math in nepali

!! bl] v @) ;Ddsf ;ª\Vofx¿ / ;ªV\ ofª\sx¿ (

!! b]lv @) ;Ddsf uGtL

!) sf] ;dx" agfcfF} M

d/] f] ul0ft, sIff ! 93

!! bl] v @) ;Ddsf uGtL

oxfF sltcf]6f v/fof] 5g\ <

dfly !) / $ cf6] f v/fof] 5g\ .
!) / $ ldnfpbF f !$ xG' 5 . o;nfO{ rfw} elgG5 .

bz Ps bz Ps bz Ps bz Ps bz Ps
!! afx| t]x| !$ kGw|

!! !$
P3f/ rfw}

bz Ps bz Ps bz Ps bz Ps bz Ps
@)

;fx] | ;q c7f/ pGgfO; la;

94 d/] f] ul0ft, sIff !

uGtL u//] nV] g'xf;] \ M

bz Ps !!
!!

bz Ps

bz Ps

bz Ps

d/] f] ul0ft, sIff ! bz Ps

95

uGtL u/]/ n]Vgx' f];\ M bz Ps
bz Ps
96 bz Ps
bz Ps
bz Ps

d/] f] ul0ft, sIff !

df ;ª\Vof eg{x' f];\ M

!) / # ldnfpbF f x'G5 .

!) / & ldnfpbF f x'G5 .

!) / !) ldnfpFbf xG' 5 .

!) / ldnfpFbf !% x'G5 .

@) ;Ddsf ;ªV\ ofx¿ uGtL ug'{xf];\ M

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

tn lbOPsf j:t'x¿ uGtL ug{x' f];\ M

:ofp

d]/f] ul0ft, sIff ! rsn]6

97

tflnsf k"/f ug'x{ f;] \ M

! bz / ! Ps ≠ !! P3f/

!! !!

! bz / @ Ps ≠ !@ afx|

!@ !@

!# !# ! bz / # Ps ≠ !# tx] |

98 d]/f] ul0ft, sIff !

tflnsf k/" f ug{'xf;] \ M

! bz / $ Ps ≠ !$ rf}w
!$

! bz / % Ps ≠ !% kGw|
!%

!^ ! bz / ^ Ps ≠ !^ ;f]x|

d/] f] ul0ft, sIff ! 99

tflnsf k/" f ug{x' f];\ M

! bz / & Ps ≠ !& ;q
!&

! bz / * Ps ≠ !* c7f/
!*

100 d/] f] ul0ft, sIff !

tflnsf k/" f ugx{' f];\ M

! bz / ( Ps ≠ !( pGgfO;
!(

@ bz ≠ @) la;
@)

d]/f] ul0ft, sIff ! 101

l7s cufl8 s] cfpF5 <

!$ !% !@ !*
!! !& @)

l7s k5fl8 s] cfpF5 < !%
!*
!! !#
!% !^
!& !$ !@ !!

;fgf] ;ª\VofnfO{ nufpg'xf;] \ M & !&
!) !*
!& !* !$ !%
d/] f] ul0ft, sIff !
@) !( !* !&

7n' f] ;ª\VofnfO{ nufpgx' f];\ M

( !( * !@
!! !% ( !$

102

larsf] ;ª\Vof eg{'xf];\ M !% !&

!@ !$

!) !@ !* @)

!! !# !# !%

cufl8 / k5fl8sf ;ª\Vofx¿ egx'{ f;] \ M

!@ !%

!^ !*

!( !$

vfnL 7fpF eg{'xf;] \ M

!) !@ !# !%

!% !^ !( @)

!^ !% !$ !@

d/] f] ul0ft, sIff ! 103

;ae} Gbf ;fgf] ;ªV\ ofnfO{ nufpgx' f];\ M

!@ !# !! !$ !# !^

!$ !# !@ !# !& !(

!! !& !* !( @) !#

!% !$ !& !) !* !(

;a}eGbf 7'nf] ;ª\VofnfO{ nufpgx' f];\ M

!@ !# !$ !$ !! !&

!# !% !@ !( !% !$

!* !^ !$ !^ @) !$

!$ !^ !! !@ !% !(

104 d/] f] ul0ft, sIff !

