padasalai’s centum coaching team special question paper mathematics · 2014-11-29 ·...
TRANSCRIPT
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PADASALAI’S CENTUM COACHING TEAM
Special Question Paper Mathematics
STD: XII Marks :200, Time : 3 Hrs.
Section – A (answer all Questions) 40x1=40
1.
3
2
1
A vdpy; TAA d; juk; fhz;f
a) 3 b) 0 c) 1 d) 2
2.
541
3k1
231
vd;w mzpf;F Neh;khW cz;L vdpy; kd; kjpg;G(fs;)
a)k VNjDk; xU nka;naz; b) 4k c) 4k d) 4k
3. xU rJu mzp A d; thpir n vdpy; Aadj vd;gJ
a) 2A b) nA c) 1nA d) A
4. A kw;Wk; B vd;w mzpfs; ngUf;fYf;F cfe;jitahapd; TAB =
a) TT BA b) TT AB c) AB d) BA
5. a f;Fk; b f;Fk; ,ilg;gl;l Nfhzk; 120° NkYk; mtw;wpd; vz;zsTfs; KiwNa 32, a . b MdJ
a) 3 b) 3 c) 2 d) 2
3
6. k4j3i2
, kcjbia
Mfpa ntf;lh;fs; nrq;Fj;J ntf;lHfshapd;>
a) a = 2, b = 3, c = -4 b) a = 4, b = 4, c = 5 c) a = 4, b = 4, c = -5 d)a = -2, b =3, c =4
7. kjiPR 2 , kjiSQ 23 vdpy; ehw;fuk; PQRS d; gug;G
a) 35 b) 310 c) 2
35 d) 2
3
8. b d; kPJ a d; tPoy; kw;Wk; a d; kPJ b d; tPoYk; rkkhapd; a + b kw;Wk; a - b f;F ,ilg;gl;l Nfhzk;
a) 2
b)
3
c)
4
d)
3
2
9. kjim 2 kw;Wk; kji 294 vd;gd nrq;Fj;J ntf;lHfs; vdpy; m ,d; kjpg;G
a) -4 b) 8 c) 4 d) 12
10. kji 295 , kjim 2 vd;gd nrq;Fj;J ntf;lHfs; vdpy; m ,d; kjpg;G
a) 16
5 b)
16
5 c)
5
16 d)
5
16
11. 122 yx vdpy; iyx
iyx
1
1d; kjpg;G
a) iyx b) x2 c) iy2 d) iyx
12.
100100
2
31
2
31
iid; kjpg;G
a) 2 b) 0 c) -1 d) 1 13. a = 3 + i kw;Wk; z = 2 – 3i vdpy; cs;s az, 3az kw;Wk; -az vd;gd xU Mh;fd; jsj;jpy; a) nrq;Nfhz Kf;Nfhzj;jpd; Kidg;Gs;spfs; b) rkgf;f Kf;Nfhzj;jpd; Kidg;Gs;spfs; c) ,U rkgf;f Kf;Nfhzj;jpd; Kidg;Gs;spfs; d) xNu Nfhliktd.
14. i2
3,d; nka; kw;Wk; fw;gidg; gFjpfs;
a) 0, 3/2 b) 3/2, 0 c) 2, 3 d) 3, 2
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15. 044x32y3x16 22 vd;gJ
a) xU ePs;tl;lk; b) xU tl;lk;. c) xU gutisak; d) xU mjpgutisak; 16. (2,-3) vd;w Kid x = 4 vd;w ,af;Ftiuiaf; nfhz;l gutisaj;jpd; nrt;tfy ePsk; a) 2 b) 4 c) 6 d) 8
17. 1y8x2 vd;w gutisaj;jpd; Kid
a)
0,
8
1 b)
0,
8
1 c)
8
1,0 d)
8
1,0
18. xy 42 -,d; nrt;tfyj;jpd; rkd;ghL
a) x = 1 b) y = 1 c) x = 4 d) y = -1 19. MjpapypUe;J xU Neh;f;Nfhl;by; x njhiytpy; efUk; Gs;spapd; jpirNtfk; v vdTk; a+bv2=x2vdTk; nfhLf;fg;gl;Ls;sJ. ,q;F a kw;Wk; b khwpypfs; mjd; KLf;fkhdJ
a)x
b b)
x
a c)
b
x d)
a
x
20. = 1 / t vDk; tistiuf;F Gs;sp (-3, -1/3 ) vd;w Gs;spapy; nrq;Nfhl;bd; rkd;ghL a) 80273 t b) 80275 t c) 80273 t d) t1
21.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
22.° C ntg;gepiyapy; “ l “ kP ePsKs;s xU cNyhfj; Jz;bd; rkd;ghL 20000004.000005.01 l vdpy;
100°C -y; l-,d; khW tPjk; a) Cm00013.0 b) Cm00023.0 c) Cm00026.0 d) Cm00033.0
23. u = sin-1
22
44
yx
yx kw;Wk; f = sin u vdpy; rkgbj;jhd rhh;G f d; gb
a) 0 b) 1 c) 2 d) 4
24. u = ,
yx
1
22
vdpy; x x
u
+ y y
u
a) u2
1 b) u c) u2
3 d) – u
25.
