
Study Case : Q. 1 to 5 
We all love to eat pizzas, especially kids. And a variety of pizzas are available in India which have been modified according to Indian taste and menu. From the Greeks to the Egyptians, from the Persians to the Indians, there have been incarnations of pizza served throughout history, Flatbreads, naan, and plakountos are all early preparations that could be considered cousins to the modem pizza, but there isn't a consensus as to which is first and whether these could even be considered precursors to pizza at all. 
Consider two pizzas, both of equal diameter, namely, 12 inches. The first pizza marked (i) has been cut into equal slices, whereas the second pizza, marked (ii) has been cut into eight equal slices. 

Based on the above information, answer the following questions. 
The area of one slice in pizza, marked (I), is:
A)
\[6\pi \,sq.\] inches done
clear
B)
\[8\pi \,sq.\] inches done
clear
C)
\[10\pi \,sq.\] inches done
clear
D)
None of these done
clear
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The perimeter of the pizza slice shown in (I), is:
A)
\[(\pi +12)\] inch done
clear
B)
\[(\pi +10)\] inch done
clear
C)
\[(2\pi +10)\]inch done
clear
D)
\[(2\pi +12)\] inch done
clear
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The ratio of area of slice to the area of remaining pizza in (l) is:
A)
\[5:1\] done
clear
B)
\[1:5\] done
clear
C)
\[2:5\] done
clear
D)
\[5:3\] done
clear
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The ratio of areas of each slice of pizza (I) and (II), is:
A)
\[3:4\] done
clear
B)
\[5:3\] done
clear
C)
\[4:3\] done
clear
D)
\[2:5\] done
clear
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The relation between area of a sector A length of the arc \[l,\] angle \[\theta \] subtended by the arc at the centre and radius of circle, is:
A)
\[\frac{1}{2}lr\] done
clear
B)
\[lr\] done
clear
C)
\[\frac{1}{3}lr\] done
clear
D)
\[\frac{1}{2}l{{r}^{2}}\] done
clear
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Study Case : Q. 6 to 10 
Sara hold a Japanese folding fan in her hand as shown in the figure. It is shaped like a sector of a circle and made of a thin material such as paper or feather. The inner and outer radii are \[\text{3 cm}\] and \[\text{5 cm}\] respectively. The fan has three colours i.e., red, blue and green. 

Based on the above information, answer the following questions: 
If the region containing blue colour makes an angle of \[80{}^\circ \]at the centre, then find the area of the region having blue colour.
A)
\[9.17\,c{{m}^{2}}\] done
clear
B)
\[10.1\,c{{m}^{2}}\] done
clear
C)
\[11.17\,c{{m}^{2}}\] done
clear
D)
\[13.17\,c{{m}^{2}}\] done
clear
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If the region containing green colour makes an angle of \[60{}^\circ \] at the centre, then find the area of the region having green colour.
A)
\[6.2c{{m}^{2}}\] done
clear
B)
\[8.38\,c{{m}^{2}}\] done
clear
C)
\[9.9\,c{{m}^{2}}\] done
clear
D)
\[11.12\,c{{m}^{2}}\] done
clear
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If the region containing red colour makes an angle of \[20{}^\circ \]at the centre, then find the perimeter of the region containing red colour.
A)
\[\text{2}.\text{9 cm}\] done
clear
B)
\[\text{4}.\text{2 cm}\] done
clear
C)
\[\text{5}.\text{4 cm}\] done
clear
D)
\[\text{6}.\text{79 cm}\] done
clear
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Find the area of the region having radius \[3\,cm\].
A)
\[12.57\,c{{m}^{2}}\] done
clear
B)
\[14.8\,c{{m}^{2}}\] done
clear
C)
\[20\,c{{m}^{2}}\] done
clear
D)
\[26.57\,c{{m}^{2}}\] done
clear
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The region given in the figure represents:
A)
minor sector done
clear
B)
major sector done
clear
C)
minor segment done
clear
D)
major segment done
clear
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Study Case : Q. 11 to 15 
A garden bed is shown below. It is a rectangle with semicircular ends. It has a concrete circular fountain at the centre as shown. Grass is grown in the garden bed at all places except the central fountain region. 


