Page 1
v ~ ~ d 111tl1'l11 04 fiWVIftltTVI1
[ ·n1"''1!"~rmfltJ 1 oo ) I
~ c!t::t ~ c! ~Hl'U1'UUYl~'t1 18 Q:JJfll'Vf'Ufi 2560
n~n 11.30 - 13.30 cu. ' ~ q~
'IJ6 .......................... .......•.. UliJ~fJil ................................... &il'llf1U~U61J .............................. .
' q v trtllll'Yitr~'U •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 'H~~tr~'U •••••••••••••••••••••••••••••••••••••
. ~ tllAfUl'H
1. iM'~t'li'l~t>lJtl~u~~,m ~tuvlJ ~'Vlff. ·;h~·;wuu1'Vl1-:~tl~u~t~v1ti''lJnT~~,,ih.~m'l 'Vlfl~tllJ "W. ff. 2557 mh.:~ttl~ .:~Tii'fl v • 1 "' <11!1 1!1 1!1 .I "~ 1!1 .I """ d "" " "" 2. 'HUJ'Wl 'Vl'lff"W'VllJtltlt> 'li'ltl ~umunttl~l'l'li'ltl ~umwtmtfl'YIHl'Wfl~l'Jfl'lf'Wfl
t'li'1l1'v.:~~t>lJ 1flm~fl'lllfl
3. ..1nJfifl~vn uuVinm"W 11~t> ~~mm~ ulJlJ'Yifl~t>'lJ 11~v m~fiTt:H·h~t>lJ hwt~fl'lllfl ..
v v ..'1 "=" v . I""...... • "" ~ .:1 't'ilftf;f !'lJl"~lJH lHU'U~IJ{JlJVI tY'Yift. tll\1VIl!UUt111 VI~U
" 1. ,,_hh~mff~~~t~lJi'W'l1V1'lflir'W"ll1~tll'Jfl'l1V1'lf1
2. u~.:~ 1tlv.:~~muf1nlll'llo.:~~t'li'l~o'lJ ~~t>filruum'l'Vll-:~1irv .. 3. u ~'I'Wt)~fll'j ru ~1~J'W !tlv.:~~mu'W~fllJfffllll t~t!tl'l~fltllJ fll'l i' lJt~lfffllll~tJ 4. ~,, il u t1~ m11 no 1111 1v i u m w ~tfiflf111l1 t iY v111mHh ~'lJlJ m'l 'Yifl fft>'lJu ~~ ~'Vlff.
vem~11if Li:h..~~-n~'Vli-n'tl'l~mu\mc;J~'tluYl1'lm~f1im~1LL~'l'll1~ ('il~~-fn11~~1"11'W) " n11vl1~1~1'elvf~LLU~~~1'elLtltlLLYif~1'Uvf·m~h'l ,::CJn~1LU'WPI~lin~n.!)~l.J1tl
Page 2
tl I " Cl<:lu tl J"'fo u u _,. Cl I ... !II UlJlJ'YIYJ(;f6lJUlJ1~Q 'l:::(;f~fll'n61YIN111;llJi')'Y11i'YIHfll'lfttl'U1 tlQlJ'i;T11:::fll'll'lUUl
tl I -Q J Q.l ct Q.l QJ Q.l 4 ~I c::l ct Sl u .:t Q.l
fiW~ft1(;fYJ'l'U6~Ufll'lUU'l:::YitJ'VUlJ1iUlJfttl'U1u'YI 6 \ij1lJlJ1~1!1Ufll'll1UUlU11:::~1'V1Yl
' :, Q.l ct ~ Ji Q.l
'V1~'Vt.! 't111tl\JYI'lUtlUtl11Hfll'lfttl'U1'1.1U'nU!1U ~'YI1ifttl'.i1'V 2551
., ... ...,...... " 0 "
·nua:::l6UY~UtJtJ'YIYII;ltltJ uuunY~I;l6tJ~tJtJt.!lJ 30 11u1 ~1u1u 40 'Utl
