Sample.. ~u est-fort PO-f>e..

,- 8
CE)<.pl O.rLa..-tlo ns)

1. (b)
' • Al
l~ lln.e.. u segm e..n.±: -101n...1n.q
'
Ta.llinq 4:he. cna±ios OS ~ ~ •'(\. whlc.h. th.e oof n± p d.1-vide..s
ft~ B, ~~ h.o..v-e. ~ c.o-o...,-dlncJ:e.S
I

-
r V I)

oF p o.s X.1 -tu, ., Yt-t ~'I,

V

L ~+, IL+l -

o1· (a..) The o "fdlna±e.

. of oc pof nt Q
(J
',ve.Sfts d11:>i:o.nc.e.. ~~om th.e..
:x:.- <l.)C.is. 5o, the.. d...lb -conc.e. af- ( ~,"r) fTOrYl :r.-a...~,s ' •
,s t .
•
3. (d) Points Q."r e. g,ven ·a.s C.3,-ot) o.nd (-3,~)
.• . ·oisto.ncev:::. ✓ (.X2,-.X.1)t.-t- ( 'fz.-'-11)~
. r
,
-,_ f (_2, +3)~ + Lo{ +ot) L
:.. J 36 + I b
-- [Se{
4. (c) G;ven
.
e..9 u.o.Loon IS ::.(__'-Sox..+ ...t:J.. S ~ O·
H)¥ lhis v,) C. ha_v~ D = f(-30)1.- Y){~~s-

=-- J 900 - 90-0

-- 0 '

. '
Hence 'Y ootS o...;e (l..eal o.n.d e.q u.a.L o.S D ==o.
-
' -- I

l
!
 - - -- -- - - -·--•-

5. Ccl) \/o,Lurne. oF. cuboid _, length. )( Boe.ctdt h 'I- H e.ighJ:; .

. V --
-
-
. • 1 .. \/o)ume. ol=- 8-Y,ck _., C(S)lll ·2S)(b .
I -:
- \ b 8 il • S- c_rrf>
Yo Lu.me 0~ tAlail -- e Oo)( b ~ol.- s Oo)(

-- Io 9 OOOoaC.M 3
II f • So, t-he numbe.'Y. of 8-Yic~ -:::. , oQ 00000-==- 6t, 00
I

f
I 681·5
I
••
I
- ..
~- (d) Aolth mei:i. c rn.ea.n = Q., + Q:'2. + 0..3 ~ • • • • Q. n
'
f
J; J
n
'

I - - Sn ': (SuM of n. re"t'ms)

n
-
I .
-- rv~(n+ t) (_ Sn -:: ~ ( n •fl))
(1 -
- - ,- -
H t.nce A..,..~ th me:l:t c. n-t'(.o.n :t- ni-,
- -
.t_
. . ,
- - '

- -- ~-r
1· (b) y~ {Li 6)1 - (~ 4) 1 \1 , .rti./' '··
'.
=-
-- _16-=l--b- S7/-_J__=_ ✓ \Oo -- 10 ;'
p/./
2-6
Y' \
'C,l'Y\ /

~
I
- - - -
Hence "t"o.cUos - lo cm.
-- -
 a. (d) We. ~Ot..Q -th~ c{~(3 ~ -<-:t· l=>rt--.Z ::. -tf S0 ~ ,\S ' .. .
. ol
l

5 -
(-<-~) ~ (~+ ~) +(o{-f:3)~-{ + (-( +~) '>( o( ==-0
( o{ - ~
2 2
) + ~ 1. - -< ~ + ozi. + ~ a -==- o
3o{.~ - ~2.:. 0
V
s
p ui.ttn.Q. 0(::: ~
2 2
3XS-~zo -:') f> = sJ3
. ..
•- . G{ = s;, I•,e, ·- I~ ../3 ; .
! i ·_ • .. ..
f
' ' I

' ... I

9· (~) Wt k.rroLu -cha1 mi n1u:i:c.. ho..nd '

lh o n.e. rn; n..u±e..J c..o'/e-YS
6 0.
. '. JI ) • I
... A n;1 \e. .&ub te..n.d ~d ,n
' 3_5 rrn.i ru..des :;_ C6 '/... 3 r:}).=~\o •
...

