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question_answer1)
If the area of circle inscribed in an equilateral triangle is \[48\pi \] square units then what is the perimeter of that triangle?
A)
\[17\sqrt{3}\] units done
clear
B)
\[36\]units done
clear
C)
\[72\]units done
clear
D)
\[48\sqrt{3}\] units done
clear
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question_answer2)
If the perimeter of a semi-circular protractor is 36 cm, what is its diameter?
A)
11 cm done
clear
B)
13 cm done
clear
C)
15 cm done
clear
D)
14 cm done
clear
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question_answer3)
In the given figure, two circles of radii 7 cm each are shown. ABCD is a rectangle and AD and BC are the radii. What is the area of shaded region?
A)
\[20\text{ }c{{m}^{2}}\] done
clear
B)
\[21\text{ }c{{m}^{2}}\] done
clear
C)
\[19\text{ }c{{m}^{2}}\] done
clear
D)
\[18\text{ }c{{m}^{2}}\] done
clear
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question_answer4)
A race track is in the form of a circular ring that has inner and outer circumferences are 500 m and 599 m respectively. What is the width of the track?
A)
11 m done
clear
B)
22 m done
clear
C)
15.75 m done
clear
D)
10.75 m done
clear
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question_answer5)
What is the Perimeter of the shaded region?
A)
264 cm done
clear
B)
352 cm done
clear
C)
500 cm done
clear
D)
528 cm done
clear
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question_answer6)
The minute hand of a wall clock is of length 10.5 cm. What is the area covered by it in 60 minutes?
A)
\[346.5\text{ }c{{m}^{2}}\] done
clear
B)
\[340\text{ }c{{m}^{2}}\] done
clear
C)
\[355\text{ }c{{m}^{2}}\] done
clear
D)
\[342\text{ }c{{m}^{2}}\] done
clear
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question_answer7)
Four horses are tethered at four corners of a square plot of 42 m so that they just cannot reach one another. The area left ungrazed is:
A)
\[378\,{{m}^{2}}\] done
clear
B)
\[438\,{{m}^{2}}\] done
clear
C)
\[786\,{{m}^{2}}\] done
clear
D)
None of these done
clear
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question_answer8)
The diagram shows two concentric circles. The chord of the large circle is a tangent to the small circle and has length 2k. What is the area of the shaded region?
A)
\[\pi {{k}^{2}}\] done
clear
B)
\[3\pi {{k}^{2}}\] done
clear
C)
\[5\pi {{k}^{2}}\] done
clear
D)
\[2\pi {{k}^{2}}\] done
clear
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question_answer9)
If the circumferences of a circle is increased by 50%, by what percent will its area be increased?
A)
75% done
clear
B)
100% done
clear
C)
125% done
clear
D)
150% done
clear
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question_answer10)
Figure ABCD is a square with side 10 cm. BMD is an arc of a circle with centre C. BND is an arc of a circle with centre A. What is the area of the shaded region?
A)
\[\left( 100-25\pi \right)\text{ }c{{m}^{2}}\] done
clear
B)
\[\left( 100-50\pi \right)c{{m}^{2}}\] done
clear
C)
\[\left( 50\pi -100 \right)c{{m}^{2}}\] done
clear
D)
\[\left( 25\pi -100 \right)\text{ }c{{m}^{2}}\] done
clear
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question_answer11)
An equilateral triangle has a circle inscribed in it and is circumscribed by a circle. There is another equilateral triangle inscribed in the inner circle. What is the ratio of the areas of the outer circle and the inner equilateral triangle?
A)
\[\frac{16\pi }{3\sqrt{3}}\] done
clear
B)
\[\frac{8\pi }{2\sqrt{3}}\] done
clear
C)
\[\frac{24\pi }{3\sqrt{3}}\] done
clear
D)
None of these done
clear
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question_answer12)
The top of dining table is rectangular, 2k units long and k units wide, with two semicircles along the breadth. What is the area of table?
A)
\[\frac{\pi +4{{k}^{2}}}{4}\] done
clear
B)
\[\frac{(\pi +4)}{4}{{k}^{2}}\] done
clear
C)
\[\left( \frac{\pi +8}{4} \right){{k}^{2}}\] done
clear
D)
\[2(\pi +4){{k}^{2}}\] done
clear
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question_answer13)
In the given figure, PQRS is a square of diagonal \[7\sqrt{2}\,cm\]. With P as the centre, the arc QMS is drawn. What is the area of the shaded region \[(in\,\,c{{m}^{2}})\]?
