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cau;ju tpQ;Qhd gpupTf;fhd jD\; ntspaPL - ngsjpftpay; tpdhf;fSk; tpilfSk; - 5 -
TANUS ntspaPL
A / L Physics
LIGHT tpdhj;njhFg;G - 01
xsp KwpT
01. tspapypUe;J fz;zhbf;Fs; xspf;fjpu; efu;tijg; glk; fhl;Lfpd;wJ. ,J njhlu;ghd
gpd;tUk; $w;Wf;fisf; fUJf.
A. fz;zhbapy; xspf;fjpupd; fjp tspapYk; FiwthFk;.
B. gLNfhzj;ij khw;Wk; NghJ KwpNfhzk; Fwpj;j xU ngWkhdj;jpYk; FiwtfNt
,Uf;Fk;.
C. tspapYk; fz;zhbapYk; mt;nthspf;fjpupd;
kPbwd; rkdhFk;.
Nkw;Fwpj;j $w;Wf;fspy;>
(1) A khj;jpuk; cz;ikahdJ.
(2) B khj;jpuk; cz;ikahdJ.
(3) B, C Mfpad khj;jpuk; cz;ikahdit.
(4) A, B Mfpad khj;jpuk; cz;ikahdit.
(5) A, B, C Mfpa vy;yhk; cz;ikahdit.
02. fz;zhb;Fw;wp xd;wpDs; tsp ntw;wplk; xd;W
cs;sJ. fz;zhbapDs; efUk; PO vDk;
xspf;fjpupd; rupahd ghijia fhl;LtJ>
(1) OA
(2) OB
(3) OC
(4) OD
(5) OE
03. ,U epwq;fis nfhz;l fjpu; tspapypUe;J fz;zhbf;Fs; EioAk; NghJ ,U
epwq;fshf gpupe;J nry;tij glk; fhl;Lfpd;wJ.
A. fjpu;fs; a, b ,d; jug;gl;l fz;zhbf;fhd jdpKwpTr;Rl;bfs; KiwNa na, n
b
vdpd; na > n
b MFk;.
B. fjpu;fs; a, b ,d; jug;gl;l fz;zhbapDs; fjpfs; KiwNa Va, V
b vdpd; V
a > V
b
MFk;.
C. fjpu;fs; a, b ,d; miyePsq;fs; KiwNa a,
b
vdpd; a >
b MFk;.
Nkw;Fwpj;j $w;Wf;fspy;>
(1) A khj;jpuk; cz;ikahdJ.
(2) A, B khj;jpuk; cz;ikahdJ.
(3) A, C Mfpad khj;jpuk; cz;ikahdit.
(4) B, C Mfpad khj;jpuk; cz;ikahdit.
(5) A, B, C Mfpa vy;yhk; cz;ikahdit.
M. C. Q
P
O
A BC
D
E
ab
cau;ju tpQ;Qhd gpupTf;fhd jD\; ntspaPL - ngsjpftpay; tpdhf;fSk; tpilfSk; - 6 -
04. Xu; Mw;wpy; ePu;g;gug;gpypUe;J 0.8 m Moj;jpYk;> fiuapypUe;J 0.6 m fpilj;Jhuj;jpYk;
rpwpa kPndhd;W cs;sJ. fiuapYs;s fpilj;jiuapd; kl;lj;jpw;F Mw;wpy; ePu;
cz;L. fiuapypUe;J Mff; $baJ vt;tsT Jhuj;jpy; cs;sNghJ> 1.5 m
caukhd kdpjd; kl;Lkl;lhf me;j kPidf; fhzKbAk;?
(ePupd; KwpTr; Rl;b 43
)
(1) 2.00 m (2) 1.50 m (3) 1.25 m
(4) 1.00 m (5) 2.50 m
05. ghj;jpuk; xd;wpy; 6 cm jbg;ghd fz;zhbf; Fw;wp xd;wpw;F NkNy 4 cm Moj;jpw;F
ePu; ,Uf;fpd;wJ. fz;zhbf; Fw;wpapd; mbapypUf;Fk; xU nghUs; NkNyapUe;J
ghu;f;Fk; xUtUf;F vt;tsT cau;e;J Njhd;Wk;? ( w g34n , n
3 2 )
(1) 2 cm (2) 2.5 cm (3) 3 cm
(4) 3.5 cm (5) 7.0 cm
06. tspapy; ,Ue;J nry;Yk; xspf;fjpu; xd;W rkhe;jug; gf;fq;fis cila 1 cm
jbg;ghd fz;zhbf; Fw;wpnahd;wpd; xU Kfj;jpy; 60o gLNfhzj;jpy; gLfpd;wJ.
fz;zhbapd; KwpTr;Rl;b 3 Mf ,Ug;gpd; fz;zhbf; Fw;wpapy; ,Ue;J ntspNaWk;
fjpupd; gf;fg; ngau;r;rp>
(1) 0 (2) 3
cm3
(3) 1
cm3
(4) 2 3
cm3
(5) 3 3
cm3
07. 1.5 KwpTr;Rl;b cila fz;zhbahyhd Xu; miuf; Nfhsj;ij mjd; mr;R
topNa tisgug;gpd; gf;fkpUe;J Nehf;Fk; NghJ 10 cm cau; jbg;G nfhz;ljhff;
fhzg;gLfpd;wJ. mjid mr;R topNa jsg;gug;gpd; gf;fkpUe;J Nehf;Fk; NghJ
mjd; Njhw;wj; jbg;G
(1) 10
cm3
(2) 10
cm7
(3) 20
cm7
(4) 20
cm3
(5) tistpdhiu njupe;jhyd;wpf; $wKbahJ.
cau;ju tpQ;Qhd gpupTf;fhd jD\; ntspaPL - ngsjpftpay; tpdhf;fSk; tpilfSk; - 7 -
08. A ahdJ ePupDs; miuthrp Moj;jpy; cs;s Gs;spahFk;. ePupd;cauk; 4 m ck;
ePupd; KwpTr;Rl;b 43 ck; Mapd; fz;Zf;F A ahdJ jput Nkw;gug;gpypUe;J
vt;tsT cauj;jpy; ,Ug;gjhfj; njd;gLk;?