Ane.Q blue.pt b'J the. m.i~te..., ~ d ',n , 35 min.u±e.s

- ~\o "t ~~ ~· c, o )2. ~ , a 3 •~ crn~
•• '··J_;
3bO J
1 I• I
-
I J-'• J ~ '

Io. (k>) , 1-+...lo.n 2 e, == _!>•e. ct- e -) ~ i.d ent-~ tLi ) \ I

. ; ,· I
' V
' .•. l + i:.o.n 2. e i ==- , h~c1-1e1 -·l.
- I •
.. l
I
1 '
J

-
. Ae.c 2 e II
~e.c.2..&, ;...
~

. i • l
I
I '.L~,

\
. - '
 1.1. ( b ') In !)ABC , -k.o.n 60° -- h I
A-
I

""
Be.
.
~ ~ =- h ~ h::: Cfofi" m h ~
' 9orn n
6o~r
"V
90 rr,

I~. (Q) The. q •rve.n ~~sttm . of e.q u..a.±io n s is oF -bh.e. f o...-m.

V - .
a.,x.+b ,'J + C:. 0 e.9.. (D lS ct:x:.+3'J- t-= O
, ..
Q., ot. ;- ~ 'f + C2. :.. 0 ~_(D ,s 6x.+ ~'I-' l =- o
w~ hoor~,
.
~ =t- 3 =t= -1-
6 c; IJ

• C 1e ctYl'J a., -::1:- 'b, - ' '

. q2- b, • ' I

•
So, lhe. 91ven f>'lbttm oF e...q u n..i:ions hos 0.... LULi 9. ue.. ~o \o·b'.o n.
V I .

,i. Cb") Giv~n L &f' A :=. <X.T • , He-re t-P&Pt = 9 01) { •·: 'P& i s to.n9 en½: J V

rn ~ P 9-A, L9P-A+ L P9A+L &A-P~ 190°

~to -+ 9 0° + LQ.AP-== )80°
......
'v

~---
L~AP= )so·- l\':J-
-=- 63~
0
~4 /
\
\o.
'
I

-
'
)
~

' -..
 • l
I~. (Cl..) rn 6 ABC, 0 E \\ SC .
• ~D ::. AE-
.1' • •
DB EC
,
' I CB\J Ba.sic fnopo-Ytt onaJl~ Theo-Y-e.m)
=} X. :c..+ 2
X.-2
-
:x.-'
l
-- I

_.:c) :x:. ex-,) =- (:x:+f)(.::c -2.)

~) ::X:.2.. - X =. x.2- 4 ~ :X::.-= 4
. . ... '
i I~ :. '
I
'

15, (b) Wh~n we appl'.:f AA o/lule to both i:,,,ia.ng \ es., W)e,. \..0\ 11 ~ind
- V

ilia.± both· tttio..nfl les a..-Ye s, m\la:)' ', F\ A o/UJ...le.. does not .&e.e. the.
V

plci.ce rnent oF o.n.>1 \es o.nd· ~e. d~n'l n.ee.d, a. hide. i:o pYove Ll•
-
) J ; -
I I b- (b) '2o.dius = '1cm &, H e..iah..t h = ~ 4 c.l'Y'.

~e. k.no1..u ,
.
'l, V
i :., ")' 2. + h 1 =} e =- 1-t + c~ 4)t.~ l '- =- bot s .
• ,# .l=-ot£cm
,. I • I t .
I
I • I
I

.
CSA oF cor.e IS "-YI =} -t~ ~ -lS X1-
'
~
I
1- '
I
-- S So C-M2..

I
 17/-· (a)" A--rea. of ~e.c.to-Y- - "K'r'- e I
-
,
(He"le fJ - 9o')
.

