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Padasalai.Net’s Special – Centum Coaching Team Question Paper 2017-2018

tFg;G : XII CENTUM SPECIAL TEST Neuk; : 3 kzp ghlk; : fzpjk; kjpg;ngz;fs;: 200

I. Choose the correct answer: - 40×1=40

1. + - vd;w ntf;lu; xU %iytpl;lkhfTk;> -3 +4 vd;w ntf;liu xU gf;fkhfTk; nfhz;l ,izfuj;jpd; gug;G

a. 10 b. 6 c.

d. 3

2. vd;gd a, b, c Mfpatw;iw kl;Lf;fshff; nfhz;l tyf;if mikg;gpy; xd;Wf;nfhd;W nrq;Fj;jhd ntf;lu;fs;

vdpy; [ ] d; kjpg;G

a. a2 b

2 c

2 b. 0 c.

d. abc

3. = + vd;w rkd;ghL Fwpg;gJ

a. kw;Wk; Gs;spfis ,izf;Fk; Neu;NfhL b. xoy jsk; c. yoz jsk; d. zox jsk;

4. - kw;Wk; - vd;w ntf;lu;fSf;F ,ilg;gl;l Nfhzk;

a.

b.-

c.-

d.

5. MjpapypUe;J ( +4 +12 )= 26 vd;w jsj;jpw;F tiuag;gl;l nrq;Fj;jpd; ePsk;

a. 2 b.

c. 26 d.

6. (-4> 4) vd;w Gs;spapypUe;J y2=16xf;F tiuag;gLk; ,U

njhLNfhLfSf;F ,ilNaAs;s Nfhzk; a. 45

o b. 30

o c.60

o d.90

o

7. 9x2+16y

2=144 vd;w $k;G tistpd; ,af;F tl;lj;jpd; Muk;

a. b. 4 c. 3 d. 5

8. xy = c2vd;w nrt;tf mjpgutisaj;jpy; ‘t1’ vd;w

Gs;spaplj;Jr; nrq;NfhL kPz;Lk; mt;tistiuia ‘t2’–y; re;jpf;fpwJ vdpy; t1

3 t2 a. 1 b. 0 c. -1 d. -2

9. y = 3x2+3sin x vd;w tistiuf;F x = 0 tpy; njhLNfhl;bd;

rha;T a. 3 b. 2 c. 1 d. -1

10. x3-2x

2+3x+8 vd;w mjpfupf;Fk; tPjkhdJ x mjpfupf;Fk;

tPjj;ijg; Nghy; ,Uklq;F vdpy; x-d; kjpg;Gfs;

a. (-

, -3) b. (

, -3) c. (-

, 3) d. (

, 1)

11. NfhLfs; y = x, y = 1 kw;Wk; x = 0Mfpait Vw;gLj;Jk; gug;ig mr;irg; nghWj;Jr; Row;wg;gLk; NghJ cUthFk; jplg;nghUspd; fd msT

a.

b.

c.

d.

12.

+

vd;w tistiuapd; tpy;ypd; ePsk; a. 48 b. 24 c. 12 d. 96

13.

dx

a.

b.

c.

d.

14.

+5y1/3

= x vd;gjpd; tupir> gb KiwNa

a. 2, 1 b. 1, 2 c. 1, 6 d. 1, 3

15.

– y tan x =cos x d; njhiff; fhuzp

a. sec x b. cos x c. etan x

d. cot x

16. (G, .) vd;w Fyj;jpy; G = {1, -1, i, -i} vdpy; -1 ,d; tupir

a. -1 b. 1 c. 2 d. 0

17. f(x) =

kw;nwq;fpYk;

vd;gJ epfo;jfT mlu;j;jp rhu;G vdpy; k d; kjpg;G

a.

b.

c.

d.

18. var (4X+3) vd;gJ

a. 7 b. 16 var (X) c. 19 d. 0

19. xU rktha;g;G khwp X gha;rhd; gutiyg; gpd;gw;WfpwJ> NkYk; E (X

2) = 30

a. 6 b. 5 c. 30 d. 25

20. ,ay;epiyg; gutiyg; nghWj;J fPo;f;fz;ltw;wpy; vJ / vit rup? I. X = (ruhrup) vd;w Nfhl;bw;F rkr;rPuhdJ II. xU Kfl;Lg; guty; III. ruhrup = ,ilepiy msT = KfL IV. X = ruhrup

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a. I, II kl;Lk; b. II, IV kl;Lk; c. I, II, III kl;Lk; d. ,it midj;Jk;;

21. A vd;w xU jpirapyp mzpapd; tupir 3> jpirapyp k 0 vdpy; A

-1vd;gJ

a.

I b.

I c.