Based on the above information, answer the following questions: 
The area of the concrete circular fountain at the centre is:
A)
\[77\,{{m}^{2}}\] done
clear
B)
\[308\,{{m}^{2}}\] done
clear
C)
\[154\,{{m}^{2}}\] done
clear
D)
\[616\,{{m}^{2}}\] done
clear
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The area of one semicircular end of the garden bed is:
A)
\[\text{3}0\text{8 }{{\text{m}}^{\text{2}}}\] done
clear
B)
\[\text{154 }{{\text{m}}^{\text{2}}}\] done
clear
C)
\[\text{616 }{{\text{m}}^{\text{2}}}\] done
clear
D)
\[\text{77 }{{\text{m}}^{\text{2}}}\] done
clear
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Area of the garden bed where grass is grown is:
A)
\[616\,{{m}^{2}}\] done
clear
B)
\[294\,{{m}^{2}}\] done
clear
C)
\[381\,{{m}^{2}}\] done
clear
D)
\[458\,{{m}^{2}}\] done
clear
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The outer perimeter of the lawn is:
A)
\[86\,m\] done
clear
B)
\[114\,m\] done
clear
C)
\[130\,m\] done
clear
D)
\[172\,m\] done
clear
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Suppose we have a pavement all around the garden bed of which \[1\,m\] as shown below. The area of the pavement is: 

A)
\[(21+15\pi )\,{{m}^{2}}\] done
clear
B)
\[(42+15\pi )\,{{m}^{2}}\] done
clear
C)
\[(4215\pi )\,m\] done
clear
D)
\[(84+30\pi )\,{{m}^{2}}\] done
clear
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Study Case : Q. 16 to 20 
Shiva made a painting on a square chart paper ABCD. The painting is made up of squares, semicircular arcs (painted with flowers) and arcs of quadrant of circles as shown below. He painted the same type of region with same colours. 

Based on the above information, answer the following questions: 
Find the total area of the region which is painted with flowers:
A)
\[90.8\,c{{m}^{2}}\] done
clear
B)
\[100.57\,c{{m}^{2}}\] done
clear
C)
\[\text{1}0\text{5}.\text{6 c}{{\text{m}}^{\text{2}}}\] done
clear
D)
\[\text{111}.\text{2}0\text{ c}{{\text{m}}^{\text{2}}}\] done
clear
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Find the area of all quadrant given in the figure.
A)
\[190\,c{{m}^{2}}\] done
clear
B)
\[198.14\,c{{m}^{2}}\] done
clear
C)
\[201.14\,c{{m}^{2}}\] done
clear
D)
\[222.14\,c{{m}^{2}}\] done
clear
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Find the area of the region which is painted green.
A)
\[\text{1}00.\text{57 c}{{\text{m}}^{\text{2}}}\] done
clear
B)
\[\text{111}.\text{57 c}{{\text{m}}^{\text{2}}}\] done
clear
C)
\[\text{12}0\,\text{c}{{\text{m}}^{\text{2}}}\] done
clear
D)
\[\text{128}\text{.57 c}{{\text{m}}^{2}}\] done
clear
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Find the area of the region which is painted blue.
A)
\[\text{46}.\text{86 c}{{\text{m}}^{\text{2}}}\] done
clear
B)
\[\text{48 c}{{\text{m}}^{\text{2}}}\] done
clear
C)
\[\text{5}0.\text{86 c}{{\text{m}}^{\text{2}}}\] done
clear
D)
\[\text{54}.\text{86 c}{{\text{m}}^{\text{2}}}\] done
clear
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Find the total Length of the boundary of the region which is painted green.
A)
\[\text{128}\text{.57 cm}\] done
clear
B)
\[\text{132}.\text{56 cm}\] done
clear
C)
\[\text{145}.\text{57 cm}\] done
clear
D)
\[\text{15}0\text{ cm}\] done
clear
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Study Case : Q. 21 to 25 
A man wanted attractive design on the front door of his house. So, he asked a painter to paint the design as per specifications provided by him. Four equal circles were inscribed inside a square PQRS of side 28 cm as shown in the figure below: 
(i)  (ii) 
The diameter of each circle is:
A)
\[\text{3}.\text{5 cm}\] done
clear
B)
\[\text{7 cm}\] done
clear
C)
\[\text{12 cm}\] done
clear
D)
\[14\ cm\] done
clear
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Area of smaller square ABCD formed by joining the centres A, B, C and D of the four circles, is
A)
\[\text{49 c}{{\text{m}}^{\text{2}}}\] done
clear
B)
\[\text{196 c}{{\text{m}}^{\text{2}}}\] done
clear
C)
\[\text{824 c}{{\text{m}}^{\text{2}}}\] done
clear
D)
\[\text{12}.\text{25 c}{{\text{m}}^{\text{2}}}\] done
clear
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Refer to figure I area of the shaded region is:
A)
\[\text{154 c}{{\text{m}}^{\text{2}}}\] done
clear
B)
\[\text{3}0\text{8 c}{{\text{m}}^{\text{2}}}\] done
clear
C)
\[\text{616 c}{{\text{m}}^{\text{2}}}\] done
clear
D)
\[\text{77 c}{{\text{m}}^{\text{2}}}\] done
clear
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Area of the shaded portion in figure II, is:
A)
\[\text{154 c}{{\text{m}}^{\text{2}}}\] done
clear
B)
\[\text{66 c}{{\text{m}}^{\text{2}}}\] done
clear
C)
\[\text{42 c}{{\text{m}}^{\text{2}}}\] done
clear
D)
\[\text{21 c}{{\text{m}}^{\text{2}}}\] done
clear
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Cost of painting of the circular regions with centre A, B, C and D at Rs.5.00 per sq. cm.
A)
\[\text{Rs}.\text{1232}0.00\] done
clear
B)
\[\text{Rs}.\text{3}0\text{8}0.00\] done
clear
C)
\[\text{Rs}.\text{616}0.00\] done
clear
D)
\[\text{Rs}.\text{154}0.00\] done
clear
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Study Case : Q. 26 to 30 
Kritika bought a pendulum clock for her living room. The clock contains a small pendulum of length\[\text{15cm}\] 
The minute hand and hour hand of the clock are \[\text{9 cm}\] and \[\text{6 cm}\] long respectively. 

