X_SQP - 85656767 Explanationsclass10.pdf

class 10 maths

1. 1.
o1·
3.
4.
.
(b)
l~
oF
(a..)
Sample.. ~u est-fort PO-f>e..,-8
C E)<.pl O.rLa..-tlo ns)
T a.llinq 4:he. cna±ios OS ' ~ ~
•
whlc.h. th.e oof n± p d.1-vide..s
'(\.
lln.e.. u
I
e..n.±: ' • Al ft~ B, ~~ h.o..v-e. ~ c.o-o...,-dlncJ:e.S segm -101n...1n.q
V I) V -
p o.s r X.1 -tu, ., Yt-t ~'I,
L ~+, IL+l -
The o "f dlna±e. of oc pof nt '
Q ,ve.S fts d11:> i:o.nc.e.. ~~om th.e..
.
(J
:x:.-<l.)C.is. 5o, the.. d...lb -conc.e. af-( ~,"r) fTOrYl
'
• t . :r.-a...~,s ,s
(d) Points
•
C.3,-ot) o.nd (-3,~) Q."r e. g,ven ·a.s
• ·oisto.ncev:::. ✓ (.X2,-.X.1)t.-t-( 'fz.-'-11)~ . .
.
,
f (_2, + 3)~ + Lo{ +ot) L
r -
,_
:.. J 36 + I b
-[Se{
-
(c) G;ven e..9 u.o.Lo on
.
::.(__'-Sox..+ ...t:J.. S ~ O· IS
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
!

2. --·--•-
-----
- - -==
-
5. Ccl) \/o,Lurne. oF cuboid length. )( Boe.ctdth 'I-H e.ighJ:;
.
_,
--.
V -
.
\/o)ume. ol=-8-Y,ck -C(S)lll·2S)(b .
• 1 .. _., .
I -:
-
b 8 il • S-c_rrf>
Yo Lu.me 0~ tAlail -e Oo)( b Oo)( ~ol.-s -
-Io 9 OOOoaC.M
3
-
II f
•
So, t-he numbe.'Y. of 8-Yic~ -:::. , oQ 00000-==-6t, 00
I
I 681·5
I ••
f
-
I ..
~-(d) Aolth mei:i. c rn.ea.n = Q., + Q:'2. + 0..3
~ • • • • Q. n
'
f n
'
J;
J
I -Sn ': (SuM of n. re"t'ms) --
n
I .
-
(_ Sn -:: ~( n •fl)) -rv~(n+t)
-
(1 -
--
,- -
H t.nce A..,..~ th me:l:t c. n-t'(.o.n :t-ni-,
--
.t_
.
'
,
.
- -
I
--- ~-r
1·
(b) y~ {Li 6)
1
-(~ 4)
1
\1 , .rti./' '··
=-_16-=l--b-S7/-_J__=_ ✓\Oo p/./ Y'

-10
;'
-'. --
2-6 'C,l'Y /
I
~
- - - -
Hence "t"o.cUos lo cm. -
-- -

3. a. (d) We. ~Ot..Q -th~ c{~(3 ~ -<-:t· l=>rt--.Z ::. -tf S0 ~ ,\S
'
.. .
l
ol 5 . --
(-<-~) ~ (~+ ~) +(o{-f:3)~-{ + (-( + ~) '>( o( ==-0
( o{
2
-~
2
) + ~ 1. --< ~ + ozi. + ~ a -==-o
3o{.~ -~2.:. 0 p ui.ttn.Q. 0(::: s ~
2 2
3XS-~zo -:') f> = sJ3
V
• G{ = s;, I • ,e, · -I~ ../3 ; .
. .
.
f
'
! i ·_
•-. .. ..
'
I
' ... I
9· (~) Wt k.rroLu -cha1 mi n
1u:i:c.. ho..nd
'
lh o n.e. J rn; n..u±e.. c..o'/e-YS
6 0.
. '. JI ) • I
.
A n;1 \e. .&ub te..n.d ~d ' 3_5 rrn.i ru..des :;_ C 6 '/... 3 r:}). = ~\o
•
. . ,n
...
Ane.Q blue.pt b'J the. m.i~te..., ~d
'
, 35 min.u±e.s ,n
-~\o "t ~~ ~· c, o )2. ~ , a 3 • ~ crn~
•• '··J_;
3bO 1 -
I
J-' • J ~ '
J I• I
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 J . .
- I • .. l 1 '
- Ae.c
2 e ~e.c.2..&,
~
I ;... ~ ..
I
.
• l
I
i
'.L~,
I

