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8/12/2019 14. Statistics
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LGO@VMKQLGR
R A J Q O H G X @J O B P^ -E
LGXMALGX@FV
7
VXGX@VX@FV
@OXRJHQFX@JO@o figss @], wa mgva stuh`ah gbjut tma prasaotgt`jo je c`vao hgtg `o tma ejrl je uocrjupah us waii gs crjupah
eraquaofy h`str`but`jos. Sa mgva gisj stuh`ah mjw tj raprasaot tma stgt`st`fgi hgtg `o tma ejrl je vgr`jus crgpms
sufm gs bgr crgpms, m`stjcrgls goh eraquaofy pjiycjos. @o ghh`t`jo, wa mgva stuh`ah tma lagsura je faotrgitaohaof`as sufm gs lago, lah`go goh ljha je uocrjupah hgtg.
@o tm`s fmgptar, wa smgii h`sfuss gbjut lago, lah`go goh ljha je crjupah hgtg. Sa smgii gisj h`sfuss tma fjofapt
je fuluigt`va eraquaofy, fuluigt`va eraquaofy h`str`but`jo goh fuluigt`va eraquaofy furva (jc`va).
LAGO JE QOCRJQ^AH HGXGSa kojw tmgt tma lago je jbsarvgt`jos `s tma sul je tma vgiuas je gii tma jbsarvgt`jos h`v`hah by tma tjtgi oulba
je jbsarvgt`jos `.a., `e x7,x2,x6,, xogra o jbsarvgt`jos, tmao
lago,o
xxxxx o
.....627 jro
x
x
o
77
7
, wmara
o
x77
7haojtas tma sul x7 + x2 x6+ + xo.
H`raft latmjh Vmjrt-fut latmjh jr Gssulah-lago latmjh Vtap-hav`gt`jo latmjh. LAGO JE CRJQ^AH HGXG H`raft latmjh
@e x7,x2,x6,, xogra o jbsarvgt`jos w`tm raspaft`va eraquaof`as e 7,e 2,e 6,..,e otmao lago, )(x hae`oah by
o
oo
eeee
xexexexex
....
.....
627
662277 jr
o
o
e
xe
x
77
7
77
77
, wmara
o
oeeeee77
6277 ..... .
Xj e`oh lago je crjupah Hgtg
Xma ejiijw`oc staps smjuih ba ejiijwah `o e`oh`oc tma gr`tmlat`f lago je crjupah hgtg by h`raft latmjh.
VXA^-74 E`oh tma figss lgrk (x`) je agfm figss us`oc, 2
i`li`l `tQppar`tijwar
x`
VXA^-24 Fgifuigta ex`ejr agfm `
VXA^-64 Qsa tma ejrluig 4 lago,
o
o
e
xe
x
77
7
77
77
,
VMJRXFQXLAXMJHJRGVVQLAHLAGOLAXMJH@o tm`s fgsa, tj fgifuigta tma lago, wa ejiijw tma ejiijw`oc staps 4
VXA^-74 E`oh tma figss lgrk (x`) je agfm figss us`oc
2
i`li`l `tQppar`tijwarx
`
VXA^-24 Fmjjsa g su`tgbia vgiua je x``o tma l`hhia gs tma gssulah lago goh haojta `t by g.
VXA^-64 E`oh h`< x` g ejr agfm `
VXA^-84 E`oh e h`ejr agfm `
VXA^-14 E`oh o < 7e
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LGO@VMKQLGR
R A J Q O H G X @J O B P^ -E
LGXMALGX@FV
2
VXA^-54 Fgifuigta tma lago, )(x by us`oc tma ejrluigO
hegx
`` .
VXA^-HAU@GX@JOLAXMJHVjlat`las, tma vgiuas je x goh e gra sj igrca tmgt tma fgifuigt`jo je lago by gssulah lago latmjh bafjlas qu`ta
`ofjovao`aot. @o tm`s fgsa, wa ejiijw tma ejiijw`oc staps4
VXA^-74 E`oh tma figss lgrk (x`) je agfm figss us`oc,2
i`li`l `tQppar`tijwarx`
VXA^-24 Fmjjsa g su`tgbia vgiua je x``o tma l`hhia gs tma gssulah lago goh haojta `t by g.
VXA^-64 E`oh m < (uppar i`l`t ijwar i`l`t) ejr agfm figss.
VXA^-84 E`ohm
gxu ``
ejr agfm figss.
VXA^-14 E`oh eu`ejr agfm `.
VXA^-54 Fgifuigta, tma lago by us`oc tma ejrluig
O
uegx
``m, wmara `eO
Ax.7 E`oh tma lago je tma ejiijw`oc hgtg 4
Vji. Sa lgy prapgra tma tgbia gs c`vao baijw 4
Lago, 8.278>
=15
7
7
o
`
`
o
`
``
e
xe
x
Ax.2 Xma ejiijw`oc h`str`but`jo smjws tma hg`iy pjfkat giijwgofa je fm`ihrao je g ijfgi`ty. Xma lago pjfkat giijwgofa`s Rs. 7=. E`oh tma l`ss`oc eraquaofy e.
Figss @otarvgi >-= =-75 75-28 28-62 62-8>
Eraquaofy 5 3 7> = 0
Figss @otarvgi Eraquaofy (e) Figss lgrk (x`) ex`
>-=
=-75
75-28
28-6262-8>
5
3
7>
=0
8
72
2>
2=65
28
=8
2>>
228628
8>`e =15`xe
Hg`iy pjfkat giijwgofa (`o Rs.) 77-76 76-71 71-73 73-70 70-27 27-26 26-21
Oulbar je fm`ihrao 3 5 0 76 e 1 8
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LGO@VMKQLGR
R A J Q O H G X @J O B P^ -E
LGXMALGX@FV
6
Vji. Sa lgy prapgra tma tgbia gs c`vao baijw 4
Hg`iy pjfkat
giijwgofa
Oulbar je
Fm`ihrao (e)
Figss lgrk (x`) ex`
77-76
76-71
71-7373-70
70-27
27-26
26-21
3
5
076
e
1
8
72
78
757=
2>
22
28
=8
=8
788268
2>e
77>
05
ee 88 exe `` 2>312
Lago,e
e
e
xe
xo
`
`
o
`
``
88
2>312
7
7
C`vao, lago < 7=
2>2>3127=30288
2>3127=
eee
e
e
Ax.6 E`oh tma l`ss`oc eraquaof`as e7 goh e2 o tma tgbia c`vao baijw, t `s ba`oc c`vao tmgt tma lago je tma c`vao
eraquaofy h`str`but`jo s 1>.
Vji. Sa lgy prapgra tma tgbia gs c`vao baijw 4
Figss Oulbar je (e) Figss lgrk (x`) ex`
>-2>
2>-8>
8>-5>
5>-=>
=>-7>>
73
e7
62
e2
70
7>
6>
1>
3>
0>
73>
6>e7
75>>
3>e2
737>
275= eee 27 3>6>68=> eexe ``
Lago,27
277
5=
3>6>68=>
ee
ee
e
xe
x`
o
`
``
Figss >-2> 2>-8> 8>-5> 5>-=> =>-7>> Xjtgi
Eraquaofy 73 e7 62 e2 70 72>
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LGO@VMKQLGR
R A J Q O H G X @J O B P^ -E
LGXMALGX@FV
8
C`vao, lago < 1>
2727
27
27 3>6>68=>1>1>68>>5=
3>6>68=>1> eeee
ee
ee
2>e7 2>e2< => e7 e2< 8 (`)
Goh
275= eee` 72> < 5= + e7+e2 \72>[ 7 e e7+ e2< 12 (``)
Ghh`oc (7) goh (2), wa cat 2e7< 15 e7< 2= e2< 28Maofa, ejiijw`oc l`ss`oc eraquaof`as e7 goh e2 gra 2= goh 28 raspaft`vaiy.
Ax.8 Xma ejiijw`oc tgbia c`vas tma lgrks sfjrah by 7>> stuhaots o g figss tast 4
Vji. Sa lgy prapgra tma tgbia w`tm gssulah lago, g < 61 gs c`vao baijw 4
Lrks Oj.je stuhaots (e) Figss lgrk (x`) h`< x` g < x` 61 eh`
>-7>
7>-2>
2>-6>
6>-8>
8>-1>
1>-5>
72
7=
23
2>
73
5
1
71
21
6> < g
81
11
6>
2>
7>
>
7>
2>
65>
65>
23>
>
73>
72>
O < 7>> 3>>``he
Lago, 2=3617>>
)3>>(61
O
hegx
``
Ax.1 Xm`rty wjlao wara axgl`oah `o g mjsp`tgi by g hjftjr goh tma oulbar je magrt bagts par l`outa, wara rafjrhah
goh sullgr`zah gs ejiijws. E`oh tma lago magrt bagts par l`outa ejr tmasa wjlao, by us`oc gssulah.