A)
\[\frac{49}{4}(\pi -2)\] done
clear
B)
\[\frac{49}{4}(\pi -1)\] done
clear
C)
\[\frac{49}{4}(\pi -3)\] done
clear
D)
\[\frac{49}{2}(\pi -2)\] done
clear
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question_answer14)
A circular garden of radius is 15 m is surrounded by a circular path of width 7 m. If the path is to be covered with tiles at a rate of Rs. 10 per\[{{m}^{2}}\], then what is the total cost of the work?
A)
Rs. 8410 done
clear
B)
Rs. 7140 done
clear
C)
Rs. 8140 done
clear
D)
Rs. 7410 done
clear
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question_answer15)
Find the area of the shaded region, given that the radius of each circle is equal to 5 cm.
A)
\[(400-100\pi )\] done
clear
B)
\[(360-100\pi )\] done
clear
C)
\[(231-100\pi )\] done
clear
D)
\[(400-50\pi )\] done
clear
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question_answer16)
What is area of the shaded figure below?
A)
\[\frac{\pi }{\sqrt{3}}{{a}^{2}}\] done
clear
B)
\[\frac{\pi {{a}^{2}}}{16}\] done
clear
C)
\[\frac{\left( \pi -\sqrt{2} \right)}{4}{{a}^{2}}\] done
clear
D)
\[\frac{2\sqrt{3}}{\pi }{{a}^{2}}\] done
clear
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question_answer17)
A circle is inscribed is an equilateral triangle. If the in-radius is 21 cm, what is the area of the triangle?
A)
\[1100\sqrt{3}\,c{{m}^{2}}\] done
clear
B)
\[1323\sqrt{3}\,c{{m}^{2}}\] done
clear
C)
\[1369\sqrt{3}\,c{{m}^{2}}\] done
clear
D)
\[1442\sqrt{3}\,c{{m}^{2}}\] done
clear
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question_answer18)
In the given figure ABC is an equilateral triangle and C as the centre of the circle. A and B lie on the circle. What is the area of the shaded region, if the diameter of the circle is 28 cm?
A)
\[\left( 102\frac{2}{3}-49\sqrt{3} \right)c{{m}^{2}}\] done
clear
B)
\[\left( 103\frac{2}{3}-4998\sqrt{3} \right)c{{m}^{2}}\] done
clear
C)
\[\left( 109-38\sqrt{3} \right)cm\] done
clear
D)
None of these done
clear
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question_answer19)
A square shaped bus shelter is supported on four circular poles. The circumferences of each pole are 'x' m and the length of each side of the shelter is 'y' m. find the area of the unsupported part of the shelter.
A)
\[\left( {{x}^{2}}-\frac{{{y}^{2}}}{\pi } \right){{m}^{2}}\] done
clear
B)
\[\left( {{y}^{2}}+\frac{{{x}^{2}}}{\pi } \right){{m}^{2}}\] done
clear
C)
\[\left( {{x}^{2}}+\frac{{{y}^{2}}}{\pi } \right){{m}^{2}}\] done
clear
D)
\[\left( {{y}^{2}}-\frac{{{x}^{2}}}{\pi } \right){{m}^{2}}\] done
clear
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question_answer20)
Four identical semicircles are drawn inside a big square as shown in the figure. Each side of the big square is 14 cm long. |
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What is the area of the shaded region? (Use \[\pi =\frac{22}{7}\] )
A)
\[125\text{ }c{{m}^{2}}\] done
clear
B)
\[112\text{ }c{{m}^{2}}\] done
clear
C)
\[173\text{ }c{{m}^{2}}\] done
clear
D)
\[159\text{ }c{{m}^{2}}\] done
clear
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question_answer21)
The figure given is made up of a rectangle, identical semicircle(s) and quadrant (s). |
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What is the area of the un-shaded portion? (Use \[\pi =\frac{22}{7}\])
A)
\[1350\text{ }c{{m}^{2}}\] done
clear
B)
\[1154\text{ }c{{m}^{2}}\] done
clear
C)
\[1400\text{ }c{{m}^{2}}\] done
clear
D)
\[{{21}^{2}}\times \left( 6-\pi \right)\text{ }c{{m}^{2}}\] done
clear
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question_answer22)
An ink pen, with a cylindrical barrel of diameter 2 cm and height 10.5 cm, completely filled with ink, can be used to write 4950 words. How many words can be written using 400 ml of ink?
