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question_answer1)
If the sum of the circumferences of two circles with radii \[{{R}_{1}}\] and \[{{R}_{2}}\] is equal to the circumference of a circle of radius R, then
A)
\[{{R}_{1}}+{{R}_{2}}=R\] done
clear
B)
\[{{R}_{1}}+{{R}_{2}}>R\] done
clear
C)
\[{{R}_{1}}+{{R}_{2}}<R\] done
clear
D)
Nothing definite can be said about the relation among \[{{R}_{1}},\,{{R}_{2}}\]and R. done
clear
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question_answer2)
In covering a distance s m, a circular wheel of radius r m makes ......... revolution.
A)
\[\frac{2s}{\pi r}\] done
clear
B)
\[\frac{s}{2\pi r}\] done
clear
C)
\[\frac{s}{\pi r}\] done
clear
D)
None of these done
clear
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question_answer3)
The distance travelled by a circular wheel of diameter d cm in one revolution is equal to ............ cm.
A)
\[\frac{\pi d}{2}\] done
clear
B)
\[2\pi d\] done
clear
C)
\[\frac{\pi d}{4}\] done
clear
D)
\[\pi d\] done
clear
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question_answer4)
The perimeter of a square circumscribing a circle of radius a cm is equal to ............ cm.
A)
8a done
clear
B)
4a done
clear
C)
2a done
clear
D)
\[\frac{a}{2}\] done
clear
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question_answer5)
The radii of two circles are 13 cm and 6 cm, respectively. Then, the radius of the circle which has circumference equal to sum of the circumferences of the two circles is
A)
17cm done
clear
B)
19cm done
clear
C)
7cm done
clear
D)
11cm done
clear
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question_answer6)
The circumference of a circle exceeds the diameter by 25.8 cm, then the radius of the circle is
A)
6.02 cm done
clear
B)
5.02 cm done
clear
C)
4.02 cm done
clear
D)
5.58 cm done
clear
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question_answer7)
If the perimeter of a protractor is 72 cm, then its area is
A)
\[12\text{ }c{{m}^{2}}\] done
clear
B)
\[13\,c{{m}^{2}}\] done
clear
C)
\[14\,c{{m}^{2}}\] done
clear
D)
None of these done
clear
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question_answer8)
The short and long hands of a clock are 6 cm and 8 cm long, respectively. Then, the sum of the distance travelled by their tips in 1 day is [take\[\pi =22/7\]]
A)
1282.29 cm done
clear
B)
1228.30 cm done
clear
C)
1382.30 cm done
clear
D)
1198.20 cm done
clear
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question_answer9)
The radius of the wheel of a bus is 25 cm. If the speed of the bus is 33 km/h, then how many revolutions will the wheel make in 1 min?
A)
250 done
clear
B)
520 done
clear
C)
420 done
clear
D)
350 done
clear
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question_answer10)
Areas of two circles are equal. Is it necessary that their circumferences are equal?
A)
True done
clear
B)
False done
clear
C)
Cannot say done
clear
D)
Partially True/False done
clear
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question_answer11)
Circumference of two circles are equal. Is it necessary that their areas be equal?
A)
True done
clear
B)
False done
clear
C)
Cannot say done
clear
D)
Partially True/False done
clear
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question_answer12)
The numerical value of the area of a circle is greater than the numerical value of its circumference.