Lgrk >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5>
Oj. je Vtuhaots 72 2= 23 2> 73 5
Oj. je magrt bagts
par l`outa 51-5= 5=-37 37-38 38-33 33-=> =>-=6 =6-=5
Eraquaofy 2 8 6 = 3 8 2
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LGO@VMKQLGR
R A J Q O H G X @J O B P^ -E
LGXMALGX@FV
1
Vji. Sa lgy prapgra tma tgbia w`tm gssulah lago, g < 61 gs c`vao baijw 4
Lago, 0.311
2
1.316>
72
1.31
O
he
gx ``
Ax.5 E`oh tma lago je tma ejiijw`oc h`str`but`jo by stap-hav`gt`jo latmjh 4
Vji. Sa lgy prapgra tma tgbia w`tm gssulah lago g < 72> gs c`vao baijw 4
Lago, 2.7721
157
1
602>
7>>
2>)60(72>
m
O
uegx
``
Oj. je magrt bagts
par l`outa
Oj.je wjlao (e) Figss lgrk (x`) h`< x` g
< x` 31.1
eh`
51-5=
5=-37
37-38
38-33
33-=>
=>-=6
=6-=5
2
8
6
=
3
8
2
55.1
50.1
32.1
31.1 < g
3=.1
=7.1
=8.1
0
5
6
>
6
5
0
7=
28
0
27
28
7=
O < 6> 72``he
Figss 1>-3> 3>-0> 0>-77> 77>-76> 76>-71> 71>-73>
Eraquaofy 7= 72 76 23 = 22
Figss Eraquaofy (e) Figss lgrk (x`) 2>
72>
```
x
m
gxu
eu`1>-3>
3>-0>
0>-77>
77>-76>
76>-71>
71>-73>
7=
72
76
23
=
22
5>
=>
7>>
72> < g
78>
75>
6
2
7
>
7
2
18
28
76
>
=
88
O < 7>> 60``ue
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LGO@VMKQLGR
R A J Q O H G X @J O B P^ -E
LGXMALGX@FV
5
Ax.3 E`oh tma lago lgrks erjl tma ejiijw`oc hgtg 4
Vji. Sa lgy prapgra tma tgbia gs c`vao baijw 4
Lago, 87.8==1
878>
O
xex
``
Ax.= E`oh tma lago lgrks je stuhaots erjl tma ghdj`o`oc eraquaofy h`str`but`jo tgbia.
Lgrks Oj. je Vtuhaots
Gbjva > =>
Gbjva 7> 33
Gbjva 2> 32
Gbjva 6> 51
Gbjva 8> 11
Gbjva 1> 86
Gbjva 5> 26
Gbjva 3> 75
Gbjva => 7>
Gbjva 0> =
Gbjva 7>> >
Lgrks
Baijw
7>
Baijw
2>
Baijw
6>
Baijw
8>
Baijw
1>
Baijw
5>
Baijw
3>
Baijw
=>
Baijw
0>
Ba
7
Oj. je Vtuhaots 1 0 73 20 81 5> 3> 3= =6 z
Lgrks Oj. je stuhaots Figss @otarvgi e Figss lgrk
(x`)
ex`
Baijw 7>
Baijw 2>
Baijw 6>
Baijw 8>
Baijw 1>
Baijw 5>
Baijw 3>
Baijw =>
Baijw 0>
Baijw 7>>
1
0
73
20
81
5>
3>
3=
=6
=1
>-7>
7>-2>
2>-6>
6>-8>
8>-1>
1>-5>
5>-3>
3>-=>
=>-0>
0>-7>>
1
8
0
72
75
71
7>
=
1
2
1
71
21
61
81
11
51
31
=1
01
21
5>
221
82>
32>
=21
51>
5>>
821
70>
O < =1 878>`xe
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LGO@VMKQLGR
R A J Q O H G X @J O B P^ -E
LGXMALGX@FV
3
Vji. Sa lgy prapgra tma tgbia gs c`vao baijw 4
Lago, 7.17721.17=>
8>0>
O
xex
``(gpprjx)
Ax.0 E`oh tma gr`tmlat`f lago je tma ejiijw`oc eraquaofy h`str`but`jo.
Vji. Xma c`vao sar`as s `o `ofius`va ejrl. Sa lgy prapgra tma tgbia `o axfius`va ejrl w tm gssulah lago g < 82 gs
c`vao baijw 4
Lgrks Oj. je stuhaots Figss @otarvgi e Figss lgrk (x`) ex`
Gbjva >
Gbjva 7>
Gbjva 2>Gbjva 6>
Gbjva 8>
Gbjva 1>
Gbjva 5>
Gbjva 3>
Gbjva =>
Gbjva 0>
Gbjva 7>>
=>
33
3251
11
86
26
75
7>
=
>
>-7>
7>-2>
2>-6>6>-8>
8>-1>
1>-5>
5>-3>
3>-=>
=>-0>
0>-7>>
7>>-77>
6
1
37>
72
2>
3
5
2
=
>
1
71
2161
81
11
51
31
=1
01
7>1
71
31
73161>
18>
77>>
811
81>
73>
35>
>
O < =>
8>0>``xe
Figss 21-20 6>-28 61-60 8>-88 81-80 1>-18 11-10
Eraquaofy 78 22 75 5 1 6 8
Figss Eraquaofy (e) Figss lgrk (x`) h`< x` g < x` 31.1 eu`
28.1-20.1
20.1-68.1
68.1-60.1
60.1-88.1
88.1-80.1
80.1-18.1
18.1-10.1
78
22
75
5
1
6
8
23
62
63
82 < g
83
12
13
71
7>
1
>
1
7>
71
27>
22>
=>
>
21
6>
5>
O < 3> 601``he
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R A J Q O H G X @J O B P^ -E
LGXMALGX@FV
=
Lago, 65.653>
2181
3>
601208>
3>
)601(82
O
hegx `
`(gpprjx)
LAH@GO JE G CRJQ^AH HGXGLAH@GO4 @t `s g lagsura je faotrgi taohaofy wm`fm c`vas tma vgiua je tma l`hhia ljst jbsarvgt`jo `o tma hgtg. @o
g crjupah hgtg, `t `s ojt pjss`bia tj e`oh tma l`hhia jbsarvgt`jo by ijjk`oc gt tma fuluigt`va eraquaof`as gs tmal`hhia jbsarvgt`jo w`ii ba sjla vgiua `o g figss `otarvgi. @t `s, tmaraejra, oafassgry tj e`oh tma vgiua `os`ha g figsstmgt h`v`has tma wmjia h`str`but`jo otj twj mgivas.
LAH@GOFIGVV4 Xma figss wmjsa fuluigt`va eraquaofy `s cragtar tmgo2
O`s fgiiah tma lah`go figss.
Xj fgifuigta tma lah`go je g crjupah hgtg, wa ejiijw tma ejiijw`oc staps 4VXA^-74 ^rapgra tma fuluigt`va eraquaofy tgbia fjrraspjoh`oc tj tma c`vao eraquaofy h`str`but`jo goh jbtg`o
`eO .
VXA^-24 E`oh2
O
VXA^-64 Ijjk gt tma fuluigt`va eraquaofy dust cragtar tmgo
2
Ogoh e`oh tma fjrraspjoh`oc figss (Lah`go figss)
VXA^-84 Qsa tma ejrluig Lah`go, me
FO
L
2
Smara < Ijwar i`l`t je lah`go figss.E < Eraquaofy je tma lah`go figss.F < Fuluigt`va eraquaofy je tma figss prafah`oc tma lah`go figss.m < V`za je tma lah`go figss.
`eO Ax.7>. E`oh tma lah`go je tma ejiijw`oc eraquaofy h`str`but`jo 4
Vji. Gt e`rst wa prapgra g fuluigt`va eraquaofy h`str`but`jo tgbia gs c`vao baijw 4
Mara, O < 7>>
2
O< 1>
Xma fuluigt`va eraquaofy dust cragtar tmgo 1> `s 58 goh tma fjrraspjoh`oc figss `s 2>-6>.
Vj, tma lah`go figss `s 2>-6>.
< 2>, O < 7>>, F < 2=, e < 65 goh m < 7>
Lgrks >-7> 7>-2> 2>-6> 6>-8> 8>-1> XjtgiOj. je Vtuhaots = 2> 65 28 72 7>>
Lgrks Oulbar je stuhaots (e) Fuluigt`va eraquaofy
>-7>
7>-2>
2>-6>
6>-8>
8>-1>
=
2>
65
28
72
=
2=
58
==
7>>
O < 7>>
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LGO@VMKQLGR
R A J Q O H G X @J O B P^ -E
LGXMALGX@FV
0
Xmaraejra, lah`go me
FO
2
7.650
261
0
117=>
0
11
2>65
7>22
2>7>65
2=1>
2>
Ax.77 G i`ea `osurgofa gcaot ejuoh tma ejiijw`oc hgtg ejr h`str`but jo je gcas je 7>> pji`fy mjihars. Fgifuigta tma lah`g
gca, `e pji`f`as gra c`vao joiy tj parsjos mgv`oc gca 7= yagrs jowgrhs but iass tmgo 5> yagrs.
