गणित कक्षा १

hf]8f ldnfpg'xf];\ M

uGgx' f];\ / hf]8f ldnfpgx' f];\ M

&
(
^
*

d/] f] ul0ft, sIff ! 43

jm| d};uF cfpg] ;ª\Vofªs\ /fv/] vfnL 7fpF eg{x' f;] \ M

!#%
&(

@$
^*

#%
^(

44 d]/f] ul0ft, sIff !

z"Go %

;Fu;Fu} ufcf}F M

kfrF cf]6f k/]jf rf/f] l6Kb} 5g\ . 45
p8o\ f] Pp6f k/]jf afFsL slt 5g\ <

rf/cf]6f k/]jf rf/f] l6Kb} 5g\ .
p8\of] Pp6f k/]jf afsF L slt 5g\ <

tLgcf6] f k/]jf rf/f] l6Kb} 5g\ .
p8\of] Pp6f k/]jf afsF L slt 5g\ <

bO' {cf]6f k/]jf rf/f] l6Kb} 5g\ .
p8o\ f] Pp6f k/]jf afsF L slt 5g\ <

Pscf]6f k/]jf rf/f] l6Kb} 5 .
p8o\ f] Pp6f k/]jf afsF L slt 5 <

d]/f] ul0ft, sIff !

5nkmn u/fF} / n]vfF} M

zG" o

46 d/] f] ul0ft, sIff !

uGtL u/L n]Vg'xf;] \ M

¿vdf sltcf]6f r/f 5g\ < 47
kfv] /Ldf sltcf6] f xf;F 5g\ <
aG] rdf slt hgf dflg;5g\ <

d/] f] ul0ft, sIff !

leq ePsf e]8f / afvf| uGtL u/L n]Vgx' f];\ M

48 d]/f] ul0ft, sIff !

k|Tos] 6«d] f ePsf j:tx' ¿ uGtL u/L nV] g'xf];\ M

d/] f] ul0ft, sIff ! 49

^ bz

bz

50 d]/f] ul0ft, sIff !

uGtL u/L ;ªV\ ofªs\ n]Vgx' f;] \ M

nV] g'xf;] \ M

) ! @ # $ % ^ & * ( !)

d]/f] ul0ft, sIff ! 51

df l7s ;ª\Vofª\s n]Vgx' f;] \ M %
$
%
% %

@# ^
% @$

!$ ^

^ ^

^ d]/f] ul0ft, sIff !
!

^
$

52

df l7s ;ª\Vofªs\ nV] gx' f];\ M

&

& ! / ^ ldnfpbF f & x'G5 .
$ / ldnfpFbf & xG' 5 .
!^ @ / ldnfpFbf & xG' 5 .
& # / ldnfpbF f & xG' 5 .
% / ldnfpbF f & x'G5 .
$
&

@
&

#
&

%

& ^ / ldnfpFbf & xG' 5 .
^
53
d/] f] ul0ft, sIff !

df l7s ;ª\Vofª\s n]Vgx' f];\ M

*

* **
% $!

* * # / ldnfpbF f * x'G5 .
@ & ^ / ldnfpbF f * xG' 5 .

(

( ( ((
% !
^@
*/ ldnfpFbf ( x'G5 .
#/ ldnfpFbf ( x'G5 . & / ldnfpbF f ( xG' 5 .
$ / ldnfpFbf ( xG' 5 .
54
d]/f] ul0ft, sIff !

!) agfpgx' f;] \ M

!/(

/
/

/

/

/

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afs;df ;xL cªs\ eg'{xf;] \ M 55

& df yKbf !) x'G5 .
( df yKbf !) x'G5 .
$ df yKbf !) x'G5 .
@ df yKbf !) x'G5 .

d]/f] ul0ft, sIff !

& of]ukmn !) ;Dd cfpg] hf8]

!) ;Ddsf] uGtL

dflysf] lrqaf6 ug/] ;ª\Vof n]Vgx' f];\ M

56 d]/f] ul0ft, sIff !