2/
03/53/5
3/5
xsinxcos
xcos dx d; kjpg;G
a) 2 b) 4 c) 0 d)
26. 1
0
4)x1(x dx d; kjpg;G.
a) 1/ 12 b) 1/30 c) 1/ 24 d) 1/ 20
27. 4/
0
3 xdx2cos d; kjpg;G
a) 2 / 3 b) 1/ 3 c) 0 d) 32
28. dxxI nn sin vdpy; nI
a) 21 1
cossin1
n
n In
nxx
n b) 2
1 1cossin
1
n
n In
nxx
n
c) 21 1
cossin1
n
n In
nxx
n d) n
n In
nxx
n
1cossin
1 1
29. QPydx
dy vd;w tiff;nfO rkd;ghl;bd; njhiff; fhuzp cos x vdpy; P d; kjpg;G
a) – cot x. b) cot x c) tan x d) – tan x.
30. m < 0 Mf ,Ug;gpd; 0dx
mxdy
d; jPh;T
a) x = cemy. b) x = ce-my. c) x = my + c. d) x = c. 31. 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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32. 2xydx
dy vd;w tiff;nfOr; rkd;ghl;bd; thpir kw;Wk; gb
a) 1,1 b) 1,2 c) 2,1 d) 0,1 33. xU $l;Lf; $w;W %d;W jdpf;$w;Wfisf; nfhz;ljhf ,Ug;gpd;> nka;al;ltizapYs;s epiufspd; vz;zpf;if
a) 8 b) 6 c) 4 d) 2 34.epge;jidf; $w;W qp f;F rkhdkhdJ
a) p v q. b) p v ~ q c) ~p v q. d) p ^ q. 35. p apd; nka;kjpg;G T kw;Wk; q d; nka;kjpg;G F vdpy; gpd;tUtdtw;wpy; vit nka;kjpg;G T vd ,Uf;Fk;? (i) p v q (ii) ~ p v q iii) p v ~q iv) p ^ ~ q. a) (i), (ii), (iii) b) (i), (ii),(iv) c) (i), (iii), (iv) d) (ii), (iii), (iv) 36. gpd;tUk; $w;Wfspy; nka;kjpg;Gfs; i. Cl;bahdJ jkpo;ehl;by; cs;sJ kw;Wk; 3 + 4 = 8 ii. Cl;bahdJ jkpo;ehl;by; cs;sJ kw;Wk; 3 + 4
= 7 iii. Cl;bahdJ Nfushtpy; cs;sJ kw;Wk; 3 + 4 = 7 iv. Cl;bahdJ Nfushtpy; cs;sJ kw;Wk; 3 + 4
= 8 a) F,T,F,F b) F,F,F,T c) T,T,F,F d) T,F,T,F
37. f(x) =
x,x16
1A
2vd;gJ X vd;w njhlh; rktha;g;G khwpapd; xU epfo;jfT mlh;j;jp rhh;G (p.d.f)
vdpy; A d; kjpg;G a) 16 b) 8 c) 4 d) 1 38. X vd;w rktha;g;G khwpapd; epfo;jfT epiwr;rhh;G guty; gpd;tUkhW.
x -2 3 1
P(X=x) 6 4 12
d; kjpg;G a) 1 b) 2 c) 3 d) 4 39. X vd;w rktha;g;G khwpapd; epfo;jfT guty; gpd;tUkhW
x 0 1 2 3 4 5
P(X=x) ¼ 2a 3a 4a 5a ¼ 41 xP d; kjpg;G
a) 10 / 21 b) 2 / 7 c) 1/ 14 d) 1/ 2 40. xU jdpepiy rktha;g;G khwp a) KbTw;w fzj;jpd; kjpg;Gfisg; ngWfpwJ b) Fwpg;gpl;l xU ,ilntspapYs;s vy;yh kjpg;GfisAk; ngWfpwJ c) vz;zpylq;fh kjpg;Gfisg; ngWfpwJ d) xU KbTw;w my;yJ vz;zplj;jf;f kjpg;Gfisg; ngWfpwJ
Section – B Answer any 10 only Note 55th question is compulsory (10x6=60)
41.
