gj;jhk; tFg;G fzpjk; - edu.newsbundles.comΒ Β· π ) 2 β 8 + 12 = 0 ππ ) 2 2 β3 + 4 = 0 ,...
Transcript of gj;jhk; tFg;G fzpjk; - edu.newsbundles.comΒ Β· π ) 2 β 8 + 12 = 0 ππ ) 2 2 β3 + 4 = 0 ,...
X β MATHS QUESTION BANK Page 1
β fzf;Ffs; nra;tjpd; %yk; fzpjj;ijf; fw;Nghk; "
gj;jhk; tFg;G
fzpjk;
tpdh - tq;fp jahhpg;G :
rp.rf;jpNty; , M.Sc.,B.Ed.,
gl;ljhhp Mrphpah; ,
muR Nky; epiyg; gs;sp,
,uhkpak;gl;b, β 635 302
ghg;gpnul;bg;gl;b, ( tl;lk; )
jh;kGhp . ( khtl;lk; )
njhiyNgrp vz; : 94439 50993
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X β MATHS QUESTION BANK Page 2
Kf;fpa ,uz;L kjpg;ngz; tpdhf;fs;
ghlk; : 1. fzq;fSk; rhh;GfSk;
1. π΄ = β10 , 0 , 1 , 9 , 2 , 4 , 5 , π΅ = β1 ,β2 , 5 , 6 , 2 , 3 vd;w fzq;fSf;F gpd;tUtdtw;iw rhpghh;.
i ) fzq;fspd; Nrh;g;G ghpkhw;Wg;; gz;G cilaJ. ii ) fzq;fspd; ntl;L ghpkhw;Wg;; gz;G cilaJ.
2. A = 1 , 2 , 3 , 4 , 5 , B = 3 , 4 , 5 , 6 , C = { 5 , 6 , 7 , 8 } vdpy; A βͺ B βͺ C = A βͺ B βͺ C vd;gijr; rhpghh;.
3. A = { a , b , c , d } B = { a , c , e } kw;Wk; C = { a , e } vdpy; A β© B β© C = A β© B β© C vd;gijr; rhpghh;.
4. A β B vdpy; A βͺ B = B vdf; fhl;Lf. ( ntz;glj;ij gad;gLj;jTk; )
5. A β B vdpy; A β© B kw;Wk; A β₯ B Mfpatw;iwf; fhz;f. ( ntz;glj;ij gad;gLj;jTk; )
6. ntz;glq;fis gad;gLj;jp A β© B βͺ A \ B = A vd;gijr; rhpghh;.
7. A , B kw;Wk; C Mfpa %d;W fzq;fSf;F gpd;tUtdtw;iw tpsf;Fk; ntz;glq;fs; tiuf.
i A β© B β© C ii A kw;Wk; π΅ vd;gd C - d; cl;fzq;fs;.NkYk; mit ntl;lhf; fzq;fs;.
iii A β© B \ C iv B βͺ C \ A v A βͺ B β© C vi C β© B βͺ A
8. nfhLf;fg;gl;Ls;s f = 1 , 3 , 2 , 5 , 4 , 7 , 5 , 9 , 3 , 1 vDk; rhh;gpw;F kjpg;gfk; kw;Wk; tPr;rfk; Mfpatw;iwf; fhz;f.
9. π = 12 , 2 , 13 , 3 , 15 , 3 , 14 , 2 , 17 , 17 vd;w rhh;gpy; 2 kw;Wk; 3 Mfpatw;wpd; Kd; cUf;fisf; fhz;f.
10. π = π , β2 , β5 , π , 8 , π , π , β1 vd;gJ rkdpr; rhh;ig Fwpf;fpwJ vdpy; a , b , c kw;Wk; d Mfpatw;wpd; kjpg;igf;
fhz;f.
ghlk; : 2. nka;naz;fspd; njhlh;thpirfSk; njhlh;fSk;
11. xU $l;Lj;njhlh;thpirapd; Kjy; cWg;G 6 kw;Wk; nghJ tpj;jpahrk; 5 vdpy; mj;njhlh;thpirAk;
mjd; nghJ cWg;igAk; fhz;f.
12. 125 , 120 , 115 , 110 , .......... vd;w $l;Lj; njhlh;thpirapd; nghJ tpj;jpahrj;ijAk; 15 tJ cWg;igAk; fhz;f.
13. 2 , 3 3 , 5 3 vd;w $l;Lj;njhlh; thpirapd; 12 tJ cWg;G ahJ?
14. 4 , 9 , 14 , .......... vd;w $l;Lj;njhlh; thpirapd; 17 tJ cWg;G ahJ?
15.13 My; tFgLk; <hpyf;f kpif KO vz;fspd; vz;zpf;ifiaf; fhz;f.
16. 5 + 11 + 17 + .......... + 95 vd;w $l;Lj;njhlhpd; $Ljy; fhz;f.
17. 1 + 2 + 3 + ............ + 45 d; $Ljy; fhz;f.
18. 2 + 4 + 6 + .......... + 100 d; $Ljy; fhz;f.
19. 7 + 14 + 21 + ........... + 490 d; $Ljy; fhz;f.
20. 12 + 2 2 + β¦β¦β¦ . . + 25 2 d; $Ljy; fhz;f.
21. 13 + 2 3 + β¦β¦β¦ . . + 20 3 d; $Ljy; fhz;f.
ghlk; : 3.,aw;fzpjk;
22. njhFKiw tFj;jiy gad;gLj;jp gpd;tUtdtw;wpd; <T , kPjp fhz;f.
i ) ( π₯ 3 + π₯ 2 β 3π₯ + 5 ) Γ· ( π₯ β 1 ) ii ) ( 3π₯ 3 β 2π₯ 2 + 7π₯ β 5 ) Γ· ( π₯ + 1 ) ) πππ ) ( π₯ 3 + π₯ 2 β 7π₯ β 3 ) Γ· ( π₯ β 3 )
23. π₯ 3 β 6π₯ 2 + 11π₯ β 6 vd;w gy;YWg;Gf; Nfhitf;F ( π₯ β 1 ) xU fhuzpah vd Muha;f.
24. π₯ 3 + 6π₯ 2 + 11 + 6 vd;w gy;YWg;Gf; Nfhitf;F ( π₯ + 1 ) xU fhuzpah vd Muha;f.
25. RUf;Ff .6π₯2β 54
π₯ 2 + 7π₯ + 12
26. RUf;Ff. π₯ 3β 27
π₯ 2 β 9
27. RUf;Ff π₯
π₯ + 1 Γ·
π₯ 2
π₯ 2β 1
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X β MATHS QUESTION BANK Page 3
28. 7 + 3 kw;Wk; . 7 β 3 Mfpatw;iw %yq;fshff; nfhz;l ,Ugbr; rkd;ghl;bid mikf;f.
29. RUf;Ff .6π₯2+ 9π₯
3π₯ 2β 12π₯
30. xU ,Ugb gy;YWg;Gf; Nfhitapd; G+r;rpaq;fspd; $Ljy ; β 4 kw;Wk; mjd; ngUf;fw;gyd; 3 vdpy; mf;Nfhitiaf; fhz;f.
31. xU ,Ugb gy;YWg;Gf; Nfhitapd; G+r;rpaq;fspd; $Ljy; 1
3 kw;Wk; mjd; ngUf;fw;gyd; β
1 3
vdpy; mf;Nfhitiaf; fhz;f.
32. gpd;tUk; rkd;ghLfspd; %yq;fspd; jd;ikiaf; fhz;f.
π ) π₯ 2 β 8π₯ + 12 = 0 ππ ) 2π₯ 2 β 3π₯ + 4 = 0 , πππ ) 9π₯ 2 + 12π₯ + 4 = 0 ππ£ ) π₯ 2 β 11π₯ β 10 = 0 , π£ ) 2π₯ 2 + 5π₯ + 5 = 0
ghlk; : 4.mzpfs;
33. π΄ = 8 51 β3
24
vdpy; π΄ π kw;Wk; π΄ π π
Mfpatw;iwf; fhz;f.
34. π΄ = 2 34 1 5 0
vdpy; A β d; epiu epuy; khw;W mzpiaf; fhz;f.
35. π₯ 5 45 9 1
= 3 5 π§5 π¦ 1
vdpy; x , y kw;Wk; z Mfpatw;wpd; kjpg;G fhz;f.
36. A = 5 6 β21 0 4
32
kw;Wk; B = 3 β1 42 8 2
73
vdpy; A + B If; fhz;f.
37. A = 2 3
β9 5 β
1 57 β1
vdpy; A β d; $l;ly; Neh;khW mzpiaf; fhz;f.
ghlk; : 5.Maj;njhiy tbtpay;
38. ( - 6 , 4 ) kw;Wk; ( 2 , 6 ) Mfpa Gs;spfis ,izf;Fk; Nfhl;Lj; Jd;bd; eLg;Gs;sp fhz;f.
39. ( 3 , 0 ) kw;Wk; ( - 1 , 4 ) Mfpa Gs;spfis ,izf;Fk; Nfhl;Lj ;Jd;bd; eLg;Gs;sp fhz;f.