'
-. -

4. 1.1. ( b ') In !)ABC, -k.o.n 60° h A-
I
-
I
-
-
Be.
""
.
~ ~ =-h ~ h::: Cfofi" m h ~
' 9orn 6o~r
n
"V
90 rr,
I~. (Q) The.
•
~~sttm. of e.q u..a.±io n s is oF -bh.e. f o...-m. q rve.n
V -
a.,x.+b,'J + C:. 0 e.9. (D
.
ct:x:.+3'J-t-= O lS
.
Q., ot. ;-~ 'f + C2. :.. 0 ~_(D ,s 6x.+ ~'I-' l =-o
, ..
w~ hoor~,
~ =t-3 =t= -1-
.
6 c; I J
• C 1 e ctYl'J a., -::1:-'b,
-
' '
.
q2- b, • ' I
So, lhe.
•
f>'lbttm oF e...q u n..i:ions hos LULi 9 ue.. ~o \o·b'.o n . 91ven 0....
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-
0
~4/ \o.
' '
~
-=-63~

I
)
'
-
-..

5. ~
~· - -.
:
I~. (Cl..) rn 6 ABC, 0 E SC
• l
.
•
~D ::. AE-' • •
.1
DB EC
,
C B\J Ba.sic fnopo-YttonaJl~ Theo-Y-e.m)
'
I
=} X. -:c..+ 2
X.-2 :x.-'
-
--
l I
=-(:x:+f)(.::c-2.) _.:c) :x:. ex-,)
~) ::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
.
"-YI
=}
~ -lS X1-cor.e IS -t~
~
' I
1-
I
'
-S So C-M2.. -
I

6. -
. ,
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~~~
I
~~ / ~<r.
.;
-dl. ,;i__ X ot. ){ y
I
- 1/5v-
½
lb"' ,~) :tt
'
I ,/, >,-
I
-IS½ m~
A ~
8
-
J
2-.0l'Y ~
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, ; V
2 =: 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
' not-di"isi bl~ b\J 1 e ,
IS

7. o<O ., (a.) Both As.se-rtLon CA.") o.nd ~o.so n ('2-) -o...ire twe. ond
£ea.son ce)
.
IS the. co--rrec-1: e,.xplo.tu,J.ton. of
(A).
-
c1J:s A-8
Acco-Yd i ng to BPT if a. line DE" po..,a..Llel to ec
-
o.n.d Ac cu: D &. E rhen Line OE divides AB I a.nd AC ,n th.a..
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
.
Q ·,ven as, ,s
l '
V
FC.x) =-It-(x.2--(~+ s)x.+ ~ a) ,
'-" he.., e. k.
.
0¥l'J c.onstant IS
,
I • I
I
°t'+ -~.: ~ , o{J3=-I He.-e
I '
( .
-,
I
·F-(~) -:. k (:X
1
-ot:c.+I)
I
~ . l
I
'
'
I I
. . J t '
' J (
,,
'
'
I
..
'
I
~
. -

.
'

8. -.
·
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
/" '---.,
"·"
I ...,, . /
• I
•. -Ya.d .:us~ ·,of o.. clycle ~ 1
:
/
i
I .
'
~ tha.t lo A'S '+'-f =-· 9 0 0 -· --U), ..
I
• •
1 s O I u.,'e:. k..rto""3 -
l".l
....
/;;
.,_ J
the. 0Jt9' e. l'1 a. . .
tS '9 0° sem,-'C.L 'YC. e.
~
-
\, // So LC. BA =-9 o·.
• • 0
-~
~ / _/.'~
.....
LC BA+ LOA B,~ L AtB =-l 9o'
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 • .
Bui 90
0
• I
, • I
OAB+'f=
. ' ,
I I '
Th e:ref oire, LOAB+-'j = LoAB+-n ~ ---
F-Yom cj'.) & (i,) .
-. .•
'r\= '1 .
-
' . '
Hence LA-c.B = LBAT• .
-
'
• I . ,
'
>
I
'
23- PoZ>c?>(b1e o~c.omes : ~ H H, H.,, TH, TT ~
The.
r I .
n 1..1.f'YI b e.Y o F ouic..ome.s r~ 4-.
p--ro ba..b{ubt
-
Hence, l;he. fo,,,-eo..c.h
o~ i:hese
ou..tc.omes -I -
4
-
Hence th€! .t,-lol-eme.YLt
b.) r n C.O,s,ec ~ .
-