(1) 2 m (2) 1
m2
(3) 3
m2
(4) 3 m
(5) 1
m4
09. fz; Gs;sp A ,y; ,Uf;Fk; NghJ O [ mtjhdpj;j NghJ O ,d; tpk;gk; Nkw;
fz;zhbg;gug;gpypUe;J 1
m4
fPNo ,Ug;gjhfj; Njhd;Wfpd;wJ. fz;> B ,ypUe;J
O [ mtjhdpj;j NghJ O ,d; tpk;gk; Nkw; fz;zhbg;gug;gpy;
,Uf;ff; fhzg;gLfpd;wJ. ePupd; KwpTr;Rl;b 43 Mapd; H
,d; ngWkhdk;>
(1) 4
m9
(2) 3
m4
(3) 1 m
(4) 2 m (5) 3 m
10. ePu; Nfhsj;Jspnahd;wpy; 1 Nfhzj;jpy; gLfpd;wJ.
Xu; xspf;fjpuhdJ ,uz;L KwpTfSf;Fk;> xU
njwpg;gpw;Fk; cl;gLfpd;wJ. ,f;fjpupdJ tpyfy;
Nfhzk;>
(1) (1 -
2)( - 2
2)
(2) (1 -
2) +
(3) + 2(1 -
2)
(4) (1 -
2) + 2( -
2)
(5) 2(1 -
2) + - 2
2
11. fz;zhbapdhy; nra;ag;gl;l 15 cm gf;fKila rJuKfpf; Fw;wp xd;wpDs; cs;s
rpwpa tspf; Fkpo; xd;W xU Kfj;jpDhlhf Nehf;fg;gLifapy; Njhd;Wk; J}uk;
6 cm MFk;. vjpu; Kfj;jpDhlhf Nehf;Fifapy; Njhd;Wk; J}uk; 4 cm MFk;.
fz;zhbapd; KwpTr; Rl;b>
(1) 2.0 (2) 1.7 (3) 1.5
(4) 1.3 (5) 1.2
H
O
A
B
1
2
2 cm
2 cm
A
cau;ju tpQ;Qhd gpupTf;fhd jD\; ntspaPL - ngsjpftpay; tpdhf;fSk; tpilfSk; - 8 -
12. xspf;fjpu; ePUf;Fs; ,Ue;J fz;zhbapDhlhf nry;Yk; ghijia glk; fhl;Lfpd;wJ.
ePupd; KwpTr;Rl;biaAk;> fz;zhbapd; KwpTr;Rl;biaAk; jUtJ>
(1) 1 1
, sin sin
(2) sin 1
, sin sin
(3) sin 1
, sin sin
(4) sin , sin
(5) 1 sin
, sin sin
13. Miu 3 cm ck; KwpTr;Rl;b 3 ck; cila Nfhsnkhd;wpd; Nkw;gug;gpy; 60o
gLNfhzj;jpy; fjpu; xd;W gLfpd;wJ. fjpu; mLj;j Kfj;jpy; KwptilAkhapd;
fjpupd; tpyfy; Nfhzk;>
(1) 0o (2) 30o (3) 60o
(4) 90o (5) 180o
14. [jhd Clfj;jpypUe;J mlu;e;j Clfj;jpw;F nry;Yk; xspf;fjpupd;>
(1) Ntfk; kl;Lk; khWgLk;
(2) miyePsk; khj;jpuk; khWgLk;
(3) kPbwd; khj;jpuk; khWgLk;
(4) fjpAk; miyePsKk; khWgLk;
(5) kPbwDk; miyePsKk; khwhJ
15. Clfk; A ,ypUe;J B ,w;F miy nry;tij fhl;Lfpd;wJ. Clfk; A ,y;
gLNfhzk; 45o ,y; KwpNfhzk; 30o MFk;. A ,y; miyapd; fjp 0.283 ms-1
Mapd;> B ,y; miyapd; fjp>
(1) 0.200 ms-1
(2) 0.231 ms-1
(3) 0.347 ms-1
(4) 0.400 ms-1
(5) 0.425 ms-1
16. KwpTr;Rl;b 2 MfTs;s jputnkhd;wpDs; xUjsthb itf;fg;gl;L cs;sJ.
jputNkw;gug;gpw;F nrq;Fj;jhfg; gLk; Xu; xspf;fjpu; kPz;Lk; jputNkw;gug;ig kUtp
ntspg;gLfpd;wJ. fpilAld; jsthbapd; rha;T>
(1) 15o
(2) 30o
(3) 45o
(4) 60o
(5) 12o
ePu;
fz;zhb
45o
30o
B
A
cau;ju tpQ;Qhd gpupTf;fhd jD\; ntspaPL - ngsjpftpay; tpdhf;fSk; tpilfSk; - 9 -
16. xU khztd; ePr;ry; jlhfj;jpw;F kpf mUfpy; epw;fpd;whd. ,td; jlhfj;jpd;
mbapy; cs;s fy;iy ghu;fpd;whd;. ,jd; cz;ik Mok; x> ePupd; jdpKwpTr;Rl;b
n MFk;. ePr;ry;j; jlhfj;jpd; mbapy; ,Ue;J fy;ypd; cauk;>
(1) n
x(2) nx (3)
n
x
(4) x (5) (n 1)
n
x
17. ePu;nfhz;l jhq;fp xd;wpDs; Neu;NkNy ,Ue;J Nehf;Fk; NghJ ghj;jpuj;jpDs;
37 gq;fpw;F ePu; ,Ug;gJ Nghy; Njhd;Wfpd;wJ. ePupd; KwpTr;Rl;b 4
3 vdpd;
cz;ikahf ePu; epug;gg;gl;Ls;s gpd;dk;>
(1) 14 (2) 4
7 (3) 12
(4) 57 (5) 6
7
18. Clfk; X ,ypUe;J Clfk; Y ,w;Fr; nry;Yk; xspf; fjpu; xd;wpd; mtjpf;
Nfhzk; MFk;. Clfk; X ,y; xspapd; Ntfk; V vdpd;> Clfk; Y ,y; xspapd;
Ntfk;>
(1) V(1 - cos) (2) Vcos (3) Vsin
(4) V
sin(5)
V
cos
19. 1 m MoKs;s ePu;j; jlhfj;jpDs; xU fk;gk; epiyf;Fj;jhf itf;fg;gl;Ls;sJ.
ePu; kl;lj;jpw;F Nky; mjDauk; 1 m MFk;. ePupd; KwpTr;Rl;b 2 Mf cs;s
NghJ #upa xspahdJ fpilAld; 45o ,y; tpOk; re;ju;g;gj;jpy; jlhfj;jpd;
mbapy; cz;lhFk; epoypd; ePsk;>
(1) 1 m
(2)1
1 m2
(3)1
1 m3
(4) 1 3 m
(5) 1 2 3 m
20. ePupDs; nry;Yk; Xu; xspf;fw;iwnahd;W ePu; - tsp ,ilKfj;jpy; 30o Nfhzj;jpy;
gLfpd;wJ. ntspg;gLk; fw;iw gw;wpa gpd;tUk; $w;Wf;fspy; cz;ikahdJ>
(1)mt;nthspf;fw;iw ePupDs; KO mfj;njwpg;gilAk;.