I d. kI

22. aex + be

y = c, pe

x + qe

y = d kw;Wk; =

, =

, =

vdpy; (x, y) ,d; kjpg;G

a.

b.

c.

d.

23.

vd;w mzpapd; juk; 2 vdpy; tpd; kjpg;G

a. 1 b. 2 c. 3 d. VNjDk; xU nka;naz; 24. rkgbj;jhd Neupar; rkd;ghl;Lj; njhFg;ghdJ

a. vg;nghOJk; xUq;fikT cilajhFk; b. ntspg;gilj; jPu;T kl;LNk nfhz;Ls;sJ c. vz;zpf;ifaw;w jPu;Tfs; nfhz;Ls;sJ d. xUq;fikT cilajhf ,Uf;fj; Njitapy;iy

25. ; ( ) + ) + ( ), vdpy;

a. xU xuyF ntf;lu; b. = c. d. = + +

26.

vd;w fyg;ngz;zpd; kl;L> tPr;R KiwNa

a. e9,

b. e

9,-

c. e

6,-

d. e

9,-

27. a = 3 +i kw;wk; z = 2 – 3i vdpy; az, 3az kw;Wk; -az vd;gd Xu; Mu;fd; jsj;jpy;

a. nrq;Nfhz Kf;Nfhzj;jpd; Kidg;Gs;spfs; b. rkgf;f Kf;Nfhzj;jpd; Kidg;Gs;spfs; c. ,Urkgf;f Kf;Nfhzj;jpd; Kidg;Gs;spfs; d. xNu Nfhliktd

28. Zn = cos

+ I sin

vdpy; Z1. Z2 …… Z6 vd;gJ

a. 1 b. -1 c. I d. –i

29. | Z – Z1| = |Z – Z2| vdpy; fyg;ngz; Z ,d; epakg;ghij

a. Mjpia ikakhff; nfhz;l xU tl;lk; b. Z1 I ikakhff; nfhz;l xU tl;lk; c. Mjp topr;nry;Yk; Neu;NfhL d. Z1kw;Wk; Z2 f;fis ,izf;Fk; Nfhl;bd; nrq;Fj;J ,Urkntl;b

30. 16x2-3y

2-32x-12y-44=0 vd;gJ

a. xU ePs;tl;lk; b. xU tl;lk; c. xU gutisak; d. xu; mjpgutisak;

31. f(a) = 2, f1(a) = 1, g (a) = -J, g

1 (a) = 2 vdpy;

d; kjpg;G

a. 5 b. -5 c. 3 d. -3

32. f1(x) =0 vd;w rkd;ghl;bw;F x = x0 vd;w %ykhdJ ,ul;il tupir nfhz;Ls;sJ vdpy; x = x0 MdJ

a. ngUk Gs;sp b. rpWk Gs;sp c. tisT khw;Wg; Gs;sp d. khWepiyg; Gs;sp

33. u = y sin x vdpy;

=

a. cos x b. cos y c. sin x d. 0

34. y2(a+2x) = x

2 ( 3a-x) vd;w tistiuapd; njhiyj; njhLNfhL

a. x = 3a b. x = -

c. x =

d. x = 0

35.

x x dx ,d; kjpg;G

a. b.

c.

d.0

36. (D2-4D+4) y = e

2x d; rpwg;G jPu;T (P.I)

a.

e

2x b. xe

2x c. xe

-2x d.

e

-2x

37. m vd;w khwj;jf;f khwpypiaf; nfhz;l rkd;ghL y = emx ,d;

tiff;nfOr; rkd;ghl;by; m vd;gJ

a.

b.

c. y

1 d. y

38. ~ [p (~q)] ,d; nka; ml;ltizapy; epiufspd; vz;zpf;if

a. 2 b. 4 c. 6 d. 8

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39. gpd;tUtdtw;wpy; vJ R ,y; <UWg;Gr; nrayp my;y?

a. a * b = ab b. a * b = a – b c. a * b = d. a * b =

40. (Z9, +9) ,y;[7] ,d; tupir

a. 9 b. 6 c. 3 d. 1

II. Answer any ten questions: - 10×6=60

41. 2x – 3y + 7z = 5, 3x + y – 3z = 13, 2x + 19y – 47z = 32 xUq;fikTj; jd;ikia Muha;f.

42. Neu;khWfSf;Fupa tupir khw;W tpjpia vOjp epUgp. 43. Kf;Nfhzk; ABC ,d; cr;rpfshd A, B, C apd; epiyntf;lu;fs; ,

, vdpy; Kf;Nfhzk; ABC ,d; gug;ghdJ is

| × + × + × │

Vd epWTf. ,jdpd;Wk; , , xNu Neu;f;Nfhl;lik ntf;lu;fshapUf;f epge;jidiaf; fhz;f.