Gca
(`o yagrs)
Baijw
2>
Baijw
21
Baijw
6>
Baijw
61
Baijw
8>
Baijw
81
Baijw
1>
Baijw
11
Baijw
5>
Oj. je pji`fy
mjihars
2 5 28 81 3= =0 02 0= 7>>
Vji. Erjl tma c`vao tgbia wa fgo e`oh tma eraquaofy goh fuluigt`va eraquaofy gs c`vao baijw 4
Mara, O < 7>>
2
O< 1>
Xma fuluigt`va eraquaofy dust cragtar tmgo 1> `s 3= goh tma fjrraspjoh`oc figss `s 61-8>.
Vj, tma lah`go figss `s 51-8>.
< 2>, O < 7>>, F < 81, e < 66 goh m < 1
Xmaraejra, lah`go me
FO
2
35.6166
77=>
66
217711
66
11611
66
811>61
Maofa, tma lah`go gca `s 61.35 yagrs.
Gca (`o yagrs) Oulbar je stuhaots (e) Fuluigt`va eraquaofy
71-2>
2>-21
21-6>
6>-61
61-8>
8>-81
81-1>
1>-11
11-5>
2
8
7=
27
66
77
6
5
2
25
28
81
3=
=0
02
0=
7>>
O < 7>>
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LGO@VMKQLGR
R A J Q O H G X @J O B P^ -E
LGXMALGX@FV
7>
Ax.72 Xma iaoctm je 8> iagvas je g pigot gra lagsurah fjrraft tj tma oagrast l`ii`latar, goh tma hgtg jbtg`oah s
raprasaotah `o tma ejiijw`oc tgbia. E`oh tma lah`go iaoctm je tma iagvas.
Iaoctm
(`o ll) 77=-725 723-761 765-788 781-716 718-752 756-737 732-7=>
Oj. je iagvas 6 1 0 72 1 8 2
Vji. Xma c`vao sar`as `s `o `ofius`va ejrl. Sa lgy prapgra tma tgbia `o axfius`va ejrl goh prapgra tma fuluigt`va
eraquaofy tgbia gs c`vao baijw 4
Mara, O < 8>
2
O< 2>
Xma fuluigt`va eraquaofy dust cragtar tmgo 2> `s 20 goh tma fjrraspjoh`oc figss `s 788.1-716.1
Vj, tma lah`go figss `s 788.1-716.1
< 788.1, O < 8>, F < 73, e < 72 goh m < 0
Xmaraejra, lah`gome
FO
2
31.78521.21.78872
061.7880
72
)732>(1.788
Maofa, lah`go iaoctm je iagvas `s 785.31 ll.
Ax.76 Fgifuigta tma l`ss`oc eraquaofy g erjl tma ejiijw`oc h`str`but`jo, t `s ba`oc c`vao tmgt tma lah`go je tma
h`str`but`jo s 28.
Vji. Gt e`rst wa prapgra g fuluigt`va eraquaofy h`str`but`jo tgbia gs c`vao baijw 4
Gca (`o yagrs) >-7> 7>-2> 2>-6> 6>-8> 8>-1> Xjtgi
Oj. je parsjos (e) 1 21 g 7= 3 11+g
Fuluigt`va eraquaofy 1 6> 6>+g 8=+g 11+g
Iaoctm (`o ll) Oulbar je iagvas (e) Fuluigt`va eraquaofy
773.1-725.1
725.1-761.1
761.1-788.1
788.1-716.1
716.1-752.1
752.1-737.1737.1-7=>.1
6
1
0
72
1
82
6
=
73
20
68
6=8>
O < 8>
Gca (`o ll) >-7> 7>-2> 2>-6> 6>-8> 8>-1>
Oj. je parsjos 1 21 g 7= 3
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LGO@VMKQLGR
R A J Q O H G X @J O B P^ -E
LGXMALGX@FV
77
V`ofa tma lah`go `s 28, tmaraejra, tma lah`go figss w`ii ba 2>-6>.
Maofa, < 2>, O < 11+g, F < 6>, e < g goh m < 7>
Xmaraejra, lah`go me
FO
2
7>6>
2
11
2>28
g
g
7>2
)1(2>28
g
g
12
)1(8
g
g
8g < 1g 21 g < 21
Maofa, tma vgiua je l`ss`oc eraquaofy g `s 21.
Ax.78 Xma lah`go je tma ejiijw`oc hgtg s 121. E`oh tma vgiuas je x goh y, `e tma tjtgi eraquaofy s 7>>.
Figss @otarvgi Eraquaofy (e)
>-7>> 27>>-2>> 1
2>>-6>> x
6>>-8>> 72
8>>-1>> 73
1>>-5>> 2>
5>>-3>> y
3>>-=>> 0
=>>-0>> 3
0>>-7>>> 8
O < 7>>
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R A J Q O H G X @J O B P^ -E
LGXMALGX@FV
72
Vji. Gt e`rst wa prapgra g fuluigt`va eraquaofy h`str`but`jo tgbia gs c`vao baijw 4
Sa mgva O < 7>>
287>>35 yxyx (`)V`ofa tma lah`go `s 121, sj, tma lah`go figss `s 1>> 5>>
< 1>>, O < 7>>, F < 65 + x, e < 2> goh m < 7>>
Xmaraejra, lah`go me
FO
2
1)78(217>>2>
651>1>>121
x
x
1 < 78 x x < 0
Gisj, putt`oc x < 0 `o (7), wa cat 0 + y < 28 y < 71Maofa, tma vgiuas je x goh y gra 0 goh 71 raspaft`vaiy.
LJHA JE G CRJQ^AH HGXGLJHA 4 Ljha `s tmgt vgiua gljoc tma jbsarvgt`jos wm`fm jffurs ljst jetao `.a., tma vgiua je tma jbsarvgt`jo
mgv`oc tma lgx`lul eraquaofy.
@o g crjupah eraquaofy h`str`but`jo, `t `s ojt pjss`bia tj hatarl`oa tma ljha by ijjk`oc gt tma eraquaofy.
LJHGIFIGVV 4 Xma figss je g eraquaofy h`str`but`jo mgv`oc lgx`lul eraquaofy `s fgiiah ljhgi figss je g
eraquaofy h`str`but`jo .
Xma ljha `s g vgiua `os`ha tma ljhgi figss goh `s fgifuigtah by us`oc tma ejrluig.
Ljha < m
eee
ee
2>7
>7
2
Smara < Ijwar i`l`t je tma ljhgi figss.m < V`za je figss `otarvgi.e7< Eraquaofy je ljhgi figss.e>< Eraquaofy je tma figss prafah`oc tma ljhgi figsse2< Eraquaofy je tma figss suffaah`oc tma ljhgi figss
Figss @otarvgi eraquaofy (e) Fuluigt`va eraquaofy
>-7>>
7>>-2>>
2>>-6>>
6>>-8>>8>>-1>>
1>>-5>>
5>>-3>>
3>>-=>>
=>>-0>>
0>>-7>>>
2
1
x
7273
2>
y
0
3
8
2
3
3+x
70+x65+x
15+x
15+x+y
51+x+y
32+x+y
35+x+y
O < 7>>
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R A J Q O H G X @J O B P^ -E
LGXMALGX@FV
76
Ax71 Xma ejiijw`oc hgtg c`vas tma `oejrlgt`jo jo tma jbsarvah i`eat`las (`o mjurs) je 221 aiaftr`fgi fjlpjoaots 4
Hatarl`oa tma ljhgi i`eat`las je tma fjlpjoaots.
Vji. Mara tma figss 5>-=> mgs lgx`lul eraquaofy, sj `t `s tma ljhgi figss.
12,57,2>,5> >7 eem goh 6=2e
Xmaraejra, ljha < meee
ee
2>7
>7
2
521.51521.15>2>2>
05>2>
6=12572
12575>
Maofa, tma ljhgi i`eat`las je tma fjlpjoaots `s 51.521 mjurs.
Ax.75 C`vao baijw s tma eraquaofy h`str`but`jo je tma ma`cmts je pigyars o g sfmjji.
Ma`cmts (`o fl) 75>-752 765-751 755-75= 750-737 732-738
Oj. je stuhaots 71 77= 782 723 7=
E`oh tma gvargca ma`cmt je lgx`lul oulbar je stuhaots.
Vji. Xma c`vao sar`as `s `o `ofius`va ejrl. Sa prapgra tma tgbia `o axfuis`va ejrl, gs c`vao baijw 4
Ma`cmts (`o fl) 710.1-752.1 752.1-751.1 751.1-75=.1 75=.1-737.1 737.1-738.1
Oj. je stuhaots 71 77= 782 723 7=
Sa mgva tj e`oh tma ljha je tma hgtg.
Mara, tma figss 751.1-75=.1 mgs lgx`lul eraquaofy, sj `t `s tma ljhgi figss.