(2)mt;nthspf;fw;iw ePu;Nkw;gug;ig kUtp ntspg;gLk;.
45o
cau;ju tpQ;Qhd gpupTf;fhd jD\; ntspaPL - ngsjpftpay; tpdhf;fSk; tpilfSk; - 10 -
(3)mt;nthspf;fw;iwapd; tspapDs; ntspg;gLk; ntspg;gLfw;iwapd; mfyKk;
gLfw;iwapd; mfyKk; rkdhFk;.
(4)mt;nthspf;fw;iwapd; tspapDs; ntspg;gLk; ntspg;gLfw;iwapd; mfyk;
gLfw;iwapd; mfyj;ij tplf; Fiwthf ,Uf;Fk;.
(5)mt;nthspf;fw;iwapd; ePupDs; KO mfj;njwpg;gilAk; njwpfw;iwapd; mfyKk;
gLfw;iwapd; mfyKk; rkdhFk;.
21. ePupdJk; fz;zhbapdJk; KwpTr; Rl;bfs; KiwNa 1.3, 1.5 MFk;. fz;zhb -
ePu; ,il Kfj;jpw;Fupa mtjpf; Nfhzk; ahJ?
(1)1 1
sin1.3
(2) 1 1sin
1.5
(3) 1 1.3
sin1.5
(4) 1 1.5
sin1.3
(5) 1 1.3tan
1.5
22. KwpTr;Rl;b n1 cila ePupDhlhf xspf;fjpu; xd;W nrd;W ePu; - tspg;gug;gpy;
mtjpf;Nfhzj;jpy; gLfpd;wJ. KwpTr;Rl;b n2 cila Xu; vz;izg;glyk; ePUf;F
Nky; kpjf;ftplg;gl;lhy; ,t; xspf; fjpupd; KwpNfhzk; vz;izapy;>
(1) 1
1sin n (2)1
1
1sin
n
(3)1
2
1sin
n
(4)1 1
2
nsin
n
(5) 1 2
1
nsin
n
23. miuf;Nfhs fz;zhbf; Fw;wpapd; mtjpf;Nfhzk; 42o MFk;. Fw;wpapy; gLk;
xspf;fjpu; PO ,d; ghijia rupahf jUtJ>
(1) A
(2) B
(3) C
(4) D
(5) E
24. ePUf;Fs;spUe;J i gLNfhznkhd;wpy; js ePu; - tsp ,ilKfk; xd;wpy; gLk;
xspf;fjpu; xd;iwg; gw;wpg; gpd;tUk; $w;Wf;fs; $wg;gl;Ls;sd.
A. i MdJ o90 Mapd;> KwpTf;Nfhzk; mtjpf;NfhzkhapUf;Fk;.
B. i MdJ mtjpf;Nfhzj;jpw;Fr; rkdhapUg;gpd; njwpj;j fjpUk; Kwpe;j fjpUk;
xd;Wf;nfhd;W nrq;Fj;jhf ,Uf;Fk;.
C. i MdJ mtjpf; Nfhzj;ij tpl Fiwthdjhf ,Ug;gpd;> xspf;fjpu; KwptJld;>
KwpTf;Nfhzk; i [ tplf; $lthf ,Uf;Fk;.
NkYs;s $w;Wf;fspy; rupahdJ my;yJ rupahdit>
(1) A kl;Lk; cz;ikahdJ.
(2) B kl;Lk; cz;ikahdJ.
(3) C kl;Lk; cz;ikahdJ.
(4) A, C Mfad kl;Lk; cz;ikahdJ.
(5) B, C Mfpad kl;Lk; cz;ikahdJ.
cau;ju tpQ;Qhd gpupTf;fhd jD\; ntspaPL - ngsjpftpay; tpdhf;fSk; tpilfSk; - 11 -
25. xU epw rkhe;ju xspf;fw;iw xspapay; %yfj;jpy; gl;L fhl;lg;gl;lthW NkyhfTk;
fPohfTk; ntspNaWfpd;wJ. ,jw;Fj; Njitahd xspapd; %yfk;> nfhz;bUg;gJ>
(1)
45o
(2)
60o 60
o
(3)
45o
(4)
45o
45o
(5)
45o
45o
cau;ju tpQ;Qhd gpupTf;fhd jD\; ntspaPL - ngsjpftpay; tpdhf;fSk; tpilfSk; - 12 -
01. $l;L EZf;Ff; fhl;b xd;W 2 cm, 3 cm Ftpa ePsKila FtpT tpy;iyfisf;
nfhz;lJ. nghUspf;F Kd;dhy; 3 cm ,Ys;s nghUs; fUtpapD}L
Nehf;fg;gLfpd;wJ. ,Wjp tpk;gk; Kbtpypapy; cz;lhFkhW mJ nrg;gk;
nra;ag;gl;Ls;sJ. tpy;iyfspd; Ntwhf;fk;>
(1) 6 cm (2) 8 cm (3) 9 cm
(4) 10 cm (5) 12 cm
02. xU Nfhs kioj;JspapDs;Ns A ,y;
GFe;J B, C ,y; ,U njwpg;Gf;fSf;Fl;gl;L
D ,ypUe;J ntspg;gLk; xU epw xspf;fjpu;
xd;W cUtpy; fhzg;gLfpd;wJ. A ,y;
gLNfhzk; i ck; KwpNfhzk; r ck;
MFk;. gLfjpu; njhlu;ghf ntspg;gLfjpupd;
nkhj;j tpyfy;>
(1) i - r
(2) 4(i - r)
(3) 180o + 2i - 4r
(4) 360o + 2i - 6r
(5) 180o + 2i - 6r
03. mupaj;jpD}L gazpf;Fk; fjpupd; gLNfhzk; i1> ntspg;gLNfhzk; i
2> tpyfy;f;
Nfhzk; d MFk;. d MdJ (i1 + i
2) cld; khWgLk; tpjj;ij rupahf tiff;Fwpg;gJ>