44. (a) A(-5, 2, 5), B(-3, 6, 7), C(4, -1, 5) kw;Wk; D(2, -5, 3) Mfpaw;iw cr;rpfsha;f; nfhz;l ,izfuj;jpd; gug;Gf; fhz;f.

(b) = = = vd;w ntf;lu;fs; xU Kidapy; re;jpf;Fk; tpspk;Gfshf; nfhz;l ,izfuj;jpz;kj;jpd; fd msT fhz;f.

45. 3+3i, -3-3i, -3 + i vDk; fyg;ngz;fs; xU rkgf;f Kf;Nfhzj;ij Mu;fd; jsj;jpy; cUthf;Fk; vd;W fhl;Lf.

46.

-

=1 mjpgutisaj;jpd; VNjDk; xU Gs;spapypUe;J mjd;

njhiynjhLNfhLfspd; nrq;Fj;Jj; J}uq;fspd; ngUf;Fj; njhif

xU khwpyp vd;Wk; mjd; kjpg;G

vdTk; fhl;Lf.

47. kjpak; 2.00 kzpf;F xU rpw;We;jpd; Ntfkhdp 30 iky;fs; / kzp vdTk; 2.10 kzpf;F Ntfkhdp 50 iky;fs; / kzp vdTk; fhl;LfpwJ. 2.00 kzpf;Fk; 2.10 kzpf;Fk; ,ilg;gl;l VNjh xU rkaj;jpy; KLf;fk; rupahf 120 iky;fs; / kzp2 Mf ,Ue;jpUf;Fk; vdf; fhl;Lf.

48. (a) xU Fyj;jpd; rkdp cWg;G xUikj; jd;ik tha;e;jJ vd epUgp. (b) xU Fyj;jpy; cs;s a f;F (a

-1)

-1 = a vd epUgp.

49. y = 3x2 – 6x vd;w tistiuapd; Kfl;Lg; Gs;spfisf; fhz;f kw;Wk;

,U gf;fKk; cs;s rha;tpd; Fwpiaf; nfhz;L mjd; jd;ikia Muha;e;J mwpf.

50.

= 1 (a>b>0) vd;w ePs;tl;lk; Vw;gLj;Jk; gug;gpid Fw;wr;irg;

nghWj;Jr; Row;wpdhy; Vw;gLk; jplg;nghUspd; fd msTf; fhz;f. 51. x – mr;rpd; kPJ ikak; kw;Wk; XuyF Muk; nfhz;l tl;lj;

njhFg;gpd; tiff;nrOr; rkd;ghl;il mikf;f. 52. epUTf: p q ((~ p) q)

53. xU N[hbg; gfilfs; 10 Kiw Rz;lg;gLfpd;wd. ,U gfilfSk; xNu vz; fhl;Ltij ntw;wp vdf; nfhz;lhy; m) 4 ntw;wpfs; M) G+r;rpa ntw;wp Mfpatw;wpd; epfo;jfTf; fhz;f.

54. mnkupf;f fz;lj;jpy; n[l; tpkhdj;jpy; gazk; nra;Ak; xU egu; fh];kpf; fjpupaf;fj;jpdhy; ghjpf;fg;gLtJ xU ,ay;epiy gutyhFk;. ,jd; ruhrup 4.35 m rem MfTk;> jpl;l tpyf;fk; 0.59 m

rem MfTk; mike;Js;sJ. xU egu; 5.20 m rem f;F Nky; fh];kpf; fjpupaf;fj;jpdhy; ghjpf;fg;gLthu; vd;gjw;F epfo;jfT fhz;f.

55. (a) nka;naz; Fzfq;fisf; nfhz;l p(x) = 0 vd;w gy;YWg;Gf; Nfhitr; rkd;ghl;bd; fyg;ngz; %yq;fs; ,iznaz; ,ul;ilahfj;jhd; ,lk;ngWk; vd ep&gpf;f. (b) xU vz;zpd; n

Mk; gb %yk; fzf;fplg;gLk; NghJ Vw;gLk;

rjtPjg; gpio Njhuhakhf> me;j vz;zpd; rjtPjg; gpioapd;

klq;F MFk; vdf; fhl;Lf. III. Answer any ten questions: - 10×10=100

56. gpd;tUk; rkd;ghLfspd; njhFg;G xUq;fikT cilajh vd;gij Muha;f. xUq;fikT cilajhapd; mtw;iwj; jPu;f;f. x + y - z =1,

2x + 2y – 2z = 2, -3x – 3y + 3z = -3

57. (a) tof;fkhd FwpaPLfSld; Cos A =

epUgp.