A)
40000 done
clear
B)
60000 done
clear
C)
450000 done
clear
D)
80000 done
clear
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question_answer23)
What is the area of the sector of a circle, whose radius is 6 m and the angle at the centre is\[42{}^\circ \]?
A)
\[13.2\text{ }{{m}^{2}}\] done
clear
B)
\[14.2\text{ }{{m}^{2}}\] done
clear
C)
\[13.4\text{ }{{m}^{2}}\] done
clear
D)
\[14.4\text{ }{{m}^{2}}\] done
clear
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question_answer24)
In the given figure, ABCD is a square of side 10 cm and a circle is inscribed in it. What is the area of the shaded part? (\[in\text{ }c{{m}^{2}}\])
A)
\[\frac{100-36\pi }{41}\] done
clear
B)
\[\frac{100-25\pi }{8}\] done
clear
C)
\[\frac{100+25\pi }{8}\] done
clear
D)
None of these done
clear
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question_answer25)
The given figure shows an isosceles triangle and a semicircle with centre O. |
|
If the radius of the semicircle is 2.8 cm. What is the perimeter of the figure?
A)
15.6 cm done
clear
B)
18.8 cm done
clear
C)
16.8 cm done
clear
D)
20.4 cm done
clear
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question_answer26)
The given figure is made up of a circle and three identical semicircles. If O is the centre and XY is the diameter of the bigger circle respectively and XY is equal to 28 cm, What is the perimeter of the shaded part?
A)
67 cm done
clear
B)
50 cm done
clear
C)
80 cm done
clear
D)
15 cm done
clear
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question_answer27)
The given figure shows two identical semicircles inside a square. What is the area of the shaded region?
A)
\[15\text{ }c{{m}^{2}}\] done
clear
B)
\[21\,c{{m}^{2}}\] done
clear
C)
\[16\,c{{m}^{2}}\] done
clear
D)
\[23\,c{{m}^{2}}\] done
clear
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question_answer28)
There is a circular road round a circular garden. If the difference between the circumferences of the outer circle and the inner circle is 44 m., what is the width of the road?
A)
5 m done
clear
B)
6 m done
clear
C)
7 m done
clear
D)
8 m done
clear
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question_answer29)
A circle of radius 'b' is divided into 6 equal sectors. An equilateral triangle is drawn on the chord of each sector to lie outside the circle. What is the area of the resulting figure?
A)
\[3{{b}^{2}}\left( \pi +\sqrt{3} \right)\] done
clear
B)
\[3\sqrt{3}{{b}^{2}}\] done
clear
C)
\[3\left( {{b}^{2}}\sqrt{3}+\pi \right)\] done
clear
D)
\[\frac{3\sqrt{3}\pi {{b}^{2}}}{2}\] done
clear
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question_answer30)
What is the area of the given figure?
A)
\[115.5\text{ }c{{m}^{2}}\] done
clear
B)
\[228.5\text{ }c{{m}^{2}}\] done
clear
C)
\[154\text{ }c{{m}^{2}}\] done
clear
D)
None of these done
clear
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question_answer31)
A wire in the form of a circle of radius 42 cm is cut and again bent to form a square. What is the diagonal of the square?
A)
\[66\text{ }cm\] done
clear
B)
\[66\sqrt{3}\,cm\] done
clear
C)
\[66\sqrt{2}\,cm\] done
clear
D)
None of these done
clear
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question_answer32)
In the adjoining figure ACB is a quadrant with radius 'a'. A semicircle is drawn outside the quadrant taking AB as a diameter. What is the area of shaded region?
A)
\[\frac{1}{4}\left( \pi -2{{a}^{2}} \right)\] done
clear
B)
\[\left( \frac{1}{4} \right)\left( \pi {{a}^{2}}-{{a}^{2}} \right)\] done
clear
C)
\[\frac{{{a}^{2}}}{2}\] done
clear
D)
\[{{a}^{2}}\left( \frac{\pi -2}{2} \right)\] done
clear
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question_answer33)
There are two circles intersecting each other. Another smaller circle with centre O is lying between the common regions of two larger circles. Centres of the circle (i.e., A, O and B) are lying on a straight line. If AB = 16 cm and the radii of the larger circles are 10 cm each, what is the area of the smaller circle?