.i
r
A
B
C
D
i1
i2
d
A
(1) (2)
(3) (4) (5)
d
i + i1 2
d
i + i1 2
d
i + i1 2
d
i + i1 2
d
i + i1 2
TANUS ntspaPL
A/ L Physics
LIGHT guPl;ir - 02
Nfj;jpufzpj xspapay;
cau;ju tpQ;Qhd gpupTf;fhd jD\; ntspaPL - ngsjpftpay; tpdhf;fSk; tpilfSk; - 13 -
04. xU tpy;iyapd; Kjyhk; jiyikf; Ftpaj;jpw;F ntspNa mjpypUe;J 0.025 m
J}uj;jpy; nghUnshd;W itf;fg;gl;Ls;sJ. mjd; tpk;gk; ,uz;lhk; jiyikf;
Ftpaj;jpw;F mg;ghy; 0.10 m J}uj;jpy; Njhd;Wfpd;wJ. tpy;iyapd; Ftpaj;J}uk;>
(1) 0.040 m (2) 0.050 m (3) 0.250 m
(4) 0.300 m (5) 0.630 m
05. FtpT tpy;iy xd;wpd; Kd;dhy; 50 cm J}uj;jpy; itf;fg;gl;Ls;s nghUs; xd;wpd;
tpk;gk; jpiu xd;wpy; njspthfj; Njhd;wpaJ. tpy;iyiaAk; jpiuiaAk; mirf;fhJ
tpy;iyapd; Kd;dhy; 25 cm J}uj;jpy; itf;fg;gLk; nghUspd; tpk;gj;ij jpiuapy;
ngw;Wf;nfhs;s tpy;iyAld; Nru;f;fNtz;ba ,d;ndhU tpy;iyapd; tY>
(1) - 6 D (2) - 4 D (3) - 2 D
(4) + 2 D (5) + 4 D
06. fz;zhb mupankhd;wpDhlhfr; nry;Yk; xspf; fjpu; xd;W ,opT tpyfy;
milfpd;wJ. ,f;fjpu; ntspg;gLtJ>
(1) ,uz;lhk; Kfj;jpd; nrt;td; topNa
(2) ,uz;lhk; Kfj;ij kUtp
(3) mtjpf; Nfhzj;jpy;
(4) gLfjpUf;F rkhe;jukhf
(5) Nkw;$wg;gl;l vJTky;y
07. mupaj;jpD}L xspf;fjpupd; KwpT gw;wpa gpd;tUk; $w;Wf;fisf; fUJf.
A. gLNfhzk; mjpfupg;gpd; tpyfw; Nfhzk; Fwpj;j xU ngWkhdj;jpypUe;J Fiwe;J
,opTg;ngWkhdk; mile;j gpd; xspf;fjpu; mupaj;jpD}L KwptilahJ.
B. mupaj;jpD}L xspf;fjpu; Kwptiltjw;F mupaf; Nfhzk;> mupaj; jputpaj;jpd;
mtjpf;Nfhzj;jpd; ,Uklq;fpYk; rpwpjhf ,Uj;jy; Ntz;Lk;.
C. rpW Nfhz mupaj;jpy; rpwpa gLNfhzq;fspy; gLk; fjpu;fspy; tpyfy;fs;
rkdhapUf;Fk;.
Nkw;Fwpj;j $w;Wf;fspy;>
(1) A khj;jpuk; cz;ikahdJ.
(2) B khj;jpuk; cz;ikahdJ.
(3) C khj;jpuk; cz;ikahdJ.
(4) B, C Mfpad khj;jpuk; cz;ikahdit.
(5) A, B, C Mfpad khj;jpuk; cz;ikahdit.
08. KwpTr;Rl;b n1 cila ePupD}lhf xspf;fjpu; xd;W nrd;W ePu; - tspg;gug;gpy;
mtjpf;Nfhzj;jpy; gLfpd;wJ. KwpTr;Rl;b n2 cila Xu; vz;izg;glyk; ePUf;F
Nky; kpjf;ftplg;gl;lhy; ,t; xspf; fjpupd; KwpNfhzk; vz;izapy;>
(1) 1
1sin (n ) (2) 1
1
1sin
n
(3) 1
2
1sin
n
(4) 1 2
1
nsin
n
(5) 1 1
2
nsin
n
cau;ju tpQ;Qhd gpupTf;fhd jD\; ntspaPL - ngsjpftpay; tpdhf;fSk; tpilfSk; - 14 -
09. FtpT tpy;iy xd;wpd; Ftpaj;jpypUe;J nghUspd; Jhuk; x ,w;Fk;> mNj Gs;spapy;
,Ue;J tpk;gj;jpd; J}uk; y ,w;Fk; fPwg;gLk; tiuG>
10. xspf; fjpu; xd;W mlu;e;j Clfk; xd;wpypUe;J Ijhd Clfk; xd;wpDs; efu;fpd;wJ.
Clfj;jpd; mtjpf;Nfhzk; C vdpd; fjpupd; rhj;jpakhd cau; tpyfy; Nfhzk;>
(1) 0 (2) - C (3) - 2C
(4) 2C (5) C2
11. mupaf; Nfhzk; 70o cila mupaj;jpy; 40o gLNfhzj;jpy; cs;s NghJ ,opT
tpyfy; epiyapy; cs;sJ. mupaj;jpd; KwpTr;Rl;b>
(1)
o
o
sin40
sin20
(2)
o
o
sin40
sin25
(3)
o
o
sin40
sin30
(4)
o
o
sin40
sin35
(5)
o
o
sin40
sin45
12. 12 m Moj;jpy; ,Ue;J ePu; gug;gpD}L thdj;ij mtjhdpf;Fk; RopNahb xUtdpw;F
Njhw;wkspf;Fk; xspf; $k;gpd; Nfhzk;> (ePupd; KwpTr;Rl;b 43 ) MFk;.