!) ;Ddsf ;ªV\ ofx¿ hf]8fF} M

;Ltf;uF # cf]6f s/] f 5g\ . xl/;Fu @ cf]6f s/] f 5g\ . bj' }hgfsf]
hDdf ubf{ sltcf]6f s/] f eP <

b'j} hgfn] # cf]6f s/] f / @
cf]6f s/] f Ps} 7fpFdf /fv] eg]
hDdf % cf6] f s]/f x'G5 .
ul0ftLo jfSodf nV] bf M

# ±@ ≠ %

-tLg_ ± -bO' {_ Ö -kfFr_

pQ/ M % cf]6f s/] f

ul0ftLo jfSodf M ± ≠ pQ/ M s6] fs]6Lx¿

ul0ftLo jfSodf M ± ≠ pQ/ M s6] fs6] Lx¿

d/] f] ul0ft, sIff ! 57

hDdf slt eP < ul0ftLo jfSo agfpg'xf];\ M

±≠ ±≠

±≠ ±≠

±≠ ± ≠

hDdf sltcf]6f :ofp 5g\ <

ul0ftLo jfSodf :ofp xG' 5g\ .

ul0ftLo jfSodf :ofp xG' 5g\ .

ul0ftLo jfSodf :ofp xG' 5g\ .

58 d]/f] ul0ft, sIff !

j:t'x¿ k|of]u u/L hf8] fF} M

!±! ≠ @±! ≠
!±# ≠ !±$ ≠

#±@ ≠ #±% ≠

@±# ≠ %±@ ≠

@±& ≠ #±$ ≠

d]/f] ul0ft, sIff ! 59

hf]8g\ x' f;] \ M

@ ±# ≠ % $ ±@ ≠

% ±! ≠ % ±@ ≠
% ±$ ≠ % ±# ≠

^ ±@ ≠ $ ±^ ≠

% ±@ ≠ # ±^ ≠

% ±# ≠ & ±# ≠

60 d]/f] ul0ft, sIff !

hf8] fF} M

@ hgf ljBfyL{x¿ vl] n/xs] f lyP . ! hgf csf]{ ylkof] . ca hDdf
slt hgf ljBfyL{ eP <

ul0ftLo jfSodf M @ ± ! ≠ #

ylkPkl5 hDdf slt hgf ljBfyL{x¿ eP5g\ <

±≠

d/] f] ul0ft, sIff ! ±≠

61

ylkPkl5 slt x'G5 < ul0ftLo jfSodf n]Vg'xf];\ M

±≠ ±≠

±≠ ±≠

km" nbfgLdf tLgcf]6f k"mn 5g\ . kfrF cf6] f km" n yKbf hDdf
sltcf]6f k"mn x'G5g\ .

± ≠

hf]8g\ x' f];\ M ^±@≠
#±$≠
!±#≠ (±!≠
%±%≠
@±&≠ d]/f] ul0ft, sIff !

62

hf]8g\ 'xf;] \ M bf];f| ] k6s

slt df5f lemlsP <

klxnf] k6s

@±! ≠

klxnf] k6s bf;] |f] k6s
klxnf] k6s
@± ≠

bf];|f] k6s

±≠

hf]8\g'xf;] \ M ^±) ≠
)±$ ≠
!±) ≠ )±) ≠
%±) ≠
)±& ≠ 63

d]/f] ul0ft, sIff !

hf8] \gx' f;] \ M !±! ≠

@±) ≠

±≠ ±≠

±≠ ±≠

64 d/] f] ul0ft, sIff !

hf]8/] % agfpgx' f];\ M

% ± ) ≠%

$ ≠
±
±
≠ !

) @±

≠ ≠
±

#± ≠ 65

d]/f] ul0ft, sIff !

b'j} ;d"xsf r/f hDdf ubf{ sltcf]6f x'G5g\ <

ul0ftLo jfSodf M ^ ± # Ö ( pQ/ M ( cf]6f r/fx¿

xfdLn] o;nfO{ 7f8f] ¿kdf /fv]/ klg hf]8g\ ;S5fF} M -7f8f] ¿kdf_
^
^±#Ö( ±#

(

!#
±^ ±%

#^
±$ ±$

@^
±% ±#

% )
±# ±^

66 d/] f] ul0ft, sIff !

7f8f] ¿kdf /fv/] hf]8\g'xf];\ M

$@ & #
±! ±# ±@ ±%

!±#Ö ^±@Ö $±#Ö

±

#±$Ö *±!Ö &±@Ö
±

d/] f] ul0ft, sIff ! 67

hf]8]/ ! agfcfF} M hf]8]/ @ agfcfF} M

! @
)
)! !
!) @

hf8] /] # agfcfF} M hf8] ]/ $ agfcfF} M

# $
) )
! !
# @
@ $
#
68
d/] f] ul0ft, sIff !

hf8] /] % agfcf}F M hf]8/] ^ agfcf}F M

% ^
)
! )
@ !
# @
$ #
% ^
%
$

d]/f] ul0ft, sIff ! 69

hf]8]/ & agfcf}F M hf8] /] * agfcfF} M

& *
# )
! !
@ @
) #
$ $
& *
^ &
% ^
%
70
d]/f] ul0ft, sIff !

hf8] /] ( agfcf}F M hf]8]/ !) agfcf}F M

( !)