I ... ~6'\..!'YI 1 " 'Ut) 1-32
" 'Ut) 33-40
" '1.1611::: 2.5 fi:::UU'\.1
' ' ' . ... "'. .,...., ... " "tl 1. l'UUU'V6-t.!1lJI;lfJ11 lli'U'YIU~(;ft)lJ l;l01'\.I'YII;ltllJ U11:::116~1;ltltJ lJ'\.1111..11 tlUtJtJ'YIYJ(;ftllJ
I
..., " ... '" 0 ~" " ..., cv cv " '.i 111;l~ Yl'U t) (;Ttl lJ'Y16QY11U lJU'U tl~tl'.i::: Yll'U fl1~6lJ I 11\) tl~tl~VI'.i ~ tl1JV11l 11'U'.i111;l~ ~'U6(;ft)1J
u u 11 u nJ mm u n Y~ l;ltl u
I
, !11!11"'1...., 0 liJ!II 't1~tlUfiYI11tltlfllfltllJ IYI
5. ,dt>(;ftltJm~11 1-H'(;ftlY~n'.i:::Y~1llthV~6ulnuuuunY~(;ftltJ
Page 3
~Mi.Yl'lrl 04 fllWVlflli.YVli v VI P1 l1ih 2 . ( -- NIETS
"" 0 .:t "" 0 anlbloaournomsiinllwtom {ooM\SL.IIllll) lU!i.Yl~YI 18 fJ,_.ill'VfUfi 2560 __ .. _, __ (Nic_, !l'tll 11.30 - 13.30 U.
' ' ' .:! fHl 'H ll 1 uuuthuu s ~-;uat>n &at>n 1 ri l fltl'UnlJnnq~
X 1111 I • I I
-3 -2 -1 0 3
1. I X I < 2 2. 1-x I < 2
3. I x-11 < 4 4. I x+21 > 1
5. I X+ 2 1 = X+ 2
' a-X ·aX + 16-X ·27X 1 2.
0 ... ihh1l1 ilfiltYh1V1 111UlU~~.:J'Ulfl a =
('f (')" 2 5 2 + 2 2
1. 9 2.
81
2 4
3. 165
4. 20 4
5. 40
Page 4
'1M«1'111 04 fiWVIfll«VIi w VI P1 l1Ul 3 , T NIETS
cv J -=t cv J anlllloaoornomsiinttwiOlllO (ooMISIIIIW) 1\.U«l'l'YI 18 tp.Jill't'fUfi 2560 __ ,._, __ CI'IM<_ !Ttn 11.30 - 13.30 U.
"' J ~25J625x6y4 I cv !II ~ 3. U't'f11U !'Yilfl1.J'llfl ~
1. 25 lxy1JGI
2. 25 xyJG"l
3. 25 xyf;
4. 125 X I y If;
5. l 25 lxlyJG"l
1. x (2x)'~~
2. 3x(2x)X
3. 9x (2x)X
4. lOx J)'
Page 5
l1tll 11.30- 13.30 'U.
5. ill
a=1+J5 ill aX - a-X'
q I I~ f:ll mn
a% -x llflllfll ~ + a 3
1. 1- J5
2. J5
3. 1 + J5
4. 2 + J5
5. 3 + J5
" 6. tht11'1Hil'U1'U'\l~~ x, y u~~ z 1~ 9 .U-e:~1~~-e:~,tlihiJu'\l1~
( n)Yn • " 1. x = x fJflm'U1'Uiflli'U1fl n
2. ~x+ y = J; + .JY
4. tll X < y U~~ Z < Q U'tl1 X > y z z
Page 6
l1lll 11.30- 13.30 u •
., I I
fJU~l'l1-l'uum1r.~u3JfimnJllltl Sl 0 ov i, Sl .ot .ot Ull11llU1UfJU'l1J.J'YI~'11J.J~UJ ~J.JlO'Yiif~OfJU
1. 15 f.!U
2. 18 f.!U
3. 21 f.!U
4. 24 f.!U
5. 27 'YIU ..
