1) A square with side 5 cm, mid point of the sides are joined to form another square, if this process is repeated, find perimeter of 9th square.
2) find sum of first 1234 term of series, 1,2,1,2,2,1,2,2,2,1,2,2,2,2...
3)Z(n)=2S(n)+41, S(n)=sum of first n natural no, Find lowest number for which Z(n) is prime a)6, b)7, c)40, d)Z(n) is always prime
4)2 circles intersect at point AB, arc made by smaller circle is 90 degree and that of larger circle 60 degree, find area of intersection.
5)P is point inside triangle ABC at distance 8,6,12 cm from A,B,C respectively, find perimeter of ABC.

• 1) Ans 5/4
  can be done by half area approach.
  As for the 1st square made by joining the mid point of square with 5 cm length its area is halfed (25/2). and for the 2nd its again halfed(25/4).
  
  for 9th square area = 25*(1/2)^(n-1)=25*(1/2)^(8)
  to get the perimeter = 4*sqrt(area)
• 11 years agoHelpfull: Yes(15) No(10)
• @anurag johri
  used some fuzzy method :p
  make a grp of numbers (1),(2,1),(2,2,1),(2,2,2,1),(2,2,2,2,1)...
  >some of the numbers in the grps ll make the series 1,3,5,7... which is d series of odd numbers.
  >no of terms in every grp ll make the series 1,2,3,4,
  some of this series ll be given as n(n+1)/2 gives n=49 n for the 50th grp it will give 9 more terms all ll be 2's sum 9*2=18-----(1)
  
  using n=49 in part 1
  and it ll give u sum of 49 grps which is actually sum of 1225 terms.
  
  it ll be 49*49 = 2401 ------(2)
  total sum=some of 1225 terms + some of next 9 terms
  = 2401+18
  = 2419
  i have made a little mistake is previous 1 so exact solution is 2419
  
  
• 11 years agoHelpfull: Yes(8) No(6)
• 5)
  answer to ques. no 5.
  perimeter =2(a+b+c)=2(8+6+12)=52cm
  explanation:
  draw a triangle ABC
  given AP=8
  BP=6
  CP=12
  
  draw a perpendicular to BC from P let it is PM
  by pythagorus
  BP^2 = PM^2 + BM^2 .....(1)
  CP^2 = PM^2 + CM^2......(2)
  FROM 1 AND 2....
  CP^2 - BP^2 =CM^2 - BM^2
  12^2 - 6^2 = (CM+BM)(CM-BM)
  CM+BM = BC = 12+6 = 18
  SIMILARLY
  AB = 8+6= 14
  AC = 12+8= 20
  PERIMETER= 18+14+20 = 52cm ans.
• 11 years agoHelpfull: Yes(7) No(2)
• first square made by joining the mid point of square with 5 cm length will have side as 5/root(2)
  for second square 5/(root 2)^2
  
  for 9th square 5/(root 2)^9 = 5/8*(root 2)
  so perimeter will be 5*4/8*(root 2) = 5/2(root 2)
• 11 years agoHelpfull: Yes(6) No(4)
• QUESTION 3:
  
  when n=40 then z(n)=1640+41=1681
  which is 41 square.
  
  Ans:6
• 11 years agoHelpfull: Yes(5) No(3)
• (3) d) z(n) is always prime
  put s(n)=n*(n+1)/2
  and solve for values for 0,1,2 even -1,-2,-3
  
• 11 years agoHelpfull: Yes(4) No(4)
• 2) Ans 2418
• 11 years agoHelpfull: Yes(2) No(0)
• 4) cant be determined. more data required.
• 11 years agoHelpfull: Yes(1) No(1)
• (2) 2419
  @anurag johri
  used some fuzzy method :p
  make a grp of numbers (1),(2,1),(2,2,1),(2,2,2,1),(2,2,2,2,1)...
  part 1 >sum of the numbers in each grps ll make the series 1,3,5,7... which is d series of odd numbers.
  
  part 2 >no of terms in every grp ll make the series 1,2,3,4,
  sum of this series ll be given as n(n+1)/2 gives n=49 n for the 50th grp it will give 9 more terms all ll be 2's sum 9*2=18-----(1)
  
  using n=49 in part 1
  and it ll give u sum of 49 grps which is actually sum of 1225 terms.
  
  it ll be 49*49 = 2401 ------(2)
  total sum=some of 1225 terms + some of next 9 terms
  = 2401+18
  = 2419
  i have made a little mistake is previous 1 so exact solution is 2419
• 11 years agoHelpfull: Yes(1) No(2)
• Can anyone tell me about the approach used in 5th question ???
• 11 years agoHelpfull: Yes(1) No(0)
• side of square=5
  2nd square is 5/underroot2
  nth term of gp is ar power n-1
  a=5;r=1/under root2
  perimeter=4*5(1/under root 2)
  ===5/4 answer
• 11 years agoHelpfull: Yes(1) No(0)
• give hint to question 4 and 5
• 11 years agoHelpfull: Yes(1) No(0)
• 2)u can see 1 only in the in the sum of n consecutive no.
  therefore find n n(n+1)/2
• 11 years agoHelpfull: Yes(0) No(0)
• 2)u can see '1' only in the in the sum of n consecutive no.
  therefore find n by n(n+1)/2
• 11 years agoHelpfull: Yes(0) No(0)
• @ HARISH ye sum of series ka logic kya h bata do yaar not getting it
  
• 11 years agoHelpfull: Yes(0) No(0)
• plz, anyone explain me how question 2,4 will be solved
  
• 11 years agoHelpfull: Yes(0) No(0)
• Question no. 4 is incomplete. Radius of the smaller circle is 1 cm.
  I gave my elitmus exam on 03/09/17 and all these questions showed up.
• 7 years agoHelpfull: Yes(0) No(0)