Ax.73 Xma ljha je tma ejiijw`oc sar`as s 65. E`oh tma l`ss`oc eraquaofy e `o `t.
Figss >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5> 5>-37
Eraquaofy = 7> e 75 72 5 3
Vji. V`ofa tma ljha `s 65, sj tma ljhgi figss w`ii ba 6>-8>
eeem >7 ,75,7>,6> goh 722 e
Xmaraejra, ljha < meee
ee
2>7
>7
2
7>)2>(
)75(57>
72752
576>55
e
e
e
e
72> 5e < 75> 7>e 8e < 8> e < 7>
Maofa, tma vgiua je tma l`ss`oc eraquaofy e `s 7>.
I`eat`las (`o mjurs) >-2> 2>-8> 8>-5> 5>-=> =>-7>> 7>>-72>
Eraquaofy 7> 61 12 57 6= 20
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R A J Q O H G X @J O B P^ -E
LGXMALGX@FV
78
CRG^M@FGI. RA^RAVAOXGX@JO JE FQLQIGX@UA ERAWQAOFP H@VXR@BQX@JO
FQLQIGX@UAERAWQAOFP^JIPCJOFQRUA(JC@UA)Fuluigt`va eraquaofy `s je twj typas goh fjrraspjoh`oc tj tmasa, tma jc`va `s gisj je twj typas.
IAVV XMGO VAR@AV LJRA XMGO VAR@AV
IAVV XMGO VAR@AVXj fjostruft g fuluigt`va eraquaofy pjiycjo goh go jc`va, wa ejiijw tmasa staps 4
VXA^-7 4 Lgrk tma uppar figss i`l`t gijoc x-gx`s goh tma fjrraspjoh`oc fuluigt`va eraquaof`as gijoc y-
gx`s.
VXA^-2 4 ^ijt tmasa pj`ots fuffass`vaiy by i`oa saclaots. Sa cat g pjiycjo, fgiiah fuluigt`va eraquaofy
pjiycjo.
VXA^-6 4 ^ijt tmasa pj`ots fuffass`vaiy by sljjtm furvas, wa cat g furva fgiiah fuluigt`va eraquaofy
jr go jc`va.
G^^I@FGX@JO JE GO JC@UA
Jc`va fgo ba usah tj e`oh tma lah`go je g eraquaofy h`str`but`jo. Xj e`oh tma lah`go, wa ejiijw tmasa staps.
LAXMJH@
VXA^-7 4 Hrgw goyjoa je tma twj typas je eraquaof`as furvas jo tma crgpm pgpar.
VXA^-2 4 Fjlputa )(2
`eOO
goh lgrk tma fjrraspjoh`oc pj`ots jo tma y-gx`s.
VXA^-6 4 Hrgw g i`oa pgrgiiai tj x-gx`s erjl tma pj`ot lgrkah `o stap 2, futt`oc tma fuluigt`va eraquaofy
furva gt g pj`ot ^.
LAXMJH@@
VXA^-7 4 Hrgw iass tmgo typa goh ljra tmgo typa fuluigt`va eraquaofy furvas jo tma crgpm pgpar.
VXA^-2 4 Lgrk tma pj`ot je `otarsaft`oc (^) je tma twj furvas hrgw2o `o stap 7.
VXA^-6 4 Hrgw parpaoh`fuigr ^L erjl ^ jo tma x-gx`s. Xma x-fjjrh`ogta je pj`ot L c`vas tma lah`go .
Ax.7= Xma ejiijw`oc h`str`but jo c`vas tma hg`iy ofjla je 1> wjrkars je g egftjry.
Fjovart tma h`str`but`jo gbjva tj g iass tmgo typa fuluigt`va eraquaofy h`str`but`jo goh hrgw `ts jc`va.
Hg`iy `ofjla (`o Rs.) 7>>-72> 72>-78> 78>-75> 75>-7=> 7=>-2>>
Oj. je wjrkars 72 78 = 5 7>
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R A J Q O H G X @J O B P^ -E
LGXMALGX@FV
71
Vji. Erjl tma c`vao tgbia, wa prapgra g iass tmgo typa fuluigt`va eraquaofy h`str`but`jo tgbia, gs c`vao baijw 4
Dj`o tmasa pj`ots by g eraamgoh
furva tj cat go jc`va je iass tmgo typa.
Ax.70 Xma ejiijw`oc tgbia c`vas prjhuft`jo y`aih par maftgra je wmagt je 7>> egrls je g v`iigca.
^rjhuft`jo y`aih
(`o kc/mg) 1>-11 11-5> 5>-51 51-3> 3>-31 31-=>
Oj. je egrls 2 = 72 28 6= 75
Fmgoca tma h`str`but`jo tj ljra tmgo typa h`str`but`jo goh hrgw `ts jc`va.
Vji. Erjl tma c`vao tgbia, wa lgy prapgra ljra tmgo typa fuluigt`va eraquaofy h`str`but`jo tgbia, gs c`vao baijw 4
^rjhuft`jo ljra tmgo (`o kc/mg) 1> 11 5> 51 3> 31
Fuluigt`va eraquaofy 7>> 0= 0> 3= 18 75
Ojw, pijt tma pj`ots (1>, 7>>), (11,0=), (5>,0>), (51,3=), (3>,18) goh (31,75)
Dj`o tmasa pj`ots by g eraamgoh furva tj cat go jc`va je ljra tmgo typa.
@ofjla iass tmgo (`o Rs) 72> 78> 75> 7=> 2>>
Fuluigt`va eraquaofy 72 25 68 8> 1>
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75
Ax.2> Xma goougi prje ts agroah by 6> smjps je g smjpp`oc fjlpiax `o g ijfgi`ty c`vas r`sa tj tma ejiijw`oc h`str`but`jo
^rje`t (`o igkms Rs.) Oj. je smjps (eraquaofy)
Ljra tmgo jr aqugi tj 1
Ljra tmgo jr aqugi tj 7>
Ljra tmgo jr aqugi tj 71
Ljra tmgo jr aqugi tj 2>Ljra tmgo jr aqugi tj 21
Ljra tmgo jr aqugi tj 6>
Ljra tmgo jr aqugi tj 61
6>
2=
75
787>
3
6
Hrgw bjtm jc`vas ejr tma hgtg gbjva. Maofa, jbtg`o tma lah`go prje`t.
Vji. Sa mgva g ljra tmgo typa fuluigt`va eraquaofy h`str`but`jo tgbia. Sa lgy gisj prapgra g iass tmgo typa
fuluigt`va eraquaofy h`str`but`jo tgbia erjl tma c`vao hgtg, gs c`vao baijw 4
Ljra tmgo typa Iass tmgo typa
Ojw, pijt tma pj`ots G(1,6>), B(7>,2=), F(71,75), H(2>,78), A(21,7>), E(6>,3) goh C(61,6) ejr tma ljra tmgo typa
fuluigt`va eraquaofy goh tma pj`ots ^(7>,2), W(71,78), R(2>,75), V(21,2>), X(6>,26), Q(61,23) goh U(8>,6>) ejr
tma iass tmao typa fuluigt`va eraquaofy tgbia.
Dj`o tmasa pj`ots by g eraamgoh tj cat jc`vas ejr ljra tmgo typa goh iass tmgo typa.
Xma tjw jc`vas `otarsaft agfm jtmar gt pj`ot (73.1, 71).
Maofa, tma lah`go prje`t `s Rs. 73.1 igkms.
^rje`t ljra tmgo
(Rs. `o igkms)
Oj. je smjps
1 6>
7> 2=
71 75
2> 78
21 7>
6> 3
61 6
^rje`t iass tmgo
(Rs. `o igkms)
Oj. je smjps
7> 2
71 78
2> 77
21 2>
6> 26
61 23
8> 6>
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R A J Q O H G X @J O B P^ -E
LGXMALGX@FV
73
Ax.27 Xma ejiijw`oc hgtg c`vas tma oejrlgt`jo jo lgrks je 3> stuhaots `o g par`jh`fgi tast 4
Lgrks Iass tmgo
7>
Iass tmgo
2>
Iass tmgo
6>
Iass tmgo
8>
Iass tmgo
1>
Oj. je stuhaots 6 77 2= 8= 3>
Hrgw g fuluigt`va eraquaofy furva ejr tma gbjva hgtg goh e`oh tma lah`go.
Vji. Sa mgva g iass tmgo fuluigt`va eraquaofy tgbia. Sa lgrk tma uppar figss i`l`ts gijoc tma x-gx`s goh tma
fjrraspjoh`oc fuluigt`va eraquaofy (oj. je stuhaots) gijoc tma y-gx`s. Ojw, pijt tma pj`ots (7>,6), (2>,77),
(6>,2=), (8>,8=) goh (1>,3>). Dj`o tmasa pj`ots by g eraamgoh furva tj cat go jc`va je iass tmgo typa.
Mara, O < 3>
612
Xgka g pj`ot G(>,61) jo tma y-gx`s goh hrgw G^x-gx`s, laat`oc tma furva gt ^.
