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# Cat 2006 qs and solutions

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### Cat 2006 qs and solutions

1. 1. ! " ! " #" \$• % " & " #• % "• " " (" (• " # "• "•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• 5 " " > " F ! % : " ( # < # # " + < 7 @ < 8 B " # # > " F # ( " ( # < # # + • % ( # " < < " " • 5 <" F > " " # A ( # < =1 < # & " # # • # " "** B " " " " # < # " " , -*. / -/. + -+. 0 -0. 1 -1. "
3. 3. */ ( # # < " " ( < - .\$ -*. 1 -/. 3 -+. C -0. *0 -1. *1*+ B " < # # " " , -*. / -/. + -+. 0 -0. 1 -1. "*0 < : " " \$ -*. * -/. / -+. + -0. 0 -1. 1*1 < < # # " " -*. / -/. 1 -+. 4 -0. 3 -1. 2 - # \$ ! " : " ( ( # # : ( ( # % # # : " *== " **= % " : " *= " *= 7 : " ? # # " " # # # " : #( # " (: " " #7 " : " ( ( #• < " " : *= : " # " 5 " " # *= " # "• " # " ( **= " *= : C= # *= " # "*4 : *= : " " ( " *= " # ( " : +, -*. C= -/. *== -+. **= -0. */= -1. *+=*3 : *+== " " 1 " : 0, -*. C= -/. *== -+. **= -0. */= -1. I*2 " /= : 1 " +, -*. C= -/. *== -+. **= -0. */= -1. *+=*C " *== " : 1 " " : - 1., -*. " *= : -/. " *= : -+. : *= " -0. : /= " -1. 7/= " ( & " " " " : " , -*. +3== -/. 0=== -+. 03== -0. 1=== -1. 4===
4. 4. - ! "% # " " F ?% 7 : @ ! " ? ? " " " ( # # " ! " # / 0 1 # . ( # ( ? " " ( # ( ( " B " "# ( # " # ( " " " ( # " ! " > & ? 9%9 - #! " % . " ( *0 - CH 1. " # ! " %/* # ( " @ I " # ! " % : " # - . ! " % 7 : @ " ( " ( # \$ -*. * 1 + + -/. * 0 0 + -+. * 1 0 / -0. = 1 / + -1. = 1 / /// # ( ( # - " " . # " 7 : - " . " # - . ! " % 7 : @ " ( " ( # \$ -*. / 1 + / -/. = 1 + * -+. * 1 + / -0. / + 1 * -1. * + 1 */+ # ( " # ( # % 7 @ " # - . ! " % 7 : @ " ( " ( # \$ -*. = 1 0 * -/. = 1 / / -+. * 1 + + -0. * 1 + / -1. = 0 + //0 # ( # " " # - . ! " % 7 : @ " ( " ( # \$ -*. = 1 / / -/. = 1 0 * -+. * 1 + + -0. * 1 + / -1. * 1 0 //1 # ( ( " " " " ) " 3= " " # ! " 7 " " " ( # " -*. 3 -/. C -+. *= -0. *+ -1. *0
5. 5. . # 0\$ < " # I # " " > #( " " #/4 " " " " " " I " " ! " 9 ? 9 ! & ) # " ? "? #F " " & ) # & ) # # ( "? 9 " " -*. % J ? #A " " " " " -/. % " " " " -+. % ( ( -0. % ( " # " " -1. % ( #/3 " ? " " (# "" " " " " ( & " " & " " " 8 # " ( 5 " " # 9 ( < " ( " # -*. 7 # ! ? # ( ( -/. 7 # ! ? # ( " " -+. 7 # ! ? # " -0. 7 # ! ? # "" " ( " -1. 7 # ! ? # ?/2 ( ( # " ( ( # " @ " ( # # " " " ( # # <( " ( ? " # ( " " " -*. B ( " ? " " -/. B ( ( " " # " -+. B ( " " -0. B ( " ( " -1. B ( ? " ( " "
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
7. 7. #" " " B A " #" " " " ( " " 7 " # " " " ? # # " " " # # "? " > # " " " ( " ? # " ( # " # " " " # 9 M M ## " " " " # " " ( " F " ## " # " ? # F " " ( " " \$ F " " % ( #" " > " " " # " F \$" " " # & # " " ( 9 # " %" " " # " " " # " " M " " ( ( & " " " #" " I " " " " # F " " ( # ? M " " # " # " ( " " " " ( # ? ( > ( ( ( " ! " " ( # 7 " ( ? (+* " & " " "" # # " " " \$ -*. % " -/. " " ? # " -+. "? - # . ) # ) -0. % ? # -1. " ) #+/ %"" # # # " # " ( ( " " -*. " " " ! " " ( -/. ( " ! " # # " " " " -+. # ( 9 " " -0. ( " " " " " -1. " " " "