9. ~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
'
~ 0..c coYi.sn1,'on •. Poime
'
YB~ at.x~~~~~)l'3
Sh= ot_")(~')t~~,-
r
1-~ = ~ 'j. ~ ~ 3 ~ 3 ~ -1.
.
•
HCF = p"Yoduc.t of b m.a . .lles t power of e_a.c..h . . common
•
fo...c.lo-Y in the. nu...m be.YS i•e. -t
3
.::: 8 . p~rme.
The-Ye F o-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.
. -

10. c9 x
2
-~ kx. + ll. := o
Comp Q...., in~
'l ua.cJ,ya..i:ic
He"e
~ )ven eq. U:~ion l1'> tth. the. ~ ene-rol fo'Yrf' oF
e.ciu.a.tion, \..Vh.eYe C\.X.t-+ bx.+ c..:= o.
Q_= 8 , b= -a.lk, c..=-k. .
P, n di n3-disc,.·, mi nan l :
D = b
1
-4 QC
--
------(-~k)
1
-4)( B )(k. -==} lf ll
1
-i~"
Si nee 1i-0ots o.'Ye ,ye.oJ. 0.1 .. d e.ciual .
. •. Oiscrimino.n.-l = o
----
-----'----
pLLl D = 0
Yk
1
-?>~k'. =-o
~ 4 "-
1
= 3 ~ k
:'.) "-::. 8
Henc.e. VCl..lJte. of' "-: 9 .

11. ~ b-b) Le..t A=-( 3, -4) o.nd s ~ (\,~)
l I ' ,
•
Ai line. i:,~q me.ni AB
.
h.i sec ie.d , ~ o line .2>e.9f¥\en± LS
V
"
'
e..i the..Y-div, de_d ' ~o.±i.o OF I : eJ O'Y ~ ~ IS tn
.
'
Lv h.en AS IS dlvi de.d '
"'r"O....UO oF I ~ ot , !:.hen ' 1n
co-o-r di no.le$
r
,' (~) + ct_(.-4') -
I 1(1)+a2(3) .
3 ~
../
, .
'
I • ~ :
. -(-+----t}
J
.-·
I
- '
\_ 3 ./
"r.
. .
' Whe.n AB IS ,di. vi de.d • i'n 'YOCUO «. : 1 \::he. c. o o -yd.i no±-e..s
.
/
cl(1) +3 ~(at) +Jt (_-4) ':.-1
r
•
'
3 3 7
' '
'
I -( S -· 01
~ I
l _ -
\__ '3
,
,J
' '
"4
I
' .
!
---

12. ~-:,..
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 ~
"'
~ ~n
ft -~
IF t '-"0 o.ngles oF on.e l-riangle a."l e eoLLol -l:.o b,.uo·
anqles
V V I,,
of a.n othe.-r lh.ta.n g 'e. o/Le.spective,~, the two trian~ !es
V V 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 I ef>.
-
In ~A0B and i::,CoD
LAOS= l COD C ve.,Lc nu~ opposi ~e on.glesJ
\,I V
lSf'O = LDCO ( A l~e.Yna±e. l nte.Yior o.n_g \e.s J .
"
-::) OA0B ,v l>COD LAA c.Yiteyion)
He.nu, oA -
08
'
oc 00

13. ~8. o.) Time token b'-1 Sonic,_ lo dror1¥e.. one oound ~ IS mi n.LLte.s.
T,me to..lle.n b~ R~v, 'CO d7'ive. one. "Tou.n.d -:::..let mi nut.es.
'V
Time ta_ken b~ both to rnee..t 04oln -=-LCM of t B &, I~.
-
V
l,Je. f-ind LCM of 1S o..nd \ol using pyime. 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 -3b
.
lne.-re..foYe time. to~en b)l both to me..e..t
.
a.i CL9cun
I -
slo...Yttnq poi n.t. LC.M 0f &.. '~
-
- \8
CJ
-.-
I -3b N\,nu.½:.es.
'
---