A)
True done
clear
B)
False done
clear
C)
Cannot say done
clear
D)
Partially True/False done
clear
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question_answer13)
.Area of the largest triangle that can be inscribed in a semi-circle of radius r units is
A)
\[{{r}^{2}}\]sq units done
clear
B)
\[\frac{1}{2}{{r}^{2}}\]sq units done
clear
C)
\[2{{r}^{2}}\]sq units done
clear
D)
\[\sqrt{2}{{r}^{2}}\]sq units done
clear
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question_answer14)
If the perimeter of a circle is equal to that of a square, then the ratio of their areas is
A)
22:7 done
clear
B)
14:11 done
clear
C)
7:22 done
clear
D)
11:14 done
clear
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question_answer15)
If the area of a circle is \[2464\text{ }c{{m}^{2}}\], then the diameter of circle is
A)
57cm done
clear
B)
56cm done
clear
C)
54cm done
clear
D)
None of these done
clear
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question_answer16)
If the area of a semi-circular field is \[30800\text{ }{{m}^{2}}\], then the perimeter of the field is
A)
420cm done
clear
B)
720m done
clear
C)
580m done
clear
D)
None of these done
clear
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question_answer17)
The cost of fencing a circular field at the rate of Rs 36 per m is Rs 11880. The field is to be ploughed at the rate of Rs 0.60 per \[{{m}^{2}}\]. Then, the cost of ploughing the field is [take \[\pi =22/7\]]
A)
Rs 5197.5 done
clear
B)
Rs 866.25 done
clear
C)
Rs 10395 done
clear
D)
None of these done
clear
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question_answer18)
A circular park is surrounded by a road 21 m wide. If the radius of the park is 105 m, then the area of the road is
A)
\[1524.62\text{ }c{{m}^{2}}\] done
clear
B)
\[15246\text{ }c{{m}^{2}}\] done
clear
C)
\[15640.20\text{ }c{{m}^{2}}\] done
clear
D)
None of these done
clear
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question_answer19)
Circular footpath of width 2 m is constructed at the rate of Rs 20 per \[{{m}^{2}}\] around a circular park of radius 1500 m. Then, the total cost of construction of the footpath is [take, \[\pi =3.14\]]
A)
Rs 37705.12 done
clear
B)
Rs 18852.56 done
clear
C)
Rs 377051.2 done
clear
D)
None of these done
clear
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question_answer20)
Area of segment of a circle is less than the area of its corresponding sector?
A)
True done
clear
B)
False done
clear
C)
Cannot say done
clear
D)
Partially True/False done
clear
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question_answer21)
The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal?
A)
True done
clear
B)
False done
clear
C)
Cannot say done
clear
D)
Partially True/False done
clear
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question_answer22)
Tick the correct answer in the following question. Area of a sector of angle p (in degrees) of a circle with radius R is
A)
\[\frac{p}{180{}^\circ }\times 2\pi R\] done
clear
B)
\[\frac{p}{180{}^\circ }\times \pi {{R}^{2}}\] done
clear
C)
\[\frac{p}{360{}^\circ }\times 2\pi R\] done
clear
D)
\[\frac{p}{720{}^\circ }\times 2\pi {{R}^{2}}\] done
clear
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question_answer23)
Find the area of sector of central angle \[x{}^\circ \] of a circle with radius 4r.
A)
\[\frac{\pi x{{r}^{2}}}{45{}^\circ }\] done
clear
B)
\[\frac{2\pi x{{r}^{2}}}{360{}^\circ }\] done
clear
C)
\[\frac{2\pi x{{r}^{2}}}{45{}^\circ }\] done
clear
D)
\[\frac{4\pi x{{r}^{2}}}{180{}^\circ }\] done
clear
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question_answer24)
The area of a sector of a circle with radius 6 cm, if angle of the sector \[60{}^\circ \]is
A)
\[\frac{132}{14}c{{m}^{2}}\] done
clear
B)