@) ;Ddsf ;ªV\ ofx¿sf] hf]8 !)

hf8] f}F M

;Ltf;Fu !) cf]6f s/] f 5g\ . xl/;uF % cf6] f s/] f 5g\ . pgLx¿;Fu
hDdf slt s/] f eP <

ul0ftLo jfSodf M !) ± % ≠ pQ/ M s/] f

hf8] \gx' f;] \ M !) ± * ≠
!) ± !) ≠
!) ± @ ≠

!) ± & ≠

hDdf rsn]6sf] ;ª\Vof slt xf]nf <

!# cf]6f rsn]6 $ cf6] f rsn6]

ul0ftLo jfSodf M !# ± $ ≠ pQ/ M rsn6]

hf]8g\ 'xf;] \ M !$ ± @ ≠
!% ± $ ≠
!@ ± ! ≠
!! ± & ≠ 105

d]/f] ul0ft, sIff !

hf8] \g'xf;] \ M !@ ± % Ö
!! ± ! Ö
!@ ± @ Ö !% ± ! Ö
!@ ± & Ö ! ± !* Ö
!$ ± # Ö !) ± $ Ö
^ ± !@ Ö % ± !) Ö
# ± !$ Ö
!) ± * Ö d/] f] ul0ft, sIff !

106

lx;fa ug{x' f;] \ M

6]andf ^ cf6] f :ofp 5g\ . cfdfn] $ cf]6f yKge' of] . a'afn] klg #
cf]6f yKg'eof] . ca 6]andf hDdf sltcf]6f :ofp eP <

^

^±$

^±$±#

ul0ftLo jfSodf M ^ ± $ ± # ≠ !# cf6] f :ofp

hf]8f}F M &±#±% ≠

*±@±$ ≠

(±!±^ ≠ %±%±# ≠

@±#±$ ≠ %±@±! ≠

$±#±# ≠ * ± @ ± !) ≠

d]/f] ul0ft, sIff ! 107

lx;fa ug{x' f];\ M

ufd] f;Fu * cf]6f s]/f 5g\ . ;Gtf]if;Fu % cf6] f s/] f 5g\ . pgLx¿;Fu
hDdf sltcf6] f s]/f eP <

* cf]6f s]/f % cf6] f s/] f

ul0ftLo jfSodf M * ± % ≠ !) df uGtL ug]{ xf] eg] ;lhnf]
xG' 5 . To;}n] klxnf !) agfP/
hDdf slt xG' 5 < afFsL /xs] fnfO{ !) df hf]8fF} .

(±% ≠ !) agfpgsf nflu % cf]6f
s]/faf6 @ cf]6f s]/f 5'6\ofO{
* cf]6f s]/fdf ldnfpg]

* ± @ ± # ≠ !) ± #

!) / # ldnfpbF f xG' 5 .

pQ/ M cf6] f s]/f

108 d/] f] ul0ft, sIff !

* ± % s;/L hf]8g\ ] <

!= !) agfpgsf nflu * df hf8] \g'k5{ . * ±%

@= % nfO{ / df 56' \ofpg'xf];\ . @#
!)
#= !) agfpgsf nflu * / hf8] g\ 'xf];\ . !#

$= !) / hf]8\bf x'G5 .

o;/L klg lx;fa ug{ ;lsG5 M
*±% ≠*±@±#

≠ !) ± #
≠ !#

!) agfO{ hf]8g\ x' f];\ M

*±$ ≠ &±% ≠

(±@ ≠ ^±% ≠

d]/f] ul0ft, sIff ! 109

/ª e/L hf]8 ugx{' f];\ M !!

 d]/f] ul0ft, sIff !