14. •·
~C\. rn l:)ABD Pt
I i:.o.n boc -AB ' ~
I SD \~
I
I {3 -h ~ -
I
X h ~
I • . . -:x. -::: h • -. • ti) ~
I -rs bff( ;oC'-.. -
Q. I
I Nov.:>, in 6ABC.
-<--:(:= ➔D
"!\01')1' _,-
,
I to..n 30~ =-AB
:X..-t3o
~
'
-AB -
-ls :c.-t3o
I
::) X-t 30 -::: ~h (AB=h)
I
+3o= ✓3h
•
h r f---ro m ea . ch)
j . .
.J3
,,
- =) h+.f3 )( 5 o = ..f3 x Jg)(h
---
I
I =-:) ath :: 3o./3
~ h = tc;.{3 rn
---
I
He.nee he.i3hi of lo t..ueY
.
IS 5 rn. IS
~ --
- -
-

15. :
.
'
.3 0. We.. k.now, c.os A -
' bec..A
Also, .bt n
2
A 4-cos
2
A -=--I '
~in~A :::. \-cos2.A
.J 2ec.'A-'
1
beci..o_, ---Cl) / I -r '
"\.2. - -bin A -- -
"
~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 -
'
-l·,; ) - ---. .
.
'/be~A-
( hot'\" eq.H)
We k.now 1 i::"a.n A -
'/cot A-, TheYe.fo-.e, ton A =-✓ Aec...
2
A-, -
.

16. II ,_, . , • ' t _,
~
31. Lt. t the cost of-one bo..t be x... I
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 -cJ O O
-
(/
6 3
'
P u.±t. i.rt Q lhe va.LUL of
' '
~ e..-\: 4 ,n e.q, (I ) b,!) e..
V .., r
6x+ 6,<o,oo -=-3Soo
.
3
6:x.. = 3500-400
X. -3100 , S-So - --
G 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._)
-

17. 3~.-a) u...t.'S t,QLe. !:he. o"'Ti.g·, no..l weed cF i-Yoi. n. ~'. X ! . '
V
0 ,ilSl i no.1 s p eed
63
Time lc::LI'en .t"o t.Yo.Me,f G 3 ~rn 1 .-~i th -
-
::;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
1dinq 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
I -.
J . i . I I
:x:
2
-Y cot x.. -+. .3 x, :-I ~ b . -:::. o ~
I
-.
-
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 r bo the o, i~ ina.l o.ue.oO-R e_
V - -
~o·-e.e..d --ls ½ ~ ~m/~T.
.
I
'
'

18. ~ 3. (_o..) u_t
'Y be. the -Ya.d ius oF c:.i,y-c..le ond AB b~ 4: he. c ho'Yd,
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~+oB
2
=-A B2.
-yl+ yl.::. s 2.
fr.'--
,. ;.;
~ I r ( , lj I
=) ~ '¥"'2 -~ S" ' ' '
-=, r = s
'
'
.f2
,.
,
a
A 'Yeo.. 0~ CLYC.le. ~ 7 'Y
2
::. ~~ v S )( 5 :::.. 3 9 · Cl( c9 cm -i
1 I +
ol a.
-
I
,& e.g mu,t -::.
'
A "'Y t:: a-. of
.
A-reo.. of .be.c¼.o"t'-A--rect oF ti OA 8 n-11 rio-r
..,
9o
•
X 7\,2._ t - '>(5
1 ')(_ s
--
360• l ~ .{J_ J:i
1 -
, .
··,e-3 9 . ~ 8 1-•o1.s: -
4 4
-IL\· plS 3· 51 crn
2 , - --
ot
A"Ye~ of rr,ino, seqment
V
:: 39·~8-3-S1 ::... '3S·~I c..M~
£. e 9 ui '"l"'Y e..J cU ff e.,ren ~ -3S ·-=1l -~-si -
..
-S ~-·14 ·c m2.
I
-
' -
I
..

19. 31..t,
I
CIQ5S-In+e-tvQ.) Mid-VoJue fi1 e_q_ ue.p1,. ~ 1-t·xc
I • )
II -13 12. 3 3b
I:?>-IS- ·~
G
I 84
, s-11- / I, '
9
' rtt LJ
-
I 1 -I 9 18 •, lS tX. 3lf
f9-2.) 2.,0
I F- ~oF
a?l-23 2 2.. 5
I \' 0
- -,
9.b ot3--2S 1.4
I ½
- .
-
_ i~-~~ 4otF 2. H~ -::.1q lf -t2-of
.
l I
' ' . .
.. '
' .J
I
q·,'\l'Cn : rneo.n =-l Q
'
mea.n Ci)
,• J I
we. knot>.?, -z:F,::,c.;
I
~F-,'
=> 1 9 = 7o '-I+~ o F
'
½o+F
~ 19(4o~F) = 1oY+ r:J.. oF
~ ~f ~ I f,
-
~) F
..
8. -
. .
•
,.._