360° D c..
' - ~~ Y.. (14)1.X 90°
1 3 60"' (r, Botf~~~
~~ ~<r. .;
I

- dl. ,;i__ X ot. ){ \ y I

\ 1/5v-
/
½ lb"' ,~) :tt\
'
I
I
, / , >,-

- IS½ m~ AJ
~
2-.0l'Y\
8
~

18- (d) Volume oF 0... sphe.Y-e - ½ 7\~3

~

Le.t ., a.nd r-r2- be. th.e h.o..dti ()F the ~ bpheYeS.

So, Le....t ~, -::. .t ·x and Y1- -=. 3oc
V, -=. 4/~ 7Pr, 3 ~ r~~)s - a
Vi. 4/3 7\ , ~ @:x)3 all
.•. Y, ; V2 =: 8 : 2."f .

',. ta.) Soi:.h (A) o.n.d (R.) <U'te. t -r u.e o.nd {P..) is the Co'"ne..c±-

e")( o lo.na.:i: ion oF- A·

3Bo IS ' not- di"isi bl~ b\J 1e ,
 o<O ., (a.) Both As.se-rtLon CA.") o.nd ~o.so n ('2-) - o...ire twe. ond
ce) . (A).
£ea.son IS the. co--rrec-1: e,.xplo.tu,J.ton. of
-
Acco-Yd i ng to BPT if a. line DE" po..,a..Llel to ec c1J:s A-8
o.n.d
-
Ac cu: D &. E rhen Line OE divides AB a.nd AC
,n th.a.. I

so.me "rah: 0 .

~ ,. ( b) l f' lhe "r"OOlS 0-'T"f ~ o.nd-~ then q.LL0-d-y-0-tic

...
po 4, nomi o..l.
.
V

,s Q ·,ven as, l '

V

FC.x) =- It- (x.2-- (~+ s)x.+ ~ a) ,

.
'-" he.., e. k. IS 0¥l'J c.onstant , I • I

He.-e
I
°t'+ -~.: ~ , o{J3=-I I '
( . - ,

~
I
. ·F-(~) -:. k (:X 1 - ot:c.+I) l I
'
'
I

I
. . J t
I
' ' J (

,,
'

'
.. I

' ~
I

. -
\

. '
 2.2.. b) u...t ,LAc.B - '>'l and t
. . ·\ -
BAT -==-'-1 • c..
A • ta.n~ ~t, m,(ll.es · o..n o..n~ \e t>f 9 0° u!>Cth /" '---.,
...,,
.

"·" .,_ J
/ I
• I
I
'
•. -Ya.d .:us~ ·,of o.. clycle ~ 1
: . / i

~
I
sO =-· 9 0 0
• •1 I u.,'e:. k..rto""3 tha.t lo A'S '+'-f
the. 0Jt9' e. l'1 a. sem,- 'C.L'YC. \e. . . tS '9 0°
-· - - U), . -
....
l".l

~ \ /;;
-
So LC. BA =- 9 o·.
•
\,
~ /
//
_/.'~
LC BA+ LOA B,~ L AtB =- l 9o'
• 0
I r I I
... -~ . .....
.,
I
~"'
The..,s-ef o~e r, ~q O r-f- l.OA B + 7\ :::- ,:-a 0° '

'
.
.
So, Lo A B -r "")'\ ~ 9 o• .... - _. -tii) ~
• I •
.
0
Bui OAB +'f= 90 . ' ,• I , •
I
I
I '

Th e:refoire, LOAB+ -'j = LoAB +-n

-.
~ - -- F-Yom cj'.) & (i,) .
'r\= '1 . - '. '
.•

Hence LA-c.B = LBAT • .

- ' • I .,
' > I
'
23- PoZ>c?>(b1e o~c.o mes : ~ H H, H.,, TH, TT ~
r I
The. n 1..1.f'YI b e.Y o F ouic..o me.s .
r~ 4-.