40. ( 1 , - 1 ) kw;Wk; ( - 5 , 3 ) Mfpa Gs;spfis ,izf;Fk; Nfhl;Lj; Jd;bd; eLg;Gs;sp fhz;f.
41. ( 0 , 0 ) kw;Wk; ( 0 , 4 ) Mfpa Gs;spfis ,izf;Fk; Nfhl;Lj; Jd;bd; eLg;Gs;sp fhz;f.
42. xU tl;lj;jpd; ikak; ( - 6 , 4 ) mt;tl;lj;jpd; xU tpl;lj;jpd; xU Kid Mjpg;Gs;sp vdpy; kw;nwhU Kidiaf; fhz;f.
43. A ( 4 , - 6 ) , B ( 3 , - 2 ) kw;Wk; C ( 5 , 2 ) Mfpatw;iw cr;rpfshff;nfhz;l Kf;Nfhzj;jpd; eLf;Nfhl;L ikak; fhz;f.
44. ( 1 , 3 ) , ( 2 , 7 ) kw;Wk; ( 12 , -16 ) Mfpatw;iw cr;rpfshff;nfhz;l Kf;Nfhzj;jpd; eLf;Nfhl;L ikak; fhz;f.
45. ( 3 , 5 ) , ( - 7 , 4 ) kw;Wk; ( 10 , - 2 ) Mfpatw;iw cr;rpfshff; nfhz;l Kf;Nfhzj;jpd; eLf;Nfhl;L ikak; fhz;f.
46. ( 3 , 5 ) , ( 8 , 10 ) Mfpa Gs;spfis ,izf;Fk; Nfhl;Lj; Jz;il cl;Gwkhf 2 : 3 vd;w tpfpjj;jpy; gphpf;Fk; Gs;spiaf; fhz;f.
47. ( 3 , 4 ) , ( - 6 , 2 ) Mfpa Gs;spfis ,izf;Fk; Nfhl;Lj;Jz;il ntspg;Gwkhf 3 : 2 vd;w tpfpjj;jpy; gphpf;Fk; Gs;spiaf;
fhz;f.
fPo;f;fz;l Gs;spfis Kidfshff; nfhz;l Kf;Nfhzq;fspd; gug;G fhz;f.
48. 1 , 2 , β3 , 4 kw;Wk;;; β5 , β6
49. 0 , 0 , 3 , 0 kw;Wk; 0 , 2
50. 5 , 2 , 3 , β5 kw;Wk; ( β5 , β1 )
51. β4 ,β 5 , 4 , 5 kw;Wk; ( β1 , β6 )
thpirapy; mike;j Kf;Nfhzj;jpd; KidfSk; mit mikf;Fk; Kf;Nfhzj;jpd;
gug;gsTfSk; fPNo nfhLf;fg;gl;Ls;sd. xt;nthd;wpYk; a β tpd; kjpg;G fhz;f.
t.vz; Kidfs; gug;G
52 6 , 7 , β4 , 1 kw;Wk; ( π , βπ ) 68 r.m
53 0 , 0 , 4 , π kw;Wk; ( 6 , 4 ) 17 r.m
54 π , π , 4 , 5 kw;Wk; ( 6 , β1 ) 9 r.m
55 9 , β3 , 3 , π kw;Wk; ( β1 , 5 ) 12 r.m
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gpd;tUk; Gs;spfs; xNu Nfhl;by; mikAk; Gs;spfsh vd Muha;f.
56. π΄ 2 , 3 , π΅ 4 , 0 kw;Wk; πΆ 6 , β3
57. 4 , 3 , 1 , 2 kw;Wk; ( β2 , 1 )
58. β2 , β 2 , β6 , β2 kw;Wk; ( β2 , 2 )
fpNo nfhLf;fg;gl;l Gs;spfs; xU Nfhliktd vdpy; k β d; kjpg;G fhz;f.
59. π , β1 , 2 , 1 kw;Wk; ( 4 , 5 )
60. 2 , β5 , 3 , β4 kw;Wk; 9 , π
61. π , π , 2 , 3 kw;Wk; ( 4 , β1 )
55. rha;Tf; Nfhzk; 45 0 kw;Wk; y β ntl;L
2
5 vdf;nfhz;l Neh;f;Nfhl;bd; rkd;ghL fhz;f.
62. rha;Tf; Nfhzk; 60 0 kw;Wk; y β ntl;L 3 vdf;nfhz;l Neh;f;Nfhl;bd; rkd;ghL fhz;f.
63. rha;T - 3 kw;Wk; y β ntl;L 4 vdf;nfhz;l Neh;f;Nfhl;bd; rkd;ghL fhz;f.
64. gpd;tUk; tptuq;fSf;F Neh;NfhLfspd; rkd;ghL fhz;f.
i ) rha;T β 4 , ( 1 , 2 ) vd;w Gs;sptopr; nry;fpwJ. ii ) rha;T
2
3 , ( 5 , - 4 ) vd;w Gs;sp topr; nra;fpwJ.
65. gpd;tUk; Neh;f; NfhLfspd; rha;T kw;Wk; y ntl;Lj;Jz;L Mfpadtw;iwf; fhz;f.
π ) π¦ = π₯ + 1 ππ ) 5π₯ = 3π¦ πππ ) 4π₯ β 2π¦ + 1 = 0 ππ£ ) 10π₯ + 15π¦ + 6 = 0
66. gpd;tUk; Gs;spfs; topr;nry;Yk; Neh;f;Nfhl;bd; rkd;ghL fhz;f.
π ) β2 , 5 , 3 , 6 ππ ) 0 , β 6 , ( β8 , 2 )
66. x β mr;rpypUe;J 5 myFfs;J}uj;jpy; cs;sJk; x β mr;rpf;F ,izahdJkhd Neh;f;Nfhl;bd; rkd;ghL fhz;f.
67. ( - 5 , - 2 ) vd;w Gs;sp topr;nry;tJk; Ma mr;RfSf;F ,izahdJkhd Neh;f;Nfhl;bd; rkd;ghL fhz;f.
68.gpd;tUk; Neh;f;NfhLfspd; rha;Tfisf; fhz;f
i ) 3x + 4y β 6 = 0 ii ) y = 7x + 6 iii ) 4x = 5y + 3
69. 3x + 2y β 12 = 0 , 6x + 4y =8 = 0 Mfpa Neh;f;NfhLfs; xd;Wf;nfhd;W ,iz vd epWTf.
70. x + 2y + 11 = 0 , 3x + 6y + 2 = 0 Mfpa Neh;f;NfhLfs xd;Wf;nfhd;W ,iz vd epWTf.
71. x + 2y + 1 = 0 , 2x β y + 5 = 0 Mfpa Neh;f;NfhLfs; xd;Wf;nfhd;W nrq;Fj;J vd epWTf.
72. 5x β 2y β 9 = 0 , ay + 2x β 11 = 0 Mfpa Neh;f;NfhLfs; xd;Wf;nfhd;W nrq;Fj;J vdpy; a β tpd; kjpg;G fhz;f.
ghlk; : 6.tbtpay;
73. β π΄π΅πΆ y; π·πΈ β π΅πΆ kw;Wk;
π΄π·
π·π΅=
2
3 AE = 3.7 nr.kP vdpy; EC - If; fhz;f.
74. D kw;Wk; E Mfpa Gs;spfs; KiwNa gf;fq;fs; AB kw;Wk; AC fspy; π·πΈ β π΅πΆ vd;wpUf;FkhW mike;Js;sd.
i ) AD = 6 nr.kP , DB = 9 nr.kP kw;Wk; AE = 8 nr.kP vdpy; AC β fhz;f.
ii ) AD = 8 nr.kP , AB = 9 nr.kP kw;Wk; AE = 12 nr.kP vdpy; CE β fhz;f.
75. AD vd;gJ β π΄π΅πΆ β y; β π΄ d; cl;Gw Nfhz ,Urkntl;b.mJ BC I D - y; re;jpf;fpwJ.
i ) π΅π· = 2 nr.kP π΄π΅ = 5 nr.kP π·πΆ = 3 nr.kP vdpy; AC β fhz;f.
ii ) AB = 5.6 nr.kP AC = 6 nr.kP DC = 3 nr.kP vdpy; BC β fhz;f.
76. gpd;tUtdtw;Ws; AD vd;gJ βπ΄π΅πΆ y; β π΄ d; Nfhz ,Urkntl;b MFkh vdr; Nrhjpf;f.
i ) AB = 4 nr.kP AC = 6 nr.kP BD = 1.6 nr.kP kw;Wk; CD = 2.4 nr.kP
ii ) AB = 6 nr.kP AC = 8 nr.kP BD = 1.5 nr.kP kw;Wk; CD = 3 nr.kP
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X β MATHS QUESTION BANK Page 5
77.fPo;f;fhZk; xt;nthU glj;jpYk; x β d; kjpg;G fhz;f.
78. xU tl;lj;jpy; AB , CD vd;Dk; ,U ehz;fs; xd;iwnahd;W cl;Gwkhf P β y; ntl;bf;nfhs;fpwJ vdpy;
i ) CP = 4 nr.kP AP = 8 nr.kP PB = 2 nr.kP vdpy; PD fhz;f.
ii ) AP = 12 nr.kP AB = 15 nr.kP NkYk; CP = PD vdpy; CD β iaf; fhz;f.