(1) 1 4sin3
(2) 1 3sin
4
(3) 1 32sin4
(4) 1 4tan3
(5) 1 32tan
4
(1)y
x
(2)y
x
f
f(3)
y
x
(4)y
x
(5)y
x
40o
70o
cau;ju tpQ;Qhd gpupTf;fhd jD\; ntspaPL - ngsjpftpay; tpdhf;fSk; tpilfSk; - 15 -
13. 1.5 KwpTr;Rl;b cila rkgf;f mupak; xd;wpd; xU Kfj;jpw;F nrq;Fj;jhf xspf;
fjpu; xd;W gLfpd;wJ. fjpupd; tpyfy; Nfhzk;>
(1) 0o (2) 30o (3) 45o
(4) 60o (5) 75o
14. xt;nthd;Wk; KwpTr;Rl;b n IAila %d;W
fz;zhb mupaq;fs; Fw;wp xd;iw mikf;Fk;
tz;zk; glj;jpw; fhl;lg;gl;Ls;sd. fjpupd;
gLNfhzk; 1 MFk;. mJ sin(
1) =
n
2 vDk;
njhlu;igj; jpUg;jpg;gLj;Jfpd;wJ. gLfjpUf;Fk;
ntspg;gLfjpUf;Fk; ,ilg;gl;l tpyfw; Nfhzk;
ahjha; ,Uj;jy; Ntz;Lk;?
(1) 0 (2) 6
(3) 4 (4) 3
(5) 2
15. ePupd; KwpTr;Rl;b 43 MfTk;> tspapNy xspapd; Ntfk; 3 x 108 m s-1 MfTk;
,Ug;gpd;> ePupNy xspapd; Ntfk;>
(1) 2.25 x 108 m s-1 (2) 3 x 108 m s-1 (3) 4 x 108 m s-1
(5) 4.25 x 108 m s-1 (5) 1.2 x 109 m s-1
16. xspf;fjpu; xd;W Nfhs tspf; Fop xd;iwf;
nfhz;l fz;zhbf; Fw;wp xd;WD}lhf cUtpy;
fhl;lg;gl;L cs;sthW nry;fpd;wJ. FopapNy
xspf;fjpupd; ghijia kpfr; rpwe;j Kiwapy;
tiff;Fwpg;gJ>
(1) A (2) B
(3) C (4) D
(5) E
17. 60o mupaf; NfhzKila fz;zhb mupak;
xd;wpd; xU Kfj;jpw;F nrt;tdhfg; gLfpd;w
Xu; xspf;fjpu; OA MFk;. ,f; fjpuhdJ
,uz;lhtJ Kfj;jpNy B ,w; gl;l gpd;du;
ngUk;ghYk;>
(1) BP topNa nry;yf;$Lk;.
(2) BQ topNa nry;yf;$Lk;.
(3) BR topNa nry;yf;$Lk;.
(4) BS topNa nry;yf;$Lk;.
(5) BT topNa nry;yf;$Lk;.
60o
1
30o 45
o
45o
60o
E
A
B
C
D
O
A
cau;ju tpQ;Qhd gpupTf;fhd jD\; ntspaPL - ngsjpftpay; tpdhf;fSk; tpilfSk; - 16 -
18. xU kdpjdpd; ghu;it tPr;R 1 m ,ypUe;J 5 m tiuahFk;. ,k; kdpjdpd; ghu;it
tPr;ir rhjhuz kdpjg;ghu;it tPr;rhf khw;Wtjw;fhf %f;Ff; fz;zhb mzpfpd;whd;.
,t; %f;Ff; fz;zhbapy; tpy;iyfs; nghUj;j Ntz;ba tpjj;ij gpd;tUtdtw;Ws;
rupahff; fhl;LtJ> (,U fz;fSk; xNu FiwghLilad)
19. rpwpjsT jputnkhd;wpid nfhz;bUf;Fk; 30 cm FtpaePsKila Fopthb xd;wpd;
mr;RtopNa Xu; xspg;nghl;L efu;j;jg;gl;lJ. nghl;L MbapypUe;J 50 cm J}uj;jpy;
,Uf;Fk; NghJ nghl;Lk; mjdJ tpk;gKk; guitapd;ikapd;wp nghUe;jf;
fhzg;gl;lJ. mj;jputj;jpd; KwpTr;Rl;b>
(1) 1.0 (2) 1.2 (3) 43
(4) 1.4 (5) 53
20. gdpf;fl;bapdhy; cUthf;fg;gl;l mupakhdJ 1.48 KwpTr; Rl;bia cila
vz;nzapDs; mkpo;j;jg;gl;bUf;fpd;wJ. gdpf;fl;bapd; KwpTr;Rl;b 1.31 MFk;.
cUtpy; fhl;bathW xU epw xspf;fjpu; xdW gLfpd;wJ. fjpu; nry;Yk; ghijia
rupahff; Fwpg;gJ.
(4) (5)
(1) (2) (3)
FopT
FtpT
FtpT
FopT
FtpT
FopT
FopT
FtpT FtpT
FopT
cau;ju tpQ;Qhd gpupTf;fhd jD\; ntspaPL - ngsjpftpay; tpdhf;fSk; tpilfSk; - 17 -
21. mupaj; jpuprpakhdpapy; Ntzpau; mstpilfs; ,uz;bd; kPJ thrpg;Gf;fs;
vLf;fg;gLfpd;wd. gpd;tUtdtw;Ws; vjidr; nrk;ikahf;Ftjw;fhf ,t;thW
nra;ag;gLfpd;wJ?
(1) Ntzpau; mstpilfspd; nrk;ikapd;ik.
(2) guitapd;ik (,lkhW Njhw;w tOf;fs;)
(3) mupa Nkirapd; ikak;> tl;l mstpil ikaj;Jld; nghUe;jhik.
(4) Nkirapd; ikak;> mupaj;jpd; mbapd; ikaj;Jld; nghUe;jhik.
(5) mupaj;jpd; mbapd; ikak;> njhiyfhl;bapd; Row;rp mr;Rld; nghUe;jhik.