( ± @ ≠



^ ± ^ ≠



( ± ^ ≠



( ± * ≠



( ± ( ≠



& ± % ≠

110

lx;fa ug'{xf;] \ M

;Ltf;uF # cf]6f s]/f 5g\ . xl/;uF * cf6] f s/] f 5g\ . pgLx¿;Fu
hDdf sltcf6] f s/] f eP <

# cf]6f s/] f * cf6] f s/] f

* nfO{ 6'jm| o\ fP/ !) agfP/
hf]8fF} M
#±*≠#±&±!

≠ !) ± !
≠ !!

# nfO{ 6j' |m\ofP/ klg !) agfpg ;lsG5 .
#±*≠!±@±*

≠ ! ± !)

≠ !!

ul0ftLo jfSodf M ( ± # ≠

hDdf slt x'G5 <

@±( ≠ $±* ≠

^±* ≠ *±( ≠

d/] f] ul0ft, sIff ! 111

lx;fa ug'{xf;] \ M

hDdf sltcf]6f r/fx¿ 5g\ <

( cf]6f r/f ^ cf6] f r/f

ul0ftLo jfSodf M ( ± ^ ≠ !% pQ/ M !% cf6] f r/f

7f8f] ¿kdf /fv/] hf]8g\ ] cEof; u/fF} M (
±^
( ± ^ ≠ !% !%

* ± # Ö !! &±%Ö ^±*Ö

±

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

112

hf]8g\ 'xf;] \ M

(* ( * &

±@ ±# ±# ±$ ±%

&( * * (

±& ±% ±% ±^ ±$

** ( ( (

±* ±& ±^ ±& ±(

!@ !# !$ !^ !%
±$ ±# ±$ ±$ ±$

d/] f] ul0ft, sIff ! 113

hf8] \g'xf];\ M df s'g ;ªV\ of /fVbf !% xG' 5 <

df s'g ;ªV\ of /fVbf !@ xG' 5 <

&

+
)+ !+
$ + !@ ^ + ( + !% + &
!!
df sg' ;ªV\ of /fVbf !& xG' 5 < ^ +
!#
!
!)
df sg' ;ª\Vof /fVbf @) x'G5 <

+ + + +
+
!! !# @)

!& +

+ d]/f] ul0ft, sIff !

!%

114

@) ;Ddsf ;ªV\ ofx¿sf] 36fp !!

36fcfF} M

;Ltf;uF !@ cf6] f s/] f lyP . pgn]
@ cf]6f vfOg\ . ca sltcf6] f s/] f
afFsL /x] <

ul0ftLo jfSodf M !@ – @ ≠ pQ/ M s]/f

36fpgx' f];\ M !^ – ^ ≠
!% – % ≠
!# – # ≠
!* – * ≠ !% cf6] f rsn]6

!% cf]6f rsn6] sf] yk' |fa] f6 # cf6] f
aR] bf sltcf6] f rsn6] afFsL /x] <

ul0ftLo efiffdf M !% – # ≠ pQ/ M rsn6]

36fpgx' f;] \ M !^ – ! ≠
!& – $ ≠
!# – @ ≠
!( – # ≠ 115

d]/f] ul0ft, sIff !

hf8] / 36fp

6]andf hDdf & cf]6f :ofp 5g\ . cfdfn] @ cf6] f :ofp lemSge' of] .
To;kl5 afafn] # cf6] f :ofp lemSg'eof] eg] 6]andf sltcf6] f :ofp afFsL
/x] <

&

&–@

&–@–#

ul0ftLo jfSodf– & – @ – # Ö @ pQ/ M @ cf]6f :ofp

slt afFsL x'G5 <

%–@–! ≠ *–@–@ ≠

(–$–# ≠ *–%–! ≠

^–$–! ≠ $–!–! ≠

&–!–$ ≠ !) – @ – # ≠

116 d/] f] ul0ft, sIff !

36fpg'xf];\ M

k;ndf hDdf !@ cf]6f l;;fsnd 5g\ . ( cf6] f l;;fsnd k;n]n]
ar] ]5 . sltcf6] f l;;fsnd afFsL /x] <

!) af6 36fpbF f ;lhnf] x'G5 .

!@ egs] f] !) / @ xf] .

!) af6 ( 36fcf}F .

ca ! / @ afFsL /xG5 .