544
434
221
A -f;F> 1 AA vdf; fhl;Lf.
42. gpd;tUk; mzpfspd; juk; fhz;f
6721
3142
4321
43. xNu mbg;gf;fKk;> xNu ,iz NeHf;NfhLfSf;Fk; ,ilg;gl;l ,izfuq;fs; rkgug;Gilait
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vd;gij ntf;lH Kiwapy; epWTf.
44. tof;fkhd FwpaPl;LfSld; Kf;Nfhzk; ABC y;bc
acbA
2cos
222 vd ep&gp.
45. 1z ,d; tPr;R6
kw;Wk; 1z ,d; tPr;R
32
vdpy; 1z vd epWTf.
46. n vd;gJ kpif KO vz; vdpy; 6
cos233 1 nii nnn vd ep&gpf;f
47. gutisa Mbapd; Ftpak; mjd; ikaj;jpypUe;J (Kid) 8 nr.kP njhiytpy; cs;sJ. Mbapd;
FopT 25 nr.kP vdpy; mt;thbapd; tpl;lk; fhz;f.
48. fPo;f;fz;ltw;wpf;F vy;iyf; fhz;f. x
x
x1
0
coslim
49. gpd;tUk; rhHGfs; ve;j ,ilntspfspy; FopT milfpd;wd vd;gijAk; kw;Wk; tisT khw;Wg; Gs;spfisAk;
fhz;f xxxxf 452 23
50. tifaPLfisg; gad;gLj;jp 3 65 Njhuha kjpg;Gfisf; fhz;f.
51. kjpg;gpLf:
dx
xfxf
xf
2
0 cossin
sin
52. yx, vd;w Gs;spapy; rha;T x
y1 vdf; nfhz;L>(1,0) vd;w Gs;sp topahfr; nry;yf; $ba tistiuapd;
rkd;ghl;ilf; fhz;f.
53. qpqP ~~ xU nka;ikah vd;gjid nka; ml;ltiziaf; nfhz;L jPHkhdpf;f.
54. pqqpqp ~~ vdf; fhl;Lf
55. xU gfil ,UKiw cUl;lg;gLfpwJ.mjd; Nky; cs;s vz; xw;iwg;gil vz;zhf ,Uj;jy; ntw;wpahff;
fUjg;gLfpwJ. ntw;wpapd; epfo;jfTg; gutypd; ruhrhp kw;Wk; gutw;gbiaf; fhz;f.
(m)
xU gha;]hd; gutypy; 32 XPXP vdpy; 5XP If; fhz;f. .050.03 egiven
Section – C answer any 10 only 70th question is compulsory (10x10=100)
56. xU igapy; &.1 kw;Wk; &.2> kw;Wk; &.5 ehzaq;fs; cs;sd. &gha; 100 kjpg;gpw;F nkhj;jk; 30 ehzaq;fs;
cs;sd. mt;thwhapd; xt;nthU tifapYk; cs;s ehzaq;fspd; vz;zpf;ifia fhz;f
57. sin A − B = sinA cosB − cosA sinB vd ntf;lH Kiwapy; ep&gp
58. ntl;Lj;Jz;L tbtpy; xU jsj;jpd; rkd;ghl;ilj; jUtpf;f
59. 𝑥2 − 2𝑥 + 4 = 0 -,d; %yq;fs; 𝛼 kw;Wk; 𝛽 vdpy; 𝛼𝑛 − 𝛽𝑛 = 𝑖2𝑛+1 sin 𝑛𝜋
3 mjpypUe;J α9 − β9 kjpg;ig
ngWf
60. xU njhq;F ghyj;jpd; fk;gp tlk; gutisa tbtpypYs;sJ. mjd; ePsk; 40 kPl;lH MFk;. topg;ghijahdJfk;gp
tlj;jpd; fPo;kl;lg; Gs;spapypUe;J 5 kPl;lH fPNo cs;sJ. fk;gp tlj;ijj; jhq;Fk; J}z;fspd; cauq;fs; 55 kPl;lH
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vdpy;>30 kPl;lH cauj;jpy; fk;gp tlj;jpw;F xU Jiz jhq;fp $Ljyhff; nfhLf;fg;gl;lhy; mj;Jizj;jhq;fpapd;
ePsj;ijf; fhz;f
61. 16𝑥2 + 9𝑦2 + 32𝑥 − 36𝑦 = 92vd;w ePs;tl;lj;jpd; ikaj; njhiyj;jfT> ikak;> Ftpaq;fs;> cr;rpfs; Mfpatw;iwf;
fhz;f. NkYk; mjd; tistiuia tiuf.
