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XII Std fzpjk;
fhyk; : 3 kzp nkhj;j kjpg;ngz;fs; 200
mwpTiu
(i) midj;J tpdhf;fSk; rhpahf gjpthfp cs;sjh vd;gjid rhpghh;j;Jf;
nfhs;sTk;. mr;Rg;gjptpy; FiwapUg;gpd; miwf; fz;fhzpg;gghshplk;
cldbahfj; njhptpff;fTk;
(ii) ePyk; my;yJ fUg;G ikapid kl;LNk vOJtjw;Fg; gad;gLj;j Ntz;Lk;.
glq;fs; tiutjw;F ngd;rpy; gad;gLj;jTk;
gFjp m
Fwpg;G :
(i) midj;J tpdhf;fSf;Fk; tpilaspf;f
(ii) nfhLf;fg;gl;l ehd;F tpilfspy; kpfTk; Vw;Gila tpilapid
Njh;e;njLj;J FwpaPl;Lld; tpilapidAk; Nrh;j;J vOJ.
40x1=40
1. xU rJu mzp A d; thpir n vdpy; Aadj vd;gJ
a) 2A b) nA c) 1nA d) A
2. kjpg;gpl Ntz;ba %d;W khwpfspy; mike;j %d;W Nehpa mrkgbj;jhd rkd;ghl;Lj; njhFg;gpy; 0 kw;Wk; 0 x , 0y
kw;Wk; 0z vdpy; njhFg;Gf;fhd jPh;T
a) xNu xU jPh;T b) ,uz;L jPh;Tfs; c) vz;zpf;ifaw;w jPh;Tfs ;d) jPh;T ,y;yhik 3. x
2/3 + y
2/3 = 4 vd;w tistiuapd; tpy;ypd; ePsk;
a) 48 b) 24 c) 12 d) 96
4. m < 0 Mf ,Ug;gpd; 0dx
mxdy
d; jPh;T
a) x = cemy
. b) x = ce-my
. c) x = my + c. d) x = c. 5. Mjpg;Gs;spia ikakhff; nfhz;l tl;lq;fspd; njhFg;gpd; tiff;nfO rkd;ghL a) x dy + y d x = 0 b) x dy – y d x = 0 c) x d x + y dy = 0 d) x d x – y d y =0
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6. xxf kw;Wk; f(1) = 2 vdpy; f(x) vd;gJ
a) )2xx(3
2 b) )2xx(
2
3 c) )2xx(
3
2 d) )2x(x
3
2
7. gpd;tUtdtw;Ws; vJ Kuz;ghlhFk; ? a) p v q. b) p ^ q c) p v ~q. d) p ^ ~q. 8. (Z9, +9) y; [7] d; thpir a) 9 b) 6 c) 3 d) 1. 9. ngUf;fy; tpjpia nghWj;J Fykhfpa xd;wpd; ehyhk; %yq;fspy; – i d; thpir a)4 b) 3 c) 2 d) 1
10 . f(x) =
elsewhere,0
3x0,kx2
vd;gJ epfo;jfT mlh;j;jp rhh;G vdpy; k d; kjpg;G
a) 1/ 3 b) 1/ 6 c) 1/ 9 d) 1/12. 11. E(X +c) = 8 kw;Wk; E (X –c) = 12 vdpy; c d; kjpg;G. a) -2 b) 4 c) -4 d) 2. 12. xU gha;]hd; gutypy; P(X = 2 ) = P(X=3) vdpy; gz;gsit d; kjpg;G a) 6 b) 2 c) 3 d) 0 13 rkgbj;jhd Nehpar; rkd;ghl;Lj; njhFg;ghdJ a) vg;NghJNk xUq;fikT cilajhFk; b) ntspg;gilj;jPHT kl;LNk nfhz;Ls;sJ c) vz;zpf;ifaw;w jPHTfs; nfhz;Ls;sJ d) xUq;fikT cilajhf ,Uf;fj; Njitapy;iy 14. ba , fis epiy ntf;lHfshf nfhz;l Gs;spfs; topahfTk; f;F ,izahfTk; mike;j jsj;jpd; Jiz myF my;yhj ntf;lH rkd;ghL
a) 0 vabar b) 0 vabr
c) 0vba d) 0bar
15. MjpapypUe;J 752 kjir vd;w jsj;jpw;F cs;s J}uk;
a) 30
7 b) 7
30 c) 7
30 d) 30
7
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16. ZZ -,d; kjpg;G a) )Im(2 Z b) )Im(2 Zi c) )Im(Z d) )Im(Zi
17. (2,4) ypUe;J 2052 22 yx vd;w ePs;tl;lj;jpw;F tiuag;gLk; njhLNfhLfspd; njhehzpd; rkd;ghL
a) 055 yx b) 055 yx c) 055 yx d) 055 yx
18. 3
1
x
xvd;w rhHgpw;F 0x -d; NghJ Nyhgpjhypd; tpjpia gad;gLj;j
,ayhJ fhuzk; 1 xxf kw;Wk; 3 xxg