79. xU tl;lj;jpy; AB , CD vd;Dk; ,U ehz;fs; xd;iwnahd;W ntspg;Gwkhf P β y; ntl;bf;nfhs;fpwJ vdpy;
i ) AB = 4 nr.kP BP = 5 nr.kP kw;Wk; PD = 3 nr.kP vdpy; CD β iaf; fhz;f.
ii ) BP = 3 nr.kP CP = 6 nr.kP kw;Wk; CD = 2 nr.kP vdpy; CD β iaf; fhz;f.
80. β PQR β d; gf;fq;fs; PQ kw;Wk; PR β fspd; kPJ mike;j Gs;spfs; S kw;Wk; T vd;f. NkYk; ππ β ππ , PR = 5.6 nr.kP kw;Wk;
ππ
ππ=
3
2 vdpy; PT fhz;f.
ghlk; : 7.Kf;Nfhztpay;
80. πππ π
πΆππ ππ π +
πΆππ π
πππ π= 1 vd;w Kw;nwhUikia epWTf.
81. 1 β πΆππ π1 + πΆππ π
= πΆππ ππ πβπΆππ‘ π vd;w Kw;nwhUikia epWTf.
82. 1 β πππ π
1 + πππ π = πππ π β π‘ππ π vd;w Kw;nwhUikia epWTf.
83. πΆππ 2 π + πππ 2 π = 2 + πππ π vd;w Kw;nwhUikia epWTf.
84. πΆππ‘ 2 π + πΆππ π = πππ 2 π vd;w Kw;nwhUikia epWTf.
85. 200 kP ePsKs;s E}ypdhy; xU fhw;whb fl;lg;gl;L gwe;Jnfhz;bUf;fpwJ. me;j E}y; jiukl;lj;Jld; 30 0 Nfhzj;ij
Vw;gLj;jpdhy; fhw;whb jiukl;lj;jpypUe;J vt;tsT cauj;jpy; gwf;fpwJ vdf; fhz;f.
( ,q;F E}y; xU Neh;f;Nfhl;by; cs;sjhf fUJf )
86. Rthpy; rha;j;J itf;fg;gl;l xU VzpahdJ jiuAld; 60 0 Nfhzj;ij Vw;gLj;JfpwJ. Vzpapd; mb Rtw;wpypUe;J 3.5 kP
J}uj;jpy; cs;sJ vdpy; Vzpapd; ePsj;ij fhz;f.
87. 30 kP ePsKs;s xU fk;gj;jpd; epoypd; ePsk; 10 3 kP vdpy; #hpadpd; Vw;wf; Nfhzj;ij ( jiu kl;lj;jpypUe;J Vw;wf; Nfhzk; )
mstpidf; fhz;f.
88. cauk; 150 nr.kP cs;s xU rpWkp xU tpsf;Ff; fk;gj;jpd; Kd;epd;wthW 150 3 nr.kP ePsKs;s epoiy Vw;gLj;Jfpwhs; vdpy;
tpsf;Ff; fk;gj;jpd; cr;rpapd; Vw;wf;Nfhzj;ijf; fhz;f.
ghlk; : 8.mstpay;
89. kuj;jpdhyhd xU jpd;kf; $k;gpd; mbr;Rw;wsT 44 kP kw;Wk; mjd; cauk; 12 kP vdpy; mj;jpd;kf; $k;gpd; fdmsitf; fhz;f.
90. xU jpd;k Neh;tl;l cUisapd; Muk; 14 nr.kP kw;wk; cauk; 8 nr.kP vdpy; tisgug;G kw;Wk; nkhj;j gug;G Mfpatw;iwf; fhz;f.
91. 98.56 r.nr.kP Gwgug;Gf; nfhz;l xU jpd;kf; Nfhsj;jpd; Muj;ijf; fhz;f.
92. xU ,ilf;fz;l tbtpyhd thspapd; Nkw;Gw kw;Wk; mbg;Gw Muq;fs; KiwNa 15 nr.kP kw;Wk; 8 nr.kP .NkYk; mjd;
Mok; 63 nr.kP vdpy; mjd; nfhs;ssit ypl;lhpy; fhz;f. Ο = 22
7
93. xU Neh;tl;l cUisapd; tisgug;G 704 r.nr.kP kw;Wk; mjd; cauk; 8 nr.kP vdpy; mt;TUisapd; fd msitf; fhz;f.
94. xU Nfhsj;jpd; fdmsT mjd; Gwg;gug;Gf;Fr; rkk; vdpy; mjd; tpl;lj;ijf; fhz;f.
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X β MATHS QUESTION BANK Page 6
95. xU jpd;kf; $k;gpd; Muk; kw;Wk; rhAauk; KiwNa 20 nr.kP kw;Wk; 29 nr.kP vdpy; mj;jpd;kf; $k;gpd; fd msitf; fhz;f.
96. cUisapd; Muk; 14 nr.kP cauk; 8 nr.kP vdpy; cUisapd; fd msitf; fhz;f.
97. xU jpz;k miuf;Nfhsj;jpd; nkhj;jGwgug;G 675 π r.nr.kP vdpy; mjd; tisgug;G fhz;f.
98. xU jpd;k cUisapd; Muk; 14 nr.kP kw;Wk; cauk; 30 nr.kP vdpy; cUisapd; fd msitf; fhz;f.
99. 448 π f.nr.kP fdmsT nfhz;l xU jpz;k Neh;tl;l cUisapd; cauk; 7 nr.kP mt;TUisapd; tpl;lj;ijf; fhz;f.
100. xU jpz;k Neh;tl;l cUisapd; Muk; 7 nr.kP kw;Wk; cauk; 20 nr.kP vdpy;
i ) cUisapd; tisgug;G ii ) cUisapd; nkhj;jg; gug;G fhz;f.
101. 8.4 nr.kP tpl;lk; nfhz;l xU Nfhstbt jpz;k cNyhf vwpFz;bd; fd msitf; fhz;f.
102. 62.37 f.nr.kP fd msTf; nfhz;l xU jpz;k Neh;tl;l cUisapd; cauk; 4.5 nr.kP vdpy; mt;TUisapd; Muj;ij fhz;f.
103. xU jpz;k Neh;tl;l cUisapd; fd msT 98 π f.nr.kP kw;Wk; mjd; cauk; 8 nr.kP vdpy; mt;TUisapd; tisgug;ig fhz;f.
104. xU jpz;k miuf;Nfhsj;jpd; tisgug;G 2772 r.nr.kP vdpy; mjd; nkhj;jgug;igf; fhz;f.
105. xU Neh;tl;l jpz;kf; $k;gpd; cauq;fspd; tpfpjk; 1 : 3 kw;Wk; mtw;wpd; Muq;fspd; tpfpjk; 3 : 1 vdpy; mtw;wpd; fd
msTfspd; tpfpjj;ijf; fhz;f.
101. xU jpz;k Neh;tl;l cUisapd; nkhj;j Gwgug;G 660 r.nr.kP mjd; tpl;lk; 14 nr.kP vdpy; cUisapd; cauj;ijAk; ,
tisgug;igAk; fhz;f.
106. ,uz;L jpz;k miuf;Nfhsq;fspd; Muq;fs; 3 : 5 vd;w tpfpjj;jpy; cs;sd vdpy; mf;Nfhsq;fspd; tisgug;Gfspd; tpfpjk;
fhz;f.
107. xU jpz;k Neh;tl;l $k;gpd; fdmsT 4928 f.nr.kP mjd; cauk; 24 nr.kP vdpy; $k;gpd; Muk; fhz;f.
108. xU Neh;tl;l $k;gpd; fdmsT 216 π f.nr.kP kw;Wk; mf;$k;gpd; Muk; 9 nr.kP vdpy; mjd; cauk; fhz;f.
ghlk; : 11.Gs;spapay;
109. Kjy; 13 ,ay; vz;fspd; jpl;l tpyf;fj;ijf; fhz;f.
110. xU Gs;sp tpuuj;jpd; khWghl;Lf; nfO 57 kw;Wk; jpl;ltpyf;fk; 6.84 vdpy; mjd; $l;Lr;ruhrhpiaf; fhz;f.
111. 43 , 24 , 38 , 56 , 22 , 39 , 45 Mfpa Gs;sptptuq;fspd; tPr;R kw;Wk; tPr;Rf; nfO Mfpatw;iwf; fhz;f.
112. fz;lwpe;j Gs;sp tptuj; njhFg;gpYs;s 20 kjpg;Gfspd; jpl;ltpyf;fk; 5 vd;f. Gs;sptptuj;jpd; xt;nthU kjpg;igAk; 2 My;
ngUf;fpdhy; fpilf;Fk; Gjpa Gs;sp tptuq;fspd; jpl;ltpyf;fk; kw;Wk; tpyf;f th;f;fr; ruhrhp Mfpatw;iwf; fhz;f.
113. ,U tptuj;njhlh;fspd; khWghl;Lf; nfOf;fs; 58 kw;wk; 69 vd;f.mtw;wpd; jpl;ltpyf;fk; KiwNa 21.2 kw;Wk; 15.6 vdpy;
mtw;wpd; $l;Lr;ruhrhpiaf; fhz;f.