Based on the above information, answer the following questions, 
Find the area swept by the minute hand in 10 minutes.
A)
\[\text{22}.\text{24 c}{{\text{m}}^{\text{2}}}\] done
clear
B)
\[\text{42}.\text{42 c}{{\text{m}}^{\text{2}}}\] done
clear
C)
\[\text{44 c}{{\text{m}}^{\text{2}}}\] done
clear
D)
\[\text{44}\text{.42 c}{{\text{m}}^{\text{2}}}\] done
clear
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If the pendulum covers a distance of \[22\,cm\] in the complete oscillation, then find the angles described by pendulum at the centre.
A)
\[40{}^\circ \] done
clear
B)
\[42{}^\circ \] done
clear
C)
\[45{}^\circ \] done
clear
D)
\[48{}^\circ \] done
clear
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Find the angles described by hour hand in 10 minutes.
A)
\[5{}^\circ \] done
clear
B)
\[10{}^\circ \] done
clear
C)
\[15{}^\circ \] done
clear
D)
\[20{}^\circ \] done
clear
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Find the area swept by the hour hand in 1 hour.
A)
\[\text{7}.\text{68 c}{{\text{m}}^{\text{2}}}\] done
clear
B)
\[\text{8}\text{.2 c}{{\text{m}}^{\text{2}}}\] done
clear
C)
\[\text{8}\text{.86 c}{{\text{m}}^{\text{2}}}\] done
clear
D)
\[\text{9}.\text{428 c}{{\text{m}}^{\text{2}}}\] done
clear
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Find the area swept by the hour hand between\[\text{11 a}.\text{m}.\]and \[\text{5 p}.\text{m}.\]
A)
\[\text{56}.\text{568 c}{{\text{m}}^{\text{2}}}\] done
clear
B)
\[\text{62 c}{{\text{m}}^{\text{2}}}\] done
clear
C)
\[\text{70 c}{{\text{m}}^{\text{2}}}\] done
clear
D)
\[\text{72 c}{{\text{m}}^{\text{2}}}\] done
clear
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Study Case : Q. 31 to 35 
A farmer has a rectangular field of length \[30\,m\] and breadth \[15\,m\]. By the farmer a pit of diameter \[7\,m\] is dug \[12\,m\] deep for rain water harvesting. The earth taken out is spread in the field. 