a) njhlHr;rpaw;wit b) tifaplj;jf;fitay;y c) 0x f;F Njwg;ngwhj tbtj;jpy; ,y;iy d) 0x f;F Njwg;ngWk; tbtj;jpy; cs;sJ
19 a
dxxf0
=
a) a
dxaxf0
b) a
dxxaf0
c) a
dxxaf0
2 d) a
dxaxf0
2
20. nzyx;mzyx;lzyx 222 vd;w rkd;ghLfs; 0 nml vDkhW mikAkhapd; mj;njhFg;gpd; jPh;T a) xNu xU G+r;rpkw;w jPh;T b) ntspg;gil jPh;T c) vz;zpf;ifaw;w jPh;T d) jPh;T ,y;yhik ngw;W ,Uf;Fk;
21. kjiPR 2 , kjiSQ 23 vdpy; ehw;fuk; PQRS d; gug;G
a) 35 b) 310 c) 2
35 d) 2
3
.22 xU NfhL x kw;Wk; y mr;Rf;fSld; kpif jpirapy; 45°, 60° Nfhzq;fis Vw;gLj;JfpwJ vdpy; z mr;Rld; mJ cz;lhf;Fk; Nfhzk;
a) 30 b) 90 c) 45 d) 60
23. kjia 32 kw;Wk; kjib 23 vdpy; a f;Fk; bf;Fk; nrq;Fj;jhf cs;s xU XuyF ntf;lH
a) 3
kji
b)
3
kji
c)
3
k2ji
d)
3
kji
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24. 1
z
1
1y
2
1x
kw;Wk;
2
1z
5
1y
3
2x
Mfpa ,U NfhLfSk;
a) ,iz b) ntl;bf;nfhs;git c) xU jsk; mikahjit d) nrq;Fj;J.
25. iz vd;w fyg;ngz;iz Mjpia nghWj;J 2
Nfhzj;jpy; fbfhu vjph;
jpirapy; Row;Wk; NghJ me;j vz;zpd; Gjpa epiy a) iz b) -iz c) -z d) z
26. 3
sin3
cos n
in
zn vdpy; 621 z.........zz vd;gJ
a) 1 b) -1 c) i d) -i
27. 062 kxx vd;w rkd;ghl;bd; xU %yk; -i +3 vdpy; kd; kjpg;G
a) 5 b) 5 c) 10 d) 10
28 x12y2 vd;w gutisaj;jpd; Ftpehzpd; ,Wjpg;Gs;spfspy; tiuag;gLk; njhLNfhLfs; re;jpf;Fk; Gs;sp mikAk; NfhL a) x - 3 =0 b) x+ 3 =0 c) y + 3 =0 d) y – 3 = 0 29. nrt;tfyj;jpd; ePsk; Jizar;rpd; ePsj;jpy; ghjp vdf; nfhz;Ls;s mjpgutisaj;jpd; ikaj;njhiyj;jfT
a) 2
3 b) 3
5 c) 2
3 d) 2
5
30 2cxy vd;w nrt;tf mjpgutisaj;jpd; njhiynjhLNfhLfs;. a) cy,cx b) cy,0x c) 0y,cx d) 0y,0x
31 y = 3x² vd;w tistiuf;F x d; Maj;njhiyT 2 vdf; nfhz;Ls;s Gs;spapy; nrq;Nfhl;bd; rha;thdJ a) 1 / 13 b) 1 / 14 c) -1 / 12 d) 1 / 12 32. xU Nfhsj;jpd; fdmsT kw;Wk; Muj;jpNyw;gLk; khWtPjq;fs; vz;zstpy; rkkhf ,Uf;Fk; NghJ Nfhsj;jpd; tisgug;G
a) 1 b) 21 c) 4 d) 34
33. y = ax³ + bx² + cx + d vd;w tistiuf;F x = 1 y; xU tisT khw;Wg;Gs;sp cz;nldpy; a) a+b = 0 b) a+ 3b = 0 c) 3 a + b = 0 d) 3a + b = 1
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34. u = xyvdpy;
x
u
f;F rkkhdJ
a) yxy-1
. b) u log x c) u log y d) xyx-1
. 35. ay² = x² (3a-x) vd;w tistiu y mr;ir ntl;Lk; Gs;spfs;. a) x = - 3a , x = 0 b) x =0, x = 3a. c) x = 0, x = a. d) d) x = 0
36. 1b
y
a
x
2
2
2
2
vd;w ePs;tl;lj;jpw;Fk; mjd; Jiz tl;lj;jpw;Fk;
,ilg;gl;l gug;G
a) bab b) baa 2 c) baa d) bab 2
37. NfhLfs; y = x, y = 1kw;Wk; x = 0 Mfpait Vw;gLj;Jk; gug;G y mr;ir nghWj;J Row;wg;gLk; jplg;nghUspd; fdmsT
a) 4 b) 2 c) 3 d) 32
38. QPxdy
dx vd;w Nehpa tiff;nfOr; rkd;ghl;by;P kw;Wk; Q Mfpait
y,d; rhHGfshf ,Ug;gpd;> jPHT a) cdxQFIFIy .. b) cdyQFIFIx ..