Page 7
18 A B
Dk- 8 ~c
18+ IO.J3 I
1. '11'U1tl
2. 18+10(J2+.J3) I
'11'U1tl
26+IO.J3 I
3. 'tnnu
26+10../2 I
4. tnnu
26+ 10( J2 +.J3) I
5. '11'U1tl
Page 8
run 11.30 - 13.30 u.
0 "" 0 0 (fHH'UvH't'l sin A = 0.6 U"~ cos A = 0.8)
1. 8 tiVI
2. 16 tiVI
3. 18 ~VI ..
4. 21 tiVI
5. 24 tiVI
Page 9
11.30- 13.30 '"·
.. ' !II !VI !II Q.l I <!!"" !V.::t c1
tll't1\!1VIH't10~'ftfl0ij\J~<tllfl'ft\!~U 20 l).JVI1 Uil1VIfl B \l~m).JVI1
B
i 2011.
1. 20-Jj l).JVI1
2. 20(1 + ~) &JJVI1
3. 20 ( 1 + J2) l).JVI1
4. 20( 1 + -!3) l).JVI1
5. 60 l).JVI1
Page 10
. o "lV !fiQ.I ~'!fl I Q.IQ.I!!
11. fll't'ilA~H't'i A, B Utl~ C l1JlAtl'1JlCJJVIfl &J.Jl1JlAlCJJV11H\Itl~ltlflil'tUY3J'ffflfi U
l~tl~ B c C Utl~ A n C = 0
1. Ans = snc
2. (AnB)UC = 0
3. (AU B) n C = B
4. A-B = C-B
5. B U C cr. A'
Page 11
12.
'tn'h 10
l1'tll 11.30- 13.30 '"·
., ., 1) lrm1uu.Uu JJ. 6 'Jflfl'UlltnhtiJu
2) flU~ll£JJlAU'U lJl·m'Uft~~n-mlUAU'U 1JHtlUft~~fl'l£Jl'U,,jAiJU
ll1l't\' U U'n'UAetfVI'UtHfl'U .,
.., q ..,
A U'n'UAetfVI'Utl..:J'UfU'l£J'U'U'U JJ. 6 .. ootoot0.1 iSI
B U'n'UAetfVI'Utl..:Jfl'U'n'U~fl'l£Jl'UAu'U
S U'n'UAetfVI'Utl..:Jfl'U~ll£JJlAU'U ., .
v .., v q 0 v c c, v " U'tl1'n..:J'tltl..:J'Utlfl11JJ'nfll't'i'UY'Ii.ltlY'Ifl'tltl.:JVIlJJUN'U.flWU1'U'U - 6tl£JA'tltl1 'U'UtlAYI
~t1,1.l~
1. u 2.
3. 4.
5.
Page 12
13. ilnn.1~111 f(x) = 4- x2 Uil~ g(x) = jx+2j
1. D I = D g Uil~ R I c Rg
2. n1 nDg = (-oo, oo) Uil~ Rl nRg = [0, 4)
3. fl'ilvJ'U~~ g ,,j~~Ufl'U X
4. fl'll~'U~~ f IV q q
VI~Ufl'U X l't'UJ~1l~l~f.Jl
5. fl'll~'U~~ f ~~nun'll~'U~~ g tnu~12~,~rn
Page 13
,,s;, 12
rnn 11.30 - 13.30 u.
y
x+y=I
1. { (x, y) I 1 ::; X ::; 3, X- I < y < } - X }
2. { (x ,y) I 1 ::; X ::; 3, X -I ::; y ::; I- X }
3. { (x, y) I 1 < X < 3, 1- X < y ::; X -I }
4. { (x,y) I 1 < X ::; 3, I- X ::; y < X -I }
5. { (x,y) I 1 < X ::; 3, 1- X ::; y ::; X -I }
Page 14
•tn~l 13
rnn 11.30 - 13.30 u .