Based on the above information, answer the following questions. 
Find the volume of the earth taken out.
A)
\[460\,{{m}^{3}}\] done
clear
B)
\[462\,{{m}^{3}}\] done
clear
C)
\[465\,{{m}^{3}}\] done
clear
D)
\[468\,{{m}^{3}}\] done
clear
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The area of the rectangular field is
A)
\[420\,{{m}^{2}}\] done
clear
B)
\[430\,{{m}^{2}}\] done
clear
C)
\[440\,{{m}^{2}}\] done
clear
D)
\[450\,{{m}^{2}}\] done
clear
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Find the area of the top of the pit.
A)
\[38.5\,{{m}^{2}}\] done
clear
B)
\[40.5\,{{m}^{2}}\] done
clear
C)
\[41.5\,{{m}^{2}}\] done
clear
D)
None of these done
clear
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The area of the remaining field is
A)
\[402.3\,{{m}^{2}}\] done
clear
B)
\[405\,{{m}^{2}}\] done
clear
C)
\[410\,{{m}^{2}}\] done
clear
D)
\[411.5\,{{m}^{2}}\] done
clear
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Find the level rise in the field.
A)
\[0.5\,m\] done
clear
B)
\[3\,m\] done
clear
C)
\[\text{1}.\text{12 m}\] done
clear
D)
\[\text{2}.\text{12 m}\] done
clear
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Study Case : Q. 36 to 40 
Gayatri have a triangle shaped grass field. At the three comers of the field, a cow a buffalo and a horse and tied separately to the pags by means of ropes of \[\text{3}.\text{5 m}\] each of graze in the field, as shown in the figure. Sides of the triangle field are \[\text{25 m},\]\[\text{24 m}\] and\[\text{7 m}\]. 

Based on the above information, answer the following questions. 
Area of triangle field is
A)
\[82\,{{m}^{2}}\] done
clear
B)
\[84\,{{m}^{2}}\] done
clear
C)
\[86\,{{m}^{2}}\] done
clear
D)
\[88\,{{m}^{2}}\] done
clear
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Area of the region grazed by the cow is
A)
\[\frac{\angle A}{360}\times \pi \times {{(3.5)}^{2}}\] done
clear
B)
\[\frac{\angle B}{360{}^\circ }\times \pi \times {{(24)}^{2}}\] done
clear
C)
\[\frac{\angle C}{360{}^\circ }\times \pi \times {{(3.5)}^{2}}\] done
clear
D)
None of these done
clear
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Area of the region grazed by the buffalo and the horse is
A)
\[\frac{(\angle A+\angle C)}{360{}^\circ }\times \pi \times {{(5.5)}^{2}}\] done
clear
B)
\[\frac{(\angle B+\angle C)}{360{}^\circ }\times \pi \times {{(5.6)}^{2}}\] done
clear
C)
\[\frac{(\angle A+\angle C)}{360{}^\circ }\times \pi \times {{(3.5)}^{2}}\] done
clear
D)
\[\frac{(\angle B+\angle C)}{360{}^\circ }\times \pi \times {{(3.5)}^{2}}\] done
clear
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Total area grazed by the cow, the buffalo and the horse is
A)
\[\text{16}.\text{25 }{{\text{m}}^{\text{2}}}\] done
clear
B)
\[\text{17}.\text{3 }{{\text{m}}^{\text{2}}}\] done
clear
C)
\[\text{18}.\text{5}\,{{\text{m}}^{\text{2}}}\] done
clear
D)
\[\text{19}.\text{25}{{\text{m}}^{\text{2}}}\] done
clear
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Find the area of the field that cannot be grazed.
A)
\[\text{6}0.\text{75 }{{\text{m}}^{\text{2}}}\] done
clear
B)
\[\text{64}.\text{75 }{{\text{m}}^{\text{2}}}\] done
clear
C)
\[\text{68 }{{\text{m}}^{\text{2}}}\] done
clear
D)
\[\text{69}.\text{75 }{{\text{m}}^{\text{2}}}\] done
clear
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