114. 50 msTfspy; kpfg;nghpa kjpg;G 3.84 fp.fp mjd; tPr;R 0.46 fp.fp vdpy; mitfspd ; kPr;rpW kjpg;igf; fhz;f.
115. xU Gs;sp tptuj;jpd; kPr;rpW kjpg;G 12.mjd; tPr;R 59 vdpy; mg;Gs;sp tptuj;jpd; kPg;ngU kjpg;igf; fhz;f.
116. xU Gs;sp tptuj; njhFg;gpd; kPg;ngU kjpg;G 7.44 kw;Wk; mjd; tPr;R 2.26 vdpy; mj;njhFg;gpd; kPr;rpW kjpg;igf; fhz;f.
117. xU FOtpy; 100 Ngh; cs;sdh;.mth;fspd; cauq;fspd; $l;Lr; ruhrhp 163.8 nr.kP kw;Wk; khWghl;L nfO 3.2 vdpy;
mth;fSila cauq;fspd; jpl;ltpyf;fk; fhz;f.
118. 59 , 46 , 30 , 23 , 27 , 40 , 52 , 35 , 29 vd;w Gs;sp tptuj;jpd; tPr;R kw;Wk; tPr;Rf; nfO fhz;f.
ghlk; : 12.epfo;jfT
119. ,U ehzaq;fs; xNu Neuj;jpy; Rz;Lk;NghJ mjpfgl;rkhf xU jiy fpilg;gjw;fhd epfo;jfT fhz;f.
120. A kw;Wk; B vd;w ,U epfo;r;rpfspy; π π΄ = 1
4 , π π΅ =
2
5 kw;Wk; π π΄ βͺ π΅ =
1
2 vdpy; π π΄ β© π΅ fhz;f.
121. Kjy; 20 ,ay; vz;fspypUe;J xU KO vz; rktha;G Kiwapy; Njh;e;njLf;fg;gLfpwJ , me;j vz; xU gfh vz;zhf
,Ug;gjw;fhd epfo;jfT fhz;f.
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X β MATHS QUESTION BANK Page 7
122. 12 ey;y Kl;ilfSld; 3 mOfpa Kl;ilfs; fye;Js;sd.rktha;g;G Kiwapy; Njh;e;njLf;fg;gLk; xU Kl;il , mOfpajhf
,Ug;gjw;fhz epfo;jfT fhz;f.
123. xU Fwpg;gpl;l ehspy; kio tUtjw;fhd epfo;jfT 0.76 vdpy; mNj ehspy; kio tuhky; ,Ug;gjw;fhz epfo;jfT fhz;f.
124. ,U gfilfs; xNu Neuj;jpy; xU Nru cUl;lg;gLk;NghJ fpilf;Fk; Kf vz;fspd; $Ljy; 3 My; kw;Wk; 4 My; tFglhky;
,Ug;gjw;fhd epfo;jfT fhz;f.
125. 3 , 5 , 7 vd;w vz;fisf; nfhz;l xU ,uz;L ,yf;f vz; mikf;fg;gLfpwJ. mt;ntz; 57 I tpl nghpajhf ,Ug;gjw;fhz
epfo;jfT fhz;f.
126. %d;W gfilfs; xNu Neuj;jpy; cUl;lg;gLtjpy; , %d;W gfilfspYk; xNu vz;zhf tUtjw;fhd epfo;jfT fhz;f.
127. xU ngl;bapy; 4 gr;ir , 5 ePyk; kw;Wk; 3 rptg;G epwg; ge;Jfs; cs;sd. rktha;g;G Kiwapy; xU ge;ij Njh;e;njLf;f mJ
gr;ir epwg; ge;jhf ,y;yhky; ,Ug;gjw;fhd epfo;jfT fhz;f.
128. A kw;Wk; B vd;gd xd;iwnahd;W tpyf;Fk; epfo;r;rpfs;.NkYk;; π π΄ = 3
5 , π π΅ =
1
5 kw;Wk; π π΄ βͺ π΅ fhz;f.
129. 1 ypUe;J 100 tiuapyhd KO vz;fspypUe;J rktha;g;G Kiwapy; Njh;e;njLf;fg;gLk; xU vz; xU KOth;f;fkhf
,Ug;gjw;fhd epfo;jfT fhz;f.
130. %d;W ehzaq;fs; xNu Neuj;jpy; Rz;lg;gLfpd;wd.,U G+f;fs; kl;Lk; fpilg;gjw;fhd epfo;jfT fhz;f
131. xU rPuhd gfil ,uz;L Kiw cUl;lg;gLfpwJ. Kf vz;fspd; $Ljy; 9 fpilf;fg; ngWtjw;fhd epfo;jfT fhz;f.
Kf;fpa Ie;J kjpg;ngz; tpdhf;fs;
ghlk; : 1. fzq;fSk; rhh;GfSk;
1. P = a , b , c , d , e , Q = a , e , i , o , u kw;Wk; R = a , c , e , g Mfpa fzq;fspd; ntl;L Nrh;g;G gz;G cilaJ vdr;
rhpghh;.
2. A = { 0 , 1 , 2 , 3 , 4 } , B = { 1 , β 2 , 3 , 4 , 5 , 6 } kw;Wk; C = { 2 , 4 , 6 , 7 } vdpy; A βͺ B β© C = A βͺ B β© A βͺ C vd;gijr; rhpghh;.
3. A = { β3 , β1 , 0 , 4 , 6 , 8 , 10 } , B = { β1 , β2 , 3 , 4 , 5 , 6 } kw;Wk; C = { β1 , 2 , 3 , 4 , 5 , 7 } vdpy;
( i ) A βͺ B β© C = A βͺ B β© A βͺ C ( ii ) A β© B βͺ C = A β© B βͺ A β© C Mfpatw;iwr; rhpghh;.
4. A = 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , B = 1 , 5 , 10 , 15 , 20 , 30 kw;Wk; C = 7 , 8 , 15 , 20 , 35 , 45 , 48 Mfpa fzq;fSf;F
A \ B β© C = A β₯ B βͺ A β₯ C vd;gijr; rhpghh;.
5. A = a , b , c , d , e , f , g , x , y , z , B = 1 , 2 , c , d , e kw;Wk; C = d , e , f , g , 2 , y vdpy;
π΄ \ π΅ βͺ πΆ = π΄ β₯ π΅ β© π΄ β₯ πΆ vd;gijr; rhpghh;.
6. gpd;tUk; fzq;fisf; nfhz;L B β khh;fdpd; fz tpj;jpahr tpjpfisr; rhpghh;.
A = 1 , 3 , 5 , 7 , 9 , 11 , 13 , 15 , B = 1 , 2 , 5 , 7 kw;Wk; C = 3 , 9 , 10 , 12 , 13
7. U = β2 ,β1 , 0 , 1 , 2 , 3 , β¦ . , 10 , A = β 2 , 2 , 3 , 4 , 5 kw;Wk; B = 1 , 3 , 5 , 8 , 9 vdpy; B β khh;fdpd; fz epug;gp tpjpfisr; rhpghh;.
8. U = a , b , c , d , e , f , g , h , A = a , b , f , g kw;Wk; B = a , b , c vdpy; B β khh;fdpd; fz epug;gp tpjpfisr; rhpghh;.
9. ntz;glq;fis gad;gLj;jp gpd;tUtdtw;iw rhpah vdr; Nrhjpj;J ghh;f;fTk;.
π A βͺ B β© C = A βͺ B β© A βͺ C ii A β© B βͺ C = A β© B βͺ A β© C ( iii ) A βͺ B β² = A β² β© B β²
ππ£ A β© B β² = A β² βͺ B β² π£ A \ B βͺ C = A β₯ B β© A β₯ C π£ π A \ B β© C = A β₯ B βͺ A β₯ C
10. π΄ = 0 , 1 , 2 , 3 kw;Wk; π΅ = 1 , 3 , 5 , 7 , 9 vd;gd ,U fzq;fs; vd;f.π βΆ π΄ β π΅ vDk; rhh;G π π₯ = 2π₯ + 1 vdf;
nfhLf;fg;gl;Ls;sJ.,r;rhh;gpid
i ) thpirNrhbfspd; fzk; ii ) ml;ltiz iii ) mk;Gf;Fwpglk; iv ) tiuglk; Mfpatw;why; Fwpf;f.
11. π΄ = 6 , 9 , 15 , 18 , 21 , kw;Wk; π΅ = 1 , 2 , 4 , 5 , 6 , π βΆ π΄ β π΅ vd;gJ π π₯ = π₯β3
3 vd tiuaWf;fg;gl;bUg;gpd; rhh;G π β I
i ) thpirNrhbfspd; fzk; ii ) ml;ltiz iii ) mk;Gf;Fwpglk; iv ) tiuglk; Mfpatw;why; Fwpf;f.