.. 15. ft1'11t~~t1u11J~hfl'~ 1 oo vt~..l &ilu~~il
1 , 2 , 4 , 7 , II , 16 , • . . , a50 , • • • , a100
I
!V olct c1 I I 't U"1'n~ti'YI 50 ( a50 ) J.Jfll&'Yil &~
1. 1,176 2. 1,226
3. 1,276 4. 1,300
5. 1,301
'j~f.I~'Yil~ 20 ill "').J~'j
1. 28o nl"').J~'j
2. 64o nl "').J~'j
3. 98o nl "').J~'j
4. I ,280 nl"&3J~1
5. 2,s6o nl",,..~'j
Page 15
17.
fX1 A = { 1, 2, 3, . .. , 10 }
B = { 4, 8, 12, 16, 20}
Utl~ C = {xi (x+1)(x-4) = 0}
2. B U C = B
3. A n B = { 4, 8 }
4. B- A={12,16,20}
5. (An C) U B = { 8, 12, 16, 20}
Page 16
't1ih 15
rnn 11.30 - 13.30 u.
Page 17
run 11.30 - 13.30 '"·
. " " ct !'I I 19. t~unnmn'Utl~VIl'U'Utl~~u.JA'I11UJ).J3j).J'l'lln Au'U x, x + 2 ua~ x + 3 '11'U1tl
X
8+3/6 I
l. '11'U1tl
8-3/6 I
2. '11'U1tl
1+/6 I
3. '11'U1tl
1-/6 I
4. '11'U1tl
5. 11 + 6/6 11u·;m
Page 18
n'tn 11.30 - 13.30 u.
0--------------------Q X
y
1. V = 2x2(2-x)
2. V = 2x2(3-x)
3. V = 2x2(4-x)
4. V = 4x(2-x)2
5. V = 4x(3 - x)2
Page 19
'11ih 18
n~n 11.30- 13.30 u.
21. y
X
0 2 3
2x 2- 4x+ 3 > 0
0 ... 1. 'tJfHll\!1\!'iJ".i.:i X
cS I 4 2. Y! = Y2 flfltln.Jt:l
4!1 X = 0 '11".Jt) X = 2
' 3. Y! <Y2
cS I 4!1 flflt:ll3.Jt:l 0 < X < 2
Q.l _J ( )2 I ; I -·· 4. <tJV11flflt1'U,t:l~fl".iln y1 = 2 x - 1 + I t:~gfllfl1lfl".iln y2 = 3
Page 20
A.l 0 X ( ) <!I I Gl !II 'I 22. 'lllflfl".ilTt lCUVIfllVI61J'\16~el'tl3Jfll".i - ~ X 4- X fl6'tf1~ I'U'\Itl&Vl 2
y
1. [0, 2] 2. [ 0, 2.5]
3. [0, 3] 4. [0,3.5]
s. [0, 4]
1. 5 2. 9
3. -7 4. -9
5. -58
Page 21
l'lih 20
run 11.30-13.30 u.
I
!II cvc:t o "''II c:t '!fiCV 24. ~lnl'Hl~A"lfJ~mU1UA~).J&UU~1'YI 1, 2, 3, ... (mO'lJUt'l~t'IH) AuU~~.fll'Vt
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1. 60,025
2. 62,525
3. 65,025
4. 66,225
5. 66,275
Page 22
R = 5e-k + 5e-2k + ... + 5e-nk n
I I
.!! ~I I "" llltl k ~~~~ e luUfllfl~'t11.Jlfl
I .. I
't1ul 21
n~1 11.30 - 13.30 u.
u~·nAt~lnunfifl~agiu1HmtJ rlaum~111mfl1~fi 8 &iJurrh1V~ (il~an1t~)
5. 5e-k [l-e~8:) 1-e
Page 23
run 11.30- 13.30 u.