A)
\[4\pi \text{ }c{{m}^{2}}\] done
clear
B)
\[2\pi \text{ }c{{m}^{2}}\] done
clear
C)
\[\frac{4}{\pi }\text{ }c{{m}^{2}}\] done
clear
D)
\[\frac{\pi }{4}\text{ }c{{m}^{2}}\] done
clear
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question_answer34)
ABCD is a squares, inside of it four circles with radius 1 cm. and touching each other are drawn. What is the area of the shaded region?
A)
\[(2\pi -3)c{{m}^{2}}\] done
clear
B)
\[(4-\pi )c{{m}^{2}}\] done
clear
C)
\[(16-4\pi )c{{m}^{2}}\] done
clear
D)
None of these done
clear
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question_answer35)
Three circles of equal radii touch each other as shown in the figure. The radius of each circle is 1 cm. What is the area of the shaded region?
A)
\[\left( \frac{2\sqrt{3}-\pi }{2} \right)c{{m}^{2}}\] done
clear
B)
\[\left( \frac{3\sqrt{2}-\pi }{3} \right)c{{m}^{2}}\] done
clear
C)
\[\frac{2\sqrt{3}}{\pi }c{{m}^{2}}\] done
clear
D)
\[\frac{\sqrt{6}}{2\pi }c{{m}^{2}}\] done
clear
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question_answer36)
A circular paper is folded along its diameter; then again it is folded to form a quadrant. Then it is cut as shown in the figure and after that the paper was reopened in the original circular shape. What is the ratio of the original paper to that of the remaining paper? (The shaded portion is cut off from the quadrant. The radius of quadrant OAB is 5 cm and radius of each semicircle is 1 cm):
A)
\[25:16\] done
clear
B)
\[25:9\] done
clear
C)
\[20:9\] done
clear
D)
\[31:25\] done
clear
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question_answer37)
ABCD is a square. A circle is inscribed in the square. Also taking A, B, C, D (the vertices of square) as the centers, four Quadrants are drawn, which are touching each other on the mid-point of the sides of square. If the Area of square is 4 cm 2, what is the area of the shaded region?
A)
\[\left( 4-\frac{3\pi }{2} \right)c{{m}^{2}}\] done
clear
B)
\[(2\pi -4)c{{m}^{2}}\] done
clear
C)
\[(4-2\pi )c{{m}^{2}}\] done
clear
D)
\[\left( \frac{7-3\pi }{2} \right)c{{m}^{2}}\] done
clear
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question_answer38)
In the adjoining diagram ABCD is a square with side 'a' cm. In the diagram the area of the larger circle with centre 'O' is equal to the sum of the areas of all the rest four circles with equal radii, whose centers are P, Q, R and S. What is the ratio between the diagonal of square and radius of a smaller circle?
A)
\[\left( 2\sqrt{2}+3 \right)\] done
clear
B)
\[\left( 2+3\sqrt{2} \right)\] done
clear
C)
\[\left( 4+3\sqrt{2} \right)\] done
clear
D)
can't be determined done
clear
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question_answer39)
In Fig, ABC is a right - angle triangle, \[\angle B=90{}^\circ ,AB=28\text{ }cm\] and \[BC=21\text{ }cm\]. With AC as diameter, a semicircle is drawn and with BC as radius, a quarter-circle is drawn. Find the area of the shaded region correct to two decimal places.
A)
\[428.75\,c{{m}^{2}}\] done
clear
B)
\[857.50\,c{{m}^{2}}\] done
clear
C)
\[214.37\,c{{m}^{2}}\] done
clear
D)
\[371.56\,c{{m}^{2}}\] done
clear
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question_answer40)
The area of the circle circumscribing three circles of unit radius touching each other is:
A)
\[(\pi /3){{\left( 2+\sqrt{3} \right)}^{2}}\] done
clear
B)
\[6\pi {{\left( 2+\sqrt{3} \right)}^{2}}\] done
clear
C)
\[3\pi {{\left( 2+\sqrt{3} \right)}^{2}}\] done
clear
D)
\[\left( \frac{\pi }{6} \right){{\left( 2+\sqrt{3} \right)}^{2}}\] done
clear
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