Tamil Nadu Trb Tet Tnpsc Class 10 Maths Question Bank for Centum Tamil Medium Download - Sslc Study Materials

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N.Krishnamoorthy, M.Sc.,B.Ed.,M.Phil., GHS Kondappanayanapalli. Krishnagiri District.

1. fzq;fSk; rhh;GfSk; xU kjpg;ngz; tpdhf;fs;:

1. A kw;Wk; B vd;gd ,uz;L fzq;fs; vd;f. AUB = A vd;gjw;F Njitahd kw;Wk; NghJkhd fl;Lg;ghL (A) 퐵 ⊆ 퐴 (B) 퐴 ⊆ 퐵 (C) 퐴 ≠ 퐵 (D) 퐴 ∩ 퐵 = 휱

2. 퐴 ⊂ 퐵 vdpy;> 퐴 ∩ 퐵 = (A) 퐵 (B) 퐴\퐵 (C) 퐴 (D) 퐵\퐴

3. P kw;Wk; Q vd;gd VNjDk; ,uz;L fzq;fs; vdpy;> 푃 ∩ 푄 = (A) {푥: 푥 ∈ 푃 my;yJ 푥 ∈ 푄} (B) {푥: 푥 ∈ 푃 kw;Wk; 푥 ∉ 푄} (C) {푥: 푥 ∈ 푃 kw;Wk; 푥 ∈ 푄} (D) {푥: 푥 ∉ 푃 kw;Wk; 푥 ∈ 푄}

4. A={푝,푞, 푟, 푠}, B={푟, 푠, 푡,푢} vdpy; A\B = (A) {푝,푞} (B) {푡,푢} (C) {푟, 푠} (D) {푝,푞, 푟, 푠}

5. n[p(A)] = 64 vdpy;> n(A) = (A) 6 (B) 8 (C)4 (D) 5

6. A , B kw;Wk; C Mfpa VNjDk; %d;W fzq;fSf;F> A∩ (BUC) = (A) (AUB) U (B∩C) (B) (A∩B) U (A∩C) (C) AU (B∩C) (D) (AUB) ∩ (BUC)

7. A , B Mfpa ,uz;L fzq;fSf;F> {(A\B) U (B\A)} ∩ (A∩B) = (A) 휱 (B) AUB (C) A∩B (D) A’∩B’

8. fPNo nfhLf;fg;gl;litfspy; jtwhd $w;W vJ? (A) A\B = A∩B’ (B) A\B = A∩B (C) A\B = (C) (AUB)∩B’ (D) A\B = (AUB) \ B

9. A , B kw;Wk; C Mfpa VNjDk; %d;W fzq;fSf;F> B\ (AUC) = (A) (A\B) ∩ ( A\C) (B) (B\A) ∩ ( B\C) (C) (B\A) ∩ ( A\C) (D) (A\B) ∩ ( B\C)

10. n(A) =20, n(B) = 30 kw;Wk; n(AUB) = 40 vdpy;> n(A∩B) = (A) 50 (B) 10 (C)40 (D) 70

11. { (x,2), (4,y) } xU rkdpr; rhh;igf; Fwpf;fpwJ vdpy;> (x,y) = (A) (2,4) (B) (4,2) (C) (2,2) (D) (4,4)

12. { (7,11), (5,a) } xU khwpypr; rhh;igf; Fwpf;fpwJ vdpy;> ‘a’ – d; kjpg;G (A) 7 (B) 11 (C)5 (D)9

13. f(x) = (-1)x vd;gJ N – ypUe;J Z – f;F tiuaWf;fg;gl;Ls;sJ. f - d; tPr;rfk; (A) {1} (B) N (C) {1,-1} (D) Z

14. f = { (6,3), (8,9), (5,3), (-1,6) } vdpy; 3 – d; Kd; cUf;fs; (A) 5 kw;Wk; -1 (B) 6 kw;Wk; 8 (C) 8 kw;Wk; -1 (D) 6 kw;Wk; 5

15. A={1,3,4,7,11} kw;Wk; B={−1,1,2,5,7,9} vd;f. f = { (1,-1), (3,2), (4,1), (7,5),(11,9) } vd;wthW mike;j rhh;G f: A → B vd;gJ (A) xd;Wf;F xd;whd rhh;G (B) Nky; rhh;G (C) ,UGwr; rhh;G (D) rhh;G my;y

16. nfhLf;fg;gl;Ls;s glk; Fwpf;Fk; rhh;G> xU (A) Nky; rhh;G (B ) ) khwpypr;; rhh;G (C) xd;Wf;F xd;whd rhh;G (D) rhh;G my;y

17. A={5,6,7} kw;Wk; B={1,2,3,4,5} vd;f. f(x) = x - 2 vd;wthW tiuaiw nra;ag;gl;l rhh;G f: A → B ,d; tPr;rfk;> ------ (A) {1,4,5} (B) {1,2,3,4,5} (C) {2,3,4} (D) {3,4,5}

18. f(x) = x2 + 5 vdpy;> f(-4) = (A) 26 (B) 21 (C)20 (D) -20

19. xU rhh;gpd; tPr;rfk; XUWg;Gf; fzkhdhy;> mJ xU (A) khwpypr; rhh;G (B) rkdpr;; rhh;G (C) ,UGwr; rhh;G (D) xd;Wf;F xd;whd rhh;G

20. f: A → B xU ,UGwr; rhh;G kw;Wk; n(A) = 5 vdpy; n(B) = (A) 10 (B) 4 (C)5 (D) 25

2. nka;naz;fspd; njhlh;thpirfSk; njhlh;fSk; xU kjpg;ngz; tpdhf;fs;:

1. gpd;tUtdtw;Ws; vJ nka;ahdf; $w;wy;y? (A) ,ay; vz;fspd; fzk; N – y; tiuaiw nra;ag;gl;l nka;naz; kjpg;Gilar; rhh;G xU njhlh;

thpirahFk;. (B ) xt;nthU rhh;Gk; xU njhlh; thpirapidf; Fwpf;Fk;. (C)xU njhlh; thpir> Kbtpyp vz;zpf;ifapy; cWg;Gf;fisf; nfhz;bUf;fyhk;. (D) xU njhlh; thpir> KbTW vz;zpf;ifapy; cWg;Gf;fisf; nfhz;bUf;fyhk;.

2. 1>1>2>3>5>8> … vd;w njhlh;tupirapd; 8 MtJ cWg;G (A) 25 (B) 24 (C)23 (D) 21

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3. , , , , … vd;w njhlh; thpirapy;> cWg;G -f;F mLj;j cWg;G

(A) (B) (C) (D)

4. a,b,c,l,m vd;gd $l;Lj; njhlh; thpirapy; ,Ug;gpd;; a-4b+6c-4l+m = (A) 1 (B) 2 (C)3 (D) 0

5. a,b,c vd;gd xU $l;Lj; njhlh; thpirapy; cs;sd vdpy;> =

(A) (B) (C) (D) 1

6. 100n +10 vd;gJ xU njhlhpd; n MtJ cWg;G vdpy;> mJ (A) xU $l;Lj; njhlh; thpir (B) xU ngUf;Fj; njhlh; thpir (C) xU khwpypj;; njhlh; thpir (D) xU $l;Lj; njhlh; thpirAk; my;y ngUf;Fj; njhlh; thpirAk; my;y

7. a1,a2,a3, …vd;gd xU $l;Lj; njhlh; thpirapy; cs;sd.NkYk; = vdpy;>13tJ cWg;G

(A) (B) 0 (C)12a1 (D) 14a1

8. a1,a2,a3, …vd;gd xU $l;Lj; njhlh; thpir vdpy; a5,a10,a15, … vd;w njhlh; thpirahdJ (A) xU ngUf;Fj; njhlh; thpir (B) xU $l;Lj; njhlh; thpir (C) xU $l;Lj; njhlh; thpirAk; my;y

ngUf;Fj; njhlh; thpirAk; my;y (D) xU khwpypj;; njhlh; thpir 9. xU $l;Lj; njhlh; thpirapd; mLj;jLj;j %d;W cWg;Gfs; k+2, 4k-6, 3k-2 vdpy;> k –d; kjpg;G

(A) 2 (B) 3 (C)4 (D) 5 10. a,b,c,l,m,n vd;gd $l;Lj; njhlh; thpirapy; cs;sd vdpy;3a+7,3b+7,3c+7,3l+7,3m+7,3n+7 vd;w njhlh; thpir

(A) xU ngUf;Fj;; njhlh; thpir (B) xU $l;Lj; njhlh; thpir (C) xU khwpypj;; njhlh; thpir (D) xU $l;Lj; njhlh; thpirAk; my;y ngUf;Fj; njhlh; thpirAk; my;y

11. xU ngUf;Fj; njhlh; thpirapy; 3 MtJ cWg;G 2 vdpy;> mjd; Kjy; 5 cWg;Gfspd; ngUf;fw;gyd; (A) 52 (B) 25 (C)10 (D) 15

12. a,b,c vd;gd xU ngUf;Fj; njhlh; thpirapypUg;gpd; vdpy;> =

(A) (B) (C) (D)

13. x,2x+2,3x+3vd;gd xU ngUf;Fj; njhlh; thpirapy; cs;sd vdpy;>5x,10x+10,15x+15 vd;w njhlh; thpirahdJ (A) xU $l;Lj; njhlh; thpir (B) xU ngUf;Fj; njhlh; thpir (C) xU khwpypj;; njhlh; thpir (D) xU $l;Lj; njhlh; thpirAk; my;y ngUf;Fj; njhlh; thpirAk; my;y

14. -3,-3,-3, … vd;w njhlh; thpirahdJ (A) xU $l;Lj; njhlh; thpir kl;Lk; (B) xU ngUf;Fj; njhlh; thpir kl;Lk; (C) xU $l;Lj; njhlh; thpirAk; my;y ngUf;Fj; njhlh; thpirAk; my;y (D) xU $l;Lj; njhlh; thpir kw;Wk; ngUf;Fj; njhlh; thpir

15. xU ngUf;Fj; njhlh; thpirapd; Kjy; ehd;F cWg;Gfspd; ngUf;fw;gyd; 256> mjd; nghJ tpfpjk; 4 kw;Wk; mjd; Kjy; cWg;G kpif vz; vdpy;> me;j ngUf;Fj; njhlh; thpirapd; 3 tJ cWg;G

(A) 8 (B) (C) (D) 16

16. xU ngUf;Fj; njhlh; thpirapy; t2 = kw;Wk; t3 = vdpy;> mjd; nghJ tpfpjk;

(A) (B) (C) 1 (D) 5

17. 푥 ≠ 0 vdpy;> 1+secx+sec2x+sec3x+sec4x+sec5x = (A) (1+secx)( sec2x+sec3x+sec4x) (B) (1+secx)( 1+sec2x +sec4x) (C) (1-secx)( secx+sec3x+sec5x) (D) (1+secx)(1+sec3x+sec4x)

18. tn=3-5n vd;gJ xU $l;Lj;njhlh; thpirapd; n MtJ cWg;G vdpy;> mf;$l;Lj;njhlh; thpirapd; Kjy; n cWg;Gfspd; $Ljy;

(A) [1− 5푛] (B) 푛(1− 5푛) (C) (1 + 5n) (D) (1 + 푛) 19. am-n,am,am+n vd;w ngUf;Fj; njhlh; thpirapd; nghJ tpfpjk; (A) am (B) a-m (C) an (D) a-n

20. 1+2+3+…n = k vdpy;> 13+23+33+ … +n3 vd;gJ (A) k2 (B) k3 (C) ( ) (D) (k+1)3

21. fPo;f;fz;l $w;Wfspy; vJ jtwhdJ?

(A) 푎 – I 푔(푘) = 푎 , ∀푘 ∈ 푁 vd tiuaWf;fg;gl;l 푔:푁 → 푅 vd;w rhh;ghf fUjyhk;. (B) xU njhlh;

thpirapy; KbTwh vz;zpf;ifapy; cWg;Gfs; ,Uf;fyhk;. (C) xU rhh;ghdJ njhlh; thpirahf ,Uf;f Ntz;ba mtrpak; ,y;iy. (D) 풇:푵 → 푹 ,q;F 풇(풙) = ퟐ풙 + ퟏ, 풙 ∈ 푹 vd;w rhh;ghdJ xU njhlh; thpir MFk;.

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22. > > > > … vd;w ngUf;Fj; njhlh; thpirapd; nghJ tpfpjk;

(m) (M) 5 (,) (<)

3.,aw;fzpjk;;

xU kjpg;ngz; tpdhf;fs;: 1. 6x-2y=3, kx-y=2 vd;w njhFg;gpw;F xNu xU jPh;T cz;nldpy;>

(A) k=3 (B) k≠3 (C)k=4 (D) k≠4 2. ,U khwpfspy; cs;s Nehpay; rkd;ghLfspd; njhFg;G xUq;fikahjJ vdpy;> mtw;wpd; tiuglq;fs;

(A) xd;wpd; kPJ xd;W nghUe;Jk; (B) xU Gs;spapy; ntl;bf;nfhs;Sk; (C) ve;jg; Gs;spapYk; ntl;bf;nfhs;shJ (D) x – mr;ir ntl;Lk;

3. x-4y = 8, 3x-12y = 24 vd;Dk; rkd;ghLfspd; njhFg;gpw;F (A) Kbtpyp vz;zpf;ifapy; jPh;Tfs; cs;sd. (B) jPh;T ,y;iy (C) xNu xU jPh;T kl;Lk; cz;L (D) xU jPh;T ,Uf;fyhk; my;yJ ,y;yhkYk; ,Uf;fyhk;

4. p(x) = (k+4)x2 +13x+3k vd;Dk; gy;YWg;Gf; Nfhitapd; xU G+r;rpak; kw;nwhd;wpd; jiyfPopahdhy;> k –d; kjpg;G (A) 2 (B) 3 (C)4 (D) 5

5. f(x) = 2x2 +(p+3)x+5 vd;Dk; gy;YWg;Gf; Nfhitapd; ,U G+r;rpaq;fspd; $Ljy; G+r;rpankdpy; p-d; kjpg;G (A) 3 (B) 4 (C)-3 (D) -4

6. x2-2x+7 vd;gij x+4 My; tFf;Fk; NghJ fpilf;Fk; kPjp (A) 28 (B)29 (C)30 (D)31 7. x3-5x2+7x-4 vd;gij x-1 My; tFf;Fk; NghJ fpilf;Fk; <T

(A) x2+4x+3 (B) x2-4x+3 (C) x2-4x-3 (D) x2+4x-3 8. (x3+1) kw;Wk; x4-1 Mfpatw;wpd; kP.ngh.t (A) x3-1 (B) x3+1 (C)x+1 (D) x-1 9. x2-2xy+y2 kw;Wk; x4-y4 Mfpatw;wpd; kP.ngh.t (A) 1 (B) x+y (C)x-y (D) x2-y2

10. x3-a3 kw;Wk; (x-a)2 Mfpatw;wpd; kP.ngh.k (A) (x3-a3)(x+a) (B) (x3-a3)(x-a)2 (C)(x-a)2(x2+ax+a2) (D) (x+a)2(x2+ax+a2)

11. k∈N vDk; NghJ ak,ak+3,ak+5 Mfpatw;wpd; kP.ngh.k (A) ak+9 (B) ak (C)ak+6 (D)ak+5

12. vd;Dk; tpfpjKW Nfhitapd; kpf RUq;fpa tbtk; (A) (B) (C) (D)

13. kw;Wk; Mfpad ,U tpfpjKW Nfhitfs; vdpy;> mtw;wpd; ngUf;fw;gyd;

(A) (B) (C) (D)

14. vd;gij My; tFf;Fk; NghJ fpilf;Fk; <T

(A) (x-5)(x-3) (B) (x-5)(x+3) (C) (x+5)(x-3) (D) (x+5)(x+3)

15. cld; If; $l;l fpilf;Fk; Gjpa Nfhit

(A) 푎 + 푎푏 + 푏 (B) 푎 − 푎푏 + 푏 (C) 푎 + 푏 (D) 푎 − 푏

16. 49(x2-2xy-y2)2 – d; th;f;f%yk;

(A) 7│푥 − 푦│ (B) 7(x+y)(x-y) (C) 7(x+y)2 (D) 7(x-y)2

17. x2+y2+z2-2xy+2yz-2zx – d; th;f;f%yk; (A) │푥 + 푦 − 푧│ (B) │푥 − 푦 + 푧│ (C) │푥 + 푦 + 푧│ (D) │푥 − 푦 − 푧│ 18. 121x4y8z6(l-m)2 – d; th;f;f%yk;

(A) 11x2y4z4 │푙 −푚│ (B) 11x4y4│푧 (푙 − 푚)│ (C) 11x2y4z6 │푙 −푚│ (D) 11x2y4 │z (푙 − 푚)│ 19. ax2+bx+c =0 vd;w rkd;ghl;bd; %yq;fs; rkk; vdpy;> c – d; kjpg;G

(A) (B) (C)− (D) −

20. x2+5kx+16 =0 vd;w rkd;ghl;bw;F nka;naz; %yq;fs; ,y;iynadpy;;>

(A) 푘 > (B) 푘 > − (C)− < 푘 < (D) 0 < 푘 <

21. 3- ia xU %ykhff; nfhz;l ,Ugbr; rkd;ghL (A) x2-6x-5=0 (B) x2+6x-5=0 (C) x2-5x-6=0 (D) x2-5x+6=0

22. x2-bx+c =0 kw;Wk; x2+bx-a =0 Mfpa rkd;ghLfspd; nghJthd %yk;

(A) (B) (C) (D)

23. a≠0, vd mike;j rkd;ghL ax2+bx+c =0 – d; %yq;fs; 훼 kw;Wk;훽 vdpy;> gpd;tUtdtw;Ws; vJ nka;ay;y?

(A) 훼 + 훽 = (B) 훼훽 = (C) 훼 +훽 = (D) + =−

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24. ax2+bx+c =0 vd;w ,Ugbr; rkd;ghl;bd; %yq;fs; 훼 kw;Wk; 훽 vdpy;> kw;Wk; Mfpadtw;iw

%yq;fshff; nfhz;l ,Ugbr;rkd;ghL (A) ax2+bx+c =0 (B) bx2+ax+c =0 (C) cx2+bx+a =0 (D) cx2+ax+b =0

25. b=a+c vdpy;> ax2+bx+c =0 vd;w rkd;ghl;bd; %yq;fs; rkk; vdpy;> (A) a=c (B) a= -c (C) a=2c (D) a=-2c

26. cWg;Gfs; 5xy kw;Wk; 28ab Mfpatw;wpd; kP.ngh.t (A) 140xyab (B) fhz ,ayhJ (C) 1 (D) 0

27. 6x2y, 9x2yz, 12x2y2z Mfpatw;wpd; kP.ngh.k (m) 36x2y2z (M) 48x2y2z2 (,)96x2y2z2 (<)72xy2z

4.mzpfs;

xU kjpg;ngz; tpdhf;fs;: 1. gpd;tUtdtw;Ws; ve;j $w;W nka;ahdjy;y?

(A) jpirapyp mzpahdJ xU rJu mzpahFk; (B ) %iytpl;l mzpahdJ xU rJu mzpahFk. (C) jpirapyp mzpahdJ xU %iytpl;l mzpahFk;. (D) %iytpl;l mzpahdJ xU jpirapyp mzpahFk;.

2. A = [aij]mxn vd;gJ xU rJu mzp vdpy;>

(A) 푚 < 푛 (B) 푚 > 푛 (C) 푚 = 1 (D) m=n

3. 3푥 + 7 5푦 + 1 2 − 3푥 = 1 푦 − 2

8 8 vdpy;> x kw;Wk; y –fspd; kjpg;Gfs; KiwNa

(A) −2,7 (B) - ,7 (C) − ,− (D) 2,−7

4. 퐴 = ( 1 − 2 3) B=−1 2−3

vdpy; A+B =

(A) ( 0 0 0) (B) 000

(C) (−14) (D) tiuaWf;fg;gltpy;iy

5. xU mzpapd; thpir 2x3 vdpy;> mt;tzpapy; cs;s cWg;Gfspd; vz;zpf;if (A) 5 (B) 6 (C)2 (D) 3

6. 8 4푥 8 = 4 2 1

1 2 vdpy;> x – d; kjpg;G (A) 1 (B) 2 (C) (D) 4

7. A – d; thpir 3x4 kw;Wk; B – d; thpir 4x3 vdpy;> BA – d; thpir (A) 3x3 (B) 4x4 (C)4x3 (D) tiuaWf;fg;gltpy;iy

8. 퐴 푋 1 10 2 = (1 2) vdpy;> A – d; thpir (A) 2x1 (B) 2x2 (C) 1x2 (D) 3x2

9. A kw;Wk; B vd;gd rJu mzpfs;. NkYk; AB = I kw;Wk; BA = I vdpy;> B vd;gJ (A) myF mzp (B) G+r;rpa mzp (C) 퐴− d; ngUf;fy; Neh;khW mzp (D) -A

10. 1 22 1

푥푦 = 2

4 vdpy;> x kw;Wk; y fspd; kjpg;G (A) 2,0 (B) 0,2 (C) 0,-2 (D) 1,1

11. 퐴 = 1− 2−3 4 kw;Wk; A+B = 0 vdpy; B =

(A) 1 −2−3 4 (B) −1 2

3 −4 (C) −1 −2−3 −4 (D) 1 0

0 1

12. 퐴 = 4 − 26 − 3 vdpy;> A2 =

(A) 16 436 9 (B) 8 −4

12 −6 (C) −4 2−6 3 (D) 4 −2

6 −3

13. A – d; thpir mxn kw;Wk; B – d; thpir pxq vd;f. A kw;Wk; B Mfpadtw;wpd; $Ljy; fhz ,aYnkdpy;> (A) m=p (B) n=q (C) n=p (D) m=p ,n=q

14. 푎 31 2

2−1 = 5

0 vdpy; a – d; kjpg;G (A) 8 (B) 4 (C)2 (D) 11

15. 퐴 = 훼 훽훾 − 훼 kw;Wk; A2 = I vdpy;>

(A) 1 + 훼2 + 훽훾 = 0 (B) 1 - 훼2 + 훽훾 = 0 (C) 1 - 훼2 - 훽훾 = 0 (D) 1 + 훼2 - 훽훾 = 0 16. A = [aij]2x2 kw;Wk; aij = i+j vdpy;> A =

(A) 1 23 4 (B) 2 3

3 4 (C) 2 34 5 (D) 4 5

6 7

17. −1 0 0 1

푎 푏푐 푑 = 1 0

0 −1 vdpy;> a,b,c kw;Wk; d Mfpatw;wpd; kjpg;Gfs; KiwNa

(A) -1,0,0,-1 (B) 1,0,0,1 (C)-1,0,1,0 (D) 1,0,0,0

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18. 퐴 = 7 21 3 kw;Wk; 퐴 + 퐵 = −1 0

2 − 4 vdpy;> mzp B =

(A) 1 00 1 (B) 6 2

3 −1 (C) −8 −21 −7 (D) 8 2

−1 7

19. ( 5 푥 1) 2−1

3= (20) vdpy;> x – d; kjpg;G

(A) 7 (B) -7 (C) (D) 0

20. A kw;Wk; B vd;gd xNu thpirAila rJu mzpfs; vdpy;> fPo;f;fz;litfspy; vJ nka;ahFk;? (A) (AB)T = ATBT (B) (ATB)T = ATBT (C) (AB)T = BA (AB)T = BTAT

5. Maj;njhiy tbtpay; xU kjpg;ngz; tpdhf;fs;:

1. (a,-b), (3a,5b) Mfpa Gs;spfis ,izf;Fk; Neh;f;Nfhl;Lj;Jz;bd; eLg;Gs;sp (A) (-a,2b) (B) (2a,4b) (C) (2a,2b) (D) (-a,-3b)

2. A(1,-3), B(-3,9) Mfpa Gs;spfis ,izf;Fk; Neh;f;Nfhl;Lj;Jz;il 1:3 vd;w tpfpjj;jpy; gphpf;Fk; Gs;sp P (A) (2,1) (B) (0,0) (C) ( ,2) (D) (1,-2)

3. A(3,4), B(14,-3) Mfpatw;iw ,izf;Fk; Neh;f;Nfhl;Lj;Jz;L x – mr;ir P ,y; re;jpf;fpwJ vdpy;> mf;Nfhl;Lj;Jz;il P gphpf;Fk; tpfpjk; (A) 4 : 3 (B) 3 : 4 (C) 2 : 3 (D) 4 : 1

4. (-2,-5), (-2,12), (10,-1) Mfpa Gs;spfis Kidfshff; nfhz;l Kf;Nfhzj;jpd; eLf;Nfhl;L ikak; (A) (6,6) (B) (4,4) (C) (3,3) (D) (2,2)

5. (1,2), (4,6), (x,6), (3,2) vd;gd ,t;thpirapy; Xh; ,izfuj;jpd; Kidfs; vdpy;> x – d; kjpg;G (A) 6 (B) 2 (C) 1 (D) 3

6. (0,0), (2,0), (0,2) Mfpa Gs;spfshy; mikAk; Kf;Nfhzj;jpd; gug;G (A) 1 rJu.myFfs; (B) 2 rJu.myFfs; (C) 4 rJu.myFfs; (D) 8 rJu.myFfs;

7. (1,1), (0,1), (0,0),(1,0) Mfpa Gs;spfshy; mikAk; ehw;fuj;jpd; gug;G (A) 3 rJu.myFfs; (B) 2 rJu.myFfs; (C) 4 rJu.myFfs; (D) 1 rJu.myFfs;

8. x – mr;Rf;F ,izahd Neh;f;Nfhl;bd; rha;Tf; Nfhzk;

(A) 0° (B) 60° (C) 45° (D) 90° 9. (3,-2), (-1,a) Mfpa Gs;spfis ,izf;Fk; Neh;f;Nfhl;bd; rha;T − vdpy;> a –d; kjpg;G

(A) 1 (B) 2 (C) 3 (D) 4 10. (-2,6), (4,8) Mfpa Gs;spfis ,izf;Fk; Neh;f;Nfhl;bw;Fr; nrq;Fj;jhd Neh;f;Nfhl;bd; rha;T

(A) (B) 3 (C) -3 (D) - 11. 9x-y-2 =0, 2x+y-9 =0 Mfpa Neh;f;NfhLfs; re;jpf;Fk; Gs;sp

(A) (-1,7) (B) (7,1) (C) (1,7) (D) (-1,-7) 12. 4x+3y-12 =0, vd;w Neh;f;NfhL y – mr;ir ntl;Lk;; Gs;sp

(A) (3,0) (B) (0,4) (C) (3,4) (D) (0,-4) 13. 7y-2x =11 vd;w Neh;f;Nfhl;bd; rha;T

(A) - (B) (C) (D) −

14. (2,-7) vd;w Gs;sp topr; nry;tJk;> x – mr;rpw;F ,izahdJkhd Neh;f;Nfhl;bd; rkd;ghL (A) x=2 (B) x=-7 (C) y=-7 (D) y=2

15. 2x-3y+6 =0 vd;w Neh;f;Nfhl;bd; x , y – ntl;Lj;Jz;Lfs; KiwNa A) 2,3 (B) 3,2 (C) -3,2 (D) 3,-2

16. xU tl;lj;jpd; ikak; (-6,4). xU tpl;lj;jpd; xU Kid (-12,8) vdpy;> mjd; kWKid (A) (-18,12) (B) (-9,6) (C) (-3,2) (D) (0,0)

17. Mjpg;Gs;sp Gs;sp topr; nry;tJk;> 2x+3y-7=0 vd;w Nfhl;bw;Fr; nrq;Fj;Jkhd Neh;f;Nfhl;bd; rkd;ghL (A) 2x+3y=0 (B) 3x-2y=0 (C) y+5=0 (D) y-5=0

18. y – mr;rpw;F ,izahdJk; (-2>5) vd;w Gs;sp topr; nry;tJkhd Neh;f;Nfhl;bd; rkd;ghL (A) x-2=0 (B) x+2=0 (C) y+5=0 (D) y-5=0

19. (2,5), (4,6), (a,a) Mfpa Gs;spfs; xNu Neh;f;Nfhl;by; mikfpd;wd vdpy;> a – d; kjpg;G (A) -8 (B) 4 (C) -4 (D) 8

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20. y=2x+k vd;w Neh;f;NfhL (1>2) vd;w Gs;sp topr; nry;fpd;wJ vdpy;> k –d; kjpg;G (A) 0 (B) 4 (C) 5 (D) -3

21. rha;T 3 MfTk;> y – ntl;Lj;Jz;L -4 MfTk; cs;s Neh;f;Nfhl;bd; rkd;ghL (A) 3x-y-4=0 (B) 3x+y-4=0 (C) 3x-y+4=0 (D) 3x+y+4=0

22. y=0 kw;Wk; x=-4 Mfpa Neh;f;NfhLfs; ntl;Lk; Gs;sp

(A) (0,-4) (B) (-4,0) (C) (0,4) (D) (4,0) 23. 3x+6y+7 =0, kw;Wk; 2x+ky =5 Mfpa Neh;f;NfhLfs; nrq;Fj;jhdit vdpy;> k – d; kjpg;G Gs;sp

(A) 1 (B) -1 (C) 2 (D) 24. fPo;f;fhZk; ve;j Gs;spfspd; njhFg;G xNu Neh;f;Nfhl;by; mikAk;?

(A) (1,-1), (-1,1), (0,0) (B) (1,-1), (-1,1), (0,1) (C) (1,-1), (-1,1), (1,0) (D) (1,-1), (-1,1), (1,1) 25. (0>0)> (1>0) kw;Wk; (0>1) Mfpatw;iw Kidfshff; nfhz;l Kf;Nfhzj;jpd; Rw;wsT

(m) √2 (M) 2 (,) 2 + √2 (<)2 −√2

6. tbtpay; xU kjpg;ngz; tpdhf;fs;:

1. ∆ ABC – d; gf;fq;fs; AB kw;Wk; AC Mfpatw;iw xU Neh;f;NfhL KiwNa D kw;Wk; E – fspy; ntl;LfpwJ. NkYk;> mf;NfhL BC – f;F ,iz vdpy; =

(A) (B) (C) (D)

2. ∆ ABC – y;; AB kw;Wk; AC – fspYs;s Gs;spfs; D kw;Wk; E vd;gd DE ∥ BC vd;wthW cs;sd. NkYk;> AD = 3 nr.kP> DB = 2 nr.kP kw;Wk; AE = 2.7 nr.kP vdpy; AC = (A) 6.5 nr.kP (B) 4.5 nr.kP (C) 3.5 nr.kP (D) 5.5 nr.kP

3. ∆ PQR –y; RS vd;gJ ∠R –d; Nfhz cl;Gw ,U rkntl;b. PQ = 6 nr.kP>;QR = 8 nr.kP>;RP = 4 nr.kP>;vdpy; PS = (A) 2 nr.kP (B) 4 nr.kP (C) 3 nr.kP (D) 6 nr.kP

4. glj;jpy; = > ∠B = 40° kw;Wk; ∠C = 60° vdpy;> ∠BAD (A) 30° (B) 50° (C) 80° (D) 40°

5. glj;jpy x – d; kjpg;ghdJ (A) 4.2myFfs; (B) 3.2 myFfs; (C) 0.8 myFfs; (D) 0.4myFfs;

6. ∆ ABC kw;Wk; ∆ DEF -fspy; ∠B =∠E kw;Wk; ∠C =∠F vdpy;> (A) = (B) = (C) = (D) =

7. nfhLf;fg;gl;l glj;jpw;Fg;> nghUe;jhj $w;wpidf; fz;lwpf. (A) ∆ ADB ~ ∆ ABC (B) ∆ ABD ~ ∆ ABC (C) ∆ BDC ~ ∆ ABC (D) ∆ ADB ~ ∆ BDC

8. 12 kP ePsKs;s xU Neh;f;Fj;jhd Fr;rp> 8 kP ePsKs;s epoiyj; jiuapy; Vw;gLj;JfpwJ. mNj Neuj;jpy; xU NfhGuk; 40 kP ePsKs;s epoiyj; jiuapy; Vw;gLj;JfpwJ vdpy;> NfhGuj;jpd; cauk; (A) 40 kP (B) 50 kP (C) 75 kP (D) 60kP

9. ,U tbnthj;j Kf;Nfhzq;fspd; gf;fq;fspd; tpfpjk; 2:3 vdpy;> mtw;wpd; gug;gsTfspd; tpfpjk; (A) 9 : 4 (B) 4 : 9 (C) 2 : 3 (D) 3 : 2

10. Kf;Nfhzq;fs; ABC kw;Wk; DEF tbnthj;jit. mtw;wpd; gug;gsTfs; KiwNa 100 nr.kP2> 49 nr.kP2 kw;Wk; BC = 8.2 nr.kP vdpy;> EF = (A) 5.47 nr.kP (B) 5.74 nr.kP (C) 6.47 nr.kP (D) 6.74 nr.kP

11. ,U tbnthj;j Kf;Nfhzq;fspd; Rw;wsTfs; KiwNa 24 nr.kP> 18 nr.kP vd;f. Kjy; Kf;Nfhzj;jpd; xU gf;fk; 8 nr.kP vdpy;> kw;nwhU Kf;Nfhzj;jpd; mjw;F xj;j gf;fk; (A) 4 nr.kP (B) 3 nr.kP (C) 9 nr.kP (D) 6 nr.kP

12. AB , CD vd;gd xU tl;lj;jpd; ,U ehz;fs;. mit ePl;lg;gLk; NghJ P – y; re;jpf;fpd;wd kw;Wk; AB = 5 nr.kP> AP = 8 nr.kP> CD = 2 nr.kP vdpy; PD = (A) 12 nr.kP (B) 5 nr.kP (C) 6 nr.kP (D) 4 nr.kP

13. glj;jpy; ehz;fs; AB kw;Wk; CD vd;gd P – y; ntl;Lfpd;wd. AB = 16 nr.kP> PD = 8 nr.kP vdpy;> PC =6 nr.kP> kw;Wk; AP > PB vdpy;> AP = (A) 8 nr.kP (B) 4 nr.kP (C) 12 nr.kP (D) 6 nr.kP

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14. P – vd;Dk; Gs;sp> tl;l ikak; O – tpypUe;J 26 nr.kP njhiytpy; cs;sJ. P – apypUe;J tl;lj;jpw;F tiuag;gl;l PT vd;w njhLNfhl;bd; ePsk; 10 nr.kP vdpy;> OT = (A) 36 nr.kP (B) 20nr.kP (C) 18 nr.kP (D) 24 nr.kP

15. glj;jpy;> ∠푃퐴퐵 = 120° vdpy;> ∠퐵푃푇 = (A) 120° (B) 30° (C) 40° (D) 60°

16. O – it ikakhf cila tl;lj;jpw;F PA, PB vd;gd ntspg;Gs;sp P - apypUe;J tiuag;gl;lj; njhLNfhLfs;. ,j;njhLNfhLfSf;F ,ilapy; cs;s Nfhzk; 40° vdpy;> ∠푃푂퐴 = (A) 70° (B) 80° (C) 50° (D) 60°

17. glj;jpy; PA, PB vd;gd tl;lj;jpw;F ntspNaAs;s Gs;sp P - apypUe;J tiuag;gl;lj; njhLNfhLfs;. NkYk; CD vd;gJ Q vd;w Gs;spapy; tl;lj;jpw;F njhLNfhL. PA = 8 nr.kP> CQ = 3 nr.kP vdpy;> PC = (A) 11 nr.kP (B) 5 nr.kP (C) 24 nr.kP (D) 38 nr.kP

18. nrq;Nfhz ∆퐴퐵퐶 - y; ∠퐵 = 90° kw;Wk; 퐵퐷 ⊥ 퐴퐶. BD = 8 nr.kP> AD = 4 nr.kP vdpy;> CD = (A) 24 nr.kP (B) 16 nr.kP (C) 32 nr.kP (D) 8 nr.kP

19. ,uz;L tbnthj;j Kf;Nfhzq;fspd; gug;gsTfs; KiwNa 16 nr.kP2> 36 nr.kP2. Kjy; Kf;Nfhzj;jpd; Fj;Jauk; 3 nr.kP vdpy;> kw;nwhU Kf;Nfhzj;jpy; mjid xj;j Fj;Jauk; (A) 6.5 nr.kP (B) 6 nr.kP (C) 4 nr.kP (D) 4.5 nr.kP

20. ,U tbnthj;j Kf;Nfhzq;fs; ∆ ABC kw;Wk; ∆ DEF Mfpatw;wpd; Rw;wsTfs; KiwNa 36 nr.kP> 24 nr.kP. NkYk;> DE=10 nr.kP vdpy;> AB= (A) 12 nr.kP (B) 20 nr.kP (C) 15 nr.kP (D) 18 nr.kP

21. nfhLf;fg;gl;l glj;jpy; cs;s ehw;fuk; APOQ –d; Rw;wsT 26 nr.kP kw;Wk; AP =10 nr.kP. O vd;gJ tl;lj;jpd; ikak;. AP kw;Wk; AQ Mfpait A apypUe;J tiuag;gLk; njhLNfhLfs; vdpy; tl;lj;jpd; Muk; (A) 6 nr.kP (B) 3 nr.kP (C) 8 nr.kP (D) 16 nr.kP

22. AB kw;Wk; CD vd;w ,U ehz;fs; xU tl;lj;jpd; cl;Gwkhf P vd;w Gs;spapy; ntl;bf; nfhs;fpd;wd. AB = 7> AP = 4> CP = 2 vdpy; CD = (m) 4 (M) 8 (,) 6 (<) 10

7. Kf;Nfhztpay; xU kjpg;ngz; tpdhf;fs;:

1. (1 − 푠푖푛 휃)푠푒푐 휃 = (A) 0 (B) 1 (C) 푡푎푛 휃 (D) 푐표푠 휃

2. (1 + 푡푎푛 휃)푠푖푛 휃 = (A) 푠푖푛 휃 (B) 푐표푠 휃 (C) 푡푎푛 휃 (D) 푐표푡 휃

3. (1 − 푐표푠 휃)(1 + 푐표푡 휃) = (A) 푠푖푛 휃 (B) 0 (C) 1 (D) 푡푎푛 휃

4. sin(90° −휃) 푐표푠휃 + cos(90° − 휃) 푠푖푛휃 = (A) 1 (B) 0 (C)2 (D) -1

5. 1− = (A) 푐표푠휃 (B) 푡푎푛휃 (C) 푐표푡휃 (D) 푐표푠푒푐휃

6. 푐표푠 푥 − 푠푖푛 푥 = (A) 2푠푖푛 푥 − 1 (B) 2푐표푠 푥 − 1 (C) 1 + 2푠푖푛 푥 (D) 1− 2푐표푠 푥

7. 푡푎푛휃 = vdpy; - d; kjpg;G

(A) 푐표푠휃 (B) 푠푖푛휃 (C) 푐표푠푒푐휃 (D) 푠푒푐휃

8. 푥 = 푎 푠푒푐휃,푦 = 푏 푡푎푛휃 vdpy; − - d; kjpg;G (A) 1 (B) −1 (C) 푡푎푛 휃 (D) 푐표푠푒푐 휃

9.

= (A) 푐표푡휃 (B) 푡푎푛휃 (C) 푠푖푛휃 (D) −푐표푡휃

10. ( ° ) + ( ° ) = (A) 푡푎푛휃 (B) 1 (C)−1 (D) 푠푖푛휃

11. glj;jpy;> AC = (A) 25 kP (B) 25√3 kP (C)

√ kP (D) 25√2 kP

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12. glj;jpy;> ∠퐴퐵퐶 = (A) 45° (B) 30° (C) 60° (D) 50°

13. xU NfhGuj;jpypUe;J 28.5 kP J}uj;jpy; epd;W nfhz;bUf;Fk; xUth; NfhGuj;jpd; cr;rpia 45° Vw;wf; Nfhzj;jpy; fhz;fpwhh;. mtUila fpilepiyg; ghh;itf;NfhL jiuapypUe;J 1.5 kP cauj;jpy; cs;sJ vdpy; NfhGuj;pd; cauk; (A) 30 kP (B) 27.5 kP (C) 28.5 kP (D) 27 kP

14. glj;jpy;> 푠푖푛휃 = vdpy;> BC = (A) 85 kP (B) 65 kP (C) 95 kP (D) 75 kP

15. (1 + 푡푎푛 휃)(1− 푠푖푛휃)(1 + 푠푖푛휃) = (A) 푐표푠 휃 − 푠푖푛 휃 (B) 푠푖푛 휃 − 푐표푠 휃 (C) ) 푠푖푛 휃 + 푐표푠 휃 (D) 0

16. (1 + 푐표푡 휃)(1− 푐표푠휃)(1 + 푐표푠휃) = (A) 푡푎푛 휃 − 푠푒푐 휃 (B) 푠푖푛 휃 − 푐표푠 휃 (C) 푠푒푐 휃 − 푡푎푛 휃 (D) 푐표푠 휃 − 푠푖푛 휃

17. (푐표푠 휃 − 1)(푐표푡 휃 + 1) + 1 = (A) 1 (B) -1 (C)2 (D) 0

18.

= (A) 푐표푠 휃 (B) 푡푎푛 휃 (C) 푠푖푛 휃 (D) 푐표푡 휃

19. 푠푖푛 휃 +

= (A) 푐표푠푒푐 휃 + 푐표푡 휃 (B) 푐표푠푒푐 휃 − 푐표푡 휃 (C) 푐표푡 휃 − 푐표푠푒푐 휃 (D) 푠푖푛 휃 − 푐표푠 휃

20. 9푡푎푛 휃 − 9푠푒푐 휃 = (A) 1 (B) 0 (C)9 (D) -9

21. 1− = (A) 푠푖푛휃 (B) 푐표푠휃 (C) −푐표푠휃 (D) - 풔풊풏휽

22. = (m) sin휃 + cos 휃 (M) sin 휃 cos 휃 (,) sin 휃 − cos 휃 (<) cosec 휃 + cot 휃

8. mstpay; xU kjpg;ngz; tpdhf;fs;:

1. 1 nr.kP MuKk; kw;Wk; 1 nr.kP cauKk; nfhz;l xU Neh; tl;l cUisapd; tisgug;G (A) 휋 nr.kP2 (B) 2휋 nr.kP2 (C) 3휋 nr.kP2 (D) 2 nr.kP2

2. Neh; tl;l cUisapd; MukhdJ mjd; cauj;jpy; ghjp vdpy; mjd; nkhj;jg; Gwg;gug;G

(A) 휋ℎ r.m (B) 휋ℎ r.m (C) 휋ℎ r.m (D) 휋ℎ r.m

3. Neh; tl;l cUisapd; mbgf;f gug;G 80 r.nr.kP. mjd; cauk; 5 nr.kP vdpy;> $k;gpd;; fdmsT

(A) 400 nr.kP3 (B) 16 nr.kP3 (C) 200 nr.kP3 (D) nr.kP3

4. xU Neh; tl;l cUisapd; nkhj;j Gwg;gug;G 200 휋 r.nr.kP. kw;Wk; mjd; Muk; 5 nr.kP vdpy;> mjd; cauk; kw;Wk; Muj;jpd; $Ljy; (A) 20 nr.kP (B) 25 nr.kP (C) 30 nr.kP (D) 15 nr.kP

5. a myFfs; MuKk; b myFfs; cauKk; nfhz;l xU Neh; tl;l cUisapd; tisgug;G (A) 휋푎 푏 r. nr.kP (B) 2휋푎푏 r. nr.kP (C) 2휋 r. nr.kP (D) 2 r. nr.kP

6. xU Neh; tl;lf; $k;G kw;Wk; Neh; tl;l cUisapd; MuKk; cauKk; KiwNa rkk; cUisapd; fd msT 120 nr.kP3 vdpy;> $k;gpd;; fdmsT (A) 1200 nr.kP3 (B) 360 nr.kP3 (C) 40 nr.kP3 (D) 90 nr.kP3

7. Neh; tl;lf; $k;gpd; tpl;lk; kw;Wk;; cauk; KiwNa 12 nr.kP> 8 nr.kP vdpy;> mjd; rhAauk; (A) 10 nr.kP (B) 20 nr.kP (C) 30 nr.kP (D) 96 nr.kP

8. Neh; tl;lf; $k;gpd; mbr;Rw;wsT kw;Wk;; rhAauk; KiwNa 120휋 nr.kP> kw;Wk; 10 nr.kP vdpy;> mjd; tisgug;G (A)1200 휋 nr.kP2 (B) 600휋 nr.kP2 (C) 300휋 nr.kP2 (D) 600 nr.kP2

9. Neh; tl;lf; $k;gpd; fdmsT kw;Wk;; mbgf;fg; gug;G KiwNa 48휋 nr.kP3> kw;Wk; 12 휋 nr.kP2 vdpy;> mjd; cauk; (A) 6 nr.kP (B) 8 nr.kP (C) 10 nr.kP (D) 12 nr.kP

10. 5 nr.kP cauKk; 48 nr.kP2 mbg;gf;fg; gug;Gk; nfhz;l xU Neh; tl;lf; $k;gpd; fdmsT (A) 240 nr.kP3 (B) 120 nr.kP3 (C) 80 nr.kP3 (D) 480 nr.kP3

11. ,uz;L cUisfspd; cauq;fs; KiwNa 1 : 2 kw;Wk; mtw;wpd; Muq;fs; KiwNa 2 : 1 Mfpa tpfpjq;fspypUg;gpd;> mtw;wpd; fd msTfspd; tpfpjk; (A) 4 : 1 (B) 1 : 4 (C) 2 : 1 (D) 1 : 2

12. 2 nr.kP MuKs;s xU Nfhsj;jpd; tisgug;G (A)8 휋 nr.kP2 (B) 16 nr.kP2 (C) 12휋 nr.kP2 (D) 16 흅 nr.kP2

13. xU jpz;k miuf; Nfhsj;jpd; tpl;lk; 2 nr.kP vdpy;> mjd; nkhj;j Gwg; gug;G (A)12 nr.kP2 (B) 12 휋 nr.kP2 (C) 4휋 nr.kP2 (D) 3 휋 nr.kP2

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14. 휋 f.nr.kP fd msT nfhz;l Nfhsj;jpd; Muk;

(A) nr.kP (B) nr.kP (C) nr.kP (D) nr.kP 15. ,uz;L Nfhsq;fspd; tisgug;Gfspd; tpfpjk; 9 : 25. mtw;wpd; fd msTfspd; tpfpjk;

(A) 81 : 625 (B) 729 : 15625 (C) 27 : 75 (D) 27 : 125 16. a myFfs; Muk; nfhz;l jpz;k miuf; Nfhsj;jpd; nkhj;jg; Gwg;gug;G

(A) 2휋 a2r.m (B) 3 휋 a2r.m (C) 3휋a r.m (D) 3 a2r.m 17. 100 휋 r.nr.kP tisgug;G nfhz;l Nfhsj;jpd; Muk;

(A) 25nr.kP (B) 100 nr.kP (C) 5 nr.kP (D) 10 nr.kP 18. xU Nfhsj;jpd; tisgug;G 36 휋 r.nr.kP vdpy;> mjd; fd msT

(A) 12 휋 nr.kP3 (B) 36 휋 nr.kP3 (C) 72 휋 nr.kP3 (D) 108 휋 nr.kP3 19. 12 휋 nr.kP2 nkhj;jg;gug;G nfhz;l jpz;k miuf;Nfhsj;jpd; tisgug;G

(A) 6휋 nr.kP2 (B) 24 휋 nr.kP2 (C) 36휋 nr.kP2 (D) 8 휋 nr.kP2 20. xU Nfhsj;jpd; MukhdJ kw;nwhU Nfhsj;jpd; Muj;jpy; ghjp vdpy; mtw;wpd; fd msTfspd; tpfpjk;

(A) 1 : 8 (B) 2 : 1 (C) 1 : 2 (D) 8 : 1 21. xU jpz;k Nfhsj;jpd; tisgug;G 24 nr.kP2. me;j Nfhsj;ij ,uz;L miuf; Nfhsq;fshfg; gphpj;jhy;

fpilf;Fk; miuf;Nfhsq;fspy; xd;wpd; nkhj;jg; Gwg;gug;G (A)12 nr.kP2 (B) 8 nr.kP2 (C) 16 nr.kP2 (D) 18 nr.kP2

22. ,uz;L $k;Gfs; rk Muq;fs; nfhz;Ls;sd. NkYk; mtw;wpd; rhAauq;fspd; tpfpjk; 4 : 3 vdpy;> tisgug;Gfspd; tpfpjk; (A) 16 : 9 (B) 8 : 6 (C) 4 : 3 (D) 3 : 4

11. Gs;spapay; xU kjpg;ngz; tpdhf;fs;:

1. 2>3>5>7>11>13>17>19>23>29 vd;w Kjy; gj;J gfh vz;fspd; tPr;R (A) 28 (B) 26 (C) 29 (D) 27

2. njhFg;gpYs;s tptuq;fspy; kpfr;rpwpa kjpg;G 14.1 kw;Wk; mt;tptuj;jpd; tPr;R 28.4 vdpy;> njhFg;gpd; kpfg; nghpa kjpg;G (A) 42.5 (B) 43.5 (C) 42.4 (D) 42.1

3. njhFg;gpYs;s tptuq;fspy; kpfg;nghpa kjpg;G 72 kw;Wk; kpfr;rpwpa kjpg;G 28 vdpy;> mj;njhFg;gpd; tPr;Rf; nfO (A) 44 (B) 0.72 (C) 0.44 (D) 0.28

4. 11 kjpg;Gfspd; ∑푥 = 132 vdpy;> mtw;wpd; $l;Lr; ruhrhp (A) 11 (B) 12 (C) 14 (D) 13

5. n cWg;Gfs; nfhz;l ve;j xU vz;fspd; njhFg;gpw;Fk; ∑(x-푥̅) = (A) ∑푥 (B) 푥̅ (C) 푛푥̅ (D) 0

6. n cWg;Gfs; nfhz;l ve;j xU vz;fspd;; njhFg;gpw;Fk; (∑푥) - 푥̅ = (A) 푛푥̅ (B) (푛 − 2)푥̅ (C) (푛 − 1)푥̅ (D) 0

7. x, y, z – d; jpl;l tpyf;fk; t- vdpy;> x+5, y+5, z+5 – d; jpl;l tpyf;fk; (A) ( B) t+5 (C) t (D) xyz

8. xU Gs;sp tptuj;jpd; jpl;l tpyf;fk; 1.6 vdpy;> mjd; tpyf;f th;f;fr; ruhrhp (A) 0.4 (B) 2.56 (C) 1.96 (D) 0.04

9. xU Gs;sp tptuj;jpd; tpyf;f th;f;f ruhrhp; 12.25 vdpy;> mjd; jpl;l tpyf;fk; (A) 3.5 (B) 3 (C) 2.5 (D) 3.25

10. Kjy; 11 ,ay; vz;fspd; tpyf;f th;f;fr; ruhrhp (A) √5 (B) √10 (C) 5√2 (D) 10

11. 10,10,10,10,10 - d; tpyf;f th;f;f ruhrhp (A) 10 (B) √10 (C) 5 (D) 0

12. 14,18,22,26,30 - d; tpyf;f th;f;fr; ruhrhp 32 vdpy; 28,36,44,52,60 - d; tpyf;f th;f;fr; ruhrhp (A) 64 (B) 128 (C) 32√2 (D) 32

13. tptuq;fspd; njhFg;G xd;wpd; jpl;l tpyf;fk; 2√2 . mjpYs;s xt;nthU kjpg;Gk; 3 My; ngUf;f fpilf;Fk; Gjpa tptuj; njhFg;gpd; jpl;l tpyf;fk; (A) √12 (B) 4√2 (C) 6√2 (D) 9√2

14. ∑(푥 − 푥̅)2 = 48, 푥̅ = 20 kw;Wk; n = 12 vdpy;> khWghl;Lf;nfO (A) 25 (B) 20 (C) 30 (D) 10

15. rpy tptuq;fspd; $l;Lr; ruhrhp kw;Wk; jpl;l tpyf;fk; KiwNa 48> 12 vdpy;> khWghl;Lf;nfO (A) 42 (B) 25 (C) 28 (D) 48

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12. epfo;jfT xU kjpg;ngz; tpdhf;fs;:

1. ∅ vd;gJ xU ,ayh epfo;r;rp vdpy;> 푃(∅) = (A) 1 (B) (C) 0 (D)

2. S vd;gJ xU rktha;g;G Nrhjidapd; $Wntsp vdpy;> 푃(푆) = (A) 0 (B) (C) (D) 1

3. A vd;w epfo;r;rpapd; epfo;jfT p vdpy;> gpd;tUtdtw;wpy; p vij epiwT nra;Ak; (A) 0 < 푝 < 1 (B) 0 ≤ 푝 ≤ 1 (C) 0 ≤ 푝 < 1 (D) 0 < 푝 ≤ 1

4. A kw;Wk; B vd;gd VNjDk; ,U epfo;r;rpfs;. NkYk; S vd;gJ rktha;g;Gr; Nrhjidapd; $Wntsp vdpy;> 푃(퐴 ∩ 퐵) = (A) 푃(퐵) − 푃(퐴 ∩ 퐵) (B) 푃(퐴 ∩ 퐵) −푃(퐵) (C) 푃(푆) (D) 푃[(퐴U퐵)’]

5. xU khztd; fzpjj;jpy; 100 kjpg;ngz; ngWtjw;fhd epfo;jfT mth; 100 kjpg;ngz; ngwhky; ,Ug;gjw;fhd epfo;jfT

(A) (B) (C) (D) 6. A kw;Wk; B vd;w ,U epfo;r;rpfspy; 푃(퐴) = 0.25, 푃(퐵) = 0.05 kw;Wk; 푃(퐴 ∩퐵) = 0.14 vdpy; 푃(퐴U퐵) =

(A) 0.61 (B) 0.16 (C) 0.14 (D) 0.6 7. 20 nghUl;fspy; 6 nghUl;fs; FiwghLilait. Rktha;g;G Kiwapy; xU nghUs; Njh;e;njLf;Fk; NghJ mJ

Fiwaw;wjhff; fpilg;gjw;fhd epfo;jfT

(A) (B)0 (C) (D) 8. A kw;Wk; B vd;gd ,uz;L xd;iwnahd;W tpyf;Fk; epfo;r;rpfs; vd;f. me;epfo;r;rpapd; $Wntsp S>

푃(퐴) = 푃(퐵) kw;Wk; 푆 = 퐴U퐵 vdpy;> 푃(퐴) =

(A) (B) (C) (D) 9. A,B kw;Wk; C vd;gd xd;iwnahd;W tpyf;Fk; %d;W epfo;r;rpfs; vd;f. mtw;wpd; epfo;jfTfs; KiwNa

, kw;Wk; vdpy;> 푃(퐴U퐵UC) = (A) (B) (C) (D) 1

10. 푃(퐴) = 0.25, 푃(퐵) = 0.50 kw;Wk; 푃(퐴 ∩ 퐵) = 0.14 vdpy; P(A Ak; my;y B Ak; my;y) = (A) 0.39 (B) 0.25 (C) 0.11 (D) 0.24

11. xU igapy; 5 fUg;G> 4 nts;is kw;Wk; 3 rptg;G epwg; ge;Jfs; cs;sd. rktha;g;G Kiwapy; Njh;e;njLf;fg;gLk; xU ge;J rptg;G epwkhf ,y;yhky; ,Ug;gjw;fhd epfo;jfT>

(A) (B) (C) (D) 12. xNu Neuj;jpy; ,U gfilfs; cUl;lg;gLfpd;wd. gfilapd; ,uz;L Kfq;fspYk; xNu vz;zhf ,Uf;f

epfo;jfT (A) (B) (C) (D) 13. xU rPuhd gfil xU Kiw cUl;lg;gLk; NghJ fpilf;Fk; gfh vz; my;yJ gF vz;zhf ,Ug;gjw;fhd

epfo;jfT> (A) 1 (B) 0 (C) (D) 14. xU ehzaj;ij %d;W Kiw Rz;Lk; Nrhjidapy; 3 jiyfs; my;yJ 3 G+f;fs; fpilf;f epfo;jfT>

(A) (B) (C) (D) 15. 52 rPl;Lfs; nfhz;l xU rPl;Lf;fl;bypUe;J xU rPl;L vLf;Fk; NghJ mJ xU V]; Mf ,y;yhkYk; kw;Wk;

xU ,uhrhthf ,y;yhkypUg;gjw;fhd epfo;jfT>

(A) (B) (C) (D) 16. xU nel;lhz;by; 53 nts;spf;fpoikfs; my;yJ 53 rdpf;;fpoikfs; tUtjw;fhd epfo;jfT

(A) (B) (C) (D) 17. xU rhjhuz tUlkhdJ 53 Qhapw;Wf;fpoikfs; kw;Wk; 53 jpq;fl;fpoikfs; nfhz;bUg;gjw;fhd epfo;jfT

(A) (B) (C) (D) 0 18. 52 rPl;Lfs; nfhz;l xU rPl;Lf;fl;bypUe;J xU rPl;L vLf;Fk; NghJ> mJ `hh;l; murpahf ,Ug;gjw;fhd

epfo;jfT> (A) (B) (C) (D) 19. xU cWjpahd epfo;r;rpapd; epfo;jfT

(A) 1 (B) 0 (C) 100 (D) 0.1 20. xU rktha;g;G Nrhjidapd; KbthdJ ntw;wpahfNth my;yJ Njhy;tpahfNth ,Uf;Fk;. mr;Nrhjidapy;

ntw;wp ngWtjw;fhd epfo;jfT Njhy;tpf;fhd epfo;jftpidg; Nghy; ,U klq;F vdpy;> ntw;wp ngWtjw;fhd

epfo;jfT (A) (B) (C) 1 (D) 0

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3. fzq;fSk; rhh;GfSk; ,U kjpg;ngz; tpdhf;fs;:

1. A = {4,6,7,8,9}, B = {2,4,6}, C = {1,2,3,4,5,6} vdpy; A∩ (BUC) fhz;f? 2. A = {4,6,7,8,9}, B = {2,4,6}, C = {1,2,3,4,5,6} vdpy; AU (B∩C) fhz;f? 3. 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}vdpy;A\ (B∩C)

fhz;f? 4. A = {4,6,7,8,9}, B ={2,4,6}, C = {1,2,3,4,5,6} vdpy; A\ ( C \ B) fhz;f? 5. P= {푎, 푏, 푐 }, Q = {푔,ℎ, 푥,푦}, R = {푎, 푒, 푓, 푠} vdpy; (i) P\ R (ii) Q∩ R (iii) R\ (P∩Q) I fhz;f? 6. ,U fzq;fspd; Nru;g;G khw;W gz;GilaJ vd ntd;;glk; %yk; ep&gp. 7. ,U fzq;fspd; ntl;L khw;W gz;GilaJ vd ntd;;glk; %yk; ep&gp. 8. A = {a,x,y,r,s}, B = {1,3,5,7,-10} Mfpa ,U fzq;fspd; Nru;g;G kw;Wk; gupkhw;W gz;GilaJ vd;gij

rupghuf;;fTk;. 9. A = {l,m,n,o,2,3,4,7}, B = {2,5,3,-2,m,n,o,p} Mfpa ,U fzq;fspd; ntl;L gupkhw;W gz;GilaJ

vd;gij rupghuf;;fTk;. 10. U = {4,8,12,16,20,24,28}, A = {8,16,24}, B = {4,16,20,28} vdpy; (AU B)| kw;Wk; (A∩ B)| If; fhz;f?. 11. A ⊂ B vdpy; AUB = B vdf; fhl;Lf. 12. A ⊂ B vdpy; A∩B kw;Wk; A \ B Mfpatw;iw fhz;f. 13. A ∩ (B \C) d; ntd;; glk; tiuf 14. (B UC) \ A d; ntd; glk; tiuf 15. A ∩ (B \C) d; ntd; glk; tiuf 16. AU (B ∩C) d; ntd; glk; tiuf 17. C∩ (B UA) d; ntd; glk; tiuf 18. A \ (B ∩C) d; ntd; glk; tiuf. 19. R={(1,3),(2,6),(3,10),(4,9)} vd;gJ xU rhu;ghFkh? rhu;G vdpy; kjpg;gfk;> Jiz kjpg;gfk;>tPr;rfk;

fhz;f. 20. Xd;Wf;nfhd;whd rhu;G>Nky; rhu;G Mfpatw;iw tiuaW. 21. khwpypr;rhu;G kw;Wk; rkdpr;rhu;gpid tiuaW. 22. A = {1,2,3,4,5}, B= N kw;Wk; f : A → B MdJ f(x) = x2 vd tiuaWf;fg;gl;Ls;sJ. f d;

tPr;rfj;jpid fhz;f. NkYk; rhu;gpd; tifiaf; fhz;f. 23. 푋 = {1,2,3,4,5},푌 = {1,3,5,7,9} vd;f. X ypUe;J Y f;fhd cwT {(1,1), (1,3), (3,5), (3,7), (5,7)} vd

tiuaWg;gpd; mJ rhh;G MFkh vd Muha;f. ,y;iy vdpy;> fhuzk; $W. 24. X={1,2,3,4} vd;f. g = {(3,1), (4,2), (2,1)} vd;w cwT X - ypUe;J X – f;F xU rhh;ghFkh vd

Muha;f. cd; tpilf;F Vw;w tpsf;fk; jUf. 25. nfhLf;fg;gl;Ls;s F= {(1,3),(2,5),(4,7),(5,9), (3,1) } vDk; rhu;gpw;F kjpg;gfk;>tPr;rfk; Mfpatw;iwf;

fhz;f. 26. A, B ,U fzq;fs;. NkYk; U vd;gJ midj;J fzk; vd;f. NkYk; n(U) = 700, n(A) = 200, n(B) =

300, n(A∩ B) =100, n(A| ∩ B|) If; fhz;f 27. n(U) = 500, n(A) = 285, n(B) = 195, n(A U B) =410, n(A| U B|) If; fhz;f 28. A = {4,5,6}, B = {5,6,7,8 }, C = {6,7,8,9} vdpy;

n(AU BU C) = n(A) + n(B) + n(C) - n(A ∩ B ) - n(B ∩ C )– n(A ∩ C ) + n(A∩ B∩ C) vd;gij rupghu;. 29. nfhLf;fg;gl;Ls;s rhu;G f = {(-1,2),(-3,1),(-5,6),(-4,3)} I i) ml;ltiz>ii) mk;Gf;Fwpg; glk;

Mfpatw;wpd; %yk; Fwpf;f. 30. Fj;Jf;NfhL Nrhjidiag; gad;gLj;jp gpd;tUk; tiuglq;fspy; vit rhh;gpidf; Fwpf;Fk; vdj;

jPh;khdpf;fTk; (ii)

31. gpd;tUk; mk;Gf;Fwp glq;fs; rhh;igf; Fwpf;fpd;wdth vdf; $W. cd; tpilf;Fj; jFe;j fhuzk; $W.

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Ie;J kjpg;ngz; tpdhf;fs;:

1. ntd;glq;fisg; gad;gLj;jp A\(BUC) = (A\B) ∩(A\C) vd;Dk; B khh;fdpd; fz tpj;jpahr tpjpia rhpghh;.

2. ntd;glq;fisg; gad;gLj;jp A\(B∩C) = (A\B) U(A\C) vd;Dk; B khh;fdpd; fz tpj;jpahr tpjpia rhpghh;.

3. ntd;glq;fisg; gad;gLj;jp (AUB)’ = A’∩B’ vd;Dk; fz epug;gpf;fhd B khh;fdpd; tpjpia rhpghh;. 4. ntd;glq;fisg; gad;gLj;jp (A∩B)’ = A’UB’ vd;Dk; fz epug;gpf;fhd B khh;fdpd; tpjpia rhpghh;. 5. ntd;glq;fisg; gad;gLj;jp A∩ (BUC) = (A∩B)U(A∩C) vd;w gq;fPl;L gz;gpid rhpghh; 6. ntd;glq;fisg; gad;gLj;jp AU (B∩C) = (AUB) ∩ (AUC) vd;w gq;fPl;L gz;gpid rhpghh; 7. A={푎, 푏, 푐,푑} B={푎, 푐, 푒} C={푎, 푒} vdpy; A∩ (BUC) = (A∩B)U(A∩C) vdf; fhl;L. 8. A={0,1,2,3,4} B={1,−2,3,4,5,6} C={2,4,6,7} vdpy; AU (B∩C) = (AUB) ∩ (AUC) vdf; fhl;L. 9. A= {1,3,5,7,9,11,13,15} B= {1,2,5,7} C= {3,9,10,12,13} vdpy; B khh;fdpd; fz tpj;jpahr tpjpfis

rhpghh;. 10. A= {푎, 푏, 푐,푑, 푒, 푓,푔, 푥,푦, 푧} B= {1,2, 푐,푑, 푒} C= {푑, 푒, 푓,푔, 2,푦} vdpy;; B khh;fdpd; fz tpj;jpahr

tpjpfis rhpghh;. 11. A= { x / -3≤ x <4 , x ЄR}, B = { x / x<5, x ЄN }, C = {-5,-3,-1,0,1,3}vdpy;A∩ (BUC) = (A∩B) U (A∩C) vdf;fhl;Lf. 12. U={푎, 푏, 푐,푑, 푒, 푓,푔,ℎ} A={푎, 푏, 푓,푔} B={푎, 푏, 푐} vdpy; B khh;fdpd; fz epug;G tpjpfis rhpghh;. 13. U={5,6,7,8,9,10,11,12,13} A={5,8,10,11} B={5,6,7,9,10} vdpy; B khh;fdpd; fz epug;G tpjpfis rhpghh;. 14. U = { 4,8,12,16,20,24,28}, A = {8,16,24}, B = {4,16,20,28}vdpy;; B khu;fdpd; fzepug;gp tpjpfis rupghu; 15. A = {5,10,15,20}, B = { 6,10,12,18,24 }, C = {7,10,12,14,21,28} vdpy; A\ (B\ C) = (A\ B) \C vd;gJ

nka;ahFkh vd Muha;f. cd; tpilf;F jf;f fhuzk; $Wf. 16. xU efuj;jpy; 85% Ngh; jkpo; nkhop> 40% Ngh; Mq;fpy nkhop kw;Wk; 20% Ngh; ,e;jp nkhop

NgRfpwhh;fs;. 32% Ngh; jkpOk; Mq;fpyKk;> 13% Ngh; jkpOk; ,e;jpAk; kw;Wk; 10% Ngh; Mq;fpyKk; ,e;jpAk; NgRfpwhh;fs; vdpy; %d;W nkhopfisAk; Ngrj; njhpe;jth;fspd; rjtPjj;jpid fhz;f.

17. xU FOtpy;; 65 khztu;fs;; fhy;ge;jhl;lKk;;> 45 Ngu; `hf;fpAk;> 42 Ngu; fpup;f;nfl;Lk; kw;Wk; 20 Ngu; fhy;ge;jhl;lKk; `hf;fpAk;> 25 Ngu;; fhy;ge;jhl;lKk; fpup;f;nfl;Lk;> 15 Ngu; `hf;fpAk; fpup;f;nfl;Lk; tpisahLfpwhu;fs;. 8 Ngu; %d;W tpisahl;LfisAk; tpisahLfpwhu;fs; vdpy;> mf;FOtpy; cs;s khztu;fspd; vz;zpf;ifia fhz;f.

18. gy;fiyf;fof khzth;fspd; fzf;nfLg;gpy;> 64 Ngh; fzpjk;> 94 Ngh; fzpg;nghwp mwptpay;> 58 Ngh;

,aw;gpay; Mfpa ghlq;fisf; fw;fpd;wdh;. 28 Ngh; fzpjKk; ,aw;gpaYk;> 26 Ngh; fzpjKk;

fzpg;nghwp mwptpaYk;> 22 Ngh; fzpg;nghwp mwptpaYk; ,aw;gpaYk; kw;Wk; 14 Ngh; %d;W

ghlq;fisAk; fw;fpd;wdh;. fzf;nfLg;gpy; fye;Jf;nfhz;l khzth;fspd; vz;zpf;ifiaf; fhz;f.

NkYk; xU ghlj;ij kl;Lk; fw;fpd;w khzth;fspd; vz;zpf;ifiaf; fhz;f.

19. xU thndhyp epiyak;; 190 khztu;fsplk; mtu;fs; tpUk;Gk; ,irapd; tiffisj; jPu;khdpf;f xU fzf;nfLg;G elj;jpaJ. 114 Ngu; Nkw;fj;jpa ,iriaAk;> 50 Ngu; fpuhkpa ,iriaAk;>41 Ngu; fu;ehlf ,iriaAk;> 14 Ngu; Nkw;fj;jpa ,iriaAk;> fpuhkpa ,iriaAk;> 15 Ngu; Nkw;fj;jpa ,iriaAk;; fu;ehlf ,iriaAk;> 11 Ngu; fu;ehlf ,iriaAk; fpuhkpa ,iriaAk;> 5 Ngu; %d;W ,irfisAk; tpUk;Gfpd;wdu; vdpy; gpd;tUtdtw;iw fhz;f.

i. ) %d;W tif ,irfisAk; tpUk;ghj khztu;fs; vz;zpf;if> ii. ) ,U tif ,irfis kl;Lk; tpUk;Gk; khztu;fspd; vz;zpf;if>

iii. ) fpuhkpa ,iria tpUk;gp Nkw;fj;jpa ,iria tpUk;ghj khztu;fspd; vz;zpf;if

20. xU fy;Y}upapy; NrUtjw;F 60 khztu;fs;; NtjpapaYk;;> 40 Ngu; ,aw;gpaypYk;; kw;Wk; 30 Ngu; capupapaypYk gjpT nra;Js;sdu;. 15 Ngu; NtjpapaypYk;; ,aw;gpaypYk;;> 5 Ngu; capupapaYk; NtjpapaypYk;> 10 Ngu;; ,aw;gaypYk; capupapaypYk; gjpT nra;Js;sdu;. %d;W ghlq;fspYk; xUtUNk gjpT nra;atpy;iy vdpy;> xU ghlj;jpw;F kl;Lk; gjpT nra;Js;s khztu;fspd; vz;zpf;ifia fhz;f.

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21. 170 thbf;ifahsu;fspy; 115 Ngu;; njhiyf;fhl;rpiaAk;> 110 Ngu; thndhypiaAk;> 130 Ngu; gj;jpupf;iffisAk; gad;gLj;Jf;fpd;wdu;. 85 Ngu; njhiyf;fhl;rp kw;Wk; gj;jpupf;ifiaAk;;> 75 Ngu; njhiyf;fhl;rp kw;Wk; thndhypiaAk; > 95 Ngu; thndhyp kw;Wk; gj;jpupf;ifiaAk;;> 70 Ngu; %d;wpidAk; gad;gLj;Jfpd;wdu; vdpy;> ntd;glj;jpy; tptuq;fisf; Fwpj;J gpd;tUtdtw;iw fhz;f.

i. ) thndhyp kl;Lk; gad;gLj;JNthu; vz;zpf;if> ii. ) njhiyf;fhl;rp kl;Lk; gad;gLj;JNthu; vz;zpf;if >

iii. )njhiyf;fhl;rp kw;Wk; gj;jpupf;ifia gad;gLj;jp thndhypia gad;gLj;jhNjhu;; vz;zpf;if

22. 4000 khztu;fs; gapYk; xU gs;spapy;; 2000 NgUf;F gpnuQ;R> 3000 NgUf;F jkpo; kw;Wk; 500

NgUf;F ,e;jpAk; njupAk;. NkYk> 1500 NgUf;F gpnuQ;R kw;Wk; jkpo;> 300 NgUf;F gpnuQ;R kw;Wk; ,e;jp;> 200 NgUf;F jkpo; kw;Wk; ,e;jp; 50 NgUf;F ,k;%d;W nkhopfSk; njupAk; vdpy; gpd;tUtdtw;iwf; fhz;f.

i. ) %d;W nkhopfSk; njupahjtu;fspd; vz;zpf;if> ii. ) VNjDk; xU nkhopahtJ njupe;jtu;fs;; vz;zpf;if >

iii. ) ,U nkhopfs; kl;LNk njupe;jtu;fs;; vz;zpf;if 23. 120 FLk;gq;fs; cs;s xU fpuhkj;jpy; 93 FLk;gq;fs; rikay; nra;tjw;F tpwifg;

gad;gLj;Jfpd;wdu;. 63 FLk;gq;fs; kz;nzz;izia gad;gLj;Jfpd;wdu;. 45 FLk;gq;fs; rikay; vupthAitg; gad;gLj;Jfpd;wdu;. 45 FLk;gq;fs; tpwF kw;Wk; kz;nzz;iz> 24 FLk;gq;fs; kz;nzz;iz kw;Wk; vupthA > 27 FLk;gq;fs; vupthA kw;Wk; tpwF Mfpaw;iw gad;gLj;Jfpd;wdu;. %d;wpidAk; gad;gLj;Jk; FLk;gq;fspd; vz;zpf;ifiaf; fhz;f.

24. A= {0,1,2,3} B= {1,3,5,7,9} vd;gd ,U fzq;fs; vd;f. f: A → B vd;Dk; rhh;G f(x) : 2x+1 vdf;

nfhLf;fg;gl;Ls;sJ. ,r;rhh;gpid (i) thpirr; Nrhbfspd; fzk; (ii) ml;ltiz (iii) mk;Gf;Fwpg; glk;

(iv) tiuglk; Mfpatw;why; Fwpf;f.

25. A={4,6,8,10} B={3,4,5,6,7} vd;gd ,U fzq;fs; vd;f. f: A → B vd;Dk; rhh;G f(x) : x+1 vdf;

tiuaWf;fg;gl;Ls;sJ. rhh;G f – I (i) thpir Nrhbfspd; fzk; (ii) ml;ltiz (iii) mk;Gf;Fwp

glk; (iv) tiuglk; Mfpatw;why; Fwpf;f.

26. A={5,6,7,8} B={−11,4,7,−10,−7,−9,−13} vd;gd ,U fzq;fs; vd;f. f :{(x,y) : y = 3-2x, x∈A, y∈B}

vd tiuaWf;fg;gl;Ls;sJ. (i) f – d; cWg;Gfis vOJf. (ii) mjd; Jiz kjpg;gfk; fhz;f. (iii)

tPr;rfk; fhz;f. (iv) vt;tifr; rhh;G vdf; fhz;f.

27. A={6,9,15,18,21} B={1,2,4,5,6} vd;gd ,U fzq;fs; vd;f. f: A → B vd;Dk; rhh;G f(x) : vd

tiuaWf;fg;gl;Ls;sJ. rhh;G f – I (i) thpir Nrhbfspd; fzk; (ii) ml;ltiz (iii) mk;Gf;Fwp

glk; (iv) tiuglk; Mfpatw;why; Fwpf;f.

28. rhh;G f : [-3,7) → R fPo;f;fz;lthW tiuaWf;fg;gl;Ls;sJ. f(x) = 4푥 − 1 ; −3 ≤ 푥 < 23푥 − 2 ; 2 ≤ 푥 ≤ 4 2푥 − 3 ; 4 < 푥 < 7

gpd;tUtdtw;iwf; fhz;f. (i) f(5)+f(6) (ii) f(1) – f (-3) (iii) f(-2)- f(4) (iv) ( ) ( )( ) ( )

29. rhh;G f : [1,6) → R fPo;f;fz;lthW tiuaWf;fg;gl;Ls;sJ. f(x) = 3푥 − 10 ; 4 ≤ 푥 < 6

2푥 − 1 ; 2 ≤ 푥 < 4 1 + 푥 ; 1 ≤ 푥 < 2

gpd;tUtdtw;iwf; fdz;f. (i) f(5) (ii) f (3) (iii) f(1) (iv f(2)- f(4) (v) 2f(5)- 3f(1)

30. rhh;G f : [-7,6) → R fPo;f;fz;lthW tiuaWf;fg;gl;Ls;sJ. f(x) = 푥 + 2푥 + 1 ;−7 ≤ 푥 < −5푥 + 5 ; −5 ≤ 푥 ≤ 2 푥 − 1 ; 2 < 푥 < 6

gpd;tUtdtw;iwf; fhz;f. (i) 2f(-4)+3f(2) (ii) f(-7) – f (-3) (iii) ( ) ( )( ) ( )

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2. nka;naz;fspd; njhlh;thpirfSk; njhlh;fSk;

,uz;L kjpg;ngz; tpdhf;fs;

1. n-tJ cWg;G nfhLf;fg;gl;L;s;s 퐶 = ( )( ) vd;w njhlu; tupirapd; Kjy; %d;W cWg;Gfisf; fhz;f.

2. F1 = F2 = 1 kw;Wk; Fn = Fn-1 + Fn-2 , n=3, 4 …… vdpy; njhlh;thpirapd; Kjy; Ie;J cWg;Gfisf; fhz;f 3. xU G+e;Njhl;lj;jpy; Kjy; tupirapy; 23 Nuh[hr; nrbfs;> ,uz;lhk; tupirapy; 21 Nuh[hr; nrbfs;>

%d;whk; tupirapy; 19Nuh[hr; nrbfs; vd;w Kiwapy; Nuh[hr; nrbfs; xU njhlu; tupirmikg;gpy; cs;sd.filrp tupirapy; 5Nuh[hr; nrbfs; ,Ug;gpd>; mg;G+e;Njhl;lj;jpy; vj;jid tupirfs;cs;sd.

4. 2010 y; xUtu; Mz;L Cjpak; &.30,000 vd gzpapy; NrUfpwhu;.NkYk; xt;nthU tUlKk; &.600 I Mz;L Cjpa cau;thf ngWfpwhu;. mtUila Mz;L Cjpak; ve;j Mz;by; &.39,000 Mf ,Uf;Fk;.

5. 125,120,115,110…vd;w $l;Lj; njhlu; tupirapd; nghJ tpj;jpahrk; kw;Wk; 15- tJ cWg;ig fhz;f? 6. √2, 3√2, 5√2 , ……vd;w $l;Lj;njhlupy; 12-tJ cWg;G fhz;f? 7. 4,9,14,……vd;w $l;Lj;njhlupy; 17-tJ cWg;G fhz;f? 8. 24,23¼ ,22½,21¾,……vd;w $l;Lj;njhlupy; 3 vj;jidahtJ cWg;G? 9. 7,13,19,………..25 vd;w $l;Lj;njhlupy; vj;jid cWg;Gfs; cs;sd? 10. xU $l;Lj;njhlh;thpirapd; 9 tJ G+[;[pak; vdpy; 19 tJ cWg;gpd; ,U klq;F 29 tJ cWg;G vd epUgp? 11. Vz; 13 My; tFgLk; <hpyf;f kpif KO vz;fspd; vz;zpf;ifiaf; fhz;f. 12. xU $l;Lj;njhlupy; t10=41, t18=73 vdpy; 27 tJ cWg;G fhz;f? 13. 1,7,13,19,…kw;Wk; 100,95,90,…Mfpa $l;Lj;njhlu; tupirfspd; n-tJ cWg;Gfs; rkk; vdpy;n-d;

kjpg;G ahJ. 14. %d;W vz;fspd; tpfpjk; 2:5:7 vd;f.Kjyhk; vz;> ,uz;lhk; vz;zpypUe;J 7 I fopj;Jg; ngwg;gLk;

vz; kw;Wk; %d;whtJ vz; Mfpad xU $l;Lj;;njhliu Vw;gLj;jpdhy; mt;ntz;fis fhz;

15. ,− , 1,−2, …. vd;w ngUf;Fj; njhlh; thpirapd; 10 tJ cWg;igAk; nghJ cWg;igAk; fhz;f?

16. , , , …. vd;w ngUf;Fj;njhlupd; nghJ tpfpjk; kw;Wk; nghJ cWg;igf; fhz;f?.

17. xU ngUf;Fj; njhlh;thpirapy; 4-tJ kw;Wk; 7-tJ cWg;Gfs; KiwNa 54 kw;Wk;1458 vdpy; mj;njhlu; tupiriaf; fhz;f?

18. xU ngUf;Fj;njhlupy; Kjy; kw;Wk; MwhtJ cWg;Gfs; KiwNa 1/3 kw;Wk;1/729 vdpy; mj;njhlu; tupiriaf; fhz;f?

19. 5,2,4/5,8/25,……vd;w ngUf;Fj;njhlupy; 128/15625 vj;jidahtJ cWg;G? 20. 1,2,4,8,……1024 vd;w ngUf;Fj;njhlupy; vj;jid cWg;Gfs; cs;sd? 21. xU Ez;Zapu; gupNrhjidapy; xt;nthU kzp NeuKk; ghf;Bupahf;fspd; vz;zpf;if ,ul;bg;ghfpwJ.

gupNrhjidapd; njhlf;fj;jpy; 30 ghf;Bupahf;fs; ,Ue;jd. 14 tJ kzp Neu Kbtpy; cs;s ghf;Bupahf;fspd; vz;zpf;ifiaf; fhz;f.

22. xU ngUf;Fj;njhlu; tupirapy; Kjy; %d;W cWg;Gfspd; $Ljy; 13 kw;Wk; mtw;wpd; tu;f;fq;fspd;;; $Ljy; 91 vdpy;;> mj;njhlu; tupiriaf; fhz;f

23. 5+11+17+………+95 vd;w $l;Lj;njhlupd; $Ljy; fhz;f 24. xU $l;Lj; njhlupy; Kjy; 14 cWg;Gfspd; $Ljy; -203 kw;Wk; mLj;j 11 cWg;Gfspd; $Ljy; -572

vdpy;> mj;njhliuf; fhz;f. 25. xU $l;Lj; njhlupy; Kjy; 11 cWg;Gfspd; $Ljy; 44 kw;Wk; mLj;j 11 cWg;Gfspd; $Ljy; 55

vdpy;> mj;njhliuf; fhz;f. 26. 24+21+18+15+……… vd;w $l;Lj;njhlupy; njhlu;r;rpahf vj;jid cWg;Gfis $l;bdhy; $Ljy; -351

fpilf;Fk;? 27. 60,56,52,48…… vd;w $l;Lj; njhlh;thpirapd; Kjy; cWg;gpypUe;J njhlu;r;rpahf vj;jid

cWg;Gfisf; $l;bdhy; $Ljy; 368 fpilf;Fk;? 28. 16 – 48 + 144 – 432 +…………. vd;w ngUf;Fj;njhlupy; cs;s Kjy; 25 cWg;Gfspd; $Ljy; fhz;f 29. 5/2+5/6+5/18+…………. vd;w ngUf;Fj;njhlupy; cs;s Kjy; 20 cWg;Gfspd; $Ljy; fhz;f 30. 2+4+8+………. vd;w ngUf;Fj;njhlupy; Kjy; cWg;gpypUe;J njhlu;r;rpahf vj;jid cWg;Gfis

$l;bdhy; $Ljy; 1022 fpilf;Fk;? 31. 3+9+27+………. vd;w ngUf;Fj;njhlupy; njhlu;r;rpahf vj;jid cWg;Gfisf; $l;bdhy; $Ljy;

1022fpilf;Fk;? 32. nghJ tpfpjk; kpif vz;zhf ,Uf;Fk; xU ngUf;Fj;njhlupy; 4 cWg;Gfs; cs;sd. Kjy; ,uz;L

cWg;Gfspd; $Ljy; 8 kw;Wk; mjd; filrp ,uz;L cWg;gfspd;$Ljy;72vdpy; mj;njhliuf; fhz;f. 33. 1+11+111+…….. vd;w KbTW njhlupy; 20 cWg;Gfs; tiu$Ljy; fhz;f. 34. 1+6+11+16+……+ x = 148 vdpy; x d; kjpg;igf; fhz;f. 35. 1+2+3+……+45 vd;w njhlupd; $Ljy; fhz;f? 36. 26+27+28+……+60 vd;w njhlupd; $Ljy; fhz;f?

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37. 2+4+6+…..+100 vd;w njhlupd; $Ljy; fhz;f? 38. 1+3+5+………….+25 cWg;Gfs; tiu $Ljy; fhz;f? 39. 31+33+…………………+53 vd;w njhlupd; $Ljy; fhz;f? 40. 12+22+32+………+252 vd;w njhlupd; $Ljy; fhz;f? 41. 12+32+52+…………………+512 vd;w njhlupd; $Ljy; fhz;f? 42. 13+23+33+………+203 -d; kjpg;G fhz;f? (my;yJ) 1+8+27+…..+8000 $Ljy; fhz;f? 43. 13+23+33+………+K3=4356 vdpy; K-d; kjpg;G fhz;f? 44. 1+2+3+………….+p= 171 vdpy; 13+23+33+…………………+p3 d; kjpg;G fhz;f? 45. 13+23+33+…………………+k3 = 8281 vdpy; 1+2+3+………….+k d; kjpg;G fhz;f?


1. xU $l;Lj; njhlh;tupirapy; 10 kw;Wk; 18 MtJ cWg;Gfs; KiwNa 41 kw;Wk; 73 vdpy; 27 MtJ cWg;igf; fhz;f.

2. xU $l;Lj;njhlu; tupirapy; %d;whtJ cWg;G 14> NkYk; xd;gjhtJ cWg;G 52 vdpy; 30-tJ cWg;G fhz;f?

3. xU ngUf;Fj;njhlupd; Kjy; cWg;G 375 kw;Wk; mjd; 4 tJ cWg;G 192 vdpy; mjd; nghJ tpfpjj;ijAk;> Kjy; 14 cWg;Gfspd; $LjiyAk; fhz;f.

4. xU ngUf;Fj;njhlupy; ,uz;lhtJ cWg;G 3 kw;Wk; mjd; nghJ tpfpjk;4/5 vdpy; Kjy; 23 cWg;Gfspd; $Ljy; fhz;f?

5. xU $l;Lj; njhlh;thpirapy; mLj;jLj;j %d;W cWg;Gfspd; $Ljy; 6 kw;Wk; mtw;wpd; ngUf;Fj; njhif -120 vdpy; mk;%d;W vz;fisf; fhz;f.

6. xU ngUf;Fj;; njhlh;thpirapy; ehd;fhtJ cWg;G kw;Wk; mjd; VohtJ cWg;G vdpy;>

mg;ngUf;Fj; njhlh; thpiriaf; fhz;f. 7. xU ngUf;Fj;; njhlh;thpirapy; 4 MtJ cWg;G kw;Wk; 7-tJ cWg;Gfs; KiwNa 54 kw;Wk; 1458

vdpy;> mj;njhlh; thpiriaf; fhz;f. 8. xU $l;Lj;njhlu; tupirapy; mLj;jLj;j %d;W cWg;Gfspd; $Ljy; 18 kw;Wk; mt;TWg;Gfspd;;

tu;f;fq;fspd; $Ljy; 140 vdpy; mk;%d;W vz;fisf; fhz;f. 9. 8 – My; tFgLk; midj;J %d;wpyf;f ,ay; vz;fspd; $Ljy; fhz;f.

10. 9 – My; tFgLk; midj;J %d;wpyf;f ,ay; vz;fspd; $Ljy; fhz;f.

11. 300 – f;Fk; 500 – f;Fk; ,ilNaAs;s 11 - My; tFgLk; midj;J ,ay; vz;fspd; $Ljy; fhz;f. 12. xU $l;Lj; njhlhpy; Kjy; 14 cWg;Gfspd; $Ljy; -203 kw;Wk; mjd; mLj;j 11 cWg;Gfspd;

$Ljy; -572 vdpy;> mj;njhliuf; fhz;f. 13. 12 - 22 + 32 - 42 + … vd;w njhlhpd; Kjy; 2n cWg;Gfspd; $Ljy; fhz;f 14. 12 - 22 + 32 - 42 + … vd;w njhlhpd; Kjy; 40 cWg;Gfspd; $Ljy; fhz;f 15. 6 + 66 + 666 + . . . vDk; njhlhpy; Kjy; n cWg;Gfspd; $Ljy; fhz;f. 16. 7+ 77 + 777 + . . . vDk; njhlhpy; Kjy; n cWg;Gfspd; $Ljy; fhz;f. 17. 0.4 + 0.94 + 0.994 + . . . vDk; njhlhpy; Kjy; n cWg;Gfspd; $Ljy; fhz;f. 18. $Ljy; fhz;f : 122 + 132 + 142 + . . . + 352 19. $Ljy; fhz;f : 12 + 32 + 52 + . . . + 512 20. $Ljy; fhz;f : 113 + 123 + 133 + . . . + 283

21. 52+72+92+…………………+392 vd;w njhlupd; $Ljy; fhz;f? 22. $Ljy; fhz;f : 7 + 14 + 21 + . . . + 490 23. 11 nr.kP> 12 nr.kP> 13 nr.kP> ... 24 nr.kP> Mfpadtw;iw KiwNa gf;fq;fshff; nfhz;l 14

rJuq;fspd; nkhj;jg; gug;G fhz;f. 24. 16 nr.kP> 17 nr.kP> 18 nr.kP> ... 30 nr.kP> Mfpadtw;iw KiwNa gf;fq;fshff; nfhz;l 15

fdrJuq;fspd; fdmsTfspd; $Ljy; fhz;f. 25. 1 + 2 + 3 + 4 + . . . + p = 171 vdpy;> 13 + 23 + 33 + . . . + p 3 – d; kjpg;igf; fhz;f. 26. 1 + 2 + 3 + 4 + . . . + n = 120 vdpy;> 13 + 23 + 33 + . . . + n 3 – d; kjpg;igf; fhz;f.

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3.,aw;fzpjk;; ,uz;L kjpg;ngz; tpdhf;fs;

1. ePf;fy; Kiwapy; jPu;f;f. 101 x+ 99 y = 499, 99x +101 y = 501. 2. FWf;Fg; ngUf;fy; Kiwapy; jPu;f;f. 2x + 7y-5 = 0 , -3x + 8y = -11. 3. RUf;Ff.

4. + –d; kjpg;G fhz;f.

5. RUf;Ff. 푋

6. RUf;Ff. ÷

7. RUf;Ff. 푋

8. RUf;Ff. ÷

9. RUf;Ff. 푋

10. RUf;Ff.

11. RUf;Ff:

12. c2-d2 , c(c-d) d; kP.ngh.t fhz;f. 13. 35x5y3z4, 49 x2yz3, 14 xy2z2 Mfpatw;wpd; kP.ngh.t. fhz;f. 14. x2 +3xy+2y2, x2 +5xy+6y2 Mfpatw;wpd; c.ngh.fh. fhz;f. 15. x4 –27a3x kw;Wk; (x -3a)2 Mfpatw;wpd; kP.ngh.t. fhz;f. 16. x3 +y3 , x3 - y3 kw;Wk; x4 +x2 y2 +y4 Mfpatw;wpd; kP.ngh.k. fhz;f. 17. 35a2c3b, 42 a3cb2, 30 ac2b3 Mfpatw;wpd; kP.ngh.k. fhz;f 18. x2y+ xy2 , x2+ xy Mfpatw;wpd; kP.ngh.k. fhz;f 19. (a -1)5 (a+3)2 , (a -2)2(a -1)3(a+3)4 Mfpatw;wpd; kP.ngh.k. fhz;f 20. x3 +x2 -7x- 3 vd;gij (x-3) My; tFf;f fpilf;Fk; <T> kPjp fhz;f 21. 3x3 +4x2 -10x+6 vd;gij (3x-2) My; tFf;f fpilf;Fk; <T> kPjp fhz;f. 22. 2x4+x3-14x2-19x+6 –d; xU fhuzp (2x+1) My; tFf;Fk;NghJ x3 +ax2 –bx-6 vd;gJ <thdhy; a -kw;Wk; b-d;

kjpg;G kw;Wk; kPjpiaf; fhz;f 23. x4 +10x3 +35x2 +50x+29 vd;w gy;YWg;gf; Nfhitia x+4 My; tFf;Fk; NghJ x3 -ax2 +bx+6 vd;gJ <thdhy; a -

kw;Wk; b-d; kjpg;G kw;Wk; kPjpiaf; fhz;f 24. x3 -6x2 +11x- 6 vd;w gy;YWg;G Nfhitf;F (x-1) xU fhuzp vd epWTf. 25. 16x2 -24x+9 d; tu;f;f %yk; fhz;f

26. ( ) ( ) ( )( ) ( ) ( )

d; tu;f;f %yk; fhz;f

27. 6x2 -5x-25 = 0 I fhuzp Kiwapy; jPu;T fhz;f. 28. x2 -7x+12 = 0 I R+j;jpu Kiwapy; jPu;T fhz;f. 29. 7+√3 kw;Wk; 7-√3 Mfpatw;iw %yq;fshff; nfhz;l ,Ugbr;rkd;ghL xd;wpid mikf;f. 30. 3+√7, 3-√7 Mfpatw;iw %yq;fshff; nfhz;l ,Ugb rkd;ghl;bid mikf;fTk;

31. √ , √ Mfpatw;iw %yq;fshff; nfhz;l ,Ugb rkd;ghl;bid mikf;fTk;

32. 3x2 - 6x + 4 = 0 vd;w rkd;ghl;bd; %yq;fs; 훼,훽 vdpy;> 훼 + 훽 d; kjpg;G fhz; 33. jPu;: √5x2+2x-3√5 = 0 34. x2 -11x-10 = 0 vDk; rkd;ghl;bd; %yq;fspd; jd;ikia Muha;f. 35. 4x2 -28x+49 = 0 vDk; rkd;ghlbd; %yq;fspd; jd;ikia Muha;f 36. x2 -2x(1+3k)+7(3+2k) = 0d;; %yq;fs; nka;naz;fs; kw;Wk;rkk; vdpy; k d;kjpg;G fhz; 37. 2x2 -10x+k = 0 d;; %yq;fs; nka;naz;fs; kw;Wk; rkk; vdpy; k d; kjpg;G fhz;f. 38. 3p2x2 -2pqx+ q2 = 0 d;; %yq;fs; nka;naz;fs; my;y vd epWTf. 39. a,b,c kw;Wk; d≠0 vd mike;j(a2+b2)x2 -2(ac+bd)x+c2+d2= 0 vd;w rkd;ghl;bd; %yq;fs; rkk; vdpy;a/b= c/d vd

epWTf. 40. 2x2 – 3x – 1 = 0 vd;w rkd;ghl;bd; %yq;fs; 훼 kw;Wk; 훽 vdpy;> NkYk; 훼-훽 - d; kjpg;igf; fhz;f. 41. rkd;ghL (1+m2)x2+2mcx+ c2 -a2 = 0 vd;w rkd;ghl;bd; %yq;fs; rkk; vdpy; c2=a2(1+m2) vd epWTf. 42. ,U njhlh;e;j xw;iwg;gil vz;fspd; $Ljy; 20 vdpy; mt;ntz;fisf; fhz;f.

Ie;J kjpg;ngz; tpdhf;fs;: 1. jPh;: 3x – 5y = -16 , 2x - 5y = 31 2. ePf;fy; Kiwapy; jPh;: 3x + 4y = -25 , 2x - 3y = 6 3. ePf;fy; Kiwapy; jPh;: 101x +99y = 499 , 99x + 101y = 501

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4. Xh; <hpyf;f vz;zpy; xd;whk; ,l ,yf;f vz;> gj;jhk; ,l ,yf;f vz;izg; Nghy; ,U klq;fhf cs;sJ. ,yf;fq;fs; ,lk; khw;wpdhy; fpilf;Fk; Gjpa vz;> nfhLf;fg;gl;l vz;iztpl 27 mjpfk; vdpy;> nfhLf;fg;gl;l <hpyf;f vz;iz fz;Lgpb.

5. 11 ngd;rpy;fs; kw;Wk; 3 mopg;ghd;fspd; nkhj;j tpiy & 50. NkYk; 8 ngd;rpy;fs; kw;Wk; 3 mopg;ghd;fspd; nkhj;j tpiy & 38 vdpy;> xU ngd;rpy; kw;Wk; xU mopg;ghdpd; tpiyiaf; fhz;f.

6. FWf;F ngWf;fy; Kiwia gad;gLj;jp gpd;tUk; rkd;ghLfis jPh;. 3x + 4y = 24 , 20x - 11y = 47 7. 3 ehw;fhypfs;; kw;Wk; 2 Nkirfspd; nkhj;j tpiy & 700. NkYk; 5 ehw;fhypfs;; kw;Wk; 3Nkirfspd; nkhj;j

tpiy & 1100 vdpy;> 2 ehw;fhypfs;; kw;Wk; 3 Nkirfspd; nkhj;j tpiyiaf; fhz;f.

8. fhuzpg;gLj;Jf: 2x3 – 3x2 – 3x + 2 vDk; Nfhitia xUgbf; fhuzpfshf fhuzpg;gLj;Jf 9. fhuzpg;gLj;Jf: x3 – 3x2 – 10x + 24 10. fhuzpg;gLj;Jf: x3 – 2x2 – 5x + 6 11. fhuzpg;gLj;Jf: x3 – 23x2 + 142x -120 12. fhuzpg;gLj;Jf: x3– 7x + 6 13. fhuzpg;gLj;Jf: 2x3 + 11x2 – 7x - 6 14. fhuzpg;gLj;Jf: x3 – 5x2 – 2x + 24 15. 6(2x2 – 3x-2), 8(4x2 + 4x+1),12(2x2 + 7x+3)Mfpa gy;YWg;Gf; Nfhitfspd; kP. ngh. t fhz;f.

16. 3x4 + 6x3 - 12x2 – 24x kw;Wk; 4x4 + 14x3 + 8x2 – 8x Mfpa gy;YWg;Gf; Nfhitfspd; kP. ngh. t fhz;f.

17. x4 + 3x3 - x – 3 kw;Wk; x3 + x2 – 5x + 3 Mfpa gy;YWg;Gf; Nfhitfspd; kP. ngh. t fhz;f.

18. 2x3 + 2x2 + 2x +2 kw;Wk; 6x3 + 12x2 + 6x + 12 Mfpa gy;YWg;Gf; Nfhitfspd; kP. ngh. t fhz;f.

19. RUf;Ff: x x

20. RUf;Ff: x x

21. RUf;Ff: ÷

22. RUf;Ff: ÷

23. P = , Q = vdpy;> - If; fhz;f.

24. tHf;f%yk; fhz;f: (6x2 + 5x - 6) (6x2 – x - 2) (4x2 + 8x + 3) 25. (2x2-5x+2) (3x2-5x-2) (6x2-x-1) d; tu;f;f Kyk; fhz;f 26. x4 - 10x3 + 37x2 - 60x + 36 - d; tHf;f%yj;ijf; fhz;f. 27. x4 - 6x3 + 19x2 - 30x + 25 - d; tHf;f%yj;ijf; fhz;f. 28. x4 -4x3 +10x2-12x +9 d; tu;f;f%yk; fhz;f 29. 9x4 - 6x3 + 7x2 - 2x + 1 - d; tHf;f%yj;ijf; fhz;f. 30. 4 + 25x2 - 12x - 24x3 +16x4 d; tHf;f%yj;ijf; fhz;f. 31. m – nx + 28x2 + 12x3 + 9 x4 – MdJ xU KO th;f;fk; vdpy; m, n Mfpatw;wpd; kjpg;Gfisf; fhz;f.

32. 4x4 - 12x3 + 37x2 + ax + b – MdJ xU KO th;f;fk; vdpy; a, b Mfpatw;wpd; kjpg;Gfisf; fhz;f.

33. ax4 - bx3 + 40x2 + 24x + 36 – MdJ xU KO th;f;fk; vdpy; a, b Mfpatw;wpd; kjpg;Gfisf; fhz;f.

34. xU vz; mjd; jiyfPop Mfpatw;wpd; $Ljy; vdpy;> me;j vz;izf; fhz;f.

35. ,uz;L kpif vz;fspd; tpj;jpahrk; 45. rpwpa vz;zpd; th;f;fk; MdJ> nghpa vz;zpd; ehd;F klq;fpw;Fr; rkk; vdpy;> me;j vz;fisf; fhz;f.

36. xU nrt;tf tbt epyk; 20 kP ePsk;> 14 kP mfyk; nfhz;lJ. mijr;Rw;wpYk; ntspg;Gwj;jpy; mike;Js;s rPuhd mfyKs;s ghijapd; gug;G 111 r.kP. vdpy; > ghijapd; mfyk; vd;d?

37. mirtw;w ePhpy; ,ae;jpug;glfpd; Ntfk; kzpf;F 15 fp.kP vd;f. mg;glF ePNuhl;lj;jpd; jpirapy; 30 fp.kP J}uk; nrd;W> gpwF vjph; jpirapy; jpUk;gp 4 kzp 30 epkplq;fspy; kPz;Lk; Gwg;gl;l ,lj;jpw;F jpUk;gp te;jhy; ePhpd; Ntfj;ijf; fhz;f.

38. xU Ntiyia nra;a A f;F B ia tpl 6 ehl;fs; Fiwthf Njitg;gLfpwJ. ,UtUk; Nrh;e;Jmt;Ntiyiar; nra;jhy; mij 4 ehl;fspy; Kbf;f ,aYk;.vdpy; B jdpNa mt;Ntiyia vj;jid ehl;fspy; Kbf;f ,aYk;?.

39. xU tUlj;jpw;F Kd;G> xUthpd; taJ mtUila kfdpd; taijg;Nghy; 8 klq;F. jw;NghJ mtUila taJ> kfdpd; tajpd; th;f;fj;jpw;Fr; rkk; vdpy;> mth;fSila jw;Nghija taijf; fhz;f.

40. 3x2 - 5x + 2 = 0 vd;w rkd;ghl;bd; %yq;fs; 훼,훽 vdpy;> gpd;tUtdtw;wpd; kjpg;Gfisf; fhz;f.

(i) + (ii) 훼 − 훽 (iii) +

41. 5x2 - px + 1 = 0 vd;w rkd;ghl;bd; %yq;fs; 훼 kw;Wk; 훽 vd;f.NkYk; 훼 - 훽 = 1 vdpy;> p – d; kjpg;igf; fhz;f. 42. 3x2 +kx -81=0 vd;w rkd;ghl;bd; xU %yk; kw;nwhU %yj;jpd; th;f;fnkdpy;> k – d; kjpg;igf; fhz;f.

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4.mzpfs;

,uz;L kjpg;ngz; tpdhf;fs; 1. aij = │2i – 3j│vd;w cWg;Gfisf; nfhz;l thpir 2x3 cs;s mzp A = [aij] –apid mikf;fTk;. 2. aij = 2i – j vd;w cWg;Gfisf; nfhz;l thpir 2x2 cs;s mzp A = [aij] –apid mikf;fTk;. 3. aij = ij vd;w cWg;Gfisf; nfhz;l thpir 2x2 cs;s mzp A = [aij] –apid mikf;fTk;.

4. aij = ׀ ׀vd;w cWg;Gfisf; nfhz;l thpir 3x2 cs;s mzp A = [aij] –apid mikf;fTk;.

5. gpd;tUk; mzpr;rkd;ghl;bypUe;J x, y kw;Wk; z – fspd; kjpg;Gfisf; fhz;f.

5푥 + 2 푦 − 4

0 4푧 + 6 = 12 −80 2

6. A= 3 25 1 kw;Wk; 퐵 = 8 −1

4 3 vdpy; C = 2A + B vd;w mzpiaf; fhz;f.

7. A= 4 −25 −9 kw;Wk; 퐵 = 8 2

−1 −3 vdpy; 6A - 3B vd;w mzpiaf; fhz;f.

8. 퐴 =2 34 15 0

vdpy; A - apd; epiu epuy; khw;W mzpiaf; fhz;f.

9. 퐴 = 8 5 21 −3 4

vdpy; AT kw;Wk; (AT)T Mfpatw;iwf; fhz;f.

10. A = 1 2 32 4 − 53 − 5 6

vdpy; (AT)T = A vd;gijr; rhpghh;f;f.

11. 퐴 = 8 3 25 9 1 kw;Wk; 퐵 = 1 −1

3 0 vdpy;> A+B ,Uf;Fkhdhy;> mjidf; fhz;f.

12. 3 −25 1 4 1

2 7 vd;w mzpfspd; ngUf;fiyf; fhz;f.

13. 2 9 − 3 4 −1 0

4 2−6 7−2 1

vd;w mzpapd; ngUf;fiyf; fhz;f. (ngUf;f KbAkhdhy;)

14. 퐴 = 5 6 − 2 31 0 4 2 kw;Wk; 퐵 = 3 −1 4 7

2 8 2 3 vdpy;> A+B -If; fhz;f.

15. A= 2 3−9 5 − 1 5

7 −1 vdpy;> A – d; $l;ly; Neh;khW mzpiaf; fhz;f.

16. 푎 23 + 푏 −1

1 = 105 vdpy; a,b ,d; kjpg;Gfis fhz;f.

17. jPh;T fhz;f. 푦

3푥 = 6 − 2푥31 + 4푦

18. 2푥 + 푦푥 − 3푦 = 5

13 vdpy; x,y ,d; jPh;Tfis fhz;f.

19. ngUf;Ff. 6−3 (2 − 7)

20. A= 3 25 1 >퐵 = 1 −2

2 3 kw;Wk; O= 0 00 0 vdpy; gpd;tUtdtw;iw rhpghh;.

i) A+B =B+A, ii) A+(-A)=0=(-A)+A 21. A= 1 3

9 −6 vdpy; AI=IA=A vd;gij rhpghh;f;f. ,q;F I vd;gJ thpir 2 nfhz;l myF mzp.

22. 1 23 3

푥 00 푦 = 푥 0

9 0 vdpy; x kw;Wk; y –fspd; kjpg;Gfis fhz;f.


1. 2X + 3Y = 2 34 0 kw;Wk; 3X+2Y = 2 −2

−1 5 vdpy; X kw;Wk; Y Mfpa mzpfisf; fhz;f.

2. A =4 1 21 −2 30 3 2

B = 2 0 46 2 82 4 6

kw;Wk; C= 1 2 −35 0 21 −1 1

vdpy; A+(B+C) = (A+B) +C vd;gij

rhpghh;.

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3. jPh;f;f: +3 =

4. jPh;T fhz;f: 3 24 5

푥푦 = 8

13

5. A = 3 2−1 4 B = −2 5

6 7 kw;Wk; C = 1 1−5 3 vdpy; A(B+C) = AB + AC vd;gij rhpghh;f;fTk;.

6. A = 1 −12 3 vdpy; A2 - 4A + 5 I2 = 0 vd epWTf.

7. A = −1 2 1 1 2 3 , B =

012

kw;Wk; C = (2 1) vdpy; (AB)C = A (BC) vd;gij rhpghh;

8. A= 3 24 0 kw;Wk; 퐵 = 3 0

3 2 vdpy; AB kw;Wk; BA Mfpatw;iwf; fhz;f. mit rkkhf

,Uf;Fkh?

9. A= 8 − 7−2 4 0 3

kw;Wk; 퐵 = 9 −3 26 −1− 5

vdpy; AB kw;Wk; BA Mfpatw;iwf; fhz;f.

10. jPh;f;f: (푥 1) 1 0−2 −3

푥5 = (0)

11. A= 1 −4−2 3 kw;Wk; 퐵 = −1 6

3 −2 vdpy; (A+B)2 ≠ A2+2AB+B2 vd epWTf.

12. A= 5 27 3 kw;Wk; 퐵 = 2 −1

−1 1 vdpy; (AB)T = BTAT vd;gij rhpghh;.

13. A= 5 37 5 X =

푥푦 kw;Wk; C = −5

−11 kw;Wk; AX = C vdpy;>x kw;Wk; y – fspd; kjpg;Gfisf; fhz;f.

14. 3 51 2

kw;Wk; 2 −5−1 3

Mfpad mzpg; ngUf;fiyg; nghUj;J xd;Wf;nfhd;W Neh;khW mzp

vd epWT.

15. A=−2 4 5

kw;Wk; 퐵 = ( 1 3 − 6) vd;w mzpfSf;F (AB)T = BTAT vd;gij rhpghh;.

16. A= 푎 푏푐 푑 kw;Wk; I2= 1 0

0 1 vdpy; A2-(a+d)A=(bc-ad)I2 vd epWTf.

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5. Maj;njhiy tbtpay;

,uz;L kjpg;ngz; tpdhf;fs; 1. (3,5) kw;Wk; (8,10) vd;w Gs;spfis Nru;f;Fk; Nfhl;Lj;Jz;bid 2:3 vd;w tpfpjj;jpy; cl;Gwkhf

gpupf;Fk; Gs;spiaf; fhz;f. 2. (-3,5) kw;Wk; (4,-9) vd;w Gs;spfis Nru;f;Fk; Nfhl;Lj;Jz;bid 1:6 vd;w tpfpjj;jpy; cl;Gwkhf

gpupf;Fk; Gs;spapd; mr;Rj;njhiyTfisf; fhz;f. 3. (3,4) kw;Wk; (-6,2) vd;w Gs;spfis ,izf;Fk;; Nfhl;Lj;Jz;bid 3:2 vd;w tpfpjj;jpy;

ntspg;;Gwkhf gpupf;Fk; Gs;spiaf; fhz;f 4. (3,0), (-1,4) vd;w Gs;spfis ,izf;Fk; Nfhl;Lj;Jz;bd; eL;g;Gs;spiaf; fhz;f. 5. (1,-1), (-5,3) vd;w Gs;spfis ,izf;Fk; Nfhl;Lj;Jz;bd; eL;g;Gs;spiaf; fhz;f. 6. A(4,-6), B(3,-2),C(5,2)Mfpa Gs;spfis cr;rpfshff; nfhz;l Kf;Nfhzj;jpd; eLf;Nfhl;L ikak;

fhz;f. 7. (1,3), (2,7) ,(12,-16) Mfpa Gs;spfis cr;rpfshff; nfhz;l Kf;Nfhzj;jpd; eLf;Nfhl;L ikak;

fhz;f 8. Gs;sp (1,3) I eLf;Nfhl;L ikakhff; nfhz;l Kf;Nfhzj;jpd; ,U Kidfs; (-7,6) kw;Wk; (8,5)

vdpy;> Kf;Nfhzj;jpd; %d;whtJ Kidiaf; fhz;f.

9. A(-6,-5), B(-6,4) vd;gd ,U Gs;spfs; vd;f. Nfhl;Lj;Jz;L AB –apd; Nky; AP = AB vd;wthW mike;Js;s Gs;sp P –iaf; fhz;f.

10. rha;T -3 MfTk; y ntl;L 4 MfTk; cs;s Neu;f;Nfhl;bd; rkd;ghL ahJ? 11. rha;Tf; Nfhzk; 450 MfTk; y ntl;L 2/5 MfTk; cs;s Neu;f;Nfhl;bd; rkd;ghL ahJ. 12. 4x-2y+1=0 vd;w Neu;f;Nfhl;bd; rha;T kw;Wk; y ntl;L fhz;f. 13. 5x+3y-15=0vd;w Neu;f;NfhlhdJ Ma mr;Rfspy; Vw;glj;Jk; ntl;Lj;Jz;Lfisf; fhz;f. 14. 2x-y+16=0 vd;w Neu;f;NfhlhdJ Ma mr;Rfspy; Vw;glj;Jk; ntl;Lj;Jz;Lfisf; fhz;f.

15. xU Neu;f;Nfhl;bd; x ntl;L kw;Wk; y ntl;L

vdpy;> mf;Nfhl;bd; rkd;ghl;il fhz;

16. Ma mr;Rfspy; 5,3 vd;w ntl;Lj;Jz;Lfis Vw;gLj;Jk; Neu;f;Nfhl;bd;rkd;ghl;il fhz;f. 17. (-1,1), (2,-4) vd;w Gs;spfis ,izf;Fk; Nfhl;bd; rkd;ghL ahJ. 18. y=7 vd;w Nfhl;bw;F nrq;Fj;jhdJk;(1>2)vd;w Gs;sp topahf nry;tJkhd Neh;Nfhl;bd; rkd;ghL

fhz;f. 19. xU tl;lj;jpd; ikak; (-6,4) mt;tl;lj;jpd; tpl;lj;jpd; xU Kidg;Gs;sp Mjpg;Gs;sp vdpy; kw;nwhU

Kidg;Gs;spiaf; fhz;f. 20. (3,-2), (7,2) vd;w Gs;spfis ,izf;Fk;; Nfhl;bd; rha;T ahJ 21. (2,-4) kw;Wk; Mjpg;Gs;spia ,izf;Fk;; Nfhl;bd; rha;T ahJ 22. rha;T -4 MfTk; (1,2) vd;w Gs;sp topahfTk; nry;Yk; Neu;f;Nfhl;bd; rkd;ghL ahJ 23. rha;T 1/3 MfTk; (-2,3) vd;w Gs;sp topahfTk; nry;Yk; Neu;f;Nfhl;bd; rkd;ghL ahJ. 24. 3x +2y -12 =0, 6x +4y +8 =0 vd;w NfhLfs; xd;Wf;nfhd;W ,izahdit vd ep&gp. 25. x +2y +1 =0, 3x +6y +2 =0 vd;w NfhLfs; xd;Wf;nfhd;W ,izahdit vd ep&gp. 26. x+ 2y+1=0, 2x -y +5 =0 vd;w NfhLfs; xd;Wf;nfhd;W nrq;Fj;J vd ep&gp. 27.

= 푥 − 푝 kw;Wk; ax +5 = 3y vd;w Neh;f;NfhLfs; xd;Wf;nfhd;W ,iz vdpy; a–d; kjpg;ig fhz;.

28. 5x- 2y-9=0,ay+2x-11=0 Mfpa NfhLfs; xd;Wf;nfhd;W nrq;Fj;J vdpy; a–d; kjpg;ig fhz;. 29. 3x-y +7=0vd;w Nfhl;bw;F ,izahfTk;;(1,-2)vd;w Gs;sp topahfTk; nry;Yk; Neu;f;Nfhl;bd; rkd;ghL fhz;f. 30. x- 2y + 3=0 vd;w Nfhl;bw;F nrq;Fj;jhfTk;(1,-2) vd;w Gs;sp topahfTk; nry;Yk; Neu;f;Nfhl;bd; rkd;ghL fhz;f. 31. A(4,-6), B(3,-2) ,C(5,2) Mfpad Kf;Nfhzk; ABC d; cr;rpfs;. cr;rp A ypUe;J tiuag;gLk;

eLf;Nfhl;bd; rkd;ghl;ilf; fhz;f 32. P(1,-3), Q(-2,5) ,R(-3,4) Mfpad Kf;Nfhzk; PQR d; cr;rpfs;. cr;rp R ypUe;J tiuag;gLk;

eLf;Nfhl;bd; rkd;ghl;ilf; fhz;f. 33. A(2,1), B(6,-1) ,C(4,11) Mfpad Kf;Nfhzk; ABC d; cr;rpfs;. cr;rp A ypUe;J tiuag;gLk;

Fj;Jf;Nfhl;bd; rkd;ghl;ilf; fhz;f 34. A(3,4) ,B(-1,2) vd;w Gs;spfisr; Nru;f;Fk; Neu;f;Nfhl;bd; ikaf;Fj;Jf;Nfhl;bd; rkd;ghl;bidf;

fhz;f


1. (7>3)>(6>1)>(8>2)kw;Wk;(p>4) vd;gd Xh; ,izfuj;jpd; thpirg;gbmike;j cr;rpfs;vdpy; p–d; kjpg;G fhz;f.

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2. gphpT R+j;jpuj;ij gad;gLj;jp (1>0)> (5>3)> (2>7) kw;Wk; (-2>4) vd;w thpirapy; vLj;Jf;nfhs;sg;gl;l Gs;spfs; Xh; ,izfuj;jpd; cr;rpfs; MFk; vd epWTf.

3. (1>2)> (-3>4) kw;Wk; (-5>-6) Mfpatw;iw Kidfshff; nfhz;l Kf;