+ V lJIV '""' 75 tl~U'U'U Ul Ufl'U &Vltl~U'U'UUfl1Jlllflfl'Jl~'J 25 fi~U'U'U
1. 6.92 tl~U'U'U
2. 12.50 fi~U'U'U
3. 77.50 tl~U'U'U
4. 82.50 fi~U'U'U
5. 141.00 tl~U'U'U
Page 24
" ' " " " fl-l-!1 l~U.IA~lfhA~~tuileuflW~eu~-!!fl~&nn..!tJ~'Un-!1 3 fl-l-!1 U'U'Uth-!!'lht'illfl~-uJ
., 0 Q.l 0 Q.l
'IHt'i'Ufl w1 , w2 Uil~ W:3 ~UJill~'U
, J ~ = W; .. £ j ' i = 1, 2, 3
wl + w2 + w3
3
fl = 0.1 5 ' p2 = 0.25 Uil~ IP; = 1 i=l
' ., ., V I .o::l .,. I o u <V .o::1 .::1.::1 I
Uil1fllA~iltiAileuflw~eu~-!!fl~UtttttJ~'UU'U'U tt1-!!ttl't'ittfleu~-!!ttm-,tlttfltttt3Jfll
1. 68.3 fl~UU'U
2. 70.7 fl~UU'U
3. 72 .0 fl~U'I-.!'1-.!
4 . 73 .7 fl~UU'I-.!
5. 74.5 fl~UU'U
Page 25
ntn 11.30 - 13.30 u.
1. 15
2. 18
3. 19
4. 20
5. 24
Page 26
run 11.30 - 13.30 u.
29.
ll1,;1.:J (x-3s,x+3s) n-hfl'u (1400, 1580)
1. X 1445 Utl~ s2 = 2025
2. X 1445 Utl~ s2 = 45
3. X 1490 Utl~ s2 = 45
4. X = 1490 Utl~ s2 = 2025
5. X 900
Page 27
,;;, 26
rnn 11.30 - 13.30 u.
"" 1~m:rnn (Ul'YI) 3 4 5 6 7 8
0 " 'illU1U\')flfll (tlU) 8 5 3 2 1 1
' I c:t "" I '1.1 c:t '1.1 I v c:t 1. flli'1HUJl'ileutlWVI I'YilfltJ 4.3 Ul'YI ).Jfitl!lU I'YilfltJ 4. Ul'YI
"" I .., "" ~I " !lUUtJ).J I'YilfltJ 3 Ul'YI Utl~ IUUfll"lfl"l~'illtJUtJtJitJ'YIHeu11
' ' .ct Q tcv .ct v tu q
2. flll'1ltltlltleutlWVII'YilfltJ 4.3 Ul'YI ).Jfitl! lU I'YilfltJ 4 Ul'YI
' I c:t "" I '1.1 c:t '1.1 I '1.1 c:t 3. flll'1ltltlltleutlWVII'YilfltJ 4.3 Ul'YI ).Jfitl!lU I'YilfltJ 4 Ul'YI
"" I .., "" ~I " " !lUUtJ).J I'YilfltJ 3 Ul'YI Utl~ IUUfll"lfl"l~'illtllltJtJitJ'Yil-!ICUltl
' I c:t "" I '1.1 c:t '1.1 I '1.1 c:t 4. tlll'1ltltlltleutlWVII'YilfltJ 4 Ul'YI ).Jfitl!lU I'YilfltJ 4 Ul'YI
' , q Q tcv ..r:t v tQ.I .c:t
5. tlll'1ltltlltleutlWVII'YilfltJ 4 Ul'YI ).Jfitl!lU I'YilfltJ 4 Ul'YI
"" I .., "" ~I " !lUUtJ).J I'YilfltJ 3 Ul'YI Utl~ luUfll"lfl"l~'illtiUtJtJitJ'Yil.:Jeu11
Page 28
run 11.30 - 13.30 u.
