paper-1-mathematics-material-ashok-kumar

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                  PAPER 1              MATHEMATICS




              ‘                      ’, ‘                  ’


                                            ………………




ம .                              ம             . B.Sc.M.A.B.Ed,
                                 (                   ),
                                 ,
                      ,
                  ம          .
                  : 9445120546
ம                     : mashokkanchi@gmail.com




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                                                P a g e | 2 | www.kalvisolai.com

                                       4. mstpay;

                                       4.1. msitfs;

        msitfs; ngUk;ghYk; tpahghu Nehf;fpNy gad;gLj;JfpNwhk;. msitfspy;
Mq;fpy kuG Kiw kw;Wk; nkl;hpf; Kiw cs;sJ. ek; ehl;by; ehk; nkl;hpf;
msitfisNa gad;gLj;JfpNwhk;.


4.1 msitfs:            ngUk;ghYk; %d;W tifahf gphpf;fyhk;. mit                   ;
                                                                              ePlly; msit>
epWj;jy; msit> nfhs;ssit xt;nthd;wppwFk; mtw;wppwfhd myF cz;L.
                                    w;          w;


   ;
ePlly; msitapd; myF                     ;
                                     kPllh;
epWj;jy; msitapd; myF                fpuhk;
nfhs;sy;; msitapd; myF
      y                              ypl;lh;

                                            ;
                                         ePllysit

                  Mq;fpy kuG                           nkl;hpf; msit
              12 mq;Fyk; = 1 mb                10 kpy;yp kPllh; = 1 nrd;b kPllh;
                                                            ;                ;
          660 mb = 1 gh;yhq;F                    100 nrd;b kPllh; = 1 kPllh;
                                                              ;          ;
              8 gh;yhq;F = 1 iky;               1000 kPllh; = 1 fpNyh kPllh;
                                                        ;                ;

                                       epWj;jy; msit
                  Mq;fpy kuG                           nkl;hpf; msit
              10 fpuhk; = 1 mTd;];               1000 kpy;yp fpuhk; = 1 fpuhk;
         16 mTd;]; = 1 gTz;L                     1000 fpuhk; = 1 fpNyh fpuhk;
              2000 gTz;L = 1 ld;                  1000 fpNyhfpuhk; = 1 ld;

                               nfhs;ssit (Kfj;jysit)

                  Mq;fpy kuG                           nkl;hpf; msit
         8 fpuhk; = 1 jput mTd;];               1000 kpy;yp ypl;lh; = 1 ypl;lh;
                                                1000             h;
       20 jput mTd;]; = 1 igd;l;                1000 ypl;lh; = 1 fpNyh ypl;lh;
                                                1000     lh;
              2 igd;l; = 1 Fthh;l;

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   ;
ePlly; msit nkl;hpf; Kiw

10   nr.kP            =     1   nr.kP
10   nr.kP            =     1   nlrp. kP
10   nlrp .kP         =     1   kP
10   kP               =     1   nlf;fh kP
10   nlf;fh kP        =     1   n`f;
                                n`flh. kP
10   n`f;
     n`flh kP         =     1   fpNyh. kP


,k;nkl;hpf; Kiwia nfhz;Nl jhd;

1000 kPllh; ;         =     1   fpNyh. kPllh;   ;
100 kPllh;
        ;             =     1   n`f;lh. kPllh;      ;
10 kPllh;
      ;               =     1   nlfh. kPllh;  ;
1/10 kPllh;
          ;           =     1             ;
                                nlrp. kPllh;
1/100 kPllh;  ;       =     1   nrd;b. kPllh;     ;
1/1000 kPllh;   ;     =     1               ;
                                kpy;yp kPllh;

vd ehk; fhz;fpNwhk;.

,Nj Nghd;wJ jhd; epWj;jy; kw;Wk; nfhs;sy; msit

                               ;
1. 4.fp.kP 475 kP vd;w msit kPllhpy; khw;Wf

jPhT:
   ;      4 fp.kP 475 kP    =         4 fp.kP + 475 kP
                            =         4000 kP + 475 kP (1 fp.kP = 1000 kP)
                            =         4475 kP

2. 10 fp 20 nr.fpuhk; = 10 vd;w msit nr.fpuhkpy; khw;Wf
    ;
 jPhT :

        10 fp. 20 nr. fpuhk; =        10 fp + 20 nr.fpuhk;
                             =        10 x100 nr.fpuhk; + 20 nr.fpuhkk; (1 fp = 100 nr.fp)
                                          100
                             =        1000 nr.fp + 20 nr.fp
                             =        1020 nr.fp

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3. xU Foe;ijf;F 200 kp.yp ghy; tPjk;> 40 Foe;ijfs; nfhz;l tFg;gpy; vy;yhf;
                                                              tFg;
Foe;ijfSf;Fk; ghy; ju Ntz;Lk; vd;why; vj;jid ypl;lh; ghy; thq;f Ntz;Lk;.

