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A spiral is made up of successive semici...

A spiral is made up of successive semicircles , with centres alternately at ' A and B , starting with centre at A , of radii 0.5 cm, 1.0 cm , 1.5 cm , 2.0 cm , ... as shown in the given figure . What is the total length of such a spiral made up to thirteen consecutive semicircles ? (Take `pi= 22/7` )

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A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ... as shown in Figure. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take pi= 22/7 ) [Hint : Length of successive semicircles is 11, 12, 13, 14, ... with centres at A, B, A, B, ..., respectively.]

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In the circle of 5cm.radius, what is the length of the arc which subtends and angle of 33^(@)15' at the centre.

Find the area of the segments shaded in figure, if PQ=24cm, PR=7cm and QR is the diameter of the circle with centre O ( Take pi=(22)/(7))

Find the area of the segment AYB shown in the adjacent figure. It is given that the radius of the circle is 21 cm and /_AOB=120^(0)(Usepi=(22)/(7) and sqrt(3)=1.732 )

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In the given figure, two concentric circles with centre O and radii 5cm and 3 cm are given, PA and PB are tangents to those circle at A and B respectively. If PA =12cm, find PB.

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KUMAR PRAKASHAN-ARITHMETIC PROGRESSION-EXERCISE 5.3
  1. In an AP : Given an=4 , d = 2 , S(n)=-14 , find n and a .

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  2. In an AP : Given a = 3 , n = 8 , S(n) = 192 , find d .

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  3. In an AP : Given l = 28 , S(n) = 144 , and there are total 9 terms...

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  4. How many terms of the AP , 9 , 17 , 25 .......must be taken to give a ...

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  5. The first term of an AP is 5, the last term is 45 and the sum is 400. ...

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  6. The first and the last terms of an AP are 17 and 350 respectively . If...

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  7. Find the sum of first 22 terms of an AP in which d = 7 and 22nd term i...

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  8. Find the sum of first 51 terms of an AP whose second and third terms a...

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  9. If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289...

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  10. Show that a(1),a(2),......a(n),.... from an AP where an is defined a...

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  11. If the sum of the first n terms of an AP is 4n - n^2 , what is the fi...

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  12. Find the sum of the first 40 positive integers divisible by 6.

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  13. Find the sum of the first 15 multiple of 8.

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  14. Find the sum of the odd numbers between 0 and 50 .

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  15. A contract on construction job specifies a penalty for delay of comple...

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  16. A sum of Rs 700 is to be used to give seven cash prizes to students of...

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  17. In a, school , students thought of planting trees in and around the sc...

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  18. A spiral is made up of successive semicircles , with centres alternate...

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  19. 200 logs are stacked in the following manner : 20 logs in the bottom r...

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  20. In a potato race, a bucket is placed at the starting point, which is ...

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