Hrgw ^L x-gx`s, `otarsaft`oc tma x-gx`s, gt L.
Xmao, JL < 66.
Maofa, tma lah`go lgrks `s 66.
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LGO@VMKQLGR
R A J Q O H G X @J O B P^ -E
LGXMALGX@FV
7=
A]ARF@VA 7 (EJR VFMJJI/BJGRH A]GLV)
JBDAFX@UA XP^A WQAVX@JOV
FMJJVAXMAFJRRAFXJOA
7. Sm`fm je tma ejiijw`oc `s g lagsura je faotrgi taohaofy :
(G) Eraquaofy (B) Fuluigt`va eraquaofy
(F) Lago (H) Figss i`l`t
2. Figss lgrk je g figss `s jbtg`oah by us`oc
(G) Figss lgrk (B)2
7[uppar i`l`t ijwar i`l`t\
(F)2
7[uppar i`l`t + ijwar i`l`t\ (H)
2
7[uppar i`l`t + ijwar i`l`t\ 7
6. Xma vgiua je
o
`
`x
7
`s
(G)2
x (B) 2 x (F) o x (H)
o
x
8. Xma lago je tma ejiijw`oc hgtg 72, 22, 62,o2`s
(G)5
)72)(7( oo (B)
5
)72)(7( ooo (F)
5
)72)(7( ooo (H)
5
)72)(7( ooo
1. Xma lago je ejiijw`oc h`str`but`jo s
(G) 7=.1> (B) 7=.1> (F) 7=.71 (H) 7=.215. Xma lago je ejiijw`oc hgtg `s 7=.31 tmao tma vgiua je p `s
(G) 27 (B) 2>.5 (F) 2> (H) 22
3. Xj e`oh lago, wa usa tma ejrluig.
(G)
o
`
`xe7
(B)
o
`
`xeO7
(F)
o
`
`xeO 7
7 (H)
o
`
``
O
xe
7
=. Sm`fm je tma ejiijw`oc fgo ojt ba hatarl`oah crgpm`fgiiy
(G) Lago (B) Lah`go (F) Ljha (H) Vtgohgrh hav`gt`jo0. @e tma lah`go je tma ejiijw`oc hgtg `s 8> tmao tma vgiua je p `s
(G) 3 (B) = (F) 0 (H) 3.5
x` 7> 72 71 21
e 2 6 3 =
x` 7> 71 p 21 6>
e 1 7> 3 = 2
Figss >- 7> 7>-6> 6>-5> 5>-=> =>-0>
Eraquaofy 1 71 6> p 2
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R A J Q O H G X @J O B P^ -E
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70
7>. Sm`fm je tma ejiijw`oc s trua:
(G) Ljha < 2lah`go Lago (B) Ljha < 6lah`go + 2Lago
(F) Ljha < 6lah`go 2Lago (H) Ojoa je tmasa
77. Ljha `s
(G) Ljst eraquaot vgiua (B) Iagst eraquaot vgiua
(F) L`hhia ljst vgiua (H) Ojoa je tmasa
72. Sm`fm je tma ejiijw`oc s trua
(G) Ljha < 2lah`go + Lago (B) Lah`go < Ljha +2
6[Lago Lah`go\
(F) Lago < Ljha +2
6[Lah`go Ljha\ (H) Lah`go < Ljha +
2
6[Lago +Lah`go\
76. @o tma ejrluig ejr ljha je g crjupah hgtg, ljha < meee
ee
2>7
>7
2 , wmara sylbjis mgva tma`r usugi
lago`oc e>raprasaots 4
(G) Eraquaofy je ljhgi figss
(B) Eraquaofy je lah`go figss
(F) Eraquaofy je tma figss prafah`oc tma ljhgi figss
(H) Eraquaofy je figss suffaah`oc tma ljhgi figss
78. Lah`go je g c`vao eraquaofy h`str`but`jo s ejuoh w`tm tma maip je g (G) Bgr crgpm (B) Jc`va (F) M`stjcrgl (H) Ojoa je tmasa
71. Xma lagsura je faotrgi taohaofy wm`fm s c`vao by tma x-fjjrh`ogta je tma pj`ot je `otarsaft`jo je tma ljra tmgo
jc`va goh iass tmgo jc`va `s
(G) Lago (B) Lah`go (F) Ljha (H) Ojoa je tmasa
Wua. 7 2 6 8 1 5 3 = 0 7>
Gos. F F F G B F F G B F
Wua. 77 72 76 78 71
Gos. G F F B B
JBDAFX@UA A]ARF@VAGOVSAR KAP
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R A J Q O H G X @J O B P^ -E
LGXMALGX@FV
2>
A]ARF@VA 2 (EJR VFMJJI/BJGRH A]GLV)
VQBDAFX@UA XP^A WQAVX@JOV
(G) LAGOJEG CRJQ^AHHGXG
7. E`oh tma lago je tma ejiijw`oc hgtg 4
(g)
(b)
2. E`oh tma lago je tma ejiijw`oc h`str`but`jo 4
(g)
(b) (`)
(``)
(```)
6. (g) Xma gr`tmlat`f lago je tma ejiijw`oc eraquaofy h`str`but`jo s 21.21. Hatarl`oa tma vgiua je p 4
(b) Xma gr`tmlat`f lago je tma ejiijw`oc eraquaofy h`str`but`jo s 83. Hatarl`oa tma vgiua je p 4
8. E`oh tma vgiua je e, tma l`ss`oc eraquaofy, `e tma lago je tma ejiijw`oc h`str`but`jo s 53.
1. (g) E`oh tma l`ss`oc eraquaof`as e7gohe2`e tma eraquaofy h`str`but`jo `s 52.= goh tma sul je gii eraquaofy `s 1>
Figss @otarvgi >-5 5-72 72-7= 7=-28 28-6>
Eraquaofy 5 = 7> 0 3
Oulbar je ^igot >-2 2-8 8-5 5-= =-7> 7>-72 72-78
Oulbar je mjusa 7 2 7 1 5 2 6
Figss @otarvgi >-7> 7>-2> 2>-6> 6>-8> 8>-1>
Eraquaofy 6 1 0 1 6
Figss @otarvgi >-7> 7>-2> 2>-6> 6>-8> 8>-1>
Eraquaofy 72 75 5 3 0
Figss @otarvgi 7>>-72> 72>-78> 78>-75> 75>-7=> 7=>-2>>
Eraquaofy 72 78 = 5 7>
Figss @otarvgi >-7>> 7>>-2>> 2>>-6>> 6>>-8>> 8>>-1>>
Eraquaofy 5 0 71 72 =
Figss >-7> 7>-2> 2>-6> 6>-8> 8>-1>
Eraquaofy 3 = p 71 8
Figss @otarvgi >-2> 2>-8> 8>-5> 5>-=> =>-7>>
Eraquaofy = 71 2> p 1
Figss @otarvgi 21-61 61-81 81-11 11-51 51-31 31-=1 =1-0=
Eraquaofy 7> 5 8 e 8 72 25
Figss >-2> 2>-8> 8>-5> 5>-=> =>-7>> 7>>-72> Xjtgi
Eraquaofy 1 e7 7> e2 3 = 1>
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R A J Q O H G X @J O B P^ -E
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27
(b) E`oh tma l`ss`oc eraquaof`as e7 goh e2`o tma ejiijw`oc hgtg `e tma lago `s25
0755 goh tma sul je tma
jbsarvgt`jo s 12.
(f) Xma lago je ejiijw`oc eraquaofy tgbia `s 16. But tma eraquaofy e7goh e2`o tma figssas 2>-8> goh 5>-=> gr
5. (g) E`oh tma lago je tma ejiijw`oc hgtg, by us`oc tma gssulah lago latmjh.
(b)
3. G figss tagfmar mgs tma ejiijw`oc gbsaotaa rafjrh je 8> stuhaots je g figss ejr tma wmjia tarl. E`oh tma lago
oulbar je hgys g stuhaot wgs gbsaot.
=. (g) E`oh tma gr`tmlat`f lago je tma ejiijw`oc eraquaofy h`str`but`jo by us`oc stap hav`gt`jo latmjh 4
(b) Xma ejiijw`oc tgbia c`vas tma i`targfy rgta (`o parfaotgca) je 61 f`t`as. E`oh tma lago i`targfy rgta.
(f) Xma h`str`but`jo smjw tma oulbar je w`fkats tgkao by bjwiars `o joa hgy fr`fkat lgtfmas. E`oh tma lago
0. (g) Xma ejiijw`oc tgbia c`vas tma h`str`but`jo je axpaoh`turas je h`eearaot egl`i`as jo ahufgt`jo. E`oh tma
lago axpaoh`tura jo ahufgt`jo je g egl`iy.