Henc e, l;he. p--ro ba..b{ ubt fo,,,- eo..c.h

o~ i:hese
ou..tc.omes I -
4
Hence th€! .t,-lol-eme.YLt b.) rn C.O,s,ec ~ .
 ~lt- q-y e.oie.s t possi b\e. Uttq th of e.a..c.h pl().(\ k.::: HCF (l\8, Sl,, "t--l)
V
'
Poime ~ 0..c coYi.sn1,' on •.
'
YB~ at.x~~~~ ~)l'3
r
Sh= ot_")(~')t~ ~,-

1-~ = ~ 'j. ~ ~ 3 ~ 3 ~ -1.

.
. •. HCF = p"Yoduc.t ofm.a..lles t power of e_a.c..h common
b
•
p~rme. fo...c.lo-Y in the. nu...m be.YS i•e. -t3 .::: 8 .

The-Ye Fo-Y-e ~-rea.±e.st poss·, b\e plOXl k's kn~th. ,s 8 m.

Now, to ~tnd tola.l nu.mbeY of plo.nks fo-nne.d b't e..ru:h. of
i:.he piece, we. di"i de t-h.e U.n9t:h • of e.o..ch piece. b'I 8.
--
l,Je. k..rl OW tho.± ~
8Xb -=- 4 B
c9"J..1 =- Sf,
.
SX9 = 7~

Theoe Fo,ye, total n.umbe-.-- oF f)La.nks f O'YYY\e_d ::. b+ 1-t-9 =- tfl~.

H e.nc.e. i:otol ot°' plo.nks ~ i I l be.. fo-rme..d.

-.
 c9 x 2 -~ kx. + ll. := o
Comp Q...., in~ ~ )ven e q .U : ~ i o n l1'> tth. the. ~ ene-rol fo'Yrf' oF

'l ua.cJ,ya..i:ic e.ciu.a.tion, \..Vh.eYe C\.X.t-+ bx.+ c..:= o.

He"e Q_= 8 , b= -a.lk, c..=- k. .
P, n di n3- disc,.·, mi nan l :
-- D= b
1
- 4 QC
1 1
- - - - - - (-~k) - 4)( B )(k. -==} lf ll - i~"

Si nee 1i-0ots o.'Ye ,ye.oJ. d e.ciual .

0.1\..

----
. •. Oiscrimino.n.-l = o
-----'----
pLLl D = 0
Yk1- ?>~k'. =-o
~ 4 "-1 = 3 ~ k
:'.) "- ::. 8

Henc.e. VCl..lJte. of' "- : 9 .

~ b- b) Le..t A=- ( 3, -4) o.nd s ~ (\,~)
, l I
• '
line. .
Ai me.ni AB LS h.i sec ie.d ,
i:,~q ~o line .2>e.9f¥\en±
V
"
'
IS e..i the..Y- div, de_d 'tn ~o.±i.o OF I : eJ O'Y ~ ~ \
.
'
Lv h.en AS IS dlvi de.d '
1n "'r"O....UO oF I ~ ot , !:.hen '

co- o-r di no.le$ - r

I 1(1)+a2(3) . ,' (~) + ct_(.-4')\
~ ../
, . I •
3 ~ :
'
. - (-+- - - -t} J
'
.-· I

\_ 3 ./
. .
"r.
' Whe.n AB IS ,di. vi de.d • i'n 'YOCUO «. : 1 \::he. c. oo -yd.i no±-e..s
.
/
':.-1 cl(1) +3 ~(at) +Jt (_-4)\ r
•
7
'
3 3
' ' '

I
-
- ( S -·, 01
\__ '3 ,J
~ I l _\

' '

"4

I
' .
!