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X β MATHS QUESTION BANK Page 8
12. π΄ = 4 , 6 , 8 , 10 , kw;Wk; π΅ = 3 , 4 , 5 , 6 , 7 π βΆ π΄ β π΅ vd;gJ π π₯ = 1
2π₯ + 1 vd tiuaWf;fg;gl;bUg;gpd; rhh;G π β I
i ) thpirNrhbfspd; fzk; ii ) ml;ltiz iii ) mk;Gf;Fwpglk; iv ) tiuglk; Mfpatw;why; Fwpf;f.
ghlk; : 2. nka;naz;fspd; njhlh;thpirfSk; njhlh;fSk;
13. xU $l;Lj;njhlh;thpirapd; 9 MtJ cWg;G G+r;rpak; vdpy; 19 tJ vWg;gpd; ,U klq;F 29 MtJ cWg;G vd epWTf.
14. xU $l;Lj;njhlh;thpirapd; 10 kw;Wk; 18 MtJ cWg;Gfs; KiwNa 41 kw;Wk; 73 vdpy; 27 tJ cWg;igf; fhz;f.
15. xU ngUf;Fj;njhlh; thpirapd; ehd;fhtJ cWg;G
2
3 kw;Wk; mjd; VohtJ cWg;G
16
81 vdpy; mg;ngUf;Fj;njhlh; thpiriaf;
fhz;f.
16. 8 β My; tFgLk; midj;J %d;wpyf;f vz;fspd; $Ljy; fhz;f.
17. 9 β My; tFgLk; midj;J %d;wpyf;f vz;fspd; $Ljy; fhz;f.
18. 300 f;Fk; 500 f;Fk; ,ilNa 11 My; tFgLk; midj;J ,ay; vz;fspd; $Ljy; fhz;f.
19. 6 + 66 + 666 + β¦β¦β¦β¦β¦.. vDk; njhlhpy; Kjy; n β cWg;Gfspd; $Ljy; fhz;f.
20. 7 + 77 + 777 + β¦β¦β¦β¦β¦.. vDk; njhlhpy; Kjy; n β cWg;Gfspd; $Ljy; fhz;f.
21. $Ljy; fhz;f. 12 2 + 13 2 + 14 2 + β¦β¦ . . + 35 2
22. $Ljy; fhz;f. 16 2 + 17 2 + 18 2 + β¦β¦ . . + 25 2
23. $Ljy; fhz;f. 16 3 + 17 3 + 18 3 + β¦β¦β¦ + 35 3
24. $Ljy; fhz;f. 11 3 + 12 3 + 13 3 + β¦β¦β¦ + 28 3
25. 11 nr.kP , 12 nr.kP , 13 nr.kP ........... 24 nr.kP Mfpadtw;iw gf;f msTfshff; nfhz;l 14 rJuq;fspd; nkhj;j gug;G fhz;f.
26. 12 nr.kP , 13 nr.kP , 14 nr.kP ........... 23 nr.kP Mfpadtw;iw gf;f msTfshff; nfhz;l 14 rJuq;fspd; nkhj;j gug;G fhz;f.
27. 16 nr.kP , 17 nr.kP , 18 nr.kP ........... 30 nr.kP Mfpadtw;iw gf;f msTfshff; nfhz;l 15 rJuq;fspd; fd msTfspd;
$Ljy; fhz;f.
ghlk; : 3.,aw;fzpjk;
gpd;tUtdtw;iw fhuzpg;gLj;Jf.
28) 2π₯3 β 3π₯2 β 3π₯ + 2 29 ) π₯3 β 3π₯2 β 10π₯ + 24 30 ) π₯3 β 2π₯2 β 5π₯ + 6 31 ) 4π₯3 β 5π₯2 + 7π₯ β 6
32 ) 2π₯3 β 9π₯2 + 7π₯ + 6 33 ) 2π₯3 + 11π₯2 β 7π₯ β 6 34 ) π₯3 β 23π₯2 + 142π₯ β 120 35 ) π₯3 + 13π₯2 + 32π₯ + 20
36 ) π₯3 β 10π₯2 β π₯ + 10 37 ) π₯3 β 5π₯2 β 2π₯ + 24
gpd;tUtdtw;wpd; th;f;f %yk; fhz;f.
38 ) π₯ 4 β 10 π₯ 3 + 37π₯ 2 β 60π₯ + 36
39 ) π₯ 4 β 6 π₯ 3 + 19π₯ 2 β 30π₯ + 25
40 ) π₯ 4 β 4 π₯ 3 + 10π₯ 2 β 12π₯ + 9
41) 4π₯ 4 + 8 π₯ 3 + 8π₯ 2 + 4π₯ + 1
42 ) 9π₯ 4 β 6π₯ 3 + 7π₯ 2 β 2π₯ + 1
43 ) 4 + 25π₯ 2 β 12π₯ β 24 π₯ 3 + 16π₯ 4
44 ) 4π₯ 4 β 12 π₯ 3 + 37π₯ 2 + ππ₯ + π MdJ xU KO th;f;fk; vdpy; a , b β d; kjpg;G fhz;f.
45) π₯ 4 β 4 π₯ 3 + 10π₯ 2 β ππ₯ + π MdJ xU KO th;f;fk; vdpy; a , b β d; kjpg;G fhz;f.
46 ) 9π₯ 4 + π π₯ 3 + 109π₯ 2 β 60π₯ + 36 MdJ xU KO th;f;fk; vdpy; a , b β d; kjpg;G fhz;f.
47) 9π₯ 4 β π π₯ 3 + 40π₯ 2 + 24π₯ + 36 MdJ xU KO th;f;fk; vdpy; a , b β d; kjpg;G fhz;f.
48 ) π β ππ₯ + 28π₯ 2 + 12 π₯ 3 + 9 π₯ 4 MdJ xU KO th;f;fk; vdpy; m , n β d; kjpg;G fhz;f.
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X β MATHS QUESTION BANK Page 9
ghlk; : 4.mzpfs;
49. jPh;T fhz;f. π¦
3π₯ =
6 β 2π₯ 31 + 4π¦
50. 5π₯ + 2 π¦ β 4
0 4π§ + 6 =
12 β80 2
vdpy; x , y kw;Wk; z - fspd; kjpg;Gfisf; fhz;f.
51. 2π₯ + π¦π₯ β 3π¦
= 5
13 vdpy; x kw;Wk; y - fspd; kjpg;Gfisf; fhz;f.
52. π΄ = 3 25 1
, π΅ = 1 β22 3
kw;Wk; π = 0 00 0
vdpy; gpd;tUtdtw;iwr; rhpghh;f;f.
π ) π΄ + π΅ = π΅ + π΄ ππ ) π΄ + βπ΄ = 0 = βπ΄ + π΄
53. π΄ = 4 1 21 β2 30 3 2
π΅ = 2 0 46 2 8 2 4 6
, πΆ = 1 2 β35 0 21 β1 1
vdpy; π΄ + π΅ + πΆ = π΄ + π΅ + πΆ vd;gijr; rhpghh;.
54. π΄ = 3 2β1 4
, π΅ = β2 5 6 7
kw;Wk; πΆ = 1 1β5 3
vdpy; π΄ π΅ + πΆ = π΄π΅ + π΄πΆ vd;gijr; rhpghh;.
55. π΄ = β2 4 5
kw;Wk; π΅ = 1 3 β6 vd;w mzpfSf;F π΄π΅ π = π΅ π π΄ π vd;gijr; rhpghh;.
56. π΄ = 1 β1 2 3
vdpy; π΄ 2 β 4π΄ + 5πΌ 2 = 0 vd epWTf.
57. π΄ = β1 2 1 1 2 3
, π΅ = 012
vdpy; πΆ = 2 1 vdpy; π΄ π΅ πΆ = π΄ π΅πΆ vd;gijr; rhpghh;.
58. π΄ = 5 2 7 3
, π΅ = 2 β1 β1 1
vdpy; π΄π΅ π = π΅ π π΄ π vd epWTf.
59. π΄ = 1 β4β2 3
kw;Wk; π΅ = β1 6 3 β2
vdpy; π΄ + π΅ 2 β π΄ 2 + 2π΄π΅ + π΅ 2 vd;gijr; rhpghh;.
60. π΄ = 3 37 6
, π΅ = 8 70 9
kw;Wk; πΆ = 2 β34 6
vdpy; ( A + B ) C kw;Wk; AC + BC vd;w mzpfisf; fhz;f.
NkYk; ( A + B ) C = AC + BC vd;gJ nka;ahFkh?
ghlk; : 5.Maj;njhiy tbtpay;
gpd;tUtdtw;iw Kidfshff; nfhz;l ehw;fuq;fspd; gug;G fhz;f.
61. 6 , 9 , 7 , 4 , 4 , 2 kw;Wk; ( 3 , 7 )
62. β3 , 4 , β5 ,β 6 , ( 4 , β1 ) kw;Wk; ( 1 , 2 )
63. β 4 , 5 , 0 , 7 , 5 , β5 kw;Wk; β4 , β2
67. ( 7 , 3 ) , ( 6 , 1 ) , ( 8 , 2 ) kw;Wk; ( P, 4 ) vd;gd Xh; ,izfuj;jpd; thpirg;gb mike;j cr;rpfs; vdpy; P - d; kjpg;igf; fhz;f.
ghlk; : 6.tbtpay;
65. Njy;]; Njw;wk; my;yJ mbg;gil tpfpj rk Njw;wj;ij vOjp epWTf.
66. Nfhz ,Urkntl;b Njw;wj;ij vOjp epWTf.
67. gpj;jhfu]; Njw;wj;ij vOjp epWTf.
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X β MATHS QUESTION BANK Page 10
ghlk; : 7.Kf;Nfhztpay;
68. Neh;Fj;jhd xU kuj;jpd; Nky; ghfk; fhw;wpdhy; Kwpe;J , mk;Kwpe;j gFjp fPNo tpOe;Jtplhky; kuj;jpd; cr;rp
jiuAld; 30 0 Nfhzj;ij Vw;gLj;JfpwJ.kuj;jpd; cr;rp mjd; mbapypUe;J 30 kP njhiytpy; jiuiaj; njhLfpwJ vdpy;
kuj;jpd; KO cauj;ijf; fhz;f.
69. flw;fiuapy; cs;s nrq;Fj;jhd ghiw xd;wpd; kPJ fl;lg;gl;Ls;s xU fyq;fiu tpsf;fj;jpy; epd;Wnfhd;bUf;Fk; xU rpWkp
fpof;F jpirapy; ,U glFfisg; ghh;fpwhs;.mg;glFfspd; ,wf;ff;Nfhzq;fs; 30 0 , 60 0 KiwNa kw;Wk; ,U glFfSf;F
,ilNa cs;s J}uk; 300 kP vdpy; fly; kl;lj;jpypUe;J fyq;fiu tpsf;ffj;jpd; cr;rpapd; J}uj;ijf; fhz;f.
[ glFfSk; fyq;fiu tpsf;fKk; xNu Neh;f;Nfhl;by; cs;sd ]
70. 60 kP cauKs;s xU NfhGuj;jpypUe;J xU fl;llj;jpd; cr;rp , mb Mfpatw;wpd; ,wf;ff;Nfhzq;fs; KiwNa 30 0 kw;Wk; 60 0
vdpy; fl;llj;jpd; cauj;ijf; fhz;f.
71. xU NfhGuj;jpd; mbapypUe;J 30 3 njhiytpy; epw;Fk; xU ghh;itahsh; , mf;NfhGuj;jpd; cr;rpapid 30 0 Vw;wf;Nfhzj;jpy;
fhz;fpwhh;. jiukl;lj;jpypUe;J mtUila fpilepiy ghh;it Nfhl;bw;F cs;s J}uk; 1.5 kP vdpy; NfhGuj;jpd; cauj;ijf; fhz;f.
72. xU NfhGuj;jpd; mbapypUe;J xU Fd;wpd; cr;rpapd; Vw;wf;Nfhzk; 60 0 vd;f. Fd;wpd; mbapypUe;J NfhGuj;jpd; cr;rpapd;
Vw;wf;Nfhzk; 30 0 kw;Wk; NfhGuj;jpd; cauk; 50 kP vdpy; Fd;wpd; cauj;ijf; fhz;f.
73. 40 nr.kP ePsKs;s xU CryhdJ xU KO miytpd;NghJ mjd; cr;rpapy; 60 0 Nfhzj;ij Vw;gLj;JfpwJ.me;j miytpy;
Cry; Fz;bd; Jtf;f epiyf;Fk; , ,Wjp epiyf;Fk; ,ilNa cs;s kpff; Fiwe;j J}uj;ijf; fhz;f.
ghlk; : 8.mstpay;
74. xU Neh;tl;l cUisapd; tisgug;G 704 r.nr.kP kw;Wk; mjd; cauk; 8 nr.kP vdpy; mt;TUisapd; fd msit ypl;lhpy;
fhz;f.
75. xU jpd;kf; Nfhsj;jpd; fdmsT 7241 1
7 f.nr.kP vdpy; , mjd; Muj;ijf; fhz;f.
76. xU rh;f;f]; $lhukhdJ cUisapd; kPJ $k;G ,ize;j tbtpy; mike;Js;sJ. $lhuj;jpd; nkhj;j cauk; 49 kP .mjd;
mbg;ghfj;jpd; tpl;lk; 42 kP .cUisg;ghfj;jpd; cauk; 21 kP NkYk; 1 r.kP fpj;jhd; Jzpapd; tpiy &.12.50 vdpy; , $lhuk;
mikf;fj; Njitahd fpj;jhd; Jzpapd; tpiyiaf; fhz;f.
77. xU jpd;k kug;nghk;ikahdJ miuf;Nfhsj;jpd; Nky; $k;G mike;j tbtpy; cs;sJ.miuf;Nfhsk; kw;Wk; $k;G Mfpatw;wpd;
Muk; 3.5 nr.kP.NkYk; nghk;ikApd; nkhj;j cauk; 17.5 nr.kP vdpy; mg;nghk;ik jahhpf;fg; gad;gLj;jg;gl;l kuj;jpd; fd
msitf; fhz;f.
78. 7 nr.kP tpl;lKs;s cUistbt Kfitapy; rpwpjsT jz;zPh; cs;sJ.mjpy; xt;nthd;Wk; 1.4 nr.kp tpl;lKs;srpy Nfhstbt
gspq;Ff; fw;fs; Nghlg;gLfpwJ.cUisapYs;s ePhpd; kl;lk; 5.6 nr.kP cau vj;jid gspq;F fw;fis Kfitapy; NghlNtz;Lk;.
79. 8 nr.kP tpl;lKk; 12 nr.kP cauKk; nfhz;l xU Neh;tl;l jpd;k ,Uk;Gf; $k;ghdJ cUf;fg;gl;L 4 kp.kP MuKs;s jpd;k Nfhs
tbt Fz;Lfshf thh;f;fg;gl;lhy; fpilf;Fk; Nfhstbt Fz;Lfspd; vz;zpf;ifiaf; fhz;f.
80. xU cs;sPlw;w Nfhsj;jpd; ntsp kw;Wk; cs; Muq;fs; KiwNa 8 nr.kP kw;Wk; 4 nr.kP . ,f;NfhskhdJ cUf;fg;gl;L 8 nr.kP
tpl;lKs;s Neh;tl;l jpz;kf; $k;ghf khw;wg;gl;lhy; $k;gpd; cauj;ijf; fhz;f.
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X β MATHS QUESTION BANK Page 11
ghlk; : 9.nra;Kiw tbtpay;
ikaj;ij gad;gLj;jp tl;lj;jpw;F njhLNfhL tiujy;
81. 3.2 nr.kP MuKs;s tl;lk; tiuf.tl;lj;jpd; Nky; P vd;w Gs;spia Fwpj;J mg;Gs;sptopNa xU njhLNfhL tiuf.
82. 4.2 nr.kP MuKs;s tl;lk; tiue;J mt;tl;lj;jpd; Nky; VNjDk; xU Gs;spiaf; Fwpf;f.tl;lj;jpd; ikaj;ij gad;gLj;jp
mg;Gs;sptopNa njhLNfhL tiuf.
njhLNfhL - ehz; Njw;wj;ij gad;gLj;jp tl;lj;jpd; Nky; mike;j Gs;spapy;
njhLNfhL tiujy;
83. 3.2 nr.kP MuKs;s tl;lk; tiuf. tl;lj;jpd; Nky; P vd;w Gs;spia Fwpj;J mg;Gs;spapy; njhLNfhL - ehz; Njw;wj;ij
gad;gLj;jp njhLNfhL tiuf.
84. 4.2 nr.kP MuKs;s tl;lk; tiue;J mt;tl;lj;jpd; Nky; VNjDk; xU Gs;spiaf; Fwpf;J. mg;Gs;spapy; njhLNfhL - ehz;
Njw;wj;ij gad;gLj;jp njhLNfhL tiuf.
tl;lj;jpw;F ntspNa mike;j Gs;spapypUe;J tl;lj;jpw;F njhLNfhl;L
Nrhbfs; tiujy;
85. 3 nr.kP MuKs;s tl;lk; tiuf.tl;lj;jpd; ikaj;jpypUe;J 7 nr.kP njhiytpy; xU Gs;spiaf; Fwpj;J , mg;Gs;spapypUe;J
tl;lj;jpw;F njhLNfhLfs; tiuf.NkYk; njhLNfhLfspd; ePsq;fis mse;J vOJf.
86. 10 nr.kP tpl;lKs;s tl;lk; tiuf.tl;lj;jpd; ikaj;jpypUe;J 13 nr.kP njhiytpy; P vd;w Gs;spia Fwpj;J mg;Gs;spapypUe;J
tl;lj;jpw;F PA kw;Wk; PB vd;w njhLNfhLfs; tiue;J mjd; ePsq;fis fzf;fpLf.
87. 6 nr.kP MuKs;s xU tl;lk; tiue;J mjd; ikaj;jpypUe;J 10 nr.kP njhiytpYs;s xU Gs;spiaf; Fwpf;f.mg;Gs;spapypUe;J
tl;lj;jpw;F njhLNfhLfs; tiue;J mjd; ePsq;fis fzf;fpLf.
88. 3 nr.kP MuKs;s xU tl;lk; tiue;J mjd; ikaj;jpypUe;J 9 nr.kP njhiytpYs;s xU Gs;spiaf; Fwpf;f.mg;Gs;spapypUe;J
tl;lj;jpw;F njhLNfhLfs; tiue;J mjd; ePsq;fis fzf;fpLf.
tl;l ehw;fuk; tiujy ;
tif : I - %d;W gf;fq;fs; kw;Wk; xU %iytpl;lk; nfhLf;fg;gLk;NghJ tl;l
ehw;fuk; tiujy;
89. π΄π΅ = 6 nr.kP π΄πΆ = 7 nr.kP π΅πΆ = 6 nr.kP kw;Wk; π΄π· = 4.2 nr.kP msTfs; nfhz;l ABCD vd;w tl;lehw;fuk; tiuf.
90. ππ = 6 .5 nr.kP ππ = 5.5 nr.kP ππ = 7 nr.kP kw;Wk; ππ = 4.5 nr.kP msTfs; nfhz;l PQRS vd;w tl;lehw;fuk; tiuf.
91. π΄π΅ = 6 nr.kP π΄π· = 4.8 nr.kP π΅π· = 8 nr.kP kw;Wk; πΆπ· = 5.5 nr.kP msTfs; nfhz;l ABCD vd;w tl;lehw;fuk; tiuf.
tif : II - ,uz;L gf;fq;fs; kw;Wk; ,uz;L %iytpl;lk; nfhLf;fg;gLk;NghJ tl;l
ehw;fuk; tiujy ;
92. ππ = 4 nr.kP ππ = 6 nr.kP ππ = 7.5 nr.kP kw;Wk; ππ = 7 nr.kP msTfs; nfhz;l PQRS vd;w tl;lehw;fuk; tiuf.
93. πΎπΏ = 5.5 nr.kP πΎπ = 5 nr.kP πΏπ = 4.2 nr.kP kw;Wk; πΏπ = 5.3 nr.kP msTfs; nfhz;l KLMN vd;w tl;lehw;fuk; tiuf.
94. πΈπΉ = 7 nr.kP πΈπ» = 4.8 nr.kP πΉπ» = 6.5 nr.kP kw;Wk; πΈπΊ = 6.6 nr.kP msTfs; nfhz;l EFGH vd;w tl;lehw;fuk; tiuf.
tif : III - %d;W gf;fq;fs; kw;Wk; xU Nfhzk; nfhLf;fg;gLk;NghJ
tl;l ehw;fuk; tiujy;.
95. π΄π΅ = 6 nr.kP π΅πΆ = 5.5 nr.kP β π΄π΅πΆ = 80 0 kw;Wk; π΄π· = 4.5 nr.kP msTfSf;F ABCD vd;w tl;lehw;fuk; tiuf.
96. ππ = 5.5 nr.kP ππ = 4.5 nr.kP β πππ = 45 0 kw;Wk; ππ = 3 nr.kP msTfSf;F PQRS vd;w tl;lehw;fuk; tiuf.
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X β MATHS QUESTION BANK Page 12
97. π΄π΅ = 7 nr.kP β π΄ = 80 0 , π΄π· = 4.5 nr.kP kw;Wk; π΅πΆ = 5 nr.kP msTfSf;F ABCD vd;w tl;lehw;fuk; tiuf
tif : IV - ,uz;L gf;fq;fs; kw;Wk; ,uz;L Nfhzq;fs; nfhLf;fg;gLk;NghJ
tl;l ehw;fuk; tiujy ;
98. πΈπΉ = 5.2 nr.kP β πΊπΈπΉ = 50 0 , πΉπΊ = 6 nr.kP kw;Wk; β πΈπΊπ» = 40 0 vd;w msTfSf;F EFGH vd;w tl;lehw;fuk; tiuf.
99. π΄π΅ = 6 nr.kP β π΄π΅πΆ = 70 0 , π΅πΆ = 5 nr.kP kw;Wk; β π΄πΆπ· = 30 0 vd;w msTfs; nfhz;l ABCD vd;w tl;lehw;fuk; tiuf.
100. ππ = 5 nr.kP β πππ = 35 0 kw;Wk; β ππ π = 70 0 , ππ = 4 nr.kP vd;w msTfs; nfhz;l PQRS vd;w tl;lehw;fuk;
tiuf.
tif : V xU gf;fk; kw;Wk; %d;W Nfhzq;fs; nfhLf;fg;gLk;NghJ
tl;l ehw;fuk; tiujy ;
101. ππ = 4 nr.kP β π = 100 0 kw;Wk; β πππ = 40 0 kW;Wk; β πππ = 70 0 vd;w msTfSf;F PQRS vd;w tl;lehw;fuk;
tiuf.
102. π΄π΅ = 5.5 nr.kP β π΄π΅πΆ = 50 0 kw;Wk; β π΅π΄πΆ = 60 0 kW;Wk; β π΄πΆπ· = 30 0 vd;w msTfSf;F ABCD vd;w tl;lehw;fuk;
tiuf.
tif : VI ,uz;L gf;fq;fs; xU Nfhzk; kw;Wk; xU ,izNfhL
nfhLf;fg;gLk;NghJ tl;l ehw;fuk; tiujy ;
103. π΄π΅ = 5.8 nr.kP β π΄π΅π· = 35 0 kw;Wk; π΄π· = 4.2 nr.kP π΄π΅ Η πΆπ· vd;w msTfs; nfhz;l ABCD vd;w tl;lehw;fuk; tiuf.
104. π΄π΅ = 6.5 nr.kP β π΄π΅πΆ = 110 0 kw;Wk; π΅πΆ = 5.5 nr.kP π΄π΅ Η πΆπ· vd;w msTfs; nfhz;l ABCD vd;w tl;lehw;fuk; tiuf.
ghlk; : 9.tiuglq;fs;
π¦ = ππ₯2 + ππ₯ + π vDk; tbtpy; mike;j ,Ugbr;rkd;ghl;bd; tiuglk; tiujy ;
fPo;f;fz;l rkd;ghLfSf;F tiuglk; tiuf.
105. π¦ = 2π₯2 106. π¦ = 3π₯2 107. π¦ = β4π₯2 108. π¦ = β3π₯2 109. π¦ = π₯ + 2 π₯ + 4 110. π¦ = 2π₯2 β π₯ + 3
ππ₯2 + ππ₯ + π = 0 vDk; tbtpy; mike;j ,Ugbr;rkd;ghl;il tiuglk; %yk; jPh;j;jy;
fPo;f;fz;ltw;iw tiuglk; %yk; jPh;f;f.
111. π₯2 β 2π₯ β 3 = 0 112. π₯2 β 3π₯ β 10 = 0 113. π₯2 β 4 = 0
114. 2π₯2 + π₯ β 6 = 0 115. π₯ β 5 π₯ β 1 = 0 116. 2π₯ + 1 π₯ β 3 = 0
117. π¦ = 2π₯2 d; tiuglk; tiue;J mjpypUe;J 2π₯2 + π₯ β 6 = 0 vd;w rkd;ghl;il jPh;f;f.
118. π¦ = π₯2 d; tiuglk; tiue;J mjpypUe;J π₯2 β 4 π₯ β 5 = 0 vd;w rkd;ghl;il jPh;f;f.
119. π¦ = π₯2 + 3π₯ + 2 d; tiuglk; tiue;J mjpypUe;J π₯2 + 2π₯ + 4 = 0 vd;w rkd;ghl;il jPh;f;f.
120. π¦ = π₯2 + 2π₯ β 3 d; tiuglk; tiue;J mjpypUe;J π₯2 β π₯ β 6 = 0 vd;w rkd;ghl;il jPh;f;f.
121. π¦ = 2π₯2 + π₯ β 6 d; tiuglk; tiue;J mjpypUe;J 2π₯2 + π₯ β 10 = 0 vd;w rkd;ghl;il jPh;f;f.
122. π¦ = π₯2 β π₯ β 8 d; tiuglk; tiue;J mjpypUe;J π₯2 β 2 π₯ β 15 = 0 vd;w rkd;ghl;il jPh;f;f.
123. π¦ = π₯2 + π₯ β 12 d; tiuglk; tiue;J mjpypUe;J π₯2 + 2 π₯ + 2 = 0 vd;w rkd;ghl;il jPh;f;f.
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X β MATHS QUESTION BANK Page 13
rpy rpwg;G tiuglq;fs;
124. fPo;f;fhZk; ml;ltizf;Fj; jFe;j tiuglk; tiue;J khwpfspd; khWghl;Lj; jd;ikia fhz;f. mk;khWghl;bd; khwpypiak;
fhz;f.
x 2 3 5 8 10
y 8 12 20 32 40
NkYk; x = 4 vdpy; y d; kjpg;G fhz;f.
125. xU kpjptz;b Xl;Lgth; A vd;w ,lj;jpypUe;J B vd;w ,lj;jpw;F xU rPuhd Ntfj;jpy; xNu topapy; ntt;NtW ehl;fspy; gazk;
nra;fpwhh;.mth; gazk; nra;j Ntfk; , mj;J}uj;jpidf; flf;f vLj;Jf;nfhz;l Neuk; Mfpatw;iwg; gw;wpa tptuq;fs;
( Ntf β fhy ) gpd;tUk; ml;ltizapy; nfhLf;fg;gl;Ls;sd.
Ntfk; ( f.kP / kzp ) 2 4 6 10 12
Neuk; ( kzpapy; ) 60 30 20 12 10
Ntf - fhy tiuglk; tiue;J mjpypUe;J .
i ) mth; kzpf;F 5 fP.kP Ntfj;jpy; nrd;why; J}uj;ijf; flf;f MFk; gaz Neuk;.
ii ) mth; ,f;Fwpg;gpl;l J}uj;ij 40 kzpNeuj;jpy; flf;f ve;j Ntfj;jpy;gazpf;f Ntz;Lk; - Mfpatw;iwf; fhz;f.
126. xU tq;fp %j;j Fbkf;fspd; itg;Gj; njhiff;F 10 % jdptl;b jUfpwJ. itg;Gj;njhiff;Fk; mjw;F Xh; Mz;Lf;Ff;
fpilf;Fk; tl;bf;Fk; ,ilNaahd njhlh;gpidf; fhl;l xU tiuglk; tiuf.mjd; %yk;
i ) &.650 itg;gj;njhiff;Ff; fpilf;Fk; tl;b kw;Wk;
ii ) &.45 tl;bahf fpilf;f tq;fpapy; nrYj;jg;glNtz;ba itg;Gj;njhif Mfpatw;iwf; fhz;f.
127. xU NgUe;J kzpf;F 40 fp.kP Ntfj;jpy; nry;fpwJ. ,jw;Fhpa J}u β fhy njhlh;gpw;fhd tiuglk; tiuf. ,jidg; gad;gLj;jp 3
kzp Neuj;jpy; ,g;NgUe;J gazpj;j J}uj;ijf; fhz;f.
128. thq;fg;gl;l Nehl;L Gj;jfq;fspd; vz;zpf;if kw;Wk; mjw;fhd tpiy tpguk; gpd;tUk; ml;ltidapy; jug;gl;Ls;sJ.
Nehl;L Gj;jfq;fspd; vz;zpf;if x 2 4 6 8 10 12
tpiy ( &.y ) 30 60 90 120 150 180
,jw;F tiuglk; tiue;J mjd; %yk;
i ) VO Nehl;Lg; Gj;jfq;fspd; tpiyiaf; fhz;f. ii ) &.165 β f;F thq;fg;gLk; Nehl;Lg; Gj;jfq;fspd; vz;zpf;ifiaf; fhz;f.
129.
Nkw;fz;l ml;ltizapy; cs;s tptuj;jpw;F tiuglk; tiue;J , mjd; %yk;
i ) x = 4 vdpy; y d; kjpg;G fhz;f. ii ) y = 12 vdpy; x d; kjpg;G fhz;f.
130. xU ypl;lh; ghypd; tpiy &.15 vd;f. ghypd; msTf;Fk; tpiyf;Fk; cs;sj; njhlh;gpidf; fhl;Lk; tiuglk; tiuf.mjidg;
gad;gLj;jp i ) tpfpjrk khwpypiaf; fhz;f. ii ) 3 ypl;lh; ghypd; tpiyiaf; fhz;f.
131. π₯π¦ = 20 , π₯ , π¦ > 0 vd;gjd; tiuglk; tiuf. mjidg; gad;gLj;jp π₯ = 5 vdpy; π¦ β d; kjpg;igAk;
π¦ = 10 vdpy; π₯ d; kjpg;igAk; fhz;f.
132
Ntiyahl;fspd; vz;zpf;if x 3 4 6 8 9 16
ehl;fspd; vz;zpf;if y 96 72 48 36 32 18
ml;ltizapy; nfhLf;fg;gl;Ls;s tptuj;jpw;fhd tiuglk; tiuf.mjd; %yk; 12 Ntiyahl;fs; mt;Ntiyia KOtJkhf
nra;J Kbf;f MFk; ehl;fspd; vz;zpf;ifia fhz;f.
x 1 3 5 7 8
y 2 6 10 14 16
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X β MATHS QUESTION BANK Page 14
ghlk; : 11.Gs;spapay;
fPo;f;fd;l Gs;sp tptuq;fSf;F jpl;ltpyf;fk; fhz;f.
133 ) 2 , 5 , 8 , 11 , 14 , 6 , 12 , 10
134 ) 65 , 58 , 53 , 50 , 50 , 63 , 52 , 55
135 ) 10 , 20 , 15 , 8 , 3 , 4
136 ) 38 , 40 , 34 , 31 , 28 , 26 , 34
137 ) 18 , 20 , 15 , 12 , 25
138 ) 20 , 18 , 32 , 24 , 26
ghlk; : 12.epfo;jfT
139. xU rPuhd gfil xU Kiw cUl;lg;gLfpwJ.gpd;tUk; epfo;r;rpfSf;fhd epfo;jfT fhz;f.
i ) vz; 4 fpilj;jy; ii ) xU ,ul;ilg;gil vz; fpilj;jy; iii ) 6 β d; gfhf; fhuzp fpilj;jy;
iv ) 4 β I tpl nghpa vz; fpilj;jy;.
140. xU rPuhd ehzak; ,uz;L Kiw Rz;lg;gLfpwJ. fPo;f;fhZk; epfo;r;rpfSf;fhd epfo;jftpid fhz;f.
i ) ,U jiyfs; fpilj;jy; ii ) Fiwe;jJ xU jiy fpilj;jy; iii ) xU G+ kl;Lk; fpilj;jy;
141. ,U rPuhd gfilfs; xU Kiw cUl;lg;gLfpd;wd. fPo;f;fhZk; epfo;r;rpfSf;fhd epfo;jftpid fhz;f.
i ) Kf vz;fspd; $Ljy; 8 Mf ,Uj;jy; ii ) Kf vz;fs; xNu vz;fshf ,Uj;jy;
iii ) Kf vz;fspd; $Ljy; 8 β I tpl mjpfkhf ,Uj;jy;.
142. ed;F fiyj;J itf;fg;gl;l 52 rPl;Lfisf; nfhz;l rPl;Lf;fl;bypUe;J rktha;g;Gr; Nrhjid Kiwapy; xU rPl;L
vLf;fg;gLfpwJ. me;j rPl;L gpd;tUgtdhf ,Uf;f epfo;jfTfisf; fhz;f.
i ) ,uhrh ii ) fUg;G ,uhrh iii ) ];NgL iv ) lakz;l; 10
143. ed;F fiyj;J itf;fg;gl;l 52 rPl;Lfisf; nfhz;l rPl;Lf;fl;bypUe;J rktha;g;Gr; Nrhjid Kiwapy; xU rPl;L
vLf;fg;gLfpwJ. me;j rPl;L gpd;tUgtdhf ,Uf;f epfo;jfTfisf; fhz;f.
i ) vLj;j rPl;L lakz;l Mf ,Uf;f ii ) vLj;j rPl;L lakz;l ,y;yhky; ,Uf;f
iii ) vLj;j rPl;L V]; rPl;lhf ,y;yhky; ,Uf;f.
144. xU ngl;bapy; 4 gr;ir , 5 epyk; kw;Wk; 3 rptg;G epwg; ge;Jfs; cs;sd. rktha;g;G Kiwapy; xU ge;ij Njh;e;njLf;f mJ
i ) rptg;G epwg; ge;jhf ,Uf;f ii ) gr;ir epwg; ge;jhf ,y;yhky; ,Uf;f Mfpatw;wpd; epfo;jfT fhz;f.
145. %d;W ehzaq;fs; xNu Neuj;jpy; Rz;lg;gLfpd;wd. epfo;jftpd; $l;ly; Njw;wj;ij gad;gLj;jp , rhpahf
,U G+f;fs; my;yJ Fiwe;jgl;rk; xU jiyahtJ fpilf;Fk; epfo;r;rpapd; epfo;jftpdif; fhz;f.
146. xU gfil ,UKiw cUl;lg;gLfpwJ.Fiwe;jJ xU cUl;lypyhtJ vz; 5 fpilg;gjw;fhd epfo;jftpidf; fhz;f.
( $l;ly; Njw;wj;ij gad;gLj;Jf )
147. 52 rPl;Lfisf; nfhz;l xU rPl;Lf;fl;bypUe;J rktha;g;G Kiwapy; xU rPl;L vLf;fg;gLk; NghJ , mr;rPl;L xU ,uhrh ( King )
my;yJ xU rptg;G epwr; rPl;lhf fpilg;gjw;fhd epfo;jftpidf; fhz;f.
148. xU igapy; 10 nts;is , 5 fUg;G , 3 gr;ir kw;Wk; 2 rptg;G epwg; ge;Jfs; cs;sd.rktha;g;G Kiwapy; Njh;e;njLf;fg;gLk;
xU ge;J , nts;is my;yJ fUg;G my;yJ gr;ir epwkhf ,Ug;gjw;fhd epfo;jftpidf; fhz;f.
Prepareb by
S.Sakthivel ., M.Sc.,B.Ed .,
B.T , Asst , Govt higher secondary school,
Ramiyampatti,
Pappireddipatti β T.K
Dharmapuri β D.T
Mobile No : 9443950993 E β Mail : [email protected]
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