[39.4\text{ }m\] done
clear
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question_answer9)
Find the area of a ring whose outer and inner radii are respectively 23 cm and 12 cm.
A)
\[1125\text{ }c{{m}^{2}}\] done
clear
B)
\[1321\text{ }c{{m}^{2}}\] done
clear
C)
\[1210\,\,c{{m}^{2}}\] done
clear
D)
\[1225\,\,c{{m}^{2}}\] done
clear
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question_answer10)
AB is a line segment of length 4 cm. P is the mid-point of AB. Circles are drawn with A, P and B as centres and radii AP = PB (see figure). The area of the shaded portion (in\[c{{m}^{2}}\]) is _____.
A)
\[6\sqrt{3}\] done
clear
B)
\[2\pi -6\sqrt{3}\] done
clear
C)
\[2\pi -3\sqrt{3}\] done
clear
D)
\[3\sqrt{3}\] done
clear
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question_answer11)
The perimeter of a sector of a circle of radius \[5.2\text{ }cm\]is\[16.4\text{ }cm\]. The area of the sector is _____.
A)
\[15.1\text{ }c{{m}^{2}}\] done
clear
B)
\[15.5\text{ }c{{m}^{2}}\] done
clear
C)
\[15.6\,c{{m}^{2}}\] done
clear
D)
\[15.9\,c{{m}^{2}}\] done
clear
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question_answer12)
Circle \[{{C}_{2}}\] passes through the centre of circle \[{{C}_{1}}\]and is tangential to it. If the area of \[{{C}_{1}}\]is \[4\text{ }c{{m}^{2}},\] then the area of \[{{C}_{2}}\] is _____.
A)
\[8\,c{{m}^{2}}\] done
clear
B)
\[8\,\sqrt{\pi \,}c{{m}^{2}}\] done
clear
C)
\[16\,c{{m}^{2}}\] done
clear
D)
\[16\sqrt{\pi }\,c{{m}^{2}}\] done
clear
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question_answer13)
In the given figure, the area of the shaded region is ___.
A)
\[3\pi \,c{{m}^{2}}\] done
clear
B)
\[6\pi \,c{{m}^{2}}\] done
clear
C)
\[9\pi \,c{{m}^{2}}\] done
clear
D)
\[7\pi \,c{{m}^{2}}\] done
clear
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question_answer14)
The ratio of the outer and inner perimeters of a circular path is\[23:22\]. If the path is 5 metres wide, the diameter of the inner circle is
A)
\[55\,m\] done
clear
B)
\[110\,m\] done
clear
C)
\[220\text{ }m\] done
clear
D)
\[~230\text{ }m\] done
clear
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question_answer15)
In the given figure, a semicircle is drawn with O as centre and AB as diameter. Semicircles are drawn with AO and OB as diameters. If \[AB=28\text{ }m,\]find the perimeter of the shaded region. \[\left[ Use\,\,\pi =\frac{22}{7} \right]\]
A)
\[70\text{ }m\] done
clear
B)
\[105\text{ }m\] done
clear
C)
\[88\text{ }m\] done
clear
D)
\[85\text{ }m\] done
clear
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question_answer16)
An oval shaped meeting table made of wood has its dimensions as shown in figure. Find the cost of polishing it at \[Rs.\text{ }3.50\]per sq. m. (Use\[\pi =3.14\])
A)
\[Rs.\,310.75\] done
clear
B)
\[Rs.\,308.91\] done
clear
C)
\[Rs.\,250.25\] done
clear
D)
\[Rs.\,360.82\] done
clear
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question_answer17)
The diameter of the driving wheel of a bus is 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 66 km per hour?
A)
200 done
clear
B)
210 done
clear
C)
250 done
clear
D)
240 done
clear
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question_answer18)
A square water tank has its sides equal to 40 m. There are four semicircular grassy plots all round it. Find the cost of turfing the plots at \[Rs.\text{ }1.25\]per sq. m.
A)
Rs.2671 done
clear
B)
Rs.4401 done
clear
C)
Rs.2512 done
clear
D)
Rs.3140 done
clear
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question_answer19)
A man runs around a circle of radius 50 m at a speed of 12 km/h. The time taken by him for going around it ten times is ___. \[(\pi =3.14)\]
A)
10 mins 42 sees done
clear
B)
12 mins 35 sees done
clear
C)
15 mins 42 sees done
clear
D)
10 mins 35 sees done
clear
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question_answer20)
A rectangular park is 100 m by 50 m. It is surrounded by semicircular flower beds all round. Find the cost of levelling the semicircular flower beds at 60 paise per\[{{m}^{2}}\].
A)
Rs.31425 done
clear
B)
Rs. 28260 done
clear
C)
Rs.352.40 done
clear
D)
Rs. 282.60 done
clear
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question_answer21)
In the given figure three circles of radius 2 cm touch one another externally. These circles are circumscribed by a circle of radius R cm. Find the value of R and the area of the shaded region in terms of \[\pi \]and \[\sqrt{3}\].
A)
\[\left\{ \frac{5\pi }{3}(5\sqrt{3}+1)-5\sqrt{3} \right\}\] done
clear
B)
\[\left\{ \frac{4\pi }{2}(4\sqrt{2}+1)-4\sqrt{2} \right\}\] done
clear
C)
\[\left\{ \frac{4\pi }{3}(4\sqrt{3}+1)-4\sqrt{2} \right\}\] done
clear
D)
\[\left\{ \frac{4\pi }{3}(4\sqrt{3}+1)-4\sqrt{3} \right\}\] done
clear
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question_answer22)
A)
(P) \[\to \](iii); (Q) \[\to \](ii); (R) \[\to \] (i) done
clear
B)
(P) \[\to \] (ii); (Q) \[\to \] (i); (R)\[\to \] (iii) done
clear
C)
(P) \[\to \] (ii); (Q) \[\to \] (iii); (R) \[\to \] (i) done
clear
D)
(P) \[\to \] (iii); (Q) \[\to \](i); (R) \[\to \] (ii) done
clear
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question_answer23)
The circumcircle of \[\Delta ABC\] with \[\angle A={{60}^{o}}\]has its centre at O and radius equal to 2 cm. Circle centered at O., touches the circumcircle and also 08 and OC. The radius of the smaller circle is (in cm)____.
A)
\[12-4\sqrt{3}\] done
clear
B)
\[\frac{6-\sqrt{3}}{2}\] done
clear
C)
\[\frac{3-\sqrt{3}}{2}\] done
clear
D)
\[4\sqrt{3}-6\] done
clear
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question_answer24)
In the given figure, ABC is a right-angled triangle, right-angled at/A. Semicircles are drawn on AB, AC and BC as diameters. Find the area of the shaded region.
A)
7 sq. units done
clear
B)
8 sq. units done
clear
C)
5 sq. units done
clear
D)
6 sq. units done
clear
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question_answer25)
In the given figure, ABCD is a square of side 10 cm. Find
(i) Area of inscribed circle |
(ii) Area of circumscribed circle |
(iii) Area of shaded region |
A)
B)
C)
D)
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