8. 8. ++ @ # " ( # " ( " " # " " ( " , -*. ( " " " " " ( # " -/. ( # " " -+. ( " " ! " -0. ( # ( M " # ( -1. ( "( ) # ! "+0 " # # # " " ? # " , -*. %" " I # " # -/. %" " " K L -+. %" " I # ( # " # K L " (" -0. %" " " " (" " I # -1. %" " I # (+1 %"" # # " # " " " " F " " , -*. " " ( M F " " -/. " " F " " " # ( ? # " -+. " " ! " # F " " ? ( -0. " " " &" " " ( F " " " # -1. " " # " " " ( & F " " ( &. 0# 2\$ # #( ( I : " I> " " " " " # #< : " < A ( " K" " # L ? # ) " # "K # " ( " L 8 " ( ( # @ < " " F F"" # 9 " # " & ? ( " 9 " F ! # # "? : " < " #B " # #" ( \$ 1= ( ? " (A " D I B # # " " &" " " &" #( " # (< ( "? ( # " & # %" # " # : " < " 7 # " ## " & K "
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
10. 10. -0. & # " " # ( " " -1. : # " " # " "+3 "" # "? # " , -*. @ # # " I " " " " " " ! " ( " -/. # & # # # " -+. ? #" # " ( " " " < -0. : (( " -1. " # " # ( ? "+2 " & " < " # -*. " " " " # " # -/. ( " " " # " # -+. ( #" " " " ) -0. # " " " # " # -1. # # # ? ( #+C "" # ) " " " , -*. 7 " ) & " ( -/. # " " " ) # # -+. ( ) # " " # -0. 7 " ) " -1. " ( < ) " # <0= " # " " # " : " < " " , -*. : " < # " -/. 8 # " #" # -+. # # ) ? # # -0. 8 ( # " < ( -1. # " ) # ". 2 2 # #( ( I : " I " " ! " " # ) " # ( " " " " ? # " " " " " # ( "! " " " " ! " # # " " " "" I " # # M " ? " " " # ( " # # "! " " ! " # # # " "
11. 11. " # ! " " " # " # ( " D " " " "# " # " " " # ! ! " " " ? " I " ! " J! " A # " " " " " ) " " " ! " % # ? " " " " ? # " # ? ( ? " " # " " #" " ! " " ( # " ( # ( # " " " " " "" # " " " " " " # " ( " " " ! " # #D " # # " " " # ? # " " " " " ! " " # I" " ( #" " " ! " " " " # " "" " "! " # 5 " ! " I " " # ( " " # " ( # # " ( " " # # " " # " # I " " ( # # " "? # "" " " " "# " # " ( " "" " " # " ! " " " " " " " ( M " " " " " " " G " # " ! " " " " " # ( " " " I " " "0* %! " " " ) # " " \$ -*. % " ( I ! ( # & # -/. % " " " # " ! " " -+. % " " " ! " & # ( -0. % " " " ! " -1. % " " " " ! " & # (
12. 12. 0/ # # # # \$ -*. % " " " ( ( " ! " " " " ( " -/. % " " ( ( I ( ! ( # & # -+. % " # # ( " -0. % # " " ! " ( -1. % # " ! " ( " ! " ( ! ( # & #0+ " # I ( " # J " ! " A J( # " A, -*. " ! " " "? ( # -/. " ! " " # " " " ( -+. " ! " " "? ( # -0. " ! " " # " " # ( ( ? & ? # # -1. " ! " " # " " "" # "00 "" # # " ! " # # , -*. " " " " " ! " -/. " " " " ! " # -+. " ! -0. " ( ( " " ! " # -1. " " " ! " #01 " # ! " # # , -*. % ( I ? -/. <( # ? ( -+. % " ) I -0. % " ( " " -1. % ( ( & ? ". 2# \$ < " I I < " " " #\$, 3 " " " " ( ( " - " " J>A. 3 " " " ? ? - " " JA.4 * 3 " ( ( ! " "" " - " " JDA.
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