c) cdyQFIFIy .. d) cdxQFIFIx ..
39. ,ul;ilg;gil kpif vz;fspd; fzk;> ngUf;fypd; fPo; a) Kbthd Fyk; b) miuf;Fyk; kl;Lk ;c) rkdpAila miuf;Fyk; kl;Lk; d) Kbtw;w Fyk; 40. X xU njhlH rktha;g;G khwp vdpy; vJ jtW? a) xfxF ' b) 0;1 FF
c) aFbFbxaP d) aFbFbxaP
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gFjp – M
Fwpg;G: (i) vitNaDk 10 tpdhf;fSf;F tpilaspf;fTk;. (ii) tpdh vz; 55 f;F fz;bg;ghf tpilaspf;fTk;. gpw tpdhf;fspypUe;J VNjDk; ehd;F tpdhf;fSf;F tpilaspf;fTk;.
10×6=60
41 gpd;tUk; rkd;ghLfspd; njhFg;G xUq;fikT cilajh vd;gij Muha;f. xUq;fikT cilajhapd; mtw;iwj; jPHf;f :
62;1832;7 zyzyxzyx
42: ; NeHkhW mzpfisf; fhz;f.
121
022
113
A
43 XH miutl;lj;jpy; cs;s Nfhzk; xU nrq;Nfhzk; ,jid ntf;lH Kiwapy; ep&gpf;f.
44 (a) Find the angle between the lines. kjijir 2475
kikir 432
(b) For any vector r prove that kkrjjriirr
45 vy;yh kjpg;GfisAk; fhz;f. 318i
46 21 , ZZ vd;w VNjDk; ,U fyg;ngz;fSf;F (i) 2
1
2
1
Z
Z
Z
Z (ii)
212
1 argargarg ZZZ
Z
vd ep&gp.
47 gutisak; xy 82 f;F2
1t vd;w Gs;spapy; njhLNfhL> nrq;NfhL
,tw;wpd; rkd;ghLfs; fhz;f.
48 222 ayx kw;Wk;
2cxy vd;w tistiufs; xd;iw xd;W nrq;Fj;jhf ntl;bf; nfhs;Sk; vdf; fhl;Lf. 49 tifaPLfisg; gad;gLj;jp 127 d; Kg;gb %yj;jpd; Njhuha kjpg;Gfis fzf;fpLf.
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50 xy vd;w tistiuapy; ,2y 0x Mfpa NfhLfSf;F ,ilg;gl;l gug;gpid y-mr;irg; nghWj;Jr; Row;wpdhy; cUthFk; jplg;nghUspd; fdmstpidf; fhz;f.
51 .,0R Kbtw;w vgPypad; Fyk; vdf; fhl;Lf. ,q;F ‘.’ vd;gJ tof;fkhd ngUf;fiyf; Fwpf;Fk;. 52 qp kw;Wk; pq rkhdkw;wit vdf; fhl;Lf 53 ,U rPuhd gfilfs; cUl;lg;gLfpd;wd. gfilfspd; Nky; cs;s vz;fspd; $l;Lj; njhifapd; vjpHghHg;gpidf; fhz;f. 54 xU fjphpaf;fg; nghUspypUe;J My;/gh Jfs;fs; ruhrhpahf 20 epkpl; fhy ,ilntspapy; 5 vd ckpog;gLfpwJ. gha;]hd; gutiyg; gad;gLj;jp Fwpg;gpl;l 20 epkpl ,ilntspapy; (i) 2 ckpoy;fs; (ii) Fiwe;jgl;rk; 2 ckpoy;fSf;fhd epfo;jfitf; fhz;f. .0067.05 e
55 (a) xU efUk; thfdj;jpd; jil (F) ,d; rkd;ghL xx
F 1005 vdpy;>
jilapd; rpWk kjpg;igf; fhz;f.