! ± @ egs] f] xf] .

ul0ftLo jfSodf M !@ – ( ≠ pQ/ M cf6] f l;;fsnd

!) agfO{ 36fpg'xf;] \ M

!# – * ≠

!! – & ≠ 117

d/] f] ul0ft, sIff !

!@ – ( slt xG' 5 <

!= !) af6 ( 36fpgsf nflu klxn] !@ !@ – (
nfO{ / df 5'6o\ fpgx' f];\ .

@= !) af6 36fp ugx'{ f];\ . @ !) – ( ≠ !

#= / ldnfpg'xf];\ .

o;/L klg lx;fa ug{ ;lsG5 M
!@ – ( ≠ @ ± !) – (

≠@±!
≠#

!) agfO{ 36fpgx' f];\ M !# – ( ≠

!@ – & ≠

!^ – ( ≠ !% – & ≠

118 d]/f] ul0ft, sIff !

36fpg'xf;] \ M

xl;gf;uF hDdf !@ cf6] f :ofp 5g\ . tLdWo] pgn] # cf]6f :ofp efOnfO{
lbOg\ . pgL;Fu hDdf sltcf6] f :ofp afsF L /x] <

!) af6 # 36fpbF f & afFsL /xG5 .
& / @ ldnfpFbf x'G5 .

o;/L lx;fa ug{ ;lsG5 M pQ/ M cf6] f :ofp
!@ – # ≠ @ ± !) – # !@ – $ ≠

≠@±&
≠(
ul0ftLo jfSodf M !@ – # ≠

!) agfO{ 36fpgx' f;] \ M

!^ – & ≠

d/] f] ul0ft, sIff ! 119

36fcf}F M

5fgfdf !@ cf]6f k/]jf lyP . # cf6] f k/]jf p8] . 5fgfdf sltcf]6f
k/]jf afsF L /x] <

ul0ftLo jfSodf M !@ – # Ö ( pQ/M ( cf]6f k/j] f
-t;] f]{ ¿kdf_
-7f8f] ¿kdf_
!@ – # Ö ( !@
–#
36fP/ 7f8f] ¿kdf /fVg'xf;] \ M (

!! – % Ö ^ !$ – ^ Ö !# – * Ö

–– –

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

120

36fpg'xf;] \ M !@
–$
!!
–! !%
!) –%

!# !*
–% –&

!&
–^

!( !$ 121
–& –&

!= rf/cf6] f /f]6L lyP . Pp6f /f]6L ss' /' nfO{ lbOof] .
ca sltcf]6f /f]6L afFsL /x] <

$–!≠

d]/f] ul0ft, sIff !

hf8] ug'{xf];\ M (±&Ö
*±*Ö
!! ± ! Ö (±(Ö
!@ ± @ Ö !$ ± $ Ö
!# ± # Ö !@ ± * Ö
!$ ± $ Ö !) ± !) Ö
!% ± % Ö
!^ ± $ Ö

36fp ug'{xf];\ M !) – ^ Ö
!@ – @ Ö
!) – % Ö !$ – # Ö
!@ – ^ Ö !^ – ( Ö
!$ – * Ö !* – * Ö
!^ – * Ö !( – ( Ö
!* – $ Ö
!( – & Ö

!= cfdfn] !% cf]6f /f]6L ksfpg'eof] . % cf6] f /f6] L d/] f] ul0ft, sIff !
5f]/LnfO{ lbge' of] . ca cfdf;Fu sltcf6] f /f]6L
afFsL /x] <

122

hf]8fF} / 36fcf}F M

6]andf hDdf ^ cf6] f :ofp 5g\ . afafn] @ cf]6f :ofp lng'eof.] kl5 cfdfn]
# cf6] f :ofp lsg/] 6a] ndf /fVg'eof] . ca 6a] ndf sltcf]6f :ofp eP <

^
^–@

^–@±#

ul0ftLo jfSodf M ^ – @ ± # Ö & pQ/ M & cf6] f :ofp

hDdf % cf6] f :ofp 5g\ . cfdfn] $ cf6] f :ofp lsGg'eof] . kl5
afafn] # cf6] f :ofp lnge' of] . ca hDdf sltcf]6f :ofp eP <