---
~-:,..
le...t'b d-Ya.t.,.:) t'r"Qp e..2.i LJ (Y) ABCD Lt., i th AB 11 DC
,o r
/ ~ o~"'
I ~
ft
~ ~n
-~ "'
IF t '-"0 o.ngles oF on.e e eoLL ol -l:.o b,.uo ·
l-rian gle a."l
I,,
V
V

anql es of a.n othe. -r lh.ta. n g 'e. o/Le. spect ive,~ , the two trian ~
V
V
!es
V
V
a.Ye c;, mi la..T.
. This ,·s • Y-e ff e. .-Ye. d to O-S .AA• si mi IQ.,it ~ cy, -\:e')'"ion for f:wo
-
,t..,.·, o..n <;l Ief>.
-
In ~A0 B and i::,Co D
LAO S= l COD Cve.,L c nu~ oppo si ~e on.gl esJ
\,I V

lSf'O = LDCO ( A l~e.Yna±e. l nte.Y ior o.n_g \e.s J .

"

-::) OA0 B ,v l>COD LAA c.Yit eyio n)

He.n u, oA - 08 '
oc 00
 ~8 . o.) Ti m e to ke n b'-1 So nic ,_ lo dror1¥e.. on e oo un d ~ IS m i n.LLte.s.
T, m e to..lle.n b~ R~ v, 'CO d7 'iv e. on e. "Tou.n.d -:::..let mi nu t.e s.
'V

Ti me ta_ ke n b~ bo th to rn ee ..t 04 ol n -=-

- LC M of t B &, I~ .
V
l,Je . f-i nd LC M of 1S o..nd \ol us in g py im e. f= a.c ..to 'Yi z.0 -ti. on ..
..,
I

L..C-M -
•
~ \S,lc:2.
; ~ °I, b 1
I
I ;
3 9, 3
3 3, I

1'
' I

Henc..e. LC .M - ~~~ ~3 ')( 3 -3 b .

lne .-r e.. foY e tim e.
I to ~e n b) l bo th to me..e..t .
CL 9c un a. i
-
slo ... Yt tnq
CJ
po i n.t.
-.- - LC .M 0f \8 &.. '~ -
I
- 3b N\,nu.½:.es.

'

-- -
•·

~C\. rn l:)ABD Pt
I i:.o.n boc - AB ' ~
I
I
SD \~
I {3 -- h \ ~
I
X h \ ~
I .• . -:x. -::: h • - . • ti) \ ~
I -rs Q. I
bff(\ ;oC'-.. -
I Nov.:>, in 6ABC. - <--:(:= ➔D "!\01')1'\ _,-
,

I to..n 30~ =- AB
:X..-t3o

~
'
-ls
- AB
:c.-t3o

I ::) X-t 30 -::: ~h (AB=h)

I
j
.• . h +3o= ✓3h rf---ro m ea,, . ch)
.J3
-
-
- -
=) h+.f3 )( 5 o = ..f3 x Jg)(h
I I =-:) ath :: 3o./3

- - ~ h = tc;.{3 rn -

. IS 5
I He.nee he.i3hi of lo t..ueY IS rn.
~
- -
- -
 :
.
'
.3 0. -
We.. k.now, c.os A
'
bec..A

Also, .bt n 2 A 4- cos 2 A -=--I '

~in~A :::. \- cos2.A

bin A - / I -r ' "\.2. - 1 beci..o_, - .J 2ec.'A-' - --Cl)

" ~ec.AJ ~ &e.<:..2. A .2>ec. A

.
• • bi" A ==-J 2>ec.2.A - t
2:ec. A
Since, ccsec A -
'
sin A
~
•. cosec A - 1:,e c.. A . . . . F---r-o m d)
✓ ~ec 2 A - 1
1
He_Te, c.o-l A - c.os A - Sec.A
Sin A -f sec2.A- t
5ec..A.

