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

1. 1
ul0ft z[ªvnf – !
;d"x (Sets)
P;Pn;L k/LIffsf] ljlzi6Ls/0f tflnsf 2065 cg';f/ æ;d"xÆ kf7af6 4 cªssf] Pp6f nfdf] pQ/
cfpg] k|Zg ;f]lwg] k|fjwfg /x]sf] 5 . oxf“ ;d"x ;DalGw dxŒjk"0f{ k|Zgx¿ pbfx/0f;lxt k|:t't
ul/Psf] 5 .
pbfx/0f : 1
olb
/ eP slt xf]nf tQf nufO e]g lrqdf
b]vfpg'xf]; .
;dfwfg M
lbOPsf], (1)
;"q cg';f/,
(1)
or, (1)
or,
or,
or,
or, 1
(1)
A B
12 8 18
9
6 7
20
C16

2. 2
pbfx/0f : 2h
75 hgfnfO{ ;f]lwPsf] k|Zgdf 55 hgfn] lrof / 25 hgfn] skmL lkpg dg k/fpg] atfP . olb 15
hgfn] b'a} dggk/]sf] atfP eg] e]g lrq agfO{ lgDg k|Zgsf] pQ/ lbg'xf]; M
(i) b'a} dg k/fpg] slt hgf /x]5g < (ii) skmL dfq dg k/fpg] slt hgf /x]5g <
;dfwfg M
oxf“, lrof / skmL dg k/fpg] dflg;x¿sf] ;d"xnfO{ qmdzM / n] hgfp“bf,
;'q cg';f/, (1)
or,
or,
or,
or,
(i) b'a} dg k/fpg] ;ªVof (1)
(ii) skmL dfq dg k/fpg] (1)
pbfx/0f M 3
Pp6f ;d'bfodf /x]sf s]xL JolStx¿nfO{ ;f]lwPsf] Pp6f k|Zgdf lrof lkpg dg k/fpg] 54 hgf,
slkm lkpg dg k/fpg] 37 hgf, b'j} lrh lkpg dg k/fpg] 18 hgf / b'j} dg gk/fpg] 27 hgf
kfOof] eg],
(i) hDdf slt JolStnfO{ of] k|Zg ;f]lwPsf] lyof] <
(ii) lrofdfq lkpg dg k/fpg] slt lyP <
(iii) k|fKt glthfnfO{ e]g lrqdf ;d]t k|:t't ug'{xf]; .
T C
35 20 5
15

3. 3
;dfwfg
oxf“, lrof dgk/fpg] ljBfyL{x¿sf] ;d"xnfO{ T / skmL dgk/fpg] ljBfyL{x¿sf] ;d"xnfO{ C
dfGbf
n(T) = 54, n(C) = 37, n n , n
(i) n
= =100 (1)
(ii) n0(T) =
= = 36 (1)
(iii) e]g lrqdf k|:t't ubf{,
(2)
pbfx/0f M 4
91 hgf ljBfyL{x¿sf] Pp6f ;d"xdf ;f]lwPsf] Pp6f k|Zgdf, ul0ft ljifo dg k/fpg] 40 hgf,
lj1fg ljifo dg k/fpg] 45 hgf, cªu|]hL ljifo dg k/fpg] 30 hgf, ul0ft / lj1fg dg k/fpg]
14, lj1fg / cªu|]hL dg k/fpg] 12, ul0ft / cªu|]hL dg k/fpg] 8 / ltg} ljifo dg k/fpg] 3
hgf kfOP eg], e]g lrq agfO{ tLgcf]6} dWo] s'g} klg ljifo dggk/fpg] ljBfyL{ ;ªVof kQf
nufpg'xf]; .
;dfwfg M
lj1fg, ul0ft / c+u|]hL ljifo dggk/fpg] ljBfyL{x¿sf] ;d"xnfO{ qmdzM S, M / E n]
hgfp“bf,
oxf“, n( ) = 91,
n( ) = 40,
n(S) = 45
n(E) = 30
n(M S) = 14
n(S E) = 12 (2)
n(M E) = 8
n(M S E) = 3
n( = ?
n( ) = n(M)+n(S)+n(E)–n(M S)–n(S E)–n(M E)+n(M S E)+n( (1)
or, 91= 40+45+30–14–12–8+3+ n(
T C
36 18 19
M S
21 11 22
3
5 9
13
E

4. 4
or, 91= 118-34+ n(
n( =91- 84
= 7 (1)
ctM tLgcf]6} dWo] s'g} klg ljifo dg gk/fpg] ljBfyL{x¿ 7 hgf /x]5g .
pbfx/0f M 5
Pp6f ;d"xdf ul/Psf] ;j]{If0fdf 50% n] :ofp dg k/fpg] / 70% n] ;'Gtnf dg k/fpg]
atfP . olb 5% n] tL b'O{ dWo] b'a} dg gk/fpg] atfP eg]
(i) dflysf] tYonfO{ e]g lrqdf k|:t't ug'{xf]; .
(ii) olb Tof] ;d'xsf 60 hgfn] b'a} dgk/fpg] atfP eg] pQm ;j]{If0fdf slthgfn] efu
lnPsf /x]5g < kQf nufpg'xf]; .
;dfwfg M
oxf“, :ofp / ;'Gtnf dgk/fpg] dflg;x¿sf]
;d"xnfO{ qmdzM A / O n] hgfp“bf, (1)
(i) oxf“, ;j{k|yd b'a} dgk/fpg] k|ltzt kQf nufpg'kb{5 .
ctM
or,
or, ...................... (2)
(ii) k|Zgcg';f/, lbOPsf]n],
..................... (1)
ctM240 hgfn] ;j]{If0fdf efu lnPsf /x]5g .
pbfx/0f : 6
110 hgfnfO{ ul/Psf] Ps ;j]{If0fdf ;a}n] b"w jf lrof lkpg] atfP . h;dWo] b"w / lrof dg
k/fpg]sf] cg'kft 3:4 /x]5 . olb 30 hgfn] b'a} lkpg] atfP eg]
(i) dflysf] tYonfO{ e]g lrqdf b]vfpg'xf]; .
(ii) lrof dfq dg k/fpg] slt hgf xf]nf <
(iii) b"w dfq dg k/fpg] slt hgf xf]nf <
;dfwfg M
oxf“, b"w / lrof dg k/fpg] dflg;sf] ;d"xnfO{ qmdzM M / T n] hgfp“bf,
U
A O

5. 5
;"q cg';f/, (1)
or,
or,
or,
or,
;= af6
lrof dfq dg k/fpg] ;ªVof
b"w dfq dg k/fpg] ;ªVof
pbfx/0f : 7
s'g} ljBfnosf 575 ljBfyL{nfO{ ;f]lwPsf] k|Zgdf xflh/L hjfkm dfq dgk/fpg] eGbf
jfbljjfb k|ltof]lutf dgk/fpg] dfq ljBfyL{ bf]Aa/ /x]5g . olb b'a} k|ltof]lutf dgk/fpg] 30
hgf / s'g} klg k|ltof]lutf dggk/fpg] 20 hgf /x]5 eg]
(i) xflh/L hjfkm k|ltof]lutf dgk/fpg]sf] ;+Vof kQf nufpg'xf]; .
(ii) jfbljjfb dfq dg k/fpg] ljBfyL{ ;+Vof kQf nufpg'x]; .
(iii) pQm tYonfO{ eg] lrqdf k|:t't ug'{xf]; .
;dfwfg M
oxf“, xflh/L hjfkm k|ltof]lutf dg k/fpg] ljBfyL{ / jfbljjfb k|ltof]lutf dg k/fpg]
ljBfyL{nfO{ qmdzM Q / D n] hgfp“bf,
U
M T
30 30 50

6. 6
;'q k|of]u ubf{,
.............. (1)
or,
or,
(1)
(i) xflh/L hjfkm dgk/fpg] ;+Vof = = 205 (1)
(ii) jfbljjfb dgk/fpg] ;+Vof =
(1)
(iii) dflysf] tYonfO{ e]g lrqdf b]vfpFbf
pbfx/0f : 8
25,000 hgfdf ul/Psf] ;j]{If0fdf 16,000 hgfn] g]kfnL rnlrq dgk/]sf] atfP / 8000 hgfn]
lxGbL rnlrq dgkg]{ atfP . olb 2000 hgfn] b'a} rnlrq dg k/]sf] atfP eg] slt k|ltztn] b'a}
rnlrq x]g{ dg gk/]sf] atfP <
;dfwfg M
oxf“, g]kfnL rnlrq / lxGbL rnlrq dg k/fpg] dflg;x¿sf] ;d"xnfO{ qmdzM
N / H n] hfp“bf,
;"q cg';f/,
U
Q D
175 30 350
20

7. 7
 b'a} rnlrq x]g{ dg gk/fpg]sf] ;ªVof
b'a} rnlrq x]g{ dg gk/fpg]sf]
pbfx/0f : 9
sIff 10 sf ljBfyL{x¿nfO{ ul/Psf] Ps ;j]{If0fdf ;+uLt dg k/fpg] 21, syf dg k/fpg] 15 /
sljtf dg k/fpg] 19 hgf /x]5g . olb ;+uLt dfq dg k/fpg] 9, syf dfq dg k/fpg] 6, ;+uLt /
syf dfq dg k/fpg] 3 / ;+uLt / sljtf dfq dg k/fpg]sf] ;ªVof 5 eP e]g lrq agfO{ lgDg
k|Zgsf] pQ/ lbg'xf]; M
(i) syf / sljtf dg k/fpg]sf] ;ªVof slt hgf /x]5g <
(ii) sljtf dfq dg k/fpg]sf] ;ªVof slt hgf /x]5g <
(iii) hDdf slt ljBfyL{nfO{ k|Zg ;f]lwPsf] lyof] <
;dfwfg M
oxf“, ;+uLt, syf / sljtf dg k/fpg] ljBfyL{sf] ;d"xnfO{ qmdzM M, S / P n] hgfp“bf,
;j{k|yd, ;d"x af6,
ctM tLgcf]6} dg k/fpg]sf] ;ªVof
;d"x af6,
ctM syf / sljtf dfq dg k/fpg]sf] ;ªVof
ctM syf / sljtf dg k/fpg]sf] ;ªVof
U
M S
9 3 6
4
5 2
8
P

8. 8
;d"x af6,
ctM sljtf dfq dg k/fpg]sf] ;ªVof = 8
(iii) hDdf k|Zg ;f]lwPsf ljBfyL{ ;ªVof =
pbfx/0f : 10
lkslgs uPsf 68 hgfdf /f]6L dg k/fpg] t/ kfp/f]6L dg gk/fpg] 27 hgf eP5 . 9 hgfn] /f]6L
/ kfp/f]6L b'a} dg kg]{ atfP5 . olb 10 hgfn] b'a} dg gkg]{ atfP eg] e]g lrq agfO{ slt hgfn]
(i) kfp/f]6L dfq dg kg]{ atfP <
(ii) kfp/f]6L dg kg]{ atfP <
;dfwfg M
oxf“, /f]6L / kfp/f]6L dg k/fpg]sf] ;d"xnfO{
qmdzM S / B n] hgfp“bf,
dfly lbOPsf] pbfx/0fx¿sf] ;xfotfn] lgDglnlvt ;d:ofx¿ ;dfwfg ug'{xf]; M
U
S B
10
27 9 22

9. 9
1. Pp6f ;d"xdf /x]sf s]xL dflg;x¿nfO{ ;f]lwPsf] Pp6f k|Zgdf bf]xf]/L uLt ;'Gg dg k/fpg]
145 hgf, nf]suLt ;'Gg dg k/fpg] 115 hgf, b'j} vfnsf uLt ;'Gg dg k/fpg] 40 hgf /
30 hgfn] b'j} vfnsf] uLt ;'Gg dg gk/fpg] kfOof] eg],
(i) hDdf slt dflg;nfO{ of] k|Zg ;f]lwPsf] lyof] <
(ii) bf]xf]/L uLt dfq ;'Gg dg k/fpg] slt lyP <
(iii) k|fKt glthfnfO{ e]g lrqdf k|:t't ug'{xf]; . pQ/ M 250, 105
2. g]kfndf cfPsf 200 hgf ko{6sx¿nfO{ eStk'/ / nlntk'/ 3'dfO;s]kl5 ;f]lwPsf] k|Zgdf
eStk'/ dg kg]{ 145 hgf, nlntk'/ dg kg]{ 80 hgf, b'j} 7fp“df dg gk/fpg] 20 hgf dfq
kfOP eg],
(i) b'j} 7fp“ dg k/fpg] slt hgf lyP <
(ii) eQmk'/ dfq dg k/fpg] slt hgf lyP <
(iii) nlntk'/ dfq dg k/fpg] slt hgf lyP <
(iv) k|fKt glthfnfO{ e]g lrqdf ;d]t b]vfpg'xf]; . pQ/ M 45, 100, 35
3. Pp6f k/LIffdf 70% ljBfyL{x¿ lj1fgdf pQL0f{, 75% ljBfyL{x¿ ul0ftdf / 5% ljBfyL{x¿
b'a} ljifodf cg'lQ0f{ eP5g . olb 220 hgf ljBfyL{x¿ b'a} ljifodf pQL0f{ eP5g eg],
(i) lbOPsf] hfgsf/LnfO{ e]glrqdf k|:t't ug'{xf]; .
(ii) hDdf k/LIffyL{sf] ;ªVof kQfnufpg'xf]; . pQ/ M 440 hgf
4. 80 hgf dflg;x¿ ePsf] Pp6f ;d"xdf sf]s / km]G6f dgk/fpg] dflg;x¿sf] cg'kft 3:4
5 . olb 24 hgfn] b'a} y/L k]o kbfy{ dgk/fp“5g / 6 hgfn] b'O{ dWo] s'g} klg k]o kbfy{ dg
k/fp“b}gg eg] e]g lrq agfO lgDglnlvt ;ªVofx¿ kQfnufpg'xf]; .
(i) sf]s dgk/fpg] dflg;x¿sf] ;ªVof
(ii) km]G6fdfq dgk/fpg] dflg;x¿sf] ;ªVof pQ/ M (i) 42 hgf (ii) 32 hgf
5. Pp6f ;d'bfodf /x]sf 1000 kl/jf/df u/]sf] ;j]{If0fdf vfgf ksfpg] OGwgsf ¿kdf ;a}n]
s'g} g s'g} Pp6f dfWod k|of]u ubf{ 450 kl/jf/n] bfp/f, 370 kl/jf/n] d66Lt]n, 300
kl/jf/n] Uof;, 50 kl/jf/n] bfp/f / d66Lt]n dfq, 30 kl/jf/n] Uof; / bfp/f dfq, 45
kl/jf/n] d66Lt]n / Uof; dfq k|of]u ubf{ /x]5g eg], e]g lrq agfO{ lgDglnlvt k|Zgx¿sf]
pQ/ lbg'xf]; M
(i) slt kl/jf/n] tLgcf]6} dfWod k|of]u ubf{ /x]5g <
(ii) slt kl/jf/n] bfp/f dfq k|of]u ubf{ /x]5g <
(iii) slt kl/jf/n] Uof; dfq k|of]u ubf{ /x]5g <
(iv) slt kl/jf/n] d66Lt]n dfq k|of]u ubf{ /x]5g < pQ/ M 5, 375, 230, 280
6. s'g} ;j]{If0fdf 50% dflg;n] lrof / 65% dflg;n] b"w dg k/fpg] atfP . olb 5% n] s'g}
klg dg gkg]{ atfP / 15 hgfn] b'a} lkpg dg k/fpg] atfP eg]

10. 10
(i) pQm tYox¿nfO{ e]g lrqdf b]vfpg'xf]; .
(ii) hDdf slthgfn] ;j]{If0fdf efu lnPsf /x]5g . -pQ/ M 75_
7. Pp6f ;j]{If0f 35% n] ;+uLt / 75% n] v]ns"b dg kg]{ atfP . olb 10% n] b'O{ dWo] s'g}
klg dg gk/fpg] atfP eg]
(i) pQm tYox¿nfO{ e]g lrqdf k|:t't ug'{xf]; .
(ii) olb ;+uLtdfq dg k/fpg] 150 eP hDdf slt hgfnfO{ ;j]{If0f ul/Psf] lyof] <
-pQ/ M 1000_
8. 750 ljBfyL{nfO{ ;f]lwPsf] Ps k|Zgdf 450 hgfn] km'6an / 300 hgfn] elnan dg k/fpg]
atfP . olb 40 hgfn] s'g} klg dg gk/fpg] atfP eg]
(i) pQm tYox¿nfO{ e]g lrqdf b]vfpg'xf]; .
(ii) b'a} v]n dg k/fpg] slthgf xf]nfg <
(iii) km'6an dfq dg k/fpg] slthgf xf]nfg < -pQ/ M 40, 410_
9. 500 s[ifsnfO{ ul/Psf] ;j]{If0fdf 350 hgfn] cfn' / 250 hgfn] Kofh /f]Kg] atfP . olb 75
hgfn] b'a} g/f]Kg] atfP eg]
(i) pQm tYox¿nfO{ e]g lrqdf b]vfpg'xf]; .
(ii) b'a} dg k/fpg] slt lyP <
(iii) Kofh dfq} /f]Kg dg k/fpg] slt xf]nfg < -pQ/ M 175, 75_
10. 150 hgfnfO{ ;f]lwPsf] Ps k|Zgdf c+u|]hL uLt dfq eGbf g]kfnL uLt dfq dg k/fpg] ;+Vof
bf]Aa/ /x]5 . olb b'a} y/Lsf uLt dg k/fpg] 20 hgf, b'a} dg gk/fpg] 10 hgf eP
(i) c+u|]hL uLt dfq dg k/fpg] slt xf]nfg <
(ii) g]kfnL uLt dg k/fpg slt xf]nfg <
(iii) lbOPsf tYox¿nfO{ e]g lrqdf b]vfpg'xf]; . -pQ/ M 30, 110_
11. 300 ljBfyL{nfO{ ul/Psf] Ps ;j]{If0fdf kf]v/f dfq 3'Dg dg k/fpg] ljBfyL{ ;+Vof lrtjg
dfq 3'g dg k/fpg] ljBfyL{ eGbf bf]Aa/ /x]5 . olb b'a} :yfg 3'Dg dg k/fpg] 10 hgf /
b'a} :yfg 3'Dg dg k/fpg] 20 hgf lyP eg]
(i) lrtjg 3'Dg dg k/fpg] slt lyP xf]nfg <
(ii) kf]v/f 3'Dg dg k/fpg] slt xf]nfg <
(iii) pQm tYox¿nfO{ e]g lrqdf b]vfpg'xf]; -pQ/ M 115, 200_
12. Pp6f ;j]{If0fdf 300 hgfn] efu lnPsf lyP h;dWo] 200 hgfn] Jof8ldG6g v]Ng dg
k/fpg] / 150 hgfn] 6]a'n 6]lg; v]Ng dg k/fpg] atfP . olb 85 hfn] b'a} v]n v]Ng dg
k/fpg] /x]5g eg]
(i) pQm tYonfO{ e]g lrqdf b]vfpg'xf]; .

11. 11
(ii) Jof8ldG6g dfq dg k/fpg]sf] ;ªVof lgsfNg'xf]; .
(iii) b'a} v]n v]Ng dg gk/fpg]sf] ;ªVof slt xf]nf < -pQ/ M 115, 35_
13. 400 ljBfyL{ dWo] 5% n] k/LIff lbPgg . hDdf ljBfyL{ ;ªVofsf] 65% ul0ftdf pQL0f{ /
50% lj1fgdf pQL0f{ eP5g . olb 50 hgf b'a} ljifodf cg'QL0f{ eP5g eg]
(i) tYox¿nfO{ e]g lrqdf b]vfpg'xf]; .
(ii) b'a} ljifodf slt hgf pQL0f{ ePsf /x]5g <
(iii) Pp6f ljifodf dfq pQL0f{ x'g]sf] ;ªVof slt /x]5g < -pQ/ M 130, 200_
14. 165 hgfnfO{ ;f]lwPsf] Ps k|Zgdf 80 hgfn] kf]v/f 3'Dg dg k/fpg] t/ n'lDagL 3'Dg dg
gk/fpg] atfP . 50 hgfn] kf]v/f 3'Dg dg gk/fpg] t/ n'lDagL 3'Dg dg k/fpg] atfP .
olb 15 hgfn] b'a} 7fp“ 3'Dg dg gk/fpg] atfP eg]
(i) dflysf] tYonfO{ e]g lrqdf b]vfpg'xf]; .
(ii) b'a} 7fp“ 3'Dg dgk/fpg] slt hgf xf]nfg < -pQ/ M 20_
15. dgsfdgf bz{g ug{ hfg ul/Psf] Pp6f ;j]{If0fdf 65% n] s]a'nsf/af6 dgsfdgf bz{g ug]{
atfP eg] 55% n] k}bn hfg dg k/]sf] atfP . olb 30% n] b'a} tl/sfaf6 hfg dg k/]sf]
atfP eg]
(i) pQm tYonfO{ e]g lrqdf b]vfpg'xf] .
(ii) xfn ghfg] lg0f{o u/]sf slt % xf]nfg < -pQ/ M 15%_
16. 80 hgf ljBfyL{nfO{ ;f]lwPsf] Ps k|Zgdf 80% n] b"w glkpg], 65% n] lrof glkpg] / 60%
n] b'a} glkpg] atfP eg] e]g lrqsf] k|of]uåf/f kQf nufpg'xf]; M
(i) b'a} k]o kbfy{ lkpg] slt k|ltztn] atfP <
(ii) sDtLdf s'g} Pp6f k]o kbfy{ lkp“5' eGg] slt hgf xf]nfg <
(iii) b'a} k]o kbfy{ lkpg] slt hgf xf]nfg < -pQ/ M 15%, 32, 12_
17. 170 hgfnfO{ ;f]lwPsf] Ps k|Zgdf ;a}n] g]kfnL jf lxGbL uLt dg k/]sf] atfP . h;dWo]
g]kfnL / lxGbL uLt dg k/fpg]sf] cg'kft 5:2 /x]5 . olb 40 hgfn] b'a} uLt dg k/]sf] atfP
eg]
(i) dflysf] tYonfO{ e]g lrqdf b]vfpg'xf]; .
(ii) g]kfnL uLt dfq dg k/]sf] slt hgfn] atfP xf]nfg <
(iii) lxGbL uLt dfq dg k/]sf] slt hgfn] atfP xf]nfg < -pQ/ M 110, 20_