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Answers to Your Questions - Page 10
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 Question.100  If the 4th term is twice the 8th term,prove that the 10th term is twice the 11th term. By sumaira, answered on 
Nov 30,2007 at 7:31 pm, I.S.T.
Answer 100 T4 = 2 (T8) 
                  a + 3d = 2 (a+7)
                  a + 3d = 2a + 14d
             or   a + 11 d = 0
             or  a = - 11d           ............(1)
                 T10 = a + 9d 
                       = - 11d + 9d            using (1)
                       = - 2d
             2(T11) = 2(a + 10d) 
                       = 2(- 11d + 10d)       using (1)
                       = 2 (-d) 
                       = -2d
   Therefore T10 = 2(T11)
 Question.101 If two equal chords of a circle intersect within the circle, prove that segments of one chord ar equal to the corresponding segments of the other chord, by Harvinder Singh, answered on Dec 02, 2007 at 9:11 p.m.
Answer 101.   Download Answer
Question.102 Lines AB and CD are parllel and P is any point between the two lines . Prove that angle ABP +angle CDP = angle DPB, by Gagandeep singh, answered on Dec 4, 2007 at 9:51 p.m.
Answer 102.   Download Answer
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Question.103  A cylinder, a cone and a hemisphere have equal base and height. Find ratio of their volumes. by V. Anusha, answered on Dec 08, 2007 at 9:00 p.m. I.S.T.
Answer 103. Since they have equal base therefore their radii are equal. 
                   Let each radius = x
                   Height of hemisphere is equal to  its radius 
                   Therefore  height of each is = x 
                   volume of cylinder : volume of cone : volume of hemisphere                                                                                                                                                          =  pie r^2 h : 1/3  pie r^2 h : 2/3 pie r^3
                                                                                                   =  h : 1/3 h : 2/3 r
                                                                                                   =  x : 1/3 x : 2/3 x
                                                                                                   =  1 : 1/3 : 2/3 
                                                                                                   =  3 : 1 : 2 
Question.104  If a  student  had  walked  1km/hr  faster ,he would  have taken  15  minutes  less  to  walk  3km.find  the  rate  at  which  he  was  walking. by Rupashree, answered on Dec 12, 2007 at 8:07 p.m.
Answer 104. Let original speed of walking = x km/h
                   according to problem 
                   3/x  -   3/(x + 1)  =  15/60         [ since time = distance/speed]
           or      3 [1/x - 1/(x+1)] = 1/4
           or      3(x+1 - x)/(x^2 + x) = 1/4
           or      3/(x^2 + x) = 1/4
           or      x^2 + x = 12
           or      x^2 + x - 12 = 0
           or      (x + 4)(x - 3) = 0
           or      x = - 4, x = 3
                   original speed of walking = 3 km/h
Question.105 How many balls, each of radius 0.5cm, can be made from a solid sphere of metal of radius 10cm by melting the sphere? by keerthanaa, answered on Dec 14, 2007 at 7:49 p.m.
Answer 105. No. of balls = Volume of metal sphere / Volume of a spherical ball
                                  =  (4/3 pie R^3)/(4/3 pie r^3)  (where R is radius of sphere and r is radius of a ball)
                                  =  R^3/ r^3
                                  =  10×10×10 / 0.5×0.5×0.5
                                  =  8000
Question.106. A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contain 880/21 m3 of air.if the internal diameter of the building is equal to its total height above the floor,find the height of the building. by Osman Farooqui, answered on Dec 15, 2007 at 6:49 p.m. 
Answer 106. Download answer 
Question.107. A tree in each year grows 4cm less than it grew in previous year. If it grew 1 metre in the first year, in how many years will it have ceased growing and what will be its height then, by Navroop Dhillon. Answered on Dec 17, 2007 at 8:27 p.m.
Answer 107. First term              = a = 100 c.m.
                   Common Difference = d = - 4  
                   Tn = 0
            or     a + (n - 1)d = 0
            or    100 + (n - 1)(- 4) = 0
            or      25 + (n - 1)(- 1)  = 0  
            or      25 - n + 1 = 0
            or      - n   =  - 26
            or         n  =   26
            Therefore it will stop growing in 26 years
            Total height = n/2 [a + l]   
                             =  13 [100 + 0]
                             =  1300 c.m.  
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Question.108.  In acute triangle PQR, PS perpendicular QR Prove that PR*PR=PQ*PQ + QR*QR - 2QR*QS, by Aashish, answered on Dec 21, 2007 at 7:21 pm IST
Answer 108.  In acute triangle PQR PS perpendicular QR. We get 2 right triangles QSP and RSP. Using Pythagoras theorem in both 
                    PR^2 = PS^2 + SR^2  ......... (i)
                    PQ^2 = PS^2 + SQ^2  ......... (ii)   
                    (ii) - (i)
                   PR^2 - PQ^2 = SR^2 - SQ^2
                   PR^2 - PQ^2 = (QR - SQ)^2 - SQ^2
                   PR^2 - PQ^2 = QR^2 + SQ^2 - 2QR*SQ - SQ^2  [Since SR = QR - QS]
                   PR^2 - PQ^2 = QR^2 - 2QR*SQ
                   PR^2 = PQ^2 + QR^2 - 2QR*SQ
Question.109. Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre of a circle by Akash Ayalani. Answered on Dec 23, 2007 at 5:38 p.m. I.S.T.                 
Answer 109. Download answer
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