Figss 78>-71> 71>-75> 75>-73> 73>-7=> 7=>-70> 70>-2>>
Eraquaofy 3 e7 2> e2 3 =
Gca (`o yagrs) >-2> 2>-8> 8>-5> 5>-=> =>-7>> Xjtgi
Oj. je pajpia 71 e7 27 e2 73 7>>
Figss @otarvgi >-7> 7>-2> 2>-6> 6>-8> 8>-1>
Eraquaofy 3 = 72 76 7>
Lgrks >-7>> 7>>-2>> 2>>-6>> 6>>-8>> 8>>-1>> 1>>-5>>
Oj. je stuhaots 2 = 72 2> 1 6
Oj. je hgys >-5 5-7> 7>-78 78-2> 2>-2= 2=-6= 6=-8>
Oj. je stuhaots 77 7> 3 8 8 6 7
Figss 8-= =-72 72-75 75-2> 2>-28 28-2= 2=-62 62-65
Oj. je stuhaots 2 72 71 21 7= 72 76 6
I`targfy rgta (`o %) 81-11 11-51 51-31 31-=1 =1-01
Oj. je f`t`as 6 7> 77 = 6
Oj. je w`fkats 2>-5> 5>-7>> 7>>-71> 71>-21> 21>-61> 61>-81>
Oj. je bjwiars 3 1 75 72 2 6
Axpaoh`tura
(`o Rs.)
7>>>-71>> 71>>-2>>> 2>>>-21>> 21>>-6>>> 6>>>-61>> 61>>-8>>> 8>>>-81>> 81>>-1>>>
Oj. je egl`i`as 28 7> 66 2= 6> 22 75 3
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(b) (`) Xj e`oh tma fjofaotrgt`jo je VJ2`o tma g`r (`o par l`ii`jo), tma hgtg wgs fjiiaftah ejr 6> ijfgi`t`as `o g
fartg`o f`ty goh `s prasaotah baijw 4
E`oh tma lago fjofaotrgt`jo je VJ2`o tma g`r.
(``) Xma ejiijw`oc tgbia smjws tmgt tma hg`iy axpaoh`tura jo ejjh je 21 mjusa mjihs `o g ijfgi`t`as. E`oh tma
lago hg`iy axpaoh`tura jo ejjh by g su`tgbia latmjh.
7>. (g) E`oh tma lago lgrks erjl tma ejiijw`oc hgtg 4
(b) Fjlputa tma lago ejr tma ejiijw`oc hgtg 4
77. (g) E`oh tma gvargca lgrks je stuhaot erjl tma ejiijw`oc hgtg 4
Fjofaotrgt`jo je
VJ2(`o ppl.)
>.>>->.>8 >.>8->.>= >.>=->.72 >.72->.75 >.75->.>2> >.2>->.28
Eraquaofy 8 0 0 2 8 2
Hg`iy axpaoh`tura
(`o Rs.)
7>>-71> 71>-2>> 2>>-21> 21>-6>> 6>>-61>
Oj. je mjusa mjihs 8 1 72 2 2
Lgrks Baijw
7>
Baijw
2>
Baijw
6>
Baijw
8>
Baijw
1>
Baijw
5>
Oj. je stuhaots 8 7> 7= 2= 8> 3>
Lgrks Iass tmgo
7>
Iass tmgo
6>
Iass tmgo
1>
Iass tmgo
3>
Iass tmgo
0>
Iass tmgo
77>
Iass tmgo
76>
Iass tmgo
71>
Oj. je stuhaots > 7> 21 86 51 =3 05 7>>
Lgrks Oj. je Vtuhaots
Gbjva > =>
Gbjva 7> 33
Gbjva 2> 32
Gbjva 6> 51
Gbjva 8> 11
Gbjva 1> 86
Gbjva 5> 26
Gbjva 3> 75
Gbjva => 7>
Gbjva 0> =
Gbjva 7>> >
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(b) E`oh tma lago wgca je tma ejiijw`oc hgtg 4
72. (g) @o g ratg`i lgrkat, eru`t vaohjrs saii`oc lgocjas kapt `o pgfk`oc bjxas. Xmasa bjxas fjotg`oah vgry`oc
oulbar je lgocjas. Xma ejiijw`oc wgs tma h`str`but`jo je lgocjas gffjrh`oc tj tma oulbar je bjxas.
E`oh tma lago oulbar je lgocjas kapt `o g pjfkat bjx.
(b) Xma ejiijw`oc hgtg smjws tmgt tma gca h`str`but`jo je pgt`aots je lgigr`g `o g v`iigca hur`oc g pgrt`fuigr
ljotm. E`oh tma gvargca gca je tma pgt`aots.
(B) LAH@GOJEG CRJQ^AHHGXG
7. E`oh tma lah`go ejr tma ejiijw`oc eraquaofy h`str`but`jo 4
(g)
(b) (`)
(``)
(f) 7>> suroglas wara rgohjliy p`fkat up erjl g ijfgi taiapmjoa h`raftiy goh tma eraquaofy h`str`but`jo je
tma oulbar je iattars `o tma Aoci`sm gipmgbats `o tma suroglas wgs jbtg`oah gs ejiijws 4
E`oh tma lah`go oulbar je iattars `o tma suroglas. E`oh tma lago oulbar je iattars `o tma suroglas.
2. (g) E`oh tma lah`go erjl tma ejiijw`oc hgtg 4
Sgcas (`o Rs.) Oj. je Sjrkars
> goh gbjva 72>
2> goh gbjva 7>=
8> goh gbjva 0>5> goh gbjva 31
=> goh gbjva 1>
7>> goh gbjva 28
72> goh gbjva 0
78> goh gbjva >
Oj. je lgocjas 1>-12 16-11 15-1= 10-57 52-58
Oj. je bjxas 71 77> 761 771 21
Gca (`o yagrs) 1-78 71-28 21-68 61-88 81-18 11-58
Oj. je fgsas 5 77 27 26 78 1
Figss @otarvgi >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5>
Eraquaofy 5 0 78 2 70 7>
Figss @otarvgi 21-61 61-81 81-11 11-51 51-31
Eraquaofy 2> 21 1 3 8
Figss @otarvgi >-= =-75 75-28 28-62 62-8> 8>-8=
Eraquaofy = 7> 75 28 71 3
Oj. je iattars 7-8 8-3 3-7> 7>-76 76-75 75-70
Oj. je Vuroglas 5 6> 8> 75 8 8
Figss crjups 77>-72> 72>-76> 76>-78> 78>-71> 71>-75> 75>-73> 73>-7=> 7=>-70> 70>-2>>
Eraquaofy 5 21 8= 32 775 5> 6= 22 6
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(b) (`) Xma ejiijw`oc h`str`but`jo c`vas tma wa`cmts je 6> stuhaots je g figss. E`oh tma lah`go wa`cmt je
tma stuhaot
(``) E`oh tma lah`go je tma ejiijw`oc eraquaofy h`str`but`jo 4
(f) Xma ejiijw`oc tgbia c`vas tma h`str`but`jo je tma i`ea t`la je 8>> oajo iglps 4
E`oh tma lah`go i`ea t`la je g iglp.
6. (g) G i`ea `osurgofa gcaot ejuoh tma ejiijw`oc hgtg ejr h`str`but`jo je gcas je 7>> pji`fy mjihars. Fgifuigta
tma lah`go gca, `e pji`f`as gra joiy c`vao tj parsjos mgv`oc gca 7= yagrs jowgrhs but iass tmgo 5> yagrs.
(b) G survay racgrh`oc tma ma`cmts (`o fl) je 17 c`ris je figss ] je g sfmjji wgs fjohuftah goh tma hgtg
jbtg`oah ejiijws 4
E`oh tma lah`go ma`cmt.
8. (g) Xma ejiijw`oc tgbia c`vas tma lgrks jbtg`oah by 1> stuhaots o g figss tast 4
E`oh tma lah`go.
(b) Xma ejiijw`oc tgbia c`vas tma pjpuigt`jo je lgias `o h`eearaot gca crjups 4
E`oh tma`r lah`go gca.
Sa`cmt (`o kc) 8>-81 81-1> 1>-11 11-5> 5>-51 51-3> 3>-31
Oj. je stuhaots 2 6 = 5 5 6 2
Lgrks >-7>> 7>>-2>> 2>>-6>> 6>>-8>> 8>>-1>> 1>>-5>> 5>>-3>> 3>>-=>> =>>-0>> 0>>-7>>>
Eraquaofy 2 1 0 72 73 2> 71 0 3 8
I`ea X`la
(`o mjurs)
71>>-2>>> 2>>>-21>> 21>>-6>>> 6>>>-61>> 61>>-8>>> 8>>>-81>> 81>>-1>>>
Oj. je iglps 78 15 5> =5 38 52 8=
Gca `o yagrs Baijw
2>
Baijw
21
Baijw
6>
Baijw
61
Baijw
8>
Baijw
81
Baijw
1>
Baijw
11
Baijw
5>
Oj. je pji`fy
mjihars
2 5 28 81 3= =0 02 0= 7>>
Ma`cmts (`o fl) Iass tmgo
78>
Iass tmgo
781
Iass tmgo
71>
Iass tmgo
711
Iass tmgo
75>
Iass tmgo
751
Oj. je c`ris 8 77 20 8> 85 17
Lgrks 77-71 75-2> 27-21 25-6> 67-61 65-8> 87-81 85-1>
Oj. je Vtuhaots 2 6 5 3 78 72 8 2
Gca crjup
(`o yagrs)
1-78 71-28 21-68 61-88 81-18 11-58 51-38
Oj. je lgias 883 6>3 230 22> 713 07 60
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1. (g) Xma ejiijw`oc tgbia c`vas tma h`str`but`jo je @W je 7>> stuhaots. E`oh tma lah`go @W.