.• . -
cot
.
A
'/be~A-\
' -- - - l·,; )

We k.now 1 i::"a.n A -- '/cot A-, TheYe.fo-.e, ton A =- ✓ Aec...2 A-, ( hot'\" eq.H)
.
 ~

31. Lt. t cost of- one bo..t be x...

the
o.n-d the C o.s.t of one bo.Ll be. ';J •
then a..cco'T d ;n>J i:o 9 u es li.on :
...,
G.:::c_ + 6'1 =
3500 - . . . . (I)

4.x.+ <;'1 =: ~4oo ~ - . - . (ii )

n-1 ul-lip!~ in~ c_q.(i) b'f ½ OJld o'i) b~ 6 we 3e.t,
-
~'-i:x-t-?4~::...,
J4ooo . . - - (iii)
~ ~ :x. + 3o ~ ::. 14 400 - - -· dv)
S LLb l-Y o..r__-lL n g e.q.(i,i) f--yo l'Y1 av) l>!) e. ~c..t
- b'I ~4oo
'
~
(/
-::: 4no
6
-- cJ O O
3 '

Pu.±t. i.rtQ lhe va.LUL of 4.., ',n e.q, (I' ) b,!) e.. ~ e..-\:
r
V
6x+ 6,<o,oo -=- 3Soo
3

6:x.. = 3500-400
--
X. 3100
G -- , S-So
3

.• . ';J - d(oo/3-=- 6 6 - t 'f o.nd X. -=- SI b • b 7J-

He...nc..e. cast oF one ba±--=- 51b·6~ c.es.)

cost of- one boJI - bb·b~ C.~s._)
-
3~.- a) u...t.'S t,QLe. !:he. o"'Ti.g·, no..l weed cF i-Yoi. n. ~'. X ! . '
Time
V

lc::LI'en .t"o t.Yo.Me,f G3 ~rn 1 .-~i th 0 ,ilSl i no.1 s p eed - 63

- ::;l....

Time t.CUt.e.n ~o c.ove, .-=F-~ k..rY' ~ith, i nc-Ye'4-sed speed·= 1-.:t.

::,c..-4- 6
( -' \

Ac c.o'"Y dinq
1 to q u e.s i:i.on : I I
-
6?,
- -:,-al ...
'?, . I '
+
-:x... x.➔ b --
. . i I
.
6?, Cue.+ b) + l-~.:r ::: '3 ~ 6_3x +a:,.B +:J-ol..:x -3 ~

-:x Coe...+ b) x 2 + b::X...

\-'

3:J-S ;-13S:x =- 3~2 + IS ::c.. • '

3:(_'2 - I '':J .:x.. - 3-=1- 8 =- 0
J
':x...2• - 3 ~ 1X.. . - I-< l, -- 0 . . J I . i I I
I

:x: 2 - Y cot x.. -+. .3 x, :- I ~ b .-:::. o ~ - .

-
X ( :x..- Lf ~) + 3 ( ~- 4-2) ==- O
C:x.-to)C:x.-4ct) ~)-·.x -=½~, -3 -
..
- I -- .
Since, ~peed c..a... n't be ne..g a±i-ve rbo the o,i~ ina.l o.ue.oO-R e_
~o·-e.e..d - -ls ½~ ~m/~T.
V - -
.
I
'
'
~ 3. (_o..) u_t be. the -Ya.d ius oF c:.i,y-c..le ond AB b~ 4: he. c ho'Yd,
'Y
LtJhtch mo..~es qo • OJ)~ \e. o.1 ce..n.he..
- ' \

AB=- S c.rY1 I
/~
In "r""ight l::,OAB, using P'-f lho.S101ros i::hem-em, / 0 \
V .... ',
OA~+oB2
-yl+ yl.::.
=- A B2.
s 2.
\~
fr.'- -
:;) ,. ;.;
~ I r ( , lj I

=) ~ '¥"'2 - ~ S" ' ' '