(or)
(b) jPHf;f: 01
1 2
1
2
2
x
y
dx
dy
gFjp – ,
Fwpg;G: (i) vitNaDk 10 tpdhf;fSf;F tpilaspf;fTk;. (ii) tpdh vz; 70 f;F fz;bg;ghf tpilaspf;fTk;. gpw tpdhf;fspypUe;J VNjDk; ehd;F tpdhf;fSf;F tpilaspf;fTk;.
10×10=100
56 NeHkhW mzp fhzy; Kiwapy; gpd;tUk; Nehpa rkd;ghl;Lj; njhFg;Gfisj; jPHf;fTk;.
. 57 xU Kf;Nfhzj;jpd; Fj;Jf;NfhLfs; xNu Gs;spapy; re;jpf;Fk; vd;gjid ntf;lH Kiwapy; epWTf.
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58 ntl;Lj;Jz;L tbtpy; xU jsj;jpd; rkd;ghl;ilj; jUtpf;f.
-,d; %yq;fs; kw;Wk; vdpy;
mjpypUe;J kjpg;ig ngWf.
vd;w mjpgutisaj;jpd; ikaj; njhiyj;jfT> ikak;> Ftpaq;fs;> cr;rpfs; Mfpatw;iwf; fhz;f. NkYk; mjd; tistiuia tiuf. 61 xU uhf;nfl; ntbahdJ nfhSj;Jk; NghJ mJ xU gutisag; ghijapy; nry;fpwJ. mjd; cr;r cauk; kP-I vl;Lk;NghJ mJ nfhSj;jg;gl;l ,lj;jpypUe;J fpilkl;l J}uk; kP njhiytpYs;sJ. ,Wjpahffpilkl;lkhf kP njhiytpy; jiuia te;jilfpwJ vdpy; Gwg;gl;l ,lj;jpy; jiuAld; Vw;gLj;jg;gLk;vwpNfhzk; fhz;f. 62 xU EioT thapypd; Nkw;$iuahdJ miu ePs;tl;l tbtj;jpy; cs;sJ. ,jd; mfyk; mb ikaj;jpypUe;J mjd; cauk; mb kw;Wk; gf;fr; RtHfspd; cauk; mb vdpy; VNjDk; xU gf;fr; RthpypUe;J mb J}uj;jpy; Nkw;$iuapd; cauk; vd;dthf ,Uf;Fk;? kw;Wk; vDk; tistiufs; xd;iwnahd;W nrq;Fj;jhf ntl;bf; nfhz;lhy;> vd ep&gpf;f. 64 tifaPLfisg; gad;gLj;jp
d; Njhuha
kjpg;igf; fzf;fpLf.
vd;w tl;lj;jpw;Fk; vd;w gutisaj;jpw;Fk; nghJthd gug;ig fhz;f. vd;w tl;l cUs;tis mjd;
mbg;gf;fj;ijg; mr;R) nghWj;J Row;Wtjhy; Vw;gLk; jplg; nghUspd; tisg;gug;igf; fhz;f
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67 jPHf;f : 68 xU ,we;jtH cliy kUj;JtH ghpNrhjpf;Fk; NghJ> ,we;j Neuj;ij Njhuhakhf fzf;fpl Ntz;bAs;sJ. ,we;jthpd; clypd; ntg;gepiy fhiy kzpastpy; vd Fwpj;Jf; nfhs;fpwhH. NkYk; kzp Neuk; fopj;J ntg;gepiy msit vdf; fhz;fpwhH. miwapd; ntg;gepiy msT (epiyahdJ) vdpy;> ,we;j Neuj;ijf; fzf;fpLf. (xU kdpj clypd; rhjhuz c\;z epiy vdf; nfhs;f).
69 ,ay;epiyg; gutypd; epfo;jfT mlHj;jpr; rhHG
vdpy; kw;Wk; ,d; kjpg;G fhz;f.
MuKs;s Nfhsj;jpDs; ngUk msT nfhs;SkhW
fhzg;gLk; $k;gpd; nfhs;ssT> Nfhsj;jpd; nfhs;sstpd;
klq;F vdf;
fhl;Lf. (or)
0 20vd;fpw fzk; mzpg;ngUf;fypd; fPo; xU Fyj;ij mikf;Fk;
vdf; fhl;Lf.
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