This material is used for teacher and student of secondary level.

1. 1
ul0ft z[ªvnf – &
aLhul0ft
P;Pn;L k/LIffsf] ljlzi6Ls/0f tflnsf 2065 cg';f/ aLhul0ftaf6 5f]6f] pQ/ cfpg] 4 cf]6f
k|||Zgsf] 8 cªs / nfdf] pQ/ cfpg] 4 cf]6f k|Zgsf] 16 cªssf] u/L hDdf 24 cªs ef/sf]
k|Zgx¿ ;f]lwg] k|fjwfg 5 .
d=; tyf n=;
P;Pn;L k/LIffdf o; kf7af6 4 cªsef/sf] Pp6f nfdf] pQ/ cfpg] k|Zg ;f]lwg] k|fjwfg /x]sf]
5 .
pbfx/0f M 1
d=;= lgsfNg'xf]; M
(SLC 2065 EDR)
;dfwfg M
klxnf] cleJoGhs
(1)
bf];|f] cleJoGhs
(1)
t];|f] cleJoGhs
(1)
∴ d=;= =
(1)
pbfx/0f M 2 d=;= lgsfNg'xf]; M /
;dfwfg M klxnf] cleJo~hs
=
-v08Ls/0f u/]sf]_ (1)
bf];|f] cleJo~hs

2. 2
-v08Ls/0f u/]sf]_ (1)
t];|f] cleJo~hs =
(1)
d=;= (1)
dflysf] pbfx/0fsf] ;xfotfn] lgDglnlvt ;d:ofx¿sf] d=;=lgsfNg'xf];M
1. / pQ/ M
2. / pQ/ M
3. / pQ/ M
4. / pQ/ M
5. / pQ/ M
6. / pQ/ M
7. / pQ/ M
pbfx/0f M 3 n=; lgsfNg' xf]; M /
;dfwfg M
klxnf] cleJo~hs
 sf] ;"q k|of]u u/]sf]  (1)
bf];|f] cleJo~hs
(1)
t];|f] cleJo~hs
 v08Ls/0f u/]sf] 
(1)

3. 3
∴ n=;= (1)
pbfx/0f M 4 n=;= lgsfNg'xf]; .
/
;dfwfg M
klxnf] cleJoGhs (1)
bf];|f] cleJoGhs
(1)
t];|f] cleJoGhs
(1)
 n=;= (1)
pbfx/0f M 5 n=; lgsfNg' xf]; M /
klxnf] cleJoGhs
(1)
bf];|f] cleJoGhs
(1)
t];|f] cleJoGhs
(1)
 n=;= (1)
dflysf] pbfx/0fx¿sf] ;xfotfn] lgDglnlvt ;d:ofx¿sf] n=;=lgsfNg'xf];
1. /
2. /
3. /
4. /
5. /

4. 4
6. /
7. /
8. /
9. /
pQ/M
1.
2.
3.
4.
5.
6.
7.
8.
9.
aLhLo leGgsf] ;/nLs/0f
P;Pn;L k/LIffdf aLhLo leGgsf] ;/nLs/0faf6 nfdf] pQ/ cfpg] 4 cªs ef/sf] Pp6f k|Zg
;f]lwg] k|fjwfg /x]sf] 5 .
pbfx/0f : 1 ;/n ug'{xf]; .
;dfwfg M
=
= (1)
=
= (1)
=
= (1)
= (1)

5. 5
pbfx/0f M 2 ;/n ug'{xf]; M
;dfwfg M
(1)
(1)
= (1)
= (1)
pbfx/0f M 3 ;/n ug'{xf]; M
;dfwfg M
(1)
(1)
(1)
(1)
dfly lbOPsf pbfx/0fsf] ;xfotf lnO{ lgDglnlvt ;d:ofx¿sf] ;/n ug'{xf]; M
1. (SLC 2063 D2) pQ/ M
2. (SLC 2065 EDR) pQ/ M
3. pQ/

6. 6
4. pQ/ M
5. (SLC 2065 A2) pQ/ M
6. pQ/ M
7. pQ/ M
3ftfªs
3ftfªs tyf tT;DaGwL ;dLs/0faf6 b'O{ cªsef/sf] 5f]6f] pQ/ cfpg] Pp6f k|Zg / 3ftfªsLo
;dLs/0f jf d"n / ;8{ tyf ;fwf/0fd"ns ;dLs/0f dWo]af6 4 cªs ef/sf] Pp6f nfdf] pQ/
cfpg] k|Zg klg ;f]lwg] k|fjwfg /x]sf] 5 .
-s_ 5f]6f] pQ/ cfpg] k|Zgx¿ M
pbfx/0f M 1 dfg lgsfNg'xf]; M
;dfwfg M
x/nfO{ c+z / c+znfO{ x/df nUbf 3ftfªssf] lrxg kl/jt{g x'G5] (1)
= [ / x'gfn] ]
= = = (1)
pbfx/0f M 2 ;/n ug'{xf]; M (2065 WDR)
;dfwfg M
=
= (1)
=
=
= 3 (1)
dflysf] pbfx/0fsf] ;xfotfn] lgDglnlvt ;d:ofx¿sf] dfg lgsfNg'xf]; M
1) pQ/ M 2) pQ/ M

7. 7
3) pQ/ M 3 4) pQ/ M
5) pQ/ M 1 6) pQ/ M 2
7) pQ/ M
-v_ nfdf] pQ/ cfpg] k|Zgx¿ M
pbfx/0f : 1 ;/n ug'{xf]; M
;dfwfg M
= (1)
= (1)
= (1)
=
= 1 pQ/ (1)
pbfx/0f M 2 ;/n ug'{xf]; M
;dfwfg M
pbfx/0f M 3 ;/n ug'{xf]; M
;dfwfg M
= (1)
= (1)
= (1)
= =
= 1 pQ/ (1)

8. 8
pbfx/0f M 4 k|dfl0ft ug'{xf]; M
;dfwfg M
= (1)
= (1)
= (1)
= = 1 (1)
pbfx/0f M 5 k|dfl0ft ug'{xf]; M olb eP k|dfl0ft u/ M
;dfwfg M
oxf“,
jf,
/
L.H.S.=
= (1)
=
= (1)
= (1)
= 1 = R.H.S. k|dfl0ft eof] . (1)
dflysf pbfx/0fsf] ;xfotfaf6 lgDglnlvt ;d:ofx¿ ;dfwfg ug'{xf]; M
1. pQ/ M 1
2. pQ/ M1
3. pQ/ M1

9. 9
4. (SLC 2063D2) pQ/ M
5. k|dfl0ft ug'{xf]; M
(i)
(ii)
6. olb eP, k|dfl0ft ug'{xf]; M
7. olb eP, k|dfl0ft ug'{xf]; M
3ftfªsLo ;dLs/0f
-s_ nfdf] pQ/ cfpg] k|Zgx¿ M
pbfx/0f M 1 xn ug'{xf]; M
;dfwfg M
jf, x'G5 . ] (1)
jf, ;femf lnPsf] . ]
jf, jf (1)
jf,
jf, (1)
∴ pQ/ (1)
pbfx/0f : 2 xn ug'{xf]; M
;dfwfg M
jf,
jf, [ kbx¿nfO{ df abn]sf] ] (1)
dfgf}“
tj,
jf, [ v08Ls/0f u/]sf] .]
jf,
jf, (1)
olb eP x'G5 .

10. 10
sf] dfg k|lt:yfkg ubf{ ∴ (1)
olb eP x'G5 .
sf] dfg k|lt:yfkg ubf{ ∴ (1)
∴ pQ/
pbfx/0f : 3 xn ug'{xf]; M
;dfwfg M cyjf,
dfgf}+
(1)
cyjf,
cyjf,
cyjf,
cyjf,
cyjf,
cyjf, (1)
cyjf, sf] dfg k|lt:yfkg ubf{]
cyjf,
∴ (1)
cyjf,
(1)
∴
dflysf] pbfx/0fx¿sf] ;xfotfn] lgDglnlvt k|Zgx¿ xn ug'{xf]; M
1. pQ/ M 1; 2 2. pQ/ M ± 2
3. pQ/ M 1, 2 4. pQ/ M 0; 2
5. pQ/ M 6. pQ/ M 3
7. pQ/ M 1, 2 8. pQ/ M -1
9. pQ/ M 2, 3 10. pQ/ M 1
11. pQ/ M ±3 12. pQ/ M 3