I ., .,
nm1uw~:00fl i11 2 1"1-r~ ur,: 00£1 2 1"1-r~ l't'hn1Jifh1~ u
1. 2 2. 3
3. 4 4. 5
5. 6
32.
25
20
, '"""" r! Utl: 3-JJJ~fl'ltll'Uti'U~ rrhn1Jifh1~
1. 1
2. 2
7 7
3. 3 4.
5
7 7
5. 6
7
Page 29
run 11.30- 13.30 u.
. . 33. ihttu~un11lt1u ABCD utr~-:J~,:jlU 1~uii~l'U AD tin 15J2 'tnhu u~1
V 4 I
~l'U AB tll1fl11'U1tl
B
D C
34.
2-JS ' 4-J9 ' 8-Jl3 ' 16-ffi ' ...
Page 30
-tttttl~~~ltlU·¥~ t-~~tttttl~M.fli e,X-X9-9If 1tll~~ X 1t!.6itttttl~ 'L/i
trJ~iM..I(,[email protected] ~It"t-lA.It tim "" "" "" "" """" "' "" "'"" "'
I I A
ttYfl.QtY 9 tl1~iHI1QlttllA. ~ ~ ' 0
ttYfl.QtY OZ t~.l!t-lllU ~l!U ttt.l!llA. "' ;o "' "" 0 .. ttYfl.QtY £Z th).l!t-lll!i ~l!U LttllA. "' I' "' "" 0 ..
ttYfl.QtY 8 ttt.l!LU. ~l!U lttllA. "' 0 0
ttYfl.QtY 0£ ttt.l!llA. ttYfl.QtY v£ lttllA. LO l"b 0 l'b 0 "
t~.l!t-lll!i Qt" ttt.l!LU. lttllA. M..I(,L@ItlA. ttYfl.QtY 09 ltt-tt"t-"Uttlfl.tc" '9£ I' no "" 1r' o o "" """" no "" 5:7 1 IT) 1 10 I I
t~tti~ttJ~.:~mt-.1\ a L.l!i ~~Deu.tth)L.l!ttl!n .,. "" ""I "" "' "' I I
h)~YR.l!tn.~l~t\fl1 ( H l.l!i ~l!U V L.l!i lttt ) tt~UiA.L.l!it-QR.t-.1\ttltYfl.~l~
~nn th)rtih)M.Jl:li ~z ttUH"De ttU~h)Deu.n~~l!~Ul.l!it-QR.Hl!Uttun U.ll~! "" "> I I "' ""I "" ITi I "" I I
t-t~tt.l!ttnnnw a LDI ~nn v L.l!i t-Lt"~tttM.i LDmntLUt-Q~lll t~rtth)ttJl:lt ooz JTi (, I ~ hv JTi JTi .,.
ttUH"Det-~~nn t~rti~M.Jl:li 00£ t-.1\ g L.ni t~rti~M.Jl:li OOI t-.1\ V l.l!t 'S£ l'b ' • l'b b' \:::7 ..
·n 0£'£1 -O£'JJ . .--. -S.l3fN~ ;o "' f"'~' "'
Lntt ~=~->·== ~ 09Sl mru.twtt~ 81 IULDntt
6Z lef (A, b1 f~Dll~~~y 170 LJlotDAtt ltt" "'
Page 31
run 11.30- 13.30 l.! •
., 39.
tl c:l <Vc:l 0 fl:::Ul.!l.!'tHl1.J 'i:lltlillfli"WWUtl.:Jl.!fU"Wl.! ~ll.!ll.! 25 fll.! aiJcu~~9ltl, tJil
60 65 65 67 70 71 73 75 76 76
79 81 83 84 85 85 88 89 90 92
95 96 99 100 100
' ' , v iJ tl r! " , r!c:l '11 P25 I l.!l tl'Wifl.! 'Yit'I'YI 25 &It'!::: iJ tl r! " , r!c:l P75 I l.!l tl"Wifl.! 'Yit'I'YI 7 5
v <::11 ·~ mn P7s - P2s 3Jflli'Yil ~