-=, r = s '
'
.f2 ,. , a

A'Yeo.. 0~ CLYC.le. ~ 7\ 'Y2 ::. ~~ v S )( 5 :::.. 3 9 · Cl( c9 cm -i

1 I + ol a.
I
A"'Y t:: a-. of
.
n-11 rio-r ,& e.g mu,t '
-
-::. A-reo.. of .be.c¼.o
.., "t'- A--rect oF ti OA 8

- - 9o • X 7\,2._ t '>(5 1 ')(_ s

360• ~ .{J_
l
J:i
1
-- ,. ··,e-3 9 . ~ 8 1- •o1.s:
4 4
, -- IL\· plS -- 3· 51 crn 2
ot
A"Ye~ of rr,ino , seqm ent :: 39·~ 8-3-S 1 ::... '3S·~ I
V
c..M~

£. e 9.. ui '"l"'Y e..J cU ff e.,ren ~ - 3S ·-=1l - ~- si

' - -- S ~-·14 ·c m2. I

.
31..t, I

CIQ5S-In+e-tvQ.) Mid-VoJue fi1 e_q_ue.p1,. ~ I •

1-t·xc )

·~
II -13 12. 3 3b
I:?>- IS- G I 84
, s-11- / I, '
9 ' rtt LJ
-
I 1 - I9 18 •, lS tX. 3lf
f9-2.) 2.,0 I F- ~oF
a?l-23 2 2.. 5 I \' 0
- -,
ot3--2S 1.4 I
½ - 9.b .
-
_ i~-~~ 4otF 2.H~
.
-::.1q lf -t2-of
.l. I
' .. ' I
'
' .J

q·,'\l'Cn : rneo.n =-l Q '

we. knot>.?, mea.n Ci) - z:F,::,c.;

,• J I

I ~F-,'

'
=> 19 = 7o '-I+~ o F
½o+F
~ 19(4o~F) = 1oY+ r:J.. oF
~ ~f ~ I f,
- ..-
~) F 8.

,.._
\ . .
•
 35. I Join oA
OA = 9cm
0L is pe:...-pend..icu..la.r eo AB,
AL-= LS - 15
-<.
- ":f-· S cm

In ilOLA b'1 p '/ thO-R O"YO. s The.OTe..fY'I :

,, -
o~+ L A'2 =- OA 2
=) OL'L ~ OA-i-LA 1
=} OL~ = 9 "t - (' s- ,2.. :::} OL2. = 81- ~a?S -- 3~ 4-~~ S
Cat ) '-f Lf
I

- :;> OL1 =9 CJ ~'> OL:~99

-
. '-t ot
I ta.n LAOL ~ AL - 15/~ - IS
·oL .Jcfoj
.f9"t/~
f---r-om AOA~P ~ to..n LAOL ~-PA ;;> tS - PA
OL m lo
=) PA -==- IS)(lo C...l"Y"
../99
~ PA: !So
-rc,c,

I
OR. u..nglh
"
oF PA--=-- rso
9· 9Y
-- ,,; c..m.

I I
 3b- (h Child 'S DaJ.i l.QtSe a.....-e
V

5
' ·' 0
I
·' s , ' °' d ,. p't 5 ,. . . . . .. to n d~s
V
1c.o'1n -l coins 3coins. lteo ins sco,ns n c:o(ns

We c.o..n ho_ve a...i:.. most- , 9 0 '

C-Olr\S

' e_. ,
I. 1+~+2>+4+S-+ .. . . . . - ~ +o n.. te.'YmS ::.190
n ( at:>< I + Cn- , ') , 7 =i9o
~
~- -
~ n Cn+1) = 3 8-o 1
~ n2-+ n - 3 80 =-0

~'> (n+~o) (_n-, 9) -= O ~ c.n+~o) cn-t 9) =- 0

=) n =-~o O"'Y n-=il9 ~ .n~-~o c,y n =-{ 9
.
St..cl rw.m be, o F coins ~a.n not be n.e__Sl o±ive..
. . . n= 19 ( ")' e.te.ctt.ng n=-- ot.o)
V

- w
. ,-
5o, nurnbe-Y of dO-t.JS=-19. ! \ '

• I s;th
(ii) 0~ , t-lum be"Y of coins fn pi5tg':t.., bo..n k on d~, ~

- n r~a..+Cn-,)dl
~n
~ L- -
~) ~15 = ,~ r ~ )( s- + ( 's-1) )<_ (5" 7
~ (...

