Mathematics Circle Revision
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Mathematics Circle Revision
English 11 leveled MCQs Free
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8 marks Long answer
Case Study 1: Governing council of a local public development authority of Dehradun decided to build an adventurous playground on the top of a hill, which will have adequate space for parking. After survey, it was decided to build rectangular playground with a semi-circular area allotted for parking at one end of the playground. The length and breadth of the rectangular playground are 14 units and 7 units, respectively. There are two quadrants of radius 2 units on one side for special seats. Based on the above information, answer the following questions: (i) What is the total perimeter of the parking area? (1m) (ii) (a) What is the total area of parking and the two quadrants? (1m) OR (b) What is the ratio of area of playground to the area of parking area? (iii) Find the cost of fencing the playground and parking area at the rate of ₹ 2 per unit. (2m)
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Total perimeter is 44 units; total area is 55.28 units$^2$; cost of fencing is ₹ 126.
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8 marks Long answer
Case Study 2: In an annual day function of a school, the organizers wanted to give a cash prize along with a memento to their best students. Each memento is made as shown in the figure and its base ABCD is shown from the front side. The rate of silver plating is ₹ 20 per $cm^2$. Based on the above, answer the following questions: (i) What is the area of the quadrant ODCO? (1m) (ii) Find the area of $\triangle AOB$. (1m) (iii) (a) What is the total cost of silver plating the shaded part ABCD? (2m) OR (b) What is the length of arc CD?
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Area of the quadrant is 7.07 cm$^2$; area of triangle AOB is 4.5 cm$^2$; cost of silver plating is ₹ 140.
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4 marks Medium answer
A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding: (i) minor segment (ii) major sector. (Use $\pi = 3.14$)
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Minor segment area is 25 cm$^2$; major sector area is 75 cm$^2$.
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4 marks Medium answer
In a circle of radius 21 cm, an arc subtends an angle of $120^\circ$ at the centre. Find: (i) the length of the arc (ii) area of the major segment formed by the arc.
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Length of the arc is 14 cm; area of the major segment is 123.54 cm$^2$.
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3 marks Medium answer
In a rectangular park measuring 50 m x 40 m, the gram panchayat plans to construct a rectangular swimming pool in the middle, surrounded by a uniform width grass strip throughout the park. Find the dimensions of the swimming pool, if the area of the grassy strip is 1184 m$^2$.
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Dimensions of the swimming pool are 30 m x 20 m.
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3 marks Medium answer
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 the area of that part of the field in which the horse can graze. (Use $\pi = 3.14$)
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Area grazed by the horse is 39.25 m$^2$.
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1 marks Short answer
The circumferences of two circles are in the ratio 4 : 5, then the ratio of their areas is:
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16 : 25
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1 marks Short answer
The hour hand of a clock is 6 cm long. The angle swept by it between 7:20 AM and 7:55 AM is:
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$\left(\frac{35}{2}\right)^\circ$
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1 marks Short answer
The arc of a circle is of length 6$\pi$ cm and the sector it bounds has an area of 24$\pi$ cm$^2$. The radius of the circle is:
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8 cm
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1 marks Short answer
The area of the circle that can be inscribed in a square of side 6 cm is:
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18$\pi$ cm$^2$
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1 marks Short answer
The area of the sector of a circle of radius 12 cm is 60$\pi$ cm$^2$. The central angle of this sector is:
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$120^\circ$
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