\[\frac{36}{7}c{{m}^{2}}\] done
clear
C)
\[\frac{132}{7}c{{m}^{2}}\] done
clear
D)
None of these done
clear
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question_answer25)
An arc of a circle is of length 5n cm and the sector it bounds has an area of \[20\,\pi \,c{{m}^{2}}\], then radius of the circle is
A)
4cm done
clear
B)
8cm done
clear
C)
12cm done
clear
D)
16cm done
clear
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question_answer26)
The length of minute hand of a clock is 14 cm. Then, the area swept by the minute hand in one minute is \[\left[ take\,\pi =\frac{22}{7} \right]\]
A)
\[28\,c{{m}^{2}}\] done
clear
B)
\[10.27c{{m}^{2}}\] done
clear
C)
\[14.7c{{m}^{2}}\] done
clear
D)
\[12.8\,c{{m}^{2}}\] done
clear
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question_answer27)
A pendulum swings through an angle \[60{}^\circ \] and describes an arc 8.8 cm in length. Then, the length of pendulum is \[\left[ use\,\pi =\frac{22}{7} \right]\]
A)
8.40cm done
clear
B)
16.8cm done
clear
C)
4.20cm done
clear
D)
8.90cm done
clear
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question_answer28)
A car has two wipers which do not overlap each other. Each wiper has a blade of length r cm sweeping through an angle of \[60{}^\circ \]. The area cleaned at each sweep of blades is
A)
\[\frac{1}{3}\pi r\,c{{m}^{2}}\] done
clear
B)
\[\frac{2}{3}\pi r\,c{{m}^{2}}\] done
clear
C)
\[\frac{1}{3}\pi {{r}^{2}}\,c{{m}^{2}}\] done
clear
D)
\[\frac{2}{3}\pi {{r}^{2}}\,c{{m}^{2}}\] done
clear
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question_answer29)
An umbrella has 8 ribs which are equally spaced (see the figure). |
Assuming umbrella to be a flat circle of radius 45 cm, then the area between the two consecutive ribs of the umbrella is |
|
A)
\[\frac{22275}{56}\,c{{m}^{2}}\] done
clear
B)
\[\frac{22275}{28}\,c{{m}^{2}}\] done
clear
C)
\[\frac{22285}{28}\,c{{m}^{2}}\] done
clear
D)
None of these done
clear
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question_answer30)
To warn ships for underwater rocks, alight house spreads a red coloured light over a sector of angle \[80{}^\circ \] to a distance of 16.5 km. Then, the area of the sea over which the ships are warned is [take \[\pi =3.14\]]
A)
\[189.97k{{m}^{2}}\] done
clear
B)
\[1899.7k{{m}^{2}}\] done
clear
C)
\[1709.73\text{ }k{{m}^{2}}\] done
clear
D)
None of these done
clear
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question_answer31)
In a circle of radius 42 cm, an arc subtends an angle of \[60{}^\circ \]at the centre. Then, the length of the arc is
A)
44cm done
clear
B)
24cm done
clear
C)
48cm done
clear
D)
46cm done
clear
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question_answer32)
In a circle of radius 28 cm, an arc subtends an angle of \[45{}^\circ \]at the centre. Then, the length of the arc and the area of the sector is
A)
\[44\text{ }cm,\text{ }154\text{ }c{{m}^{2}}\] done
clear
B)
\[22cm,154\text{ }c{{m}^{2}}\] done
clear
C)
\[22cm,308\text{ }c{{m}^{2}}\] done
clear
D)
None of these done
clear
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question_answer33)
Is the area of the circle inscribed in a square of side a cm is ............ .
A)
\[\pi {{a}^{2}}c{{m}^{2}}\] done
clear
B)
\[\frac{\pi {{a}^{2}}}{2}c{{m}^{2}}\] done
clear
C)
\[\frac{\pi {{a}^{2}}}{4}c{{m}^{2}}\] done
clear
D)
\[2\pi {{a}^{2}}c{{m}^{2}}\] done
clear
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question_answer34)
In figure, a square of diagonal 8 cm is inscribed in a circle, then the area of the shaded region is |
|
A)
\[\left( 32\pi -16 \right)\,c{{m}^{2}}\] done
clear
B)
\[\left( 16\pi -32 \right)\,c{{m}^{2}}\] done
clear
C)
\[\left( 11\pi -32 \right)\,c{{m}^{2}}\] done
clear
D)
\[\left( 16\pi -64 \right)\,c{{m}^{2}}\] done