(b) Xma iaoctm je 3> iagvas je g pigot gra lagsurah fjrraft tj tma oagrast l`ii`latar goh tma hgtg jbtg`oah `s
raprasaotah `o tma ejiijw`oc tgbia 4
E`oh tma lah`go iaoctm je tma iagvas.
5. Fgifuigta tma l`ss`oc eraquaofy e erjl tma ejiijw`oc h`str`but`jo, t ba`oc c`vao tmgt tma lah`go je tma h`str`but`jo
`s 28.
3. (g) @e tma lah`go je tma ejiijw`oc eraquaofy h`str`but`jo s 2=.1, e`oh tma l`ss`oc eraquaof`as.
(b) @e tma lah`go je tma ejiijw`oc eraquaofy h`str`but`jo s 62.1, e`oh tma vgiuas je e7goh e2.
(f) (`) Go `ofjlpiata h`str`but`jo s c`vao baijw 4
@e lah`go vgiua `s 85 goh tma tjtgi oulbar je `tals `s 26>.
)( E`oh tma l`ss`oc eraquaof`as e7goh e2.
)( E`oh tma gr`tmlat`f lago (GL) je tma fjlpiatah h`str`but`jo.(``) Xma lah`go je tma ejiijw`oc hgtg `s 2>.31 E`oh tma l`ss`oc eraquaof`as x goh y, `e tma tjtgi
eraquaofy `s 7>>
@W 31-=8 =1-08 01-7>8 7>1-778 771-728 721-768 761-788
Eraquaofy = 77 25 67 7= 8 2
Ugr`gbia 7>-2> 2>-6> 6>-8> 8>-1> 1>-5> 5>-3> 3>-=>
Eraquaofy 72 6> e7 51 e2 21 7=
Figss `otarvgi >-1 1-7> 7>-71 71-2> 2>-21 21-6> 6>-61 61-8>
Eraquaofy 3 7> x 76 y 7> 78 0
Figss >-7> 7>-2> 2>-6> 6>-8> 8>-1>
Eraquaofy 1 21 e 7= 3
Figss `otarvgi >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5> Xjtgi
Eraquaofy 1 e7 2> 71 e2 1 5>
Figss `otarvgi >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5> 5>-3> Xjtgi
Eraquaofy e7 1 0 72 e2 6 2 8>
Iaoctm
(`o ll)
77=-725 723-761 765-788 781-716 718-752 756-737 732-7=>
Oj. je iagva 7> = 76 22 3 5 8
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(F) LAH@GOJEG CRJQ^AHHGXG
7. (g) Fgifuigta tma ljha ejr tma ejiijw`oc eraquaofy h`str`but`jo.
(b) G stuhaot ojtah tma oulbar je fgrs pgss`oc tmrjucm spjt jo g rjgh ejr 7>> par`jhs agfm je 6 l`outas goh
sullgr`zah `t `o tma tgbia c`vao baijw. E`oh tma ljha je tma hgtg .
2. (g) Xma c`vao h`str`but`jo smjws tma oulbar je ruos sfjrah by sjla tjp bgtslao je tma wjrih `o joa hgy
`otarogt`jogi fr`fkat lgtfmas 4Ruos
Vfjrah
6>>>-8>>> 8>>>-1>>> 1>>>-5>>> 5>>>-3>>> 3>>>-=>>> =>>>-0>>> 0>>>-7>>>> 7>>>>-77>>>
Oj. jebgtslgo
8 7= 0 3 5 6 7 7
E`oh tma ljha je tma hgtg.
(b) (`) Xma ejiijw`oc tgbias c`vas tma gcas je tma pgt`aots ghl`ttah `o g mjsp`tgi hur`oc g yagr.
E`oh tma ljha goh tma lago je tma hgtg
(``) Xma ejiijw`oc hgtg c`vas tma h`str`but`jo je tjtgi ljotmiy mjusa mjih axpaoh`tura je 2>> egl`i`as
je g v`iigca. E`oh tma ljhgi ljotmiy axpaoh`tura je tma egl`i`as. Gisj, e`oh tma lago ljotmiy
axpaoh`tura
(f) (`) Xma ejiijw`oc h`str`but`jo c`vas tma stgta-w`sa tagfmar stuhaot rgt`j `o m`cmar safjohgry sfmjjis j
@oh`g. E`oh tma ljha goh lago je tm`s hgtg. @otarprat twj lagsuras.
(``) Xma ejiijw`oc tgbia smjws tma lgrks jbtg`oah by 7>> stuhaots je Figss ] `o sfmjji hur`oc g
pgrt`fuigr gfghal`f sass`jo. E`oh tma ljha je tm`s h`str`but`jo
Figss >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5> 5>-3> 3>-=>
Eraquaofy 1 = 3 72 2= 2> 7> 7>
Oj. je fgrs >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5> 5>-3> 3>-=>
Eraquaofy 3 78 76 72 2> 77 71 =
Gca (`o yagrs) 1-71 71-21 21-61 61-81 81-11 11-51
Oj. je pgt`aots 5 77 27 26 78 1
Axpaoh`tura
(`o Rs.)
7>>>-71>> 71>>-2>>> 2>>>-21>> 21>>-6>>> 6>>>-61>> 61>>-8>>> 8>>>-81>> 81>>-1>>>
Oj. jeegl`i`as
28 8> 66 2= 6> 22 75 3
Oj. je stuhaots
par tagfmar
71-2> 2>-21 21-6> 6>-61 61-8> 8>-81 81-1> 1>-11
Oj. jestgta/Q.X.
6 = 0 7> 6 > > 2
Lgrks Iass tmgo
7>
Iass tmgo
2>
Iass tmgo
6>
Iass tmgo
8>
Iass tmgo
1>
Iass tmgo
5>
Iass tmgo
3>
Iass tmgo
=>
Oj. je stuhaots 3 27 68 85 55 33 02 7>>
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6. (g) Fjlputa tma ljha je tma ejiijw`oc hgtg 4
(b) Fjlputa tma ljha je tma ejiijw`oc hgtg 4
8. Fgifuigta tma ljha je tma ejiijw`oc hgtg 4
1. Xma ljha je tma ejiijw`oc hgtg `s =1.3 E`oh tma l`ss`oc eraquaofy `o `t.
(F) CRG^M@FGRA^RAVAOXGX@JOJEFQLQIGX@UAERAWQAOFPH@VXR@BQX@JO7. Xma ejiijw`oc h`str`but`jo c`vas tma lgrk jbtg`oah by 7>2 stuhaots je figss ].
Fjovart tma gbjva h`str`but`jo tj g iass tmgo typa fuluigt`va eraquaofy h`str`but`jo goh hrgw `ts jc`va.
2. Xma ejiijw`oc tgbia c`vas tma h`str`but`jo je @W je 5> pup`is je figss ] `o g sfmjji.
Fjovart tma gbjva h`str`but`jo tj g ljra tmgo typa fuluigt`va eraquaofy h`str`but`jo goh hrgw `ts jc`va.6. (g) Xma ejiijw`oc tgbia c`vas tma ma`cmt je traas 4
(b) Smgt `s tma vgiua je tma lah`go je tma hgtg us oc tma crgpm `o tma c`vao e`cura, je iass tmgo jc`va goh ljr
tmgo jc`va:
Hrgw bjtm jc`vas ejr tma hgtg gbjva. Maofa, jbtg`o tma lah`go je tma hgtg.
Figss @otarvgi 7-1 5-7> 77-71 75-2> 27-21 25-6> 67-61 65-8> 87-81 85-1>
Eraquaofy 6 = 76 7= 2= 2> 76 = 5 8
Vfjra =>-0> 0>-7>> 7>>-77> 77>-72> 72>-76> 76>-78> 78>-71>
Oj. je pup`i 7= 23 8= 60 72 5 75
Sgcas (@o Rs.) 17-15 13-52 56-5= 50-38 31-=> =7-=5 =3-02
Oj. je wjrkars 72 28 8> 6> 7= = 2>
V`za 81-11 11-51 51>-31 31-=1 =1-01 01-7>1 7>1-771
Eraquaofy 3 72 73 e 62 5 7>
Lgrks >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5>
Oj. je
stuhaots
0 7> 21 1> 1 6
@W 5>-3> 3>-=> =>-0> 0>-7>> 7>>1-77> 77>-72> 72>-76>
Oj. je pup`is 2 6 1 75 78 76 3
Ma`cmt Iass tmgo
78>
Iass tmgo
781
Iass tmgo
71>
Iass tmgo
711
Iass tmgo
75>
Iass tmgo
751
Oj. je traas 8 77 20 8> 85 1>
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8. (g) Ejiijw`oc s tma gca h`str`but`jo je g crjup je stuhaots. Hrgw g fuluigt`va eraquaofy furva ejr tma hgtg
goh e`oh tma lah`go.