22. KwpTr; Rl;b 2 cila gjhu;j;jnkhd;wpdhy; Mf;fg;gl;lJk;. mupaf; Nfhzk;
30o If; nfhz;lJkhd mupnkhd;wpd; xU KwpTg; gf;fj;jpw;F nts;sp G+rg;gl;Ls;sJ.
kw;iwa Kfj;jpy; vg;gLNfhzj;jpy; gLfpd;w xspf;fjpu; kPz;Lk; mNj ghijapy;
njwpg;gpd; gpd; gazk; nra;Ak;>
(1) 60o (2) 45o (3) 30o
(4) 0o (5) 15o
23. ,ay;ghd nrg;gk; nra;ifapy; cs;s xU thdpay; njhiyfhl;bapd; ghu;itj;
Jz;bd; Nky; L ePsKs;s Neu;Nfhnlhd;W tiuag;gl;Ls;sJ. nghUs; tpy;iyapdhy;
,jd; cz;ikahd tpk;gk; xd;W cUthf;fg;gl;lJ. mjd; ePsk; Lo MFk;.
njhiyfhl;bapd; ngupjhf;Fk; tY>
(1) o
L
L(2)
o
o
L L
L L
(3)
o
o
L L
L L
(4) o
L1
L (5)
o
L1
L
24. ePu;j;jlhfnkhd;wpDs; ,Uf;Fk; RopNahb xUtu; mtuJ kpd; #spd; %yk; jlhfj;jpd;
fiuf;F mUfpy; epw;Fk; xUtUf;F rkpf;iQ xd;iw toq;f Ntz;bAs;sJ. ,J
njhlu;ghd gpd;tUk; $w;Wf;fSs; rupahdJ.
(1)xspia epiyf;Fj;jhf Nky; Nehf;fpr; nrYj;j Ntz;Lk;.
(2)xspiaf; fpilahfr; nrYj;j Ntz;Lk;.
(3)Nky; Nehf;fpAk;> epiyf;Fj;Jld; mtjpf;Nfhzj;ij tplf; Fiwe;j Nfhzj;jpYk;
xspia nrYj;j Ntz;Lk;.
(4)Nky; Nehf;fpAk;> epiyf;Fj;Jld; mtjpf;Nfhzj;ij tplf; $ba Nfhzj;jpYk;
xspia nrYj;j Ntz;Lk;.
(5)epiyf;Fj;Jld; o30 Nfhzj;jpy; xspiar; nrYj;j Ntz;Lk;.
25. thdpay; njhiyfhl;b xd;wpd; Nfhzg;ngupjhf;fj;ij mjpfupf;fr; nra;tjw;F>
(1) ghu;itj;Jz;bd; Ftpaj;Jhuj;ij mjpfupf;f Ntz;Lk;.
(2) nghUspapd; Ftpaj;Jhuj;ij Fiwf;f Ntz;Lk;.
(3) ghu;itj; Jz;bd; tYitf; Fiwf;f Ntz;Lk;.
(4) ghu;itj; Jz;Lld; xUf;F tpy;iynahd;iw Nru;f;f Ntz;Lk;.
(5) ghu;itj; Jz;Lld; tpuptpy;iy xd;iw Nru;f;f Ntz;Lk;.
cau;ju tpQ;Qhd gpupTf;fhd jD\; ntspaPL - ngsjpftpay; tpdhf;fSk; tpilfSk; - 18 -
01. rhjhuz fz; xd;wpYs;s tpy;iyapd; cau; Ftpaj;Jhuk; 2.5 cm MFk;. njspTg;
ghu;itapd; tPr;R 25 cm njhlf;fk; Kbtpyp tiuahFk;. fz;tpy;iyapd; ,opTf;
Ftpaj;Jhuk;>
(1) 25
cm11
(2) 11
cm25
(3) 25
cm9
(4) 9
cm25
(5) 1
cm4
02. xspapay; fUtpfs; rk;ge;jkhf gpd;tUk; $w;Wf;fisf; fUJf.
A. $l;L EZf;Ff;fhl;bapy; ,ay;ghd nrg;gQ; nra;if epiyapy; tpy;iyfSf;F
,ilapyhd Jhuk; ,ay;gw;w nrg;gk; nra;if epiyapYk; ghu;f;f ngupjhFk;.
B. thdpay; njhiyfhl;bapy; ,ay;ghd nrg;gQ; nra;if epiyapy; Nfhzg;
ngupjhf;fk; ,ay;gw;w nrg;gQ; nra;if epiyapYk; ghu;f;f rpwpjhFk;.
C. $l;LEZf;Ff;fhl;b> thdpay; njhiyfhl;b Mfpatw;wpy; ghu;itj; Jz;lhdJ
Xu; vspa EZf;Ff; fhl;bahfj; njhopw;gLfpd;wJ.
gpd;tUk; $w;Wf;fspy;>
(1) A khj;jpuk; cz;ikahdJ.
(2) B khj;jpuk; cz;ikahdJ.
(3) A, B Mfpad khj;jpuk; cz;ikahdit.
(4) B, C Mfpad khj;jpuk; cz;ikahdit.
(5) A, B, C Mfpad ahTk; cz;ikahdit.
03. FtpT tpy;iyapy; nghUs; F ,ypUe;J tpy;iyia Nehf;fp efUifapy; tpk;gkhdJ>
(1) KbtpypapypUe;J cUg;ngUj;J tpy;iyia Nehf;fp efUk;.
(2) KbtpypapypUe;J cUr;rpWj;J tpy;iyia Nehf;fp efUk;.
(3) F2 ,ypUe;J cUr;rpWj;J tpy;iyia Nehf;fp efUk;.
(4) F2 ,ypUe;J cUg;ngUj;J tpy;iyia Nehf;fp efUk;.
(5) F ,y; ,Ue;J tpy;iyia Nehf;fp cUg;ngUj;J efUk;.
04. Xu; EZf;Ff; fhl;bapYk;> Xu; njhiyfhl;bapYk; ,U FtpT tpy;iyfs; cs;sd.
,uz;Lk; ,ay;ghd nrg;gk; nra;ifapYs;s NghJ xj;jpUg;gJ>
(1),uz;bYk; kj;jpapYk; cUthFk; tpk;gk; cUg;ngUj;j jiyfPohd kha tpk;gk;.
(2),uz;bYk; ,Wjptpk;gkhdJ njspTg;ghu;itapd; ,opTj;Jhuj;jpy; cUthf;fg;gLk;.
TANUS ntspaPL
A/ L Physics
LIGHT guPl;ir - 03
Nfj;jpufzpj xspapay;
cau;ju tpQ;Qhd gpupTf;fhd jD\; ntspaPL - ngsjpftpay; tpdhf;fSk; tpilfSk; - 19 -
(3),uz;bYk; tpy;iyfspd; ,ilj;JhukhdJ mtw;wpd; Ftpa ePsq;fspd;
$l;Lj;njhiff;F rkdhFk;.
(4),uz;bYk; ,Wjptpk;gkhdJ jiyfPohdJ.
(5),uz;bYk; nghUspahdJ> cau; Ftpa ePsj;ijf; nfhz;bUf;Fk;.