'I -I
c:) S,s - 1 s- ....rat +r Lt 7 ==> s,s- -- 600
~
I
th
IIr - 5o, theYe 0-re t~o c.o,ns
' on l·S d~.
-
'
- ~

'iii°) Mone.'-1 ~C>.>Jed 'I(\ to d~s

V

~
'
Sn -- n -- O(a.+(n-,)d l
-
~ ... -
=} S, o ::.. \o .,.. ~ )( S- + ( 10 - I) )( 5 l
-~

ot ....

'=) S,o -- 5 \ )o+½ 5]

.
~ S,o -- S·o + ~e.'i S
~ S,o = o'l 1 s- . I '
' '
.

The-..efo')'e, mone.'j Sru,ed· '

1n lo d ~ s . :::. .f" ~ 1-~.
-

' - ~

.
' . '

'
I

I
-
l

II
 ,\
3l· ti) Totol. n.uMbe-Y oF coins ::::. c; o + Lt S +3 b +ol S + S - l '"f-o
N umbe""t" o F rls- <; coins ::. 3 b ~

'
The.-re.f o,e, 12.e.q u..ioe.d pTobo..bi lii:~ -::. '3 b
- V
- IB
I ':f o 05
'

•
(ii) Totol .num be, oF coins of- R.~-10 o.nd 12.s· 2.o .
== ~ 0 +9
-==-3h.
The_"J ef O"'f ~ r2.equ.i.-.€;d P,y-obo...bi 1.i -t:.;1 -=- 3 b :... IS·
I ':1-o a~
.

Uh) Number oF (2.s. \o coins : o2J8

p,yo bo..bi \ il>, (c.o,n of R&-=\ o) -=- c:2..-S I
'
"' I :J-o

,
. ' . fleqw.,e.d p-oobo..bi \it~
~
V
-- \-r ,p (c.oin of f2s. lo)
I I

-- I- ~8
. l"f-o

- 14 2.
j 1-=l-o
..... 'f I .
as
'I
I,
I 38· 0) ~l PS - ':;J I , - I ( J ~e . . ~

.'
II In ~ PQ.A I ) l -~,
I
I
t()...(l 4 5° -- PS- -- ~ ' ~~
~ e
~
S..A :::::(
-:,r 't~,A
l"\
V
\oorvi
\ :: ~ - .
\.;J..,
::f_ I50 r, •
'
. l ' ., ,I\
.
r---
X ::. >J - - ------ 0)

In t> p s.s
lo.n ao· ::.. p 9 - pf)__
- ';J - :(_ I

~8 X-+\oo :c.+\oo :X:-Hoo

-

1 - ::(_
~
:x_fi -=-- X-+I oo
rs -:x..-H oo
' - A I -. \ - l
• I

~ :.c. ~ to.o .• ~ ·x. - 13(,-6lrYl- ''

./B-1
~,om -the f- l 9 ,U"'('e he.iSlht 0(_
V
1
the.. lowe.Y hi::... ~Q
✓
+ QR..
.' -=-X..+ISo.= 13h·61 +ISO=- c:<8b· 61 m.
- l
-
I r

I
..
t• \' oe, Dis -lo.nc.e btlween i:::o p of t0we.Y o.nd A1 ~'s house..
c os. 4 5~ -=:: • ~ A -=: (9.A=:X..) r "l Y\ 6 6-A 1
-
VP

\....
PA PR-

'l-fi -- 136·61_:::} PA=- l36·b\

p·A
~ 9S· 62.m.
'I ..fi

I
I
<i'ii) Distance of'- Soo-y~ •s hovse ~"rem to~ e._y :
'-- SA+AB
-==-- ~+loo (~-=- I '3 <, • l, I f--yom c.h p 0..-t"~).
-=-\'3b-6\+ 1oo
-=-~3b·6 1~

- - -