clear
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question_answer35)
The area of the shaded region in figure as shown below where ABCD is a square of side 12 cm is equal to |
|
A)
\[15.43c{{m}^{2}}\] done
clear
B)
\[198c{{m}^{2}}\] done
clear
C)
\[31.72c{{m}^{2}}\] done
clear
D)
\[30.86c{{m}^{2}}\] done
clear
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question_answer36)
A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions\[20\text{ }m\text{ }\times \text{ }16\text{ }m\]. Then, the area of the field in which the cow can graze is
A)
\[154{{m}^{2}}\] done
clear
B)
\[196{{m}^{2}}\] done
clear
C)
\[228{{m}^{2}}\] done
clear
D)
\[144{{m}^{2}}\] done
clear
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question_answer37)
In the given figure, a square is inscribed in a circle of diameter d and another square is circumscribing the circle. |
Then, the ratio between area of inner square to outer square. |
|
A)
2:1 done
clear
B)
1:4 done
clear
C)
1:3 done
clear
D)
1:2 done
clear
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question_answer38)
The area of the shaded region in figure, if ABCD is a square of side 14 cm and APD and BPC are semi circles is |
|
A)
\[196\text{ }c{{m}^{2}}\] done
clear
B)
\[84c{{m}^{2}}\] done
clear
C)
\[21c{{m}^{2}}\] done
clear
D)
\[42c{{m}^{2}}\] done
clear
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question_answer39)
The area of shaded design in the given figure is (where ABCD is a square of side 10 cm and semi-circles are drawn with each of the side as diameter.) [take \[\pi =3.14\]] |
|
A)
\[57\text{ }c{{m}^{2}}\] done
clear
B)
\[67c{{m}^{2}}\] done
clear
C)
\[86\,c{{m}^{2}}\] done
clear
D)
\[52c{{m}^{2}}\] done
clear
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question_answer40)
In the given figure, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining three circles, then the area of the shaded region is |
|
A)
\[154\text{ }c{{m}^{2}}\] done
clear
B)
\[21c{{m}^{2}}\] done
clear
C)
\[42c{{m}^{2}}\] done
clear
D)
\[184c{{m}^{2}}\] done
clear
View Solution play_arrow
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question_answer41)
Is the area of the largest circle that can be drawn inside a rectangle of length a cm and breadth b cm (a > b) is ......\[c{{m}^{2}}\].
A)
\[\frac{\pi {{b}^{2}}}{4}\] done
clear
B)
\[\frac{\pi {{\alpha }^{2}}}{4}\] done
clear
C)
\[\frac{\pi \left( {{b}^{2}}-{{a}^{2}} \right)}{4}\] done
clear
D)
\[\frac{\pi {{\left( b-a \right)}^{2}}}{4}\] done
clear
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question_answer42)
In the given figure, sectors of two concentric circles of radii 7 cm and 3.5 cm are shown, then the area of the shaded region is |
|
A)
\[96.25\text{ }c{{m}^{2}}\] done
clear
B)
\[88.2\text{ }c{{m}^{2}}\] done
clear
C)
\[9.625\text{ }c{{m}^{2}}\] done
clear
D)
\[8.42\text{ }c{{m}^{2}}\] done
clear
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question_answer43)
In figure, AOB is a flower bed in the shape of a sector of a circle of radius 40 m and\[\angle AOB=60{}^\circ \]. Also, a 15 m wide concrete track is made as shown in the figure. Flower bed is made at the rate of Rs 2.40 per \[{{m}^{2}}\] and rate of making the concrete track is Rs 20 per \[{{m}^{2}}\], then the total amount spent for the job is |
[take \[\pi =3.14\]] |
|
A)
Rs 2009 done
clear
B)
Rs 53034.60 done
clear
C)
Rs 5303.460 done
clear
D)
None of the above done
clear
View Solution play_arrow
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question_answer44)
A chord of a circle of radius 10 cmsubtends a right angle at the centre. Then, the area of the minor segment is
A)
\[78.5\,c{{m}^{2}}\] done
clear
B)
\[28.5c{{m}^{2}}\] done
clear
C)
\[50c{{m}^{2}}\] done
clear
D)
\[128.5c{{m}^{2}}\] done