05. FopT tpy;iy xd;wpd; nghUs;j; Jhuk; U cld; tpk;gj;Jhuk; V khWgLk; tpjk;>
06. 60o ,id cila mupaj;jpDhL nry;Yk; gLfjpu;
fspw;Fupa vy;yh epiyfSf;FKupa tpyfy; Nfhzk;
(d) vjpu; gLNfhzk; (i) tiuG mUfpy; jug;gl;Ls;sJ.
i1 ,d; ngWkjp>
(1) 11o 30’ (2) 23o
(3) 48o 30’ (4) 67o
(5) 97o
07. Xu; ,Urkgf;f nrq;Nfhz fz;zhb mupaj;jpy; glj;jpy; fhl;bathW xU epw
xspf;fw;iw xd;W gLfpd;wJ. mupaj;jpy; ,Ue;J ntspNaWk; fjpUf;Fk; gLfjpUf;Fk;
,ilapYs;s tpyfypd; mbg;gilapy; VWtupirg;gLj;Jf.
(1) A, B, C (2) C, B, A (3) C, A, B
(4) B, A, C (5) A, C, B
08. rhjhuz kdpjf; fz;zpdhy;> nka;g;nghUnshd;W njspthf mtjhdpf;fg;gLfpd;wJ.
nghUspw;fhd tpopj;jpiuapy; Njhd;Wk; tpk;gk;>
A. vg;NghJk; cWr;rpWj;jJ.
B. vg;NghJk; nka;ahdJ.
C. vg;NghJk; jiyfPohdJ.
NkYs;s $w;Wf;fspy;>
(1) A, B Mfpad kl;Lk; rupahdit.
(2) A, C Mfpad kl;Lk; rupahdit.
(3) B, C Mfpad kl;Lk; rupahdit.
(4) A, B, C Mfpa vy;yhk; rupahdit.
(5) A, B, C Mfpa ahTk; gpioahdit.
(1)
V
(2) (3) (4) (5)
V V V V
U U U U U
d
i.
37o
i1
A B C
cau;ju tpQ;Qhd gpupTf;fhd jD\; ntspaPL - ngsjpftpay; tpdhf;fSk; tpilfSk; - 20 -
09. xspu; nghUSf;Fk; jpiuf;Fk; ,ilg;gl;l Jhuk; 50 cm MFk;. jpiuapd; jpirapy;
tpy;iy 30 cm ,w;F Clhf efu;j;jg;gLk; NghJ ,d;DNkhu; njspthd tpk;gk;
jpiuapy; Njhd;wpaJ. tpy;iyapd; Ftpa ePsk;>
(1) 8 cm (2) 13 cm (3) 16 cm
(4) 17 cm (5) 32 cm
10. xU $l;L EZf;Ff; fhl;bapd; nkhj;jg; ngupjhf;Fk; tY 15 MFk;. nghUspapd;
ngupjhf;fk; 5 MFk;. ,Wjp tpk;gk; njsptiug; ghu;itapd; ,opTj; Jhuj;jpy;
cz;lhFk; vdpd; ghu;itj; Jzpbd; Ftpaj; Jhuk;>
(1) 25 cm (2) 25
cm2
(3) 25
cm3
(4) 25
cm10
(5) 25
cm14
11. fz;zpdhy; ,U Gs;spfSf;fpilapyhd Jhuj;ij NtWgLj;jp mtjhdpg;gjw;F
mtw;Wf;fpilapyhd ,opTj;Jhuk; 1 x 10-3 m Mf ,Uf;f Ntz;Lk;. 4 x 10-5 m
,ilj; Jhuj;jpYs;s ,U Gs;spfis NtWgLj;jp mtjhdpg;gjw;Fj; Njitahd
$l;LEZf;Ff; fhl;bapd; ,opTf; Nfhzg;ngupjhf;fk;>
(1) 25 (2) 50 (3) 100
(4) 200 (5) 500
12. 20 cm Ftpaj;Jhuk; cila vspa EZf;Ff; fhl;bnahd;wpd; cau;
Nfhzg;ngupjhf;fj;jpw;Fk; ,opT Nfhzg;ngupjhf;fj;jpw;Fk; ,ilapyhd tpj;jpahrk;>
(1) 1 (2) 2 (3) 4
(4) 20 (5) 25
13. tspapypUe;J ePu;Nkw;gug;gpy; gLk; xU fjpu;
KwptiltJld; njwpg;Gk; milfpd;wJ.
njwpj;j Kwpe;j fjpu;fSf;fpilapyhd Nfhzk;
90o MFk;. jputj;jpd; KwpTr;Rl;b 3 vdpd;
fjpupd; gLNfhzk; ahJ?
(1) 0o
(2) 30o
(3) 45o
(4) 60o
(5) 90o
14. fz;zhbf; Fw;wp xd;wpd; KwpTr;Rl;b n MFk;. ntw;wplj;jpy; C fjpiaf; nfhz;l
xspf;fjpuhdJ d jbg;Gila fz;zhbf; Fw;wpapDhL gazpf;f vLj;j cau;
Neuk;>
(1)
2
2
dn
C n 1(2) 2
dn
C n 1(3)
2dn
C
(4) dn
C(5)
2
2
dn
C d 1
cau;ju tpQ;Qhd gpupTf;fhd jD\; ntspaPL - ngsjpftpay; tpdhf;fSk; tpilfSk; - 21 -
15. mr;rplg;gl;l gf;fnkhd;Wf;F kpff; fpl;lf; FtpT tpy;iynahd;W gpbf;fg;gl;bUf;fpd;wJ.
,t;tpy;iyia mg;gf;fj;Jf;Fr; rkhe;jukhfg; gpbj;Jf; nfhz;L tyg;gf;fj;jpw;F
mirf;Fk; NghJ> tpy;iyapDhlhff; fhzg;gLk; vOj;Jf;fspd; tpk;gk;> fz;
njhlu;ghf>
(1) ,lg;gf;fj;Jf;F mirAk;.
(2) tyg;gf;fj;Jf;F mirAk;.
(3) NkNy nry;Yk;.
(4) fPNo nry;Yk;.
(5) mirahJ.
