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Q. 24. Find the roots of the equation.

Sol .

Q. 25. Find the sum of all three digit numbers which are divisible by 9. 3

Sol. To find : 108 + 117 + 126 + … + 999
1st term, a = 108
Common difference, d = 117 – 108 = 9
an = 999  a + (n – 1)d = 999
108 + (n – 1).9 = 999
  (n – 1)9 = 999 – 108 = 891

SECTION D

Questions number 26 to 30 carry 6 marks each.

Q. 26. The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.

Sol. Let shorter side, AB = x m then Diagonal, AC = (x + 60) m and longer side,
BC = (x + 30) m In rt. Δ ABC,

Mathematics 2009 Question Papers Class X
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