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Question 176. The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of AP by Monila Jaipur. Answered on Oct 19, 2007 at 7:15 p.m. I.S.T
Answer 176.  T4 + T8 = 24
                         a + 3d + a + 7d = 24
               or       2a + 10d  = 24
               or       a + 5d  = 12        .................(i)
                          T6 + T10 = 44
                          a + 5d + a + 9d = 44
             or       2a + 14d  = 44
                or       a + 7d  = 22      .................(ii)
                Subtracting (i) from (ii)
                           2d = 10
                or        d = 5
                Substituting in (i)
                            a + 5× 5  = 12
                            a =  - 13
                 The first three terms are - 13, - 8, - 3

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Question 177. In a parallelogram ABCD angle A is 3x - 2 and angle C is 2x + 23.Find angle A and B, by Ketav Manik. Answered on November 8, 2008 at 9:11 p.m. I.S.T.
Answer 177. Download Answer.

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Question 178. If the heigt of the tower is 100 metre and angle of the elevation is 30 degree. Find the distance of the tower from the point of observation? by Rahul Kumar, St. Josephs school, Muzaffarpur. Answered on 24 Dec 2008
Answer 178. Let AB represent tower and C point of observation. angle ABC = 90.
tan C = AB/BC
tan 30 = 100/BC
1/sqareroot3 = 100/BC
BC = 100(squareroot3)
BC = 173 m.

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Question 179. Solve for x, 1/(x + a + b) = 1/a + 1/b + 1/x, by Simran Gill, Answered on 8 May 2009 at 5:00 p.m.
 Answer 179.                        1/(x + a + b) = 1/a + 1/b + 1/x
                                        or    1/(x + a + b) - 1/x = 1/a + 1/b
                                        or    ( x - x - a - b) / x(x + a + b) = (a + b)/ab
                                        or     - (a + b) / x(x + a + b) = (a + b)/ab
                                        or     - 1/ x(x + a + b) = 1/ab
                                        or      x^2 + ax + bx + ab = 0
                                        or       x( x+ a ) + b ( x + a) = 0
                                        or       (x + a )( x + b ) = 0
                                                   x = - a , x = - b

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Question 180. What is centroid?  by Bony Singla, Answered on 12 July 2009 at 12:46 p.m.
Answer 180.    Centroid is point of concurrence of Medians of triangle.

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Question 181. Show that one and only one out of n, n + 2 or n + 4 are divisible by 3, where n is any positive integer, by Lokesh Pradhan Bhubaneshwar. Answered on 2 August 2009 at 12:32 p.m.
Answer 181. Using euclid's division algorithm a = bq + r where 0 < = r <  b
                       let a = n and b = 3
                       n = 3q + r where 0 < = r <  3
                       if r = 0
                       n = 3q,               n  + 2 = 3q + 2,          n + 4 = 3q + 4       (here only n is divisible by 3)
                       if r = 1
                       n = 3q + 1,         n  + 2 = 3q + 3,          n + 4 = 3q + 5       (here only n + 2 is divisible by 3)
                       if r = 2
                       n = 3q + 2,         n  + 2 = 3q + 4,          n + 4 = 3q + 6       (here only n + 4 is divisible by 3)
  Therefore one and only one out of n, n + 2 or n + 4 are divisible by 3,

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Question 182. What is a Rectangle? by Shubham Maurya Varanasi. Answered on 16 August 2009 at 9:34 p.m.
Answer 182.    A Rectangle is a parallelogram whose one angle is 90 degrees.

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Question 183. AP and BQ are perpendicular to BC and AC respectively and AP = BQ. O is point of intersection of AP and BQ. Prove that AO = BO by Sneha Mariam from The Asian School Umm Al Hassam. Answered on 6 September 2009 at 7:59 a.m. I.S.T. (question was incomplete, so completed before answering)
Answer 183. Download Answer.

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Question 184. The angles of triangle are in A.P the greater angle is twice the least. Find all the angles. By Syed Zuhaib Ahmed,
MES Indian School, Doha. Answered on 13 sep 2009 at 11:35 a.m.
Answer 184. Let the angles be a, b and c where these are in A.P.
                  b - a = c - b
                  2b = a+ c
                  b = (a + c)/2 ........ (i)
                  a = 2c (given) ........(ii)
                  a + b + c = 180 ( angle sum property of triangle)
                  2c + (a + c)/2 + c = 180  [ using (i) and (ii) ]
                  3c + (2c + c)/2 = 180
 (×2)           6c + 2c + c = 360
                  9c = 360
                  c = 40
                  a = 2c = 80
                  b = (40 + 80)/2
                    =  60             

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Question 185.If the polynomials p(x) = 2x^3 + bx^2 + 3x - 5 and q(x) = x^3 + x^2 - 4x + b leave the same remainder when divided by x - 2. Find b. By Tanya Khan, Azra Public school, Hyderabad. Answered on 13 Sep 2009 at 11: 58 a.m.
Answer 185. x - 2 is a factor of p(x) and q(x),
                  therefore p(2) = q(2) = 0 by factor theorem
                  2×2^3 + b×2^2 + 3×2 - 5 = 2^3 + 2^2 - 4×2 + b
                  16 + 4b + 6 - 5 = 8 + 4 - 8 + b
                  3b = - 13
                  b = - 13/3          

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