imo selection test
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7/17/2019 imo selection test
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KVS Junior Mathematics Olympiad (JMO)
M.M. 100 Time : 3 hours
Note : Attempt all questions.
MODEL PAPER –
!. 1 Resol"e into #a$tors :
( ) ( ) ( )bacacbcba −+−+− %%%
!.& 'impli#(
( )( ) ( )( ) xa z a
x z
z a ya
z y
ya xa
y x
++−
+++
−+
++−
))**
!.3 +n 1,3&- + as as ol/ as the last to /iits o# m( irth (ear. M( ran/#ather
sai/ that that applies to him also. 2o ol/ are e
!. % A hollo $one is $ut ( a plane parallel to the ase an/ the upper portion is
remo"e/. +# the $ur"e/ sur#a$e o# the remain/er is,
4 o# the $ur"e/ sur#a$e
o# the hole $one. 5in/ the ratio o# the line sements into hi$h the $on/s
attitu/e in /i"i/e/ ( the pla$e.
!. +n trianle 678- 9 is the point at interse$tion o# 67 ith interior ise$tor
o# anle 8- an/ in the mi/ point o# 67. Pro"e that 89 ; 8 < 68 ; 78.
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!.= 'ho that
−++=+++++ 1&
103
%
= 30%
.. %
%%
3%
&%
1 η η
η
η n
!.> 5i"e letters are ritten to #i"e /i##erent persons an/ their a//resses are on
en"elopes. 5in/ in no man( a(s letters $an e pla$e/ in en"elopes so that no
letter is pla$e/ in the $orre$t en"elope.
!4. To $ir$les ith ra/ii a an/ tou$h ea$h other esternall(. Let $ e the ra/ius
o# a $ir$le hi$h tou$hes these to $ir$les as ell as a $ommon taent to to
$ir$les pro"e that
1
a
1
$
1+=
! ,. 5in/ the unit /iit o#
>>>>>>
!10. The o// numers are arrane/ in a trianular pattern as shon.
+# this pattern $ontinues #in/ the #irst numer in the- no hi$h has a sum o#
1000000.
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