(b) 2x-8y+4z=3 kw;Wk; 3x-5y+4z+10=0 vd;w jsq;fspd; ntl;Lf;NfhL topNar; nry;yf; $baJk; 3x-y-2z-4=0 vd;w jsj;jpw;F nrq;Fj;jkhdJkhd jsj;jpd; rkd;ghL fhz;f.

58.

=

=

vd;w Nfhl;il cs;slf;fpaJk;

vd;w jsj;jpw;Fr; nrq;Fj;jhfTk; mike;j jsj;jpd; ntf;lu; kw;Wk; fhu;Brpad; rkd;ghLfisf; fhz;f.

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59. fPo;f;fhZk; Gs;sp tptuq;fspd; gb fpilf;fg;ngWk; mjpgutisaj;jpd; ,af;F tl;lj;jpd; rkd;ghL fhz;f.

i)

vd;w ePs;tl;lj;jpd; ikak;> mjpgutisaj;jpd;

ikakhf mikfpwJ.

ii) mjpgutisaj;jpd; nrt;tfyj;jpd; ePsk;

kw;Wk; ikaj;

njhiyj;jfT

iii) Jizar;rpd; rkd;ghL x = 1

60. 9x2-16y

2-18x-64y-199=0 vd;w mjpgutisaj;jpd; ikaj; njhiyj;

jfT> ikak;> Ftpaq;fs;> cr;rpfs; Mfpatw;iwf; fhz;f. NkYk; mjd; tistiuia tiuf.

61. x+2y-5=0 I xU njhiyj;njhLNfhlhfTk; (6,0) kw;Wk; (-3,0) Mfpa Gs;spfs; topNa nry;yf; $baJkhd nrt;tf mjpgutisaj;jpd; rkd;ghL fhz;f.

62. x2+y

2=52, vd;w tl;lj;jpw;F 2x+3y=6 vd;w Neu;f;Nfhl;bw;F ,izahf

tiuag;gLk; njhLNfhLfspd; rkd;ghLfisf; fhz;f. 63. nfhLf;fg;gl;l xU Rw;wstpidf; nfhz;l nrt;tfq;fSs; rJuk;

kl;LNk ngUk gug;gsitf; nfhz;bUf;Fk; vdf; fhl;Lf. 64. tistiu y

2 = x kw;Wk; y = x – 2 vd;w Nfhl;bdhy; milagLk;

gug;gpidf; fhz;f. 65. y2

=4ax, vd;w gutisaj;jpd;> mjd; nrt;tfyk; tiuapyhd gug;gpid x mr;rpd; kPJ Row;Wk; NghJ fpilf;Fk; jplg;nghUspd; tisgug;igf; fhz;f.

66. xU Kg;gbg; gy;YWg;Gf; Nfhit x = -1 vDk; NghJ ngUk kjpg;G 4 MfTk;> x = 1 vDk; NghJ rpWk kjpg;G 0 MfTk; ,Ug;gpd; mf;Nfhitiaf; fhz;f.

67. x= 0 Mf ,Uf;Fk; NghJ y = 1 vd ,Uf;Fkhdhy;

(1+ex/y

)dx + ex/y

(1-x/y)dy =0 vd;w rkd;ghl;bd; jPu;T fhz;f. 68. xU NgUe;J epiyaj;jpy; xU epkplj;jpw;F cs;Ns tUk;

NgUe;Jfspd; vz;zpf;if gha;]hd; gutiyg; ngw;wpUf;fpwJ. ,q;F λ = 0.9 vdf;nfhz;L m) 5 epkpl fhy ,ilntspapy; rupahf 9 NgUe;Jfs; cs;Ns tu

M) 8 epkpl ,ilntspapy; 10f;Fk; Fiwthf NgUe;Jfs; cs;Ns tu ,) 11 epkpl ,ilntspapy; Fiwe;jgl;rk; 14 NgUe;Jfs; cs;Ns tu epfo;jfT fhz;f.

69. tof;fkhd ngUf;fypd; fPo; 1 ,d; n Mk; gb %yq;fs; Kbthd Fyj;ij mikf;Fk; vdf;fhl;Lf.

70. (a) w = u2e

v vd;w rhu;gpy; u =

kw;Wk; v = y log x, vDkhW ,Ug;gpd;

kw;Wk;

fhz;f.

b) a kw;Wk; b vd;git x2+2 +4=0 vd;w rkd;ghl;bd; %yq;fshf

,Ug;gpd; an + b

n d; kjpg;gpidf; fhz;f. ,jpypUe;J a

12+b

12 d;

kjpg;gpidj; jUtpf;f. (n vd;gJ xU KO vz;) R.RAJASEKARAN, M.SC.,B.ED.,M.PHIL.

DAYANANDA VIDYALAYA MAT HR SEC SCHOOL

KURUSILAPATTU

VELLORE DT

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