%

ul0ftLo jfSodf M % ± $ – # Ö ^ %±$
%±$–#
pQ/ M ^ cf6] f :ofp

lx;fa ug{x' f;] \ M %±!–$ ≠

^–!±$ ≠

*–#±% ≠ #±&–$ ≠

d/] f] ul0ft, sIff ! 123

!@ hf/] / lahf/] 5'6o\ fcfF} hf]/

5nkmn u/f}F M
lahf/]

!@

#$

lbOPsf] h:t} u/L @÷@ cf6] f j:t'sf] ;dx" agfO{ hf]/ / lahf]/
5'6o\ fpg'xf;] \ M

% ljhf/]

124 d/] f] ul0ft, sIff !

hf/] lahf]/

7f8f] wsf{ tfg]/ hf]/ / lahf]/ 56' \ofpg'xf];\ M

d]/f] ul0ft, sIff ! 125

hf]/ / lahf/]

#@

t];f]{ wsf{ tfGbf tn / dfly a/fa/ ePg . t];f]{ wsf{ tfGbf tn / dfly a/fa/ eof] .

%$

t];f]{ wsf{ tfGbf tn / dfly a/fa/ ePg . t];f]{ wsf{ tfGbf tn / dfly a/fa/ eof] .

t;] f]{ wsf{ tfg]/ hf]/ / lahf]/ 5'6\ofpgx' f;] \ M

^ hf]/

126 d]/f] ul0ft, sIff !

hf]/ / lahf/] ;ªV\ of 56' \ofP/ nV] g'xf];\ M

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

hf/] lahf]/

d]/f] ul0ft, sIff ! 127

!# @) ;Ddsf ;ª\Vofx¿ cIf/df

k9g\ x' f];\ / cIf/df nV] g'xf;] \ M

! Ps Ps Ps Ps

@ bO' { d/] f] ul0ft, sIff !

# tLg

$ rf/

% kfFr

^5

& ;ft

* cf7

( gf}

!) bz

!! P3f/

!@ afx|

!# t]x|

!$ rf}w

!% kGw|

!^ ;fx] |

!& ;q

!* c7f/

!( pGgfO;

@) aL;

128

tn lbOPsf ;ªV\ ofªs\ x¿nfO{ cIf/df n]Vgx' f;] \ M

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

cIf/df nl] vPsf] ;ªV\ ofnfO{ ;ª\Vofª\sdf n]Vg'xf];\ M

tLg afx|
rf/ rf}w
Ps pGgfO;
bz c7f/
5 ;fx] |

d]/f] ul0ft, sIff ! 129

!$ j|mdfTds ;ª\Vofx¿

5nkmn u/fF} M

kj| ]z åf/

aflx/ d/] f] ul0ft, sIff !

130

5nkmn u/f}F M aflx/

k|j]z åf/ 131

k|jz] åf/af6 klxnf] $ :yfgdf /x]sf hgfj/x¿

k|j]zåf/af6 rf}yf] :yfgdf /xs] f] hgfj/

nufpg'xf];\ M

k|jz] åf/af6 klxnf] # :yfgdf /x]sf hgfj/

kj| ]zåf/af6 bf];f| ] :yfgdf /xs] f] hgfj/

aflx/ lg:sg] åf/af6 rf}yf] :yfgdf /xs] f] hgfj/

aflx/ lg:sg] åf/af6 t];|f] :yfgdf /x]sf] hgfj/

d/] f] ul0ft, sIff !

x/] f}F, dn} ] slt l;s]F <
l;;fsndsf] ;ªV\ of uGtL u/L n]Vgx' f;] \ M

df ldNg] ;ªV\ of egx{' f;] \ M

!) / @ ldnfpbF f xG' 5 .
!) / ldnfpbF f !& x'G5 .