20. ,.../ -
J w I -r, I '7'11 I ,,,_ I / J
I I I -• , I/
-
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 -
I
Cat ) '-f Lf
OL
1
OL:~99
-- :;> = 9 CJ ~'>
. '-t ot
I ta.n LAOL ~ AL -15/~ -
IS
·oL
.f9"t/~ .Jcfoj
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,
OR. u..nglh oF PA--=--rso -
,,; c..m. -
I
" 9· 9Y
I I

21. _...,
"--
"
II , "- / '- '
..
3b-(h Child 'S DaJ.i l.QtSe a.....-e
V
5
' ·' 0
I
·' s , ' °' d ,.
p't 5 ,. . . . . . . to n d~s
1c.o'1n -l coins 3coins. lteo ins sco,ns
V
n c:o(ns
We ho_ve a...i:.. most-, 9 0 ' c.o..n C-Olr\S
' I. e_. , 1+~+2>+4+S-+ .. . . . . -
~ +o n.. te.'YmS ::.190
~ n ( at:>< I + C n-, ') , 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..
V
.
n= 19 ( ")' e.te.ctt.ng n=--ot.o) .. .
w -
5o, nurnbe-Y of dO-t.JS=-19.
!
. , -
'
(ii) 0~ , t-lum be"Y of
•
fn pi5tg':t bo..n k
I s;th
d~, coins on
..,
~
~n -n r~a..+Cn-,)dl -
~
L- -
~) ~15 = ,~ r ~ )( s-+ ( 's-1) )<_ (5" 7
~
(...
'I
c:) S,s -1 s-rat +r Lt 7 ==> s,s--600 - -
-
I
~
....
I
II
5o, theYe 0-re t~o
' c.o,ns on l·S
th
d~.
r
--
'

22. -
~
'
- ~
~
'iii°) Mone.'-1 ~C>.>Jed
' to d~s I(
'
V

~
Sn -n --O(a.+(n-,)dl -
~
-
...
-
=} S, o ::.. \o .,.. ~ )( S-+ ( 1 0 -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· ' lo d ~ s .. :::. .f" ~ 1-~. 1n
- '
'
-
~
' .
'
' .
I
'
I
l
-
I
I I
-

23. I I / ' / / I Y I I I I -·• I I I I I I '-' I
,
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..i oe.d pTobo..bi l ii:~ -::. '3 b -IB
- V
I ':f o 05
'
I
(ii) Totol . num be, oF
•
of-R.~-10 o.nd 12.s· 2.o . coins
== ~ 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 i l>, (c.o,n of R&-= o) -=-c:2..-S
I
'
"' I :J-o
' fleqw.,e.d p-oobo..bi \it~ -\-r ,p (c.oin of f2s. lo) . . -
, ~
V
I I
-I-~8 -
l"f-o
.
-14 2.
j 1-=l-o
..... 'f I .
as
J

24. 'I
I,
I
-
38· 0) ~l PS -':;J ~e ...
~
II
I ,
-
I
(
J -
. '
-~, In ~ PQ.A I l
I
)
t()...(l 4 5° -PS--~ ~~ -- '
I
S..A
:::::(
~
't~,A ~ e
l"
-:,r
V
\oorvi
:: ~ -
.
::f_ I 50 r, •
\.;J..,
' 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
l
'
I -. -
• I
~ :.c. ~ to.o .• ~ ·x. -
13(,-6lrYl- '
'
./B-1
~,om -the f-l 9 ,U "'('e he.iSlht 0(_
1 the.. lowe.Y hi::... ~Q + QR..
V
✓
l .' -=-X..+ISo.= 13h·61 +ISO=-c:<8b· 61 m.
--
I r
I
..
oe, Dis -lo.nc.e btlween i:::o p of t0we.Y o.nd A1 ~'s house..
t• \'
c os. 4 5 ~ -=:: • ~ A -=: (9.A=:X..) r "l Y 6 VP 6-A 1
PA PR-
\.... -
'l-fi
-136·61_:::} PA=-l36·b ~ 9S· 62.m. -
p·A
'I ..fi
I

25. rC5Z1 EC: ) ,=-:0e i:6 tetr+M: il: ifltfW
II "'-' / l 1 / ... ,
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·61~
--
-