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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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