l7s cufl8 s] cfp5F < !^ !)
!! !%
!#

7n' f] ;ªV\ ofnfO{ nufpg'xf];\ M

!# !$ !^ !@

;a}eGbf ;fgf] ;ª\VofnfO{ nufpg'xf;] \ M

!@ !# !$ !$ !! !&

132 d]/f] ul0ft, sIff !

vfnL 7fpF eg'x{ f];\ M

!! !$

hf]8\gx' f];\ M !# ± % ≠

!) ± $ ≠ !@ ± & ≠

hf]8\g'xf;] \ M @±#±%≠

(±!±%≠

!) agfO{ hf]8g\ x' f;] \ M

*±^≠ (±%≠ &±$≠

(* (^
±# ±& ±& ±%

d/] f] ul0ft, sIff ! 133

df sg' ;ªV\ of /fVbf !) x'G5 <

%

+

@ + !) + &

+

$

36fpgx' f];\ M !% – % ≠ !^ – $ ≠

!@ – @ ≠ !) – $ – @ ≠

*–$–!≠ !$ – ^ ≠ !! – * ≠
!@ – # ≠
!% !^ !*
!$ –& –* –%
–#

lx;fa ugx{' f;] \ M *±!–@≠

%–!±@≠ d/] f] ul0ft, sIff !

134

hf]/ / lahf]/ 5'6\ofpgx' f;] \ / n]Vgx' f];\ M

tn lbOPsf ;ªV\ ofªs\ x¿nfO{ cIf/df n]Vgx' f;] \ M

% !$
!@ !(

cIf/nfO{ ;ª\Vofªs\ df n]Vgx' f];\ M

;q kGw|
P3f/ tx] |

kj| z] åf/af6 kfFrfF} :yfgdf /xs] f] hgfj/df nufpg'xf;] \ M

k|j]z åf/ aflx/

aflx/ lg:sg] rfy} f] :yfgdf /x]sf] hgfj/df nufpg'xf];\ M

kj| ]z åf/ aflx/

d]/f] ul0ft, sIff ! 135

!% @! bl] v !)) ;Ddsf ;ª\Vofx¿

bz÷bz ugf}F M

@ bz ≠ @) # bz ≠ #) $ bz ≠ $)

% bz ≠ %) ^ bz ≠ ^) & bz ≠ &)

* bz ≠ *) ( bz ≠ () !) bz ≠ !))

hf]8f ldnfpg'xf];\ M ^)
$)
! bz &)
@ bz !)
# bz #)
$ bz @)
% bz %)
^ bz
& bz d/] f] ul0ft, sIff !

136

pbfx/0f x]/L vfnL 7fpF egx{' f];\ M

@ bz / ! @!

# bz #)

d]/f] ul0ft, sIff ! 137

pbfx/0f x/] L vfnL 7fpF egx{' f];\ M

# bz / ! #!

$ bz $)

138 d]/f] ul0ft, sIff !

pbfx/0f x]/L vfnL 7fpF egx{' f];\ M

$ bz / ! $! $ bz / @

$ bz / # $ bz / $

$ bz / % $ bz / ^

$ bz / & $ bz / * %)
$ bz / ( % bz

l7s cufl8 s] cfp5F <

@% #@ $*

l7s k5fl8 s] cfpF5 < $%

@@ #(

;fgf] ;ªV\ ofnfO{ nufpgx' f;] \ M

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

7'nf] ;ªV\ ofnfO{ nufpg'xf];\ M

@# @$ #% #@ $& $(

d]/f] ul0ft, sIff ! 139

larsf] ;ªV\ of eg'x{ f;] \ M @% @&

@! @#

#) #@ @* #)

$! $# $$ $^

cufl8 / k5fl8sf ;ªV\ ofx¿ eg{x' f;] \ M

@$ @*

## $#

$( #^

vfnL 7fpF eg'x{ f];\ M

@!

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

140

pbfx/0f x/] L vfnL 7fpF egx'{ f];\ M

% bz / ! %!

d]/f] ul0ft, sIff ! 141

pbfx/0f x]/L vfnL 7fpF eg'x{ f;] \ M

^ bz ^)

142 d/] f] ul0ft, sIff !