(b) G stuhaot hrgws g fuluigt`va eraquaofy furva ejr tma lgrks jbtg`oah by 8> stuhaots je g figss gs smjwo
baijw. E`oh tma lah`go lgrks jbtg`oah by tma stuhaots je tma figss.
1. Xma tgbia c`vao baijw smjws tma eraquaofy h`str`but`jo je tma sfjras jbtg`oah by 2>> fgoh`hgtas o g LFG
aotrgofa axgl`ogt`jo.
Vfjra 2>>-21> 21>-6>> 6>>-61> 61>-8>> 8>>-81> 81>-1>> 1>>-11> 11>-5>>
Oj. je
stuhaots
6> 71 81 2> 21 8> 7> 71
Hrgw fuluigt`va furva je ljra tmgo typa goh maofa e`oh lah`go.
Gca `o yagrs Oj. je stuhaots
Iass tmgo 1 65
Iass tmgo 5 3=
Iass tmgo 3 765Iass tmgo = 70>
Iass tmgo 0 21=
Iass tmgo 7> 682
Iass tmgo 77 86=
Iass tmgo 72 12>
Iass tmgo 76 1=5
Iass tmgo 78 568
Iass tmgo 71 5=8
Iass tmgo 75 3>>
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6>
A]ARF@VA 6 (EJR VFMJJI/BJGRH A]GLV)
^RAU@JQV PAGRV BJGRH WQAVX@JOV
UARPVMJRXGOVSAR XP^AWQAVX@JOV
7. Sm`fm lagsura je faotrgi taohaofy `s c`vao by tma x-fjjrh`ogta je tma pj`ot je `otarsaft`jo je tma ljra tmgo
jc`va goh iass tmgo jc`va: Haim`-2>>=
2. E`oh tma lah`go figss je tma ejiijw`oc hgtg 4 Gi-2>>=
6. E`oh tma figss lgrks je figssas 7>-21 goh 61-11 4 Ejra`oc-2>>=
8. Sr`ta tma lah`go figss je tma ejiijw`oc h`str`but`jo 4 Haim`-2>>0
1. Smgt `s tma ijwar i`l`t je tma ljhgi figss je tma ejiijw`oc eraquaofy h`str`but`jo: Ejra`oc-2>>0
VMJRXGOVSARXP^AWQAVX@JOV
7. Xma lago je tma ejiijw`oc eraquaofy h`str`but`jo `s 13.5 goh tma sul je jbsarvgt`jos `s 1>. E`oh tma l`ss`oc
eraquaof`as e7goh e24 Gi-2>>8
2. Xma ejiijw`oc tgbia c`vas tma h`str`but`jo je axpaoh`tura je h`eearaot egl`i`as jo ahufgt`jo. E`oh tma lagoaxpaoh`tura jo ahufgt`jo je g egl`iy 4 Haim`-2>>8F
Axpaoh`tura (`o Rs.) Oulbar je egl`i`as
7>>>-71>> 28
71>>-2>>> 8>
2>>>-21>> 66
21>>-6>>> 2=
6>>>-61>> 6>
61>>-8>>> 22
8>>>-81>> 75
81>>-1>>> 3
6. E`oh tma lago je tma ejiijw`oc h`str`but`jo 4 Haim`-2>>1
Lgrks Jbtg`oah >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5>
Eraquaofy = 7> 72 22 6> 7=
Figssas >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5> 5>-3>
Eraquaofy 8 8 = 7> 72 = 8
Gca (`o yagrs) >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5>
Oulbar je pgt`aots 75 76 5 77 23 7=
Figss >-2> 2>-8> 8>-5> 5>-=> =>-7>> 7>>-72>
Eraquaofy 3 e7 72 e2 = 1
Figss 8-= =-72 72-75 75-2> 2>-28 28-2= 2=-62 62-65
Oulbar je stuhaots 2 72 71 21 7= 72 76 6
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8. @e tma lago je tma ejiijw`oc hgtg `s 7=.31 e`oh tma vgiua je p 4 Gi-2>>1
1. Xma Gr`tmlat`f Lago je tma ejiijw`oc eraquaofy h`str`but`jo s 1>. E`oh tma vgiua je p 4 Haim`-2>>5
5. @e tma lago je tma ejiijw`oc s 1>, e`oh tma vgiua je e74 Haim`-2>>5
3. Xma lago je tma ejiijw`oc eraquaofy h`str`but`jo s 52.=. E`oh tma l`ss`oc eraquaofy x. Haim`-2>>3
IJOCGOVSARXP^AWQAVX@JOV
7. G survary racgrh`oc tma ma`cmts (`o fl) je 1> c`ris je figss x je g sfmjji wgs fjohuftah goh tma ejiijw`oc hgtg
wgs jbtg`oah 4 Haim`-2>>=
E`oh tma lago, lah`go goh ljha je tma gbjva hgtg.
2. E`oh tma lago, ljha goh lah`go je tma ejiijw`oc hgtg. Gi-2>>=
6. E`oh tma lago, lah`go goh ljha je tma ejiijw`oc hgtg. Ejra`co-2>>=
Figss Eraquaofy
>-1> 2
1>-7>> 6
7>>-71> 1
71>-2>> 5
2>>-21> 1
21>-6>> 6
6>>-61> 7
8. Xma ejiijw`oc tgbia c`vas tma hg`iy `ofjla je 1> wjrkars je g egftjry 4 Haim`-2>>0
x` 7> 71 p 21 6>
e 1 7> 3 = 2
Figss >-2> 2>-8> 8>-5> 5>-=> =>-7>>Eraquaofy 73 p 62 28 70
Figss >-2> 2>-8> 8>-5> 5>-=> =>-7>>
Eraquaofy 73 2= 62 e7 70
Figss >-2> 2>-8> 8>-5> 5>-=> =>-7>> 7>>-72>
Eraquaofy 1 = x 72 3 =
Ma`cmt `o fl 72>-76> 76>-78> 78>-71> 71>-75> 75>-73> Xjtgi
Oulbar je c`ris 2 = 72 2> = 1>
Figss >-7> 7>-2> 2>-6> 6>-8> 8>-1> 1>-5> 5>-3>
Eraquaofy 1 7> 7= 6> 2> 72 1
Hg`iy ofjla
(`o Rs.)
7>>-72> 72>-78> 78>-75> 75>-7=> 7=>-2>>
Oulbar je wjrkars 72 78 = 5 7>
-
8/12/2019 14. Statistics
32/32
LGO@VMKQLGR
R A J Q O H G X @J O B P^ -E
LGXMALGX@FV
62
VXGX@VX@FV A]ARF@VA (])-FBVAGOVSAR KAP
E`oh tma lago, ljha goh lah`go je tma gbjva hgtg.
1. Hur`oc tma lah`fgi fmafk-up je 61 stuhaots je g figss tma`r wa`cmts wara rafjrhah gs ejiijws 4 Gi-2>>0
Sa`cmt (`o kc) Oulbar je stuhaots
6=-8> 68>-82 2
82-88 8
88-85 1
85-8= 78
8=-1> 8
1>-12 6
Hrgw g iass tmgo typa goh g ljra tmgo typa jc`va erjl tma c`vao hgtg. Maofa jbtg`o tma lah`go wa`cmt erjl tma
crgpm.
5. E`oh tma ljha, lah`go goh lago ejr tma ejiijw`oc hgtg 4 Ejra`co-2>>0
Lgrks jbtg`oah Oulbar je stuhaots
21-61 3
61-81 67
81-1> 66
1>-11 73
11-51 77
51-31 7
UARPVMJRX GOVSAR XP^AWQAVX@JO
7. Lah`go 2.6>-8> 6. 73.1 goh 81 8. 6>-8> 1. 8>
VMJRX GOVSAR XP^AWQAVX@JO
7. e7 < =, e2< 7> 2.Rs. 2552.1 6. 70.02 8. p < 2> 1.p < 2= 5.e7< 28 3. 7>
IJOC GOVSAR XP^AWQAVX@JO
7. lago < 71>.21 ; Lah`go < 717.1 ; Ljha < 718. 2.lago < 61.35 ; Lah`go < 61.55 ; Ljha < 61.88
6. lago < 10.0 ; Lah`go < 57.5 ; Ljha < 51. 8.lago < 781.2> ; Lah`go < 76=.13 ; Ljha < 721
1. 82.2 kc 5.lago < 80.3 ; Lah`go < 8=.1 ; Ljha < 85.7
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