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ul0ft z[ªvnf – !                                      ;d"x (Sets)P;Pn;L k/LIffsf] ljlzi6Ls/0f tflnsf 2065 cg;f/ æ;d"xÆ kf7...
pbfx/0f   : 2h75 hgfnfO{  ;f]lwPsf] k|Zgdf 55 hgfn] lrof / 25 hgfn] skmL lkpg dg k/fpg] atfP . olb                   15hgf...
;dfwfg         oxf“, lrof dgk/fpg] ljBfyL{x¿sf] ;d"xnfO{   T/   skmL dgk/fpg] ljBfyL{x¿sf] ;d"xnfO{   C         dfGbf     ...
or,       91= 118-34+ n(         n(                 =91- 84                            =7                                 ...
;"q cg;f/,                                                                          (1)            or,            or,     ...
;q k|of]u ubf{,                                                           .............. (1)     or,     or,              ...
 ba} rnlrq x]g{ dg gk/fpg]sf] ;ªVof     ba} rnlrq x]g{ dg gk/fpg]sf]pbfx/0f : 9sIff 10 sf ljBfyL{x¿nfO{ ul/Psf] Ps ;j]{If...
;d"x   af6,             ctM sljtf dfq dg k/fpg]sf] ;ªVof = 8     (iii)   hDdf k|Zg ;f]lwPsf ljBfyL{ ;ªVof =pbfx/0f : 10lks...
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...
(i)    pQm tYox¿nfO{ e]g lrqdf b]vfpgxf]; .      (ii) hDdf slthgfn] ;j]{If0fdf efu lnPsf /x]5g .                          ...
(ii)    Jof8ldG6g dfq dg k/fpg]sf] ;ªVof lgsfNgxf]; .      (iii) ba} v]n v]Ng dg gk/fpg]sf] ;ªVof slt xf]nf <             ...
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Slc math series

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this is the material for the students who are preparing for slc............

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Slc math series

  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|:ttul/Psf] 5 .pbfx/0f : 1olb / eP slt xf]nf tQf nufO e]g lrqdfb]vfpgxf]; .;dfwfg M lbOPsf], (1) ;"q cg;f/, (1) or, (1) or, or, A B or, 12 8 18 or, 1 9 6 7 (1) 20 C16 1
  2. 2. pbfx/0f : 2h75 hgfnfO{ ;f]lwPsf] k|Zgdf 55 hgfn] lrof / 25 hgfn] skmL lkpg dg k/fpg] atfP . olb 15hgfn] ba} dggk/]sf] atfP eg] e]g lrq agfO{ lgDg k|Zgsf] pQ/ lbgxf]; M (i) ba} 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, T C 35 20 5 15 ;q cg;f/, (1) or, or, or, or, (i) ba} dg k/fpg] ;ªVof (1) (ii) skmL dfq dg k/fpg] (1)pbfx/0f M 3Pp6f ;dbfodf /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, bj} lrh lkpg dg k/fpg] 18 hgf / bj} dg gk/fpg] 27 hgfkfOof] 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|:tt ug{xf]; . 2
  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|:tt ubf{, T C 36 18 19 (2)pbfx/0f M 491 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] 3hgf kfOP eg], e]g lrq agfO{ tLgcf]6} dWo] sg} klg ljifo dggk/fpg] ljBfyL{ ;ªVof kQfnufpgxf]; .;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, M S n( ) = 40, n(S) = 45 21 11 22 n(E) = 30 3 5 9 n(M S) = 14 13 n(S E) = 12 (2) E 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( 3
  4. 4. or, 91= 118-34+ n( n( =91- 84 =7 (1) ctM tLgcf]6} dWo] sg} 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 bO{ dWo] ba} dg gk/fpg] atfP eg] (i) dflysf] tYonfO{ e]g lrqdf k|:tt ug{xf]; . (ii) olb Tof] ;dxsf 60 hgfn] ba} dgk/fpg] atfP eg] pQm ;j]{If0fdf slthgfn] efu lnPsf /x]5g < kQf nufpgxf]; .;dfwfg M oxf“, :ofp / ;Gtnf dgk/fpg] dflg;x¿sf] U ;d"xnfO{ qmdzM A / O n] hgfp“bf, A O (1) (i) oxf“, ;j{k|yd ba} dgk/fpg] k|ltzt kQf nufpgkb{5 . ctM or, or, ...................... (2) (ii) k|Zgcg;f/, lbOPsf]n], ..................... (1) ctM240 hgfn] ;j]{If0fdf efu lnPsf /x]5g .pbfx/0f : 6110 hgfnfO{ ul/Psf] Ps ;j]{If0fdf ;a}n] b"w jf lrof lkpg] atfP . h;dWo] b"w / lrof dgk/fpg]sf] cgkft 3:4 /x]5 . olb 30 hgfn] ba} lkpg] atfP eg] (i) dflysf] tYonfO{ e]g lrqdf b]vfpgxf]; . (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, 4
  5. 5. ;"q cg;f/, (1) or, or, or, or, ;= af6 U M T 30 30 50 lrof dfq dg k/fpg] ;ªVof b"w dfq dg k/fpg] ;ªVofpbfx/0f : 7 sg} 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 ba} k|ltof]lutf dgk/fpg] 30 hgf / sg} klg k|ltof]lutf dggk/fpg] 20 hgf /x]5 eg] (i) xflh/L hjfkm k|ltof]lutf dgk/fpg]sf] ;+Vof kQf nufpgxf]; . (ii) jfbljjfb dfq dg k/fpg] ljBfyL{ ;+Vof kQf nufpgx]; . (iii) pQm tYonfO{ eg] lrqdf k|:tt 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, 5
  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 = U Q D (1) (iii) dflysf] tYonfO{ e]g lrqdf b]vfpFbf 175 30 350 20pbfx/0f : 825,000 hgfdf ul/Psf] ;j]{If0fdf 16,000 hgfn] g]kfnL rnlrq dgk/]sf] atfP / 8000 hgfn]lxGbL rnlrq dgkg]{ atfP . olb 2000 hgfn] ba} rnlrq dg k/]sf] atfP eg] slt k|ltztn] ba}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/, 6
  7. 7.  ba} rnlrq x]g{ dg gk/fpg]sf] ;ªVof ba} rnlrq x]g{ dg gk/fpg]sf]pbfx/0f : 9sIff 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{ lgDgk|Zgsf] pQ/ lbgxf]; 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, U M S 9 3 6 4 5 2 8 P ;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 7
  8. 8. ;d"x af6, ctM sljtf dfq dg k/fpg]sf] ;ªVof = 8 (iii) hDdf k|Zg ;f]lwPsf ljBfyL{ ;ªVof =pbfx/0f : 10lkslgs 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 ba} dg kg]{ atfP5 . olb 10 hgfn] ba} 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 U oxf“, /f]6L / kfp/f]6L dg k/fpg]sf] ;d"xnfO{ S B qmdzM S / B n] hgfp“bf, 27 9 22 10dfly lbOPsf] pbfx/0fx¿sf] ;xfotfn] lgDglnlvt ;d:ofx¿ ;dfwfg ug{xf]; M 8
  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, bj} vfnsf uLt ;Gg dg k/fpg] 40 hgf / 30 hgfn] bj} 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|:tt ug{xf]; . pQ/ M 250, 1052. g]kfndf cfPsf 200 hgf ko{6sx¿nfO{ eStk/ / nlntk/ 3dfO;s]kl5 ;f]lwPsf] k|Zgdf eStk/ dg kg]{ 145 hgf, nlntk/ dg kg]{ 80 hgf, bj} 7fp“df dg gk/fpg] 20 hgf dfq kfOP eg], (i) bj} 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]vfpgxf]; . pQ/ M 45, 100, 353. Pp6f k/LIffdf 70% ljBfyL{x¿ lj1fgdf pQL0f{, 75% ljBfyL{x¿ ul0ftdf / 5% ljBfyL{x¿ ba} ljifodf cglQ0f{ eP5g . olb 220 hgf ljBfyL{x¿ ba} ljifodf pQL0f{ eP5g eg], (i) lbOPsf] hfgsf/LnfO{ e]glrqdf k|:tt ug{xf]; . (ii) hDdf k/LIffyL{sf] ;ªVof kQfnufpgxf]; . pQ/ M 440 hgf4. 80 hgf dflg;x¿ ePsf] Pp6f ;d"xdf sf]s / km]G6f dgk/fpg] dflg;x¿sf] cgkft 3:4 5 . olb 24 hgfn] ba} y/L k]o kbfy{ dgk/fp“5g / 6 hgfn] bO{ dWo] sg} klg k]o kbfy{ dg k/fp“b}gg eg] e]g lrq agfO lgDglnlvt ;ªVofx¿ kQfnufpgxf]; . (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 hgf5. Pp6f ;dbfodf /x]sf 1000 kl/jf/df u/]sf] ;j]{If0fdf vfgf ksfpg] OGwgsf ¿kdf ;a}n] sg} g sg} 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/ lbgxf]; 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, 2806. sg} ;j]{If0fdf 50% dflg;n] lrof / 65% dflg;n] b"w dg k/fpg] atfP . olb 5% n] sg} klg dg gkg]{ atfP / 15 hgfn] ba} lkpg dg k/fpg] atfP eg] 9
  10. 10. (i) pQm tYox¿nfO{ e]g lrqdf b]vfpgxf]; . (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] bO{ dWo] sg} klg dg gk/fpg] atfP eg] (i) pQm tYox¿nfO{ e]g lrqdf k|:tt 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] km6an / 300 hgfn] elnan dg k/fpg] atfP . olb 40 hgfn] sg} klg dg gk/fpg] atfP eg] (i) pQm tYox¿nfO{ e]g lrqdf b]vfpgxf]; . (ii) ba} v]n dg k/fpg] slthgf xf]nfg < (iii) km6an 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] ba} g/f]Kg] atfP eg] (i) pQm tYox¿nfO{ e]g lrqdf b]vfpgxf]; . (ii) ba} 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 ba} y/Lsf uLt dg k/fpg] 20 hgf, ba} 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]vfpgxf]; . -pQ/ M 30, 110_11. 300 ljBfyL{nfO{ ul/Psf] Ps ;j]{If0fdf kf]v/f dfq 3Dg dg k/fpg] ljBfyL{ ;+Vof lrtjg dfq 3g dg k/fpg] ljBfyL{ eGbf bf]Aa/ /x]5 . olb ba} :yfg 3Dg dg k/fpg] 10 hgf / ba} :yfg 3Dg dg k/fpg] 20 hgf lyP eg] (i) lrtjg 3Dg dg k/fpg] slt lyP xf]nfg < (ii) kf]v/f 3Dg dg k/fpg] slt xf]nfg < (iii) pQm tYox¿nfO{ e]g lrqdf b]vfpgxf]; -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]an 6]lg; v]Ng dg k/fpg] atfP . olb 85 hfn] ba} v]n v]Ng dg k/fpg] /x]5g eg] (i) pQm tYonfO{ e]g lrqdf b]vfpgxf]; . 10
  11. 11. (ii) Jof8ldG6g dfq dg k/fpg]sf] ;ªVof lgsfNgxf]; . (iii) ba} 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 ba} ljifodf cgQL0f{ eP5g eg] (i) tYox¿nfO{ e]g lrqdf b]vfpgxf]; . (ii) ba} ljifodf slt hgf pQL0f{ ePsf /x]5g < (iii) Pp6f ljifodf dfq pQL0f{ xg]sf] ;ªVof slt /x]5g < -pQ/ M 130, 200_14. 165 hgfnfO{ ;f]lwPsf] Ps k|Zgdf 80 hgfn] kf]v/f 3Dg dg k/fpg] t/ nlDagL 3Dg dg gk/fpg] atfP . 50 hgfn] kf]v/f 3Dg dg gk/fpg] t/ nlDagL 3Dg dg k/fpg] atfP . olb 15 hgfn] ba} 7fp“ 3Dg dg gk/fpg] atfP eg] (i) dflysf] tYonfO{ e]g lrqdf b]vfpgxf]; . (ii) ba} 7fp“ 3Dg dgk/fpg] slt hgf xf]nfg < -pQ/ M 20_15. dgsfdgf bz{g ug{ hfg ul/Psf] Pp6f ;j]{If0fdf 65% n] s]ansf/af6 dgsfdgf bz{g ug]{ atfP eg] 55% n] k}bn hfg dg k/]sf] atfP . olb 30% n] ba} tl/sfaf6 hfg dg k/]sf] atfP eg] (i) pQm tYonfO{ e]g lrqdf b]vfpgxf] . (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] ba} glkpg] atfP eg] e]g lrqsf] k|of]uåf/f kQf nufpgxf]; M (i) ba} k]o kbfy{ lkpg] slt k|ltztn] atfP < (ii) sDtLdf sg} Pp6f k]o kbfy{ lkp“5 eGg] slt hgf xf]nfg < (iii) ba} 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] cgkft 5:2 /x]5 . olb 40 hgfn] ba} uLt dg k/]sf] atfP eg] (i) dflysf] tYonfO{ e]g lrqdf b]vfpgxf]; . (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_ 11

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