62. mjpgutisaj;jpd; ikak; (2,4).NkYk;(2,0)topNa nry;fpwJ. ,jd; njhiyj; njhLNfhLfs;𝑥 + 2𝑦 − 12 =
0kw;Wk;𝑥 − 2𝑦 + 8 = 0 Mfpatw;wpw;F ,izahf ,Uf;fpd;wdvdpy;mjpgutisaj;jpd; rkd;ghL; fhz;f
63. ez;gfypy;𝐴vd;w fg;gy;>𝐵vd;w fg;gYf;F Nkw;Fg; Gwkhf 100 fp.kP J}uj;jpy; cs;sJ. fg;gy; 𝐴MdJ kzpf;F 35
fp.kP Ntfj;jpy; fpof;F Nehf;fpr; nry;fwJ. fg;gy; 𝐵MdJ kzpf;F 25 fp.kP Ntfj;jpy; tlf;F Nehf;fpr; nry;fpd;wJ
vdpy;> khiy 4.00 kzpf;F ,uz;L fg;gy;fSf;Fk; ,ilg;gl;l J}uk; vt;tsT Ntfkhf khWk; vd;gijf; fhz;f
64. xU %bapl;l rJu mbg;ghfk; nfhz;Ls;s (fdr; nrt;tfj;jpd;) ngl;bapd; nfhs;ssT 2000 f.nrkP> mg;ngl;bapd;
mbg;ghfk; kw;Wk; Nky; ghfj;jpw;fhd %yg; nghUl;fspd; tpiy xU r.nrkPf;F 3 kw;Wk; mjd; gf;fq;fSf;fhd %yg;
nghUl;fspd; tpiy xU rJu nr.kPf;F &. 1.50. %yg; nghUl;fspd; tpiy rpWk msT nfhs;SkhW cs;s ngl;bapd;
ePs>mfyq;fs; fhz;f
65. 𝑦 = 𝑥3 + 1vd;fpw tistiuia tiuf.
66. Muk; ‘ 𝑟 ‘ Fj;Jauk; ‘ ℎ ‘ cila $k;gpd; fdmsitf; fhz;f
67. 𝑦 = sin 𝑥vd;w tistiu 𝑥 = 0 , 𝑥 = πkw;Wk; 𝑥-mr;R Mfpatw;why; Vw;gLk; gug;gpid 𝑥-mr;rpidg; nghWj;J
Row;Wk; NghJ fpilf;Fk; jplg;nghUspd; tisgug;G 2π 2 + log 1 + 2 vd epWTf
68. ve;jnthU Gs;spapYk; rha;T 𝑦 + 2𝑥vdf; nfhz;L Mjptopahfr; nry;Yk; tistiuapd; rkd;ghL 𝑦 =
2 𝑒𝑥 − 𝑥 − 1 vdf; fhl;Lf.
69. 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 10.00 kzpastpy; 93.4 ° 𝐹vd Fwpj;Jf; nfhs;fpwhH. NkYk; 2 kzp Neuk; fopj;J ntg;gepiy msit 91.4° 𝐹 vdf; fhz;fpwhH. miwapd; ntg;gepiy msT (epiyahdJ)72° 𝐹 vdpy;> ,we;j Neuj;ijf; fzf;fpLf. (xU kdpj clypd; rhjhuz c\;z epiy 98.6° 𝐹vdf; nfhs;f).
log𝑒19.4
21.4 = − 0.0426 , log𝑒
26.6
21.4 = − 0.00945
70. 11-,d; kl;Lf;F fhzg;ngw;w ngUf;fypd;fPo; 1 , 3 , 4 , 5 , 9 vd;w fzk; xU vgPypad; Fyj;ij mikf;Fk; vdf; fhl;Lf (m)
xU ,ay;epiyg; gutypd; epfo;jfTg; guty;𝑓 𝑥 = 𝑐𝑒 − 𝑥 2 + 3𝑥 , − ∞ < 𝑋 < ∞vdpy; 𝑐 , 𝜇 , 𝜎2,tw;iwf; fhz;f
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