Latest Elitmus Aptitude Question SOLUTION: 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 s

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(#M40019654) ELITMUS Numerical Ability question Geometry Keep an EYE

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.

Asked In Elitmus manisha nayak (10 years ago)

Unsolved Read Solution (17)

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Read Solution (17) :

Harish  (10 years ago)

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)

Is this solution Helpfull? Yes (15) | No (10)  

Harish  (10 years ago)

@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

Is this solution Helpfull? Yes (8) | No (6)  

Prakash Gupta  (10 years ago)

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.

Is this solution Helpfull? Yes (7) | No (2)  

Amit Singh Shekhawat  (10 years ago)

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)

Is this solution Helpfull? Yes (6) | No (4)  

ASHISH MEHROTRA  (10 years ago)

QUESTION 3:

when n=40 then z(n)=1640+41=1681
which is 41 square.

Ans:6

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Harish  (10 years ago)

(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

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Harish  (10 years ago)

2) Ans 2418

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Harish  (10 years ago)

4) cant be determined. more data required.

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Harish  (10 years ago)

(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

Is this solution Helpfull? Yes (1) | No (2)  

yathartha mishra  (10 years ago)

Can anyone tell me about the approach used in 5th question ???

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pooja  (10 years ago)

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

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VIKASH KUMAR  (10 years ago)

give hint to question 4 and 5

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zen mano  (10 years ago)

2)u can see 1 only in the in the sum of n consecutive no.
therefore find n n(n+1)/2

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zen mano  (10 years ago)

2)u can see '1' only in the in the sum of n consecutive no.
therefore find n by n(n+1)/2

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anurag johri  (10 years ago)

@ HARISH ye sum of series ka logic kya h bata do yaar not getting it

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shruti  (10 years ago)

plz, anyone explain me how question 2,4 will be solved

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Prasanna Pradhan  (6 years ago)

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.

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