clear
View Solution play_arrow
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question_answer45)
In the given figure, ABC is an equilateral triangle inscribed in a circle of radius 4 cm with centre O, then thearea of the shaded region is |
|
A)
\[\frac{5}{3}\left( 5\pi -3\sqrt{3} \right)c{{m}^{2}}\] done
clear
B)
\[\frac{4}{3}\left( 4\pi -3\sqrt{3} \right)c{{m}^{2}}\] done
clear
C)
\[\frac{2}{3}\left( 2\pi -\sqrt{3} \right)c{{m}^{2}}\] done
clear
D)
\[\frac{7}{3}\left( 7\pi -3\sqrt{3} \right)c{{m}^{2}}\] done
clear
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question_answer46)
A memento is made as shown in the figure. Its base PBCR is silver plated from the front side at the rate of Rs 20 per\[c{{m}^{2}}\]. Then, the total cost of the silver plating is \[\left[ take\,\,\pi =\frac{22}{7} \right]\] |
|
A)
Rs 460 done
clear
B)
Rs 115 done
clear
C)
Rs 230 done
clear
D)
None of these done
clear
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question_answer47)
Find the area of the shaded region in figure, if AC = 20 cm, AB = 15 cm and O is the centre of the circle. |
\[\left[ take\,\,\pi =\frac{22}{7} \right]\] |
|
A)
\[95.54\text{ }c{{m}^{2}}\] done
clear
B)
\[95.45\,c{{m}^{2}}\] done
clear
C)
\[59.54\text{ }c{{m}^{2}}\] done
clear
D)
None of the above done
clear
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question_answer48)
In the given figure, OACBO represents a quadrant of a circle of radius 4.5 cm with centre O. Then, the area of shaded portion is [take \[\pi =22/7\]] |
|
A)
\[15.91c{{m}^{2}}\] done
clear
B)
\[9.16\text{ }c{{m}^{2}}\] done
clear
C)
\[6.75\text{ }c{{m}^{2}}\] done
clear
D)
\[22.66\text{ }c{{m}^{2}}\] done
clear
View Solution play_arrow
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question_answer49)
In this section, each question has two matching lists. Choices for the correct combination of elements from List-I and List-II are given as options [a], [b], [c] and [d] out of which one is correct. |
Figure depicts an archery target marked with its five scoring areas from the centres outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 14 cm and each of the other bands is 7 cm wide. Then match the following. |
|
| List - I | | List - II |
P. | Area of Gold score | 1. | \[462\,c{{m}^{2}}\] |
Q. | Area of Red score | 2. | \[770\,c{{m}^{2}}\] |
R. | Area of Blue score | 3. | \[154\,c{{m}^{2}}\] |
S. | Area of Black score | 4. | \[1078\,c{{m}^{2}}\] |
A)
Codes \[P\to 2,\,Q\to 1,\,R\to 4,\,S\to 3\] done
clear
B)
\[P\to 3,\,Q\to 1,\,R\to 2,\,S\to 4\] done
clear
C)
\[P\to 1,\,Q\to 4,\,R\to 2,\,S\to 3\] done
clear
D)
\[P\to 1,\,Q\to 3,\,R\to 4,\,S\to 2\] done
clear
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question_answer50)
Following question has four statements (A, B, C and D) given in Column I and five statements (p, q, r, s, t) in Column - II. Any given statement in Column - I. can have correct matching with one or more statement(s) given in Column - II.
| Column - I | | Column - II |
A. | OA = 26 cm, OC = 23 m Area of shaded region = ? | (p) | \[30\,c{{m}^{2}}\] |
B. | AD = 6.5 cm, CA = 5 cm Area of \[\Delta ABC=?\] | (q) | \[115\,{{m}^{2}}\] |
C. | BC = 6m, AB = 8 cm Area of the shaded region = ? | (r) | \[35\,c{{m}^{2}}\] |
D. | OB = 14.8 m Area of the shaded region = ? | (s) | \[0.003\,{{m}^{2}}\] |
| | (t) | \[30\,\,{{m}^{2}}\] |
A)
Codes \[\left( A \right)\to p,\,s;\,\left( B \right)\to q;\,\left( C \right)\to q;\,\left( D \right)\to r,s\] done
clear
B)
\[\left( A \right)\to q;\,\left( B \right)\to p,s;\,\left( C \right)\to p,s;\left( D \right)\to q\] done
clear
C)
\[\left( A \right)\to p,s;\,\left( B \right)\to q;\,\left( C \right)\to p,s;\,\left( D \right)\to r,s\] done
clear
D)
None of the above done
clear
View Solution play_arrow