16. R cm MiuAila cUistbt ePu;j;jhq;fp xd;wpypUe;J rPuhd tPjj;jpy; ePu;
ntspnaw;wg;gLk; NghJ ePupd; Njhw;w Mok; x cm/min vDk; tPjj;jpy; tPo;r;rpaile;jJ.
tspapdJk;> ePupdJk; KwpTr;Rl;bfs; KiwNa n1, n
2 vdpd; jhq;fpapypUe;J ePu;
ntspNaWk; tPjk; 3cm / min ,y;>
(1) 2 1
2
nx R
n (2)
2 2
1
nx R
n (3)
1
2
n2 R
n
(4) 2
1
n2 R
n (5) 2R x
17. 6 cm MiuAila fz;zhbf; Nfhsk; xd;wpd; ikaj;jpy; xU Gs;spg; nghUs;
itf;fg;gl;Ls;sJ. fz;zhbapd; KwpTr; Rl;b 1.5 MFk;. Nfhs Nkw;gug;gpypUe;J
tpk;gk; Njhd;Wk; Jhuk;>
(1) 2 cm (2) 4 cm (3) 5 cm
(4) 6 cm (5) 12 cm
18. fpilNkirapy; cs;s rkgf;f mupaj;jpy; xU
fjpu; gLtij glk; fhl;Lfpd;wJ. fjpu; fhl;ba
epiyapy; ,opT tpyfy; milAk; vdpd;>
(1) PQ fpilahf ,Uf;Fk;.
(2) QR fpilahf ,Uf;Fk;.
(3) RS fpilahf ,Uf;Fk;.
(4) PQ my;yJ RS fpilahf ,Uf;Fk;.
(5) xU fjpUNk fpilahf ,Uf;fhJ.
19. nts;nshspahdJ fz;zhb tsp ,ilKfj;jpy;
gl;L gr;ir xsp nghJ Nkw;gug;ig kUtpr; nry;tJ
fhl;lg;gl;Ls;sJ. tspapDs; ntspg;gLk; fjpu;>
(1) kQ;rs;> nrk;kQ;rs;> rptg;G vd;gdthFk;.
(2) Cjh> fUePyk;> ePyk; vd;gdthFk;.
(3) vy;yh epwf; fjpu;fSk;.
(4) gr;ir jtpu;e;j vy;yh epwf; fjpu;fSk;.
(5) vy;yh fjpu;fSk; KOTl; njwpg;gilAk;.
cau;ju tpQ;Qhd gpupTf;fhd jD\; ntspaPL - ngsjpftpay; tpdhf;fSk; tpilfSk; - 22 -
20. tspapy; nry;Yk; xspf;fjpu; xd;W tsp - jput ,ilKfk; XY ,y; gLfpd;wJ.
jputj;jpd; KwpTr; Rl;b 1 MFk;. fjpu; ab, bc vd;gtw;Wf;F ,ilapyhd Nfhzk;
MFk;. fjpu; nrt;tf fz;zhbf; Fw;wp ABCD ,DhL Kwptile;J
ntspNaWfpd;wJ. Kfk; AB MdJ XY cld; Nfhzj;ij mikf;f;fpd;wJ.
ntspg;gLfjpu; de MFk;. fz;zhbapd;
KwpTr;Rl;b 2 vdpd; fjpu;fs; ab, de
fSf;fpilapyhd Nfhzk;>
(1) 0
(2) (3)
(4) 1 1
2
sin
(5) 1 1
2
sin
21. 20 cm Ftpa ePsKk; 5 cm tpl;lKk; cila FtpT tpy;iy AB topNa ,UgFjpfshf
ntl;lg;gLfpd;wJ. glj;jpy; fhl;lg;gl;Ls;sthW tpy;iyapd; epow;wpa gFjp Gs;spg;
nghUs; P ,ypUe;J 30 cm Jhuj;jpy; NfhL XY topNa itf;fg;gLfpd;wJ. ,f;NfhL
XY MdJ tpy;iyapd; jsj;jpw;F nrq;Fj;jhf cs;sJ. Gs;spg; nghUs; P ,d;
tpk;gk; cUthFtJ>
(1) NfhL XY ,y;.
(2) NfhL XY ,w;F 1cm fPNo.
(3) NfhL XY ,w;F 1.5cm fPNo
(4) NfhL XY ,w;F 0.5cm fPNo
(5) NfhL XY ,w;F 0.5cm NkNy
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kPJ itf;fg;gl;Ls;sij cU fhl;Lfpd;wJ. P ,Ys;s g+r;rp miutl;lg; ghij
topNa glj;jpy; fhl;bathW epiyf;Fj;J
Nkw;gug;gpd; topNa 3 os-1 vd;Dk; Nfhz
Ntfj;Jld; nry;Yfpd;wJ. Q, R ,w;F ,ilNa
,Ue;J g+r;rpia mtjhdpf;Fk; mtjhdpf;F
vf;fhy ,ilntspapy; g+r;rpahdJ kiwAk;?
(1) 5 s
(2) 10 s
(3) 15 s
(4) 20 s
(5) 30 s
X Y
Air
2
1
A
B
C
D
a
b
c
d
e
5cm
2cm 2cm
X YP 30cm
A B
P
R
Q
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23. FtpT tpy;iynahd;wpdhy; cUthFk; cz;ik tpk;gj;
Jhuj;jpw;Fk; v > cUg;ngUf;fk; m ,w;Fk; ,ilNaahd
njhlu;ig mUNfAs;s tiuG fhl;Lfpd;wJ. tpy;iyapd;
Ftpaj; Jhuk;> ( v tpk;gj; Jhuj;jpd; ngWkhdj;ij kl;Lk;
Fwpf;fpd;wJ.)
(1) bc
(2) cb
(3) a (4) abc
(5) acb
24. xU njhiyfhl;b toikahd nrg;gk; nra;ifapy; cs;s NghJ mjd; cUg;ngUf;f
tY M MFk;. ,g;NghJ ghu;itj;Jz;L Jhug;nghUis Nehf;fp ,Uf;ff; $bathW
jpUg;gg;gl;L nghUspf;F mUfpy; fz;iz itj;J mtjhdpf;Fk; NghJ cUg;ngUf;f
tY>
(1) 1
M(2)
1
M 1(3)
1
M 1
(4) M 1
M 1
(5) M 1
M 1
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2n
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(1) 1 11 2
2 1
n nsin cos sin
n n
(2) 1 1
1
2
1sin n cos sin
n
(3) 1 1
2
nsin
n
(4) 1 2
1
nsin
n
(5) 1
1
1sin
n
ImI
IvI
b
a c
A B
CD
n1
n2