) )
! !
@ @
& #
$ $
# %
^ ^
( &
* *
% (
!)
d/] f] ul0ft, sIff !
71

) b]lv % ;Dd nl] vPsf] 3gfsf/ uf]6L v]nL hf]8\g'xf];\ M

) ± $Ö $ Ö
±Ö ± Ö
±Ö ± Ö
±Ö ± Ö
±Ö ± Ö
±Ö ± Ö
±Ö ± Ö
±Ö ± Ö
±Ö ± Ö
±Ö ±
d]/f] ul0ft, sIff !
72

of]ukmn % cfpg] af6f] kQf nufO{ rª\uf e6] g\ 'xf;] \ M

%±) #±@ !±# !±! !±#

@±@ @±# !±$ )±% @±@

#±! )±$ #±) $±! @±!

)±) !±$ $±! )±% #±!

!±@ @±# )±$ )±) @±@

d/] f] ul0ft, sIff ! 73

ofu] kmn !) cfpg] af6f] kQf nufO{ es0' 8f] e6] g\ x' f;] \ M

&±# $±^ (±! #±# *±!
!±% $±$ %±% @±* ^±$
!±# &±@ @±% $±! #±&
^ ± # ^ ± $ @ ± * !) ± ) ! ± (
$±% %±% $±@ @±! #±%

74 d/] f] ul0ft, sIff !

!) ;Ddsf ;ª\Vofx¿sf] 36fp *

36fp u/fF} M

;Ltf;uF % cf]6f s]/f lyP . pgn] ! cf]6f vfOg\ . ca sltcf]6f
afsF L /xo\ f] <

;Ltfn] ! cf]6f s]/f vfOg\ eg] $
cf6] f s/] f afsF L /xG5 .
ul0ftLo jfSodf n]Vbf M

% –!≠$

-kfFr_ – -Ps_ Ö -rf/_

pQ/ M $ cf]6f s/] f

9'ªu\ fdf slt Eofut' f afFsL /x] <

ul0ftLo jfSodf n]Vbf M – ≠ pQ/ M Eofu'tf

ul0ftLo jfSodf n]Vbf M – ≠ pQ/ M Eofut' f

d]/f] ul0ft, sIff ! 75

36fpgx' f];\ M

6]d« f hDdf & cf]6f :ofp 5g\ . tLdWo] tkfO{Fn] $ cf]6f :ofp efOnfO{
lbg'eof] eg] tkfOF;{ Fu hDdf sltcf6] f :ofp afsF L /xG5 <

ul0ftLo jfSodf n]Vbf M – ≠ pQ/ M :ofp

bfofkF 6l\ 6sf] lrq x]g'x{ f;] \ . sltcf]6f
k/j] f afFsL /x] <

ul0ftLo jfSodf nV] bf M – ≠ pQ/ M k/j] f

/fdn] cfk"m;uF ePsf] % cf6] f k"mnsf pQ/ M k"mnsf y'uF f
yuF' fdWo] ! cf]6f km" nsf] y'Fuf ;fyLnfO{
lbP . /fd;uF ca sltcf]6f km" nsf
yuF' f afsF L /xG5 <
ul0ftLo jfSodf n]Vbf M

–≠

lrqdf # hgf s6] fx¿ 5g\ eg] hDdf slthgf s6] Lx¿ 5g\ <

ul0ftLo jfSodf n]Vbf M – ≠ pQ/ M s6] Lx¿

76 d/] f] ul0ft, sIff !

36fcfF} M

$ af6 @ lbFbf afFsL @

af6 hfbF f afFsL
–≠

af6 p8\bf afFsL
–≠

af6 hfFbf afFsL
– ≠

d/] f] ul0ft, sIff ! 77

36fpgx' f;] \ M

@ –! ≠ !

# –! ≠

$ –@ ≠

% –$ ≠

78 d]/f] ul0ft, sIff !

36fcfF} M

;Ltf, xl/ / ljGb' k|To]s;Fu #÷# cf]6f lnrL lyP . ;Ltfn] ! cf6] f
lnrL vfOg\ . xl/n] # cf6] } lnrL vfP / ljGb'n] Pp6f klg lnrL
vfOgg\ eg] kT| os] ;Fu sltcf]6f lnrL afsF L /xG5g\ <

;Ltf

#–!≠

xl/

#– ≠

ljGb'

#– ≠

36fpg'xf];\ M *–*≠

@–@≠

&–)≠ !–)≠

$–)≠ %–%≠

!) – ) ≠ ^–)≠

d]/f] ul0ft, sIff ! 79

olb @ cf]6f k/]jf p8] eg] slt afsF L /xG5g\ <

pQ/ M $ cf6] f k/]jf

ul0ftLo jfSodf M ^ – @ ≠ $ -7f8f] ¿kdf /fv]/
o;nfO{ 7f8f] ¿kdf /fv/] klg 36fpg ;lsG5 . 36fpFbf_

^–@≠$ ^
–@
36fpg'xf;] \ M
$

$% &(
–! –# –@ –%

t];fd{] f lbPsfnfO{ 36fP/ 7f8f] ¿kdf n]Vg'xf];\ / 36fpg'xf;] \ M

*–#Ö #–@Ö ^–$Ö

–

80 d]/f] ul0ft, sIff !

36fpgx' f];\ M %
–$
%%
–@ –# *
–@
#
&
%& –#
–! –@
$ ^
–$
(^
–@ –# (
–$
*(
–# –# 81

& *
–$ –$

d]/f] ul0ft, sIff !

36fpgx' f];\ M

k"mnsf] ;ªV\ ofeGbf kt' nLsf] ;ª\Vof sltn] a9L 5 <

a9L

ul0ftLo jfSodf M & – % Ö @ pQ/ M cf]6f kt' nL

df5fsf] ;ª\VofeGbf la/fnfsf] ;ªV\ of sltn] a9L 5 <

ul0ftLo jfSodf nV] bf M – ≠
pQ/ M cf]6f la/fnf] a9L

an] 'gsf] ;ªV\ ofeGbf s]6Lsf] ;ª\Vof sltn] a9L 5 <

ul0ftLo jfSodf M pQ/ M s6] L a9L

82 d]/f] ul0ft, sIff !

36fpgx' f];\ M
s6] fsf] ;ªV\ ofeGbf ;fOsnsf] ;ª\Vof sltn] sd 5 <

sd

ul0ftLo jfSodf M ^ – $ Ö @ pQ/ M @ cf6] f ;fOsn sd

:ofpsf] ;ª\Vof s]/fsf] ;ª\VofeGbf sltn] sd 5 <

ul0ftLo jfSodf M pQ/ M :ofp sd

s;' Ls{ f] ;ª\Vof s]6fs6] Lsf] ;ªV\ ofeGbf sltn] sd 5 <

ul0ftLo jfSodf M pQ/ M s';L{ sd

d/] f] ul0ft, sIff ! 83

36fpgx' f;] \ M

s6] f / s6] Lsf] ;ª\Vofdf slt km/s 5 <

ul0ftLo jfSodf M % – # Ö @ km/s pQ/ M @ hgf s]6f a9L

Aof6«L÷;n] / 38Lsf] ;ª\Vofdf slt km/s 5 <

ul0ftLo jfSodf M pQ/ M Aof6L« ÷;n] a9L

aur}F fdf $ cf6] f ss' '/ / ! cf6] f la/fnf] 5g\ . s's'/ /
la/fnfsf] ;ª\Vofdf sltn] km/s 5 <

ul0ftLo jfSodf M pQ/ M s's/' a9L

oxfF * cf]6f s;' L{ / # cf6] f aG] r 5g\ . s';L{ / aG] rsf]
;ªV\ ofdf slt km/s 5 <

ul0ftLo jfSodf M pQ/ M s;' L{ a9L

84 d]/f] ul0ft, sIff !

36fpg'xf;] \ / hf]8f ldnfpgx' f;] \ M

#–! (( @–)
$–! #* @–!
%–! @@ (–)
!) – ! !! (–@
*–! $& *–)
$–# )^ %–!
&–! &) *–@
@–@ ^$ $–!
^–! %# (–$
(–! *% %–%

d/] f] ul0ft, sIff ! 85

36fpgx' f];\ M ^– % ≠
^– # ≠
@– @ ≠ &– ^ ≠
#– ! ≠ &– % ≠
#– @ ≠ &– @ ≠
$– ! ≠ *– @ ≠
$– @ ≠ *– $ ≠
$– # ≠ *– % ≠
%– ! ≠ *– & ≠
%– @ ≠ (– % ≠
%– # ≠ (– # ≠
%– $ ≠ !) – & ≠
%– % ≠
!) – & ≠ d/] f] ul0ft, sIff !

86

vfnL 7fpF egx{' f;] \ M –#≠ )
%– ≠$
#– ≠ ! (–&≠
–@≠#

*– ≠&

36fpFbf ! cfpg] af6f] kQf nufO{ O/h] / e6] \gx' f;] \ M

^–% #–@ *–& (–#

(–* &–$ !) – ( %–@

$–! ^–# !–) &–$

*–% &–@ %–$ &–^

d]/f] ul0ft, sIff ! 87

lx;fa u/fF} M ^*
±@ ±!
%$
±$ ±# ^*
–@ –!
%$
–$ –#

^±@Ö *±)Ö &±#Ö
^–@Ö *–)Ö &–)Ö

vfnL 7fpF eg'{xf];\ M ≠^ @ ± ≠%

#± ! ≠$ %±

#– ≠ @ $– ≠! &– ≠ $

88 d]/f] ul0ft, sIff !

lx;fa u/fF} M @ ± @≠ $

-s_ tkfOF;{ uF @ cf6] f k]lG;n 5g\ .
@ cf6] f kl] G;n pkxf/ kfpg'eof] .
ca hDdf sltcf]6f k]lG;n eP <

-v_ afn] ^ ?lkofF lbg'eof] . ±≠
cfdfn] # ?lkofF lbge' of] .
ca hDdf slt ?lkofF eof] <

-u_ d/] f] 3/df $ hgf 5f}F . d]/f] ;fyLsf] ±≠
3/df # hgf 5g\ . b'js} f] 3/df ±≠
u/L hDdf slt hgf x'G5g\ < ±≠

-3_ l5d]sLsf * cf]6f afvf| lyP .
pgn] @ cf6] f afvf| ar] 5] g\ .
ca sltcf6] f afvf| afsF L /x] <

-ª_ xKtfsf & lbgdWo] ! lbg ljBfno
hfg'kb}{g . xKtfdf hDdf slt lbg
ljBfno hfgk' 5{ <

-r_ d/] f] 3/df ( cf]6f ufO{j:t' 5g\ . ltgLx¿dWo]

@ cf6] f uf?] 5g\ . uf]?afxs]

cGo sltcf]6f ufOj{ :t' /x5] g\ < ± ≠

d]/f] ul0ft, sIff ! 89

x]/fF}, d}n] slt l;s]F <
yf/] }df l7s -_ nufpg'xf];\ M

j|md;} uF cfpg] ;ªV\ ofª\s /fv]/ vfnL 7fpF egx{' f];\ M

#%
^(

lx;fa ugx'{ f];\ M ( (
^ @
((

%!

hf8] g\ 'xf];\ M %±)≠ )±)≠

!±#≠ ^±#≠ %±%≠

#±$≠ % @)
±# ±! ±!
@
±%

90 d/] f] ul0ft, sIff !

ofu] kmn ( cfpg] af6f] kQf nufO{ es'G8f] e6] g\ 'xf];\ M

&±@ #±^ (±) #±# *±!
!±% *±! %±$ )±* ^±$
!±# &±@ @±% $±! #±&

$ ± % ^ ± # @ ± * !) ± ) ! ± (

@±& )±( $±@ @±! #±%

d/] f] ul0ft, sIff ! 91

36fpgx' f];\ M ^–$≠ (–$≠

*–#≠ &–#≠ %–!≠

*–*≠ * (%
–% –@ –$
^
–#

lx;fa u/fF} M

-s_ xl/;Fu ( cf6] f uR' rf /x5] g\ . bfhn' ] @ cf6] f u'Rrf lbge' of] . xl/;uF
sltcf]6f uR' rf eP <

-v_ /ldnf;uF ^ cf6] f :ofp lyP . pgn] # cf]6f :ofp cfÇgL alxgL
ldgfnfO{ lbOg\ . ca /ldnf;uF sltcf]6f :ofp afsF L eP <

-u_ l5ds] Lsf] 3/df & cf6] f ufO{ lyP . pgn] @ cf6] f ufO{ ar] 5] g\ . ca
sltcf]6f ufO{ afFsL /x] <

36fpg'xf];\ M

#– ≠! %± ≠^ (–&≠

@± ≠% *± ≠* ^–@≠

92 d]/f] ul0ft, sIff !