   ;
jPhT:
        1 Foe;ijf;F 200 kpyp.
        40 Foe;ijfSf;F 40 x 200 kp.yp = 800 kpyp
                                        = 8 yp
                          (1 yp = 1000 kpyp)

                                  ;
4. xU ehs; rhg;ghl;bw;F vq;fs; tPlby; 350 fpuhk; mhprp nrythfpwJ. ,d;W ehd; 5
fpNyh mhprp thq;fp te;Njd;. ,d;Dk; vj;jid ehl;fSf;F ehq;fs; ftiyg;glhky;
rhg;gplyhk;?

   ;
jPhT:
        5 fpNyh = 5000 fpuhk;
              14
        350   5000
              350               <T = 14
              1500              kPjp = 100
              1400
               100


14 ehl;fSf;Fg;g pwF 100 fpuhk; kl;LNk kpQ;Rk;

1. 10 kP 35 nr.kP vd;w msit nr.kP Mf khw;Wf
2. 3 fp.fp 4 fpuhk; vd;w msit fpuhkhf khw;Wf.
3. xU rl;ilf;F 2 kP. 25 nr.kP ePsKs;s Jzp Njitg;gLfpwJ. vdpy; 12
   rl;ilfSf;Fj; Njitahd Jzpapd; ePsk; fhz;f
4. xU ,Uk;G ehw;fhypapd; vil 5.fp.fp. 300 fp vdpy; 7 ,Uk;G ehw;fhypfspd; vil
   vd;d?


                                4.2 fhy msitfs;

fhyj;jpd; myFfs; tpehb> epkplk;> kzp> ehs;> thuk;> khjk;> Mz;L vd;W
gFf;fg;gl;Ls;sd.

1 epkplk;     =      60 tpehbfs;
1 kzp         =      60 epkplq;fs; = 60 x 60 tpehbfs;   = 3600 tpehbfs;

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1 ehs;        = 24 kzp = 1440 epkplq;fs; (24 60)
                                         (24x60)   = 86400 tpehbfs; (
                                                                    (24x60x60)
                                                                             )

1. 360 epkplq;fis kzpfshf khw;Wf
   ;
jPhT:
      360 epkplq;fs; = 360 x 1/6 kzp = 360/60 = 6 kzp


2. 3 kzp 45 epkplq;fis epkplq;fshf    khw;Wfs
   ;
jPhT
      3 kzp 45 epkplq;fs;     =       3 kzp + 45 epkplq;fs;
                              =       3x 60 epkplq;fs; + 45 epkplq;fs;
                              =       (180 + 45) epkplq;fs;
                              =       225 epkplq;fs;


3. 2 kzp 30 epkplq;fs; 15 tpehbfs; vd;gij tpehbfshf khw;Wfs
    ;
 jPhT:

2 kzp 30 epkplq;fs; 15 tpehbfs;       =       2 kzp + 30 epkplk; + 15 tpehbfs;
                                      =       2 x 60 x 60+30x60+15 tpehbfs;
                                      =       7200+ 1800 + 15 tpehbfs;
                                      =       9015 tpehbfs;


1. 30 epkplq;fs; 12 tpehbfis tpehbfshf khw;Wf
2. 2 kzp 55 epkplq;fis epkplq;fshf khw;Wf.
3. 3600 tpehbfis kzpahf khw;Wf.



                         4.3 ,uapy;Nt Neuk;> rhjhuz Neuk;

1 ehs; = 24 kzp Neuk;

      1 ehspy; cs;s 24 kzp Neuj;ijj; jhd; ,uapy;Nt Neuk; vd;W $WfpNwhk;.
,uapy;Nt Neuj;jpy; Kw;gfy; gpw;gfy; vd;W fpilahJ.

         ,uapy;Nt Neuj;ij rhjhuz Neukhf khw;w 12 kzp Neuj;ij fopf;f Ntz;Lk;.

1.       8.00 K.g. I ,uapy;Nt Neukhf khw;Wf

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        jPhT: 8.00 K.g.
           ;                = 8 kzp

2.      10.25 gp.g. I ,uapy;Nt Neukhf khw;Wf
        jPhT : 10.25 gp.g = 10.25 + 12.00 = 22.25 kzp
           ;


3.      23.10 kzpia rhjhuz Neukhf khw;Wf
        jPhT 23.10 kzp = 23.10 - 12.00 = 11.10 gp.g
           ;


4.      9.20 kzpia rhjhuz Neukhf khw;Wf
        jPhT 9 .20 kzp
           ;                = 9.20 K.g


1. ,uapy;Nt Neukhf khw;Wf
     1. 6.30 K.g            2. 1.10 gp.g

2. rhjhuz Neukhf khw;Wf
   rhjhuz
     1. 10.30 kzp           2. 23.35 kzp




                   4.4.   ehl;fs;> khjq;fs;> thuq;fs; kw;Wk; Mz;Lfs;

7 ehl;fs;             =     1 thuk;
365 ehl;fs;           =     1 Mz;L
366 ehl;fs;           =     1 Mz;L (yPg; Mz;L)
1 yPg; Mz;by;         =     gpg;uthp 29 ehl;fs;
kw;w Mz;by;           =     gpg;uthp 28 ehl;fs;


                                                     vd;
4 Mz;LfSf;F xUKiw yPg; Mz;L tUk;. xU Mz;il yPg; Mz;L vd;W vg;gb
$wyhk; vd;why; mt;thz;L 4-My; kPjkpd;wp tFgl Ntz;Lk;.

        v.fh. 2012




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1. ,tw;Ws; vJ yPg; Mz;L my;y?

    1. 1400              2. 1993        3. 2800      4. 2008

1. Mf];l; 15 Mk; Njjp Kjy; mf;Nlhgh; 27Mk; Njjp Kba vj;jid ehl;fs; vdf;
fzf;fpLf

   ;
jPhT:
        Mf];l; (31- 14)
                 (31-          =        17
        nrg;lk;gh;             =        30
        mf;Nlhgh;              =        27
        nkhj;jk;               =        74

Fwpg;G:      Mf];l; nkhj;j ehl;fs; 31 ,jpy; 15 Mk; Njjp Kjy; vd;W
Fwpg;gpl;Ls;sikahy; mjw;F Kjy; ehshd 14 I 31Tld; fopf;f Ntz;Lk;. mg;NghJ
jhd; kpjKs;s Mf];l; khj ehl;fs; fpilf;Fk;.


2. 298 ehl;fis thuq;fshf khw;Wf

jPhT:
   ;              298 ehl;fs; = 298/ 7 thuk; (1 thuk; = 7 ehl;fs;)

                  42
           7      298
                  28
                   18                   <T = 42
                   14                   kPjp = 4
                     4
= 42 thuk; 4 ehl;fs;


            2004-               2004-      ,ilapy;
3. 12 [dthp 2004-f;Fk; 7 khh;r; 2004-f;Fk; ,ilapy; cs;s ehl;fis fzf;fpLf


                  501
              4   2004
                  2004
                     0             2004 xU yPg; Mz;L gpg;uthp khjk; 29 ehl;fs;
[dthp (31 - 12)          =     19
gpg;uthp                 =     29

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khh;r;              =      6
nkhj;j ehl;fs;      =     54


Fwpg;G :               2004-                          31-
              12 [dthp 2004- vd;W Fwpg;gpl;Ls;sikahy; 31-ypUe;J 12 I fopf;f
                  2004-
Ntz;Lk;. 7 khh;r; 2004-f;Fk; ,ilapy; vd;W Fwpg;gpl;Ls;sikahy; khh;r; ehl;fs; 6 Mf
Fwpg;gpl Ntz;Lk;.


1. vit yPg; Mz;L
 1. 1992      2. 2003     3. 1997
2. 328 ehl;fis thukhf khw;Wf
3. 1996 [dthp 4 Mk; NjjpapypUe;J 1996 Vg;uy; 8Mk; Njjp Kba vj;jid ehl;fs;
vdf; fzf;fpLf (v.fh. 1 I gad;gLj;Jf)




                               4.5 Rw;wsTk;> gug;gsTk;
                               rpy Kf;fpa R+j;jpuq;fs;


1. rJuj;jpd; Rw;wsT             = 4 x gf;fk; msT
                                             msT
2. rJuj;jpd; gug;gsT            = gf;fk; x gf;fk; rJu myF
                                                      myF
3. nrt;tfj;jpd; Rw;wsT          = 2 (l xb) myF
4. nrt;tfj;jpd; gug;gsT         = lxb rJu myF ePsk; l kw;Wk; mfyk; b
5. tl;lj;jpd; Rw;wsT            = 2 πr myF
                                     r
6. tl;lj;jpd; gug;gsT           = πr 2 rJu myF
                                   r
                          π = 22/7 (m) 3.14 r vd;gJ tl;lj;jpd; Muk;

7. miutl;lj;jpd; Rw;wsT         = πr + 2r myF
                                   r    r
8. miutl;lj;jpd; gug;gsT        = ½ πr 2 rJu myF

9. Kf;Nfhzj;jpd; Rw;wsT         = AB + BC + AC myF          ABC
10. Kf;Nfhzj;jpd; gug;gsT
10.                             = ½ x mbg;gf;fk; x cauk; rJu myF
11. cUisapd; tisgug;G
11.                             = 2 πr h rJu myF

12. cUisapd; nkhj;j gug;G
12.                             = 2πr (h+r ) rJu myF

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13. cUisapd; fd msT
13.                              = πr 2h fd myF
                 r vd;gJ cUisapd; mbgf;f Muk;
                 h mjd; cauk;
14. $k;G tisgug;G
14.                              = πr ℓ myF

              ℓ vd;gJ rha;Auk;
                           uk;   ℓ= √r 2 + h2 myF

15.
15. nkhj;j gug;G                 = πr (ℓ + r )

16. fd msT
16.                              = 1/3 π      r 2h
                                          2
17.
17. Nfhsj;jpd; tisgug;G          = 4 πr       myF
                                              3
18. Nfhsj;jpd; fd msT
18.                              = 4/3 πr         fd myF
                                          2
19. miuf;Nfhsj;jpd; tisgug;G = 2 πr
19.                                           rJu myF
                                              3
20. miuf;Nfhsj;jpd; fd msT 2/3 r
20.                    msT= 2/3π                  fd myF

21. ……………. nkhj;j gug;gsT
21.                                       = 3 πr 2 rJu myF


Fwpg;G: cUisapd; fd msTf;F %d;wpy; xU gq;F $k;gpd; fd msT


gapw;rpf;fhd tpdhf;fs;

1. ePsk; 15 kP> mfyk; 10 kP cila nrt;tf tbt epyj;jpd; gug;gsT> Rw;wsT fhz;f.
2. 40kP ePsKila rJu tbt kidapd; gug;gsT> Rw;wsT fhz;f.
3. xU tpisahl;Lj;jply; nrq;Nfhz Kf;Nfhzk; tbtpy; cs;sJ. nrq;Nfhzj;ij
                                                              ;
    jhq;Fk; gf;fq;fs; 50kP> 80kP. jplypy; rpnkz;l; G+r rJu kPllUf;F &.5 tPjk; MFk;
    nkhj;j nryitf; fhz;f.
4. 3.5 kP MuKs;s tl;lj;jpd; Rw;wsT kw;Wk; gug;gsT fhz;f.
5. 14 nr.kP MuKs;s miutl;lj;jpd; Rw;wsT kw;Wk; gug;gsT fhz;f.
6. xU jpd;k cUisapd; Muk; 7 nr.kP kw;Wk; cauk; 12 nr.kP vdpy; cUisapd;
    1.tisgug;G 2. nkhj;j Gwgug;G 3. fd msT fhz;f.
7. xU jpd;k $k;gpd; Muk; kw;Wk; rhAauk; KiwNa 35 nr.kP kw;Wk; 37 nr.kP vdpy;
    $k;gpd; tisgug;G kw;Wk; nkhj;jg; Gwgug;igf; fhz;f ( π 22/7)



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8. xU jpz;k miuf;Nfhsj;jpd; nkhj;j Gwgug;G 675 π r.nr.kP vdpy; mjd;
    tisgug;igf; fhz;f
9. xU jpz;k miuf;Nfhsj;jpd; tisgug;G 277 r.nr.kP vdpy; mjd; nkhj;j Gwgug;ig
    fhz;f.
10. 98.56 r.nr.kP Gwgug;G nfhz;l xU jpz;kf; Nfhsj;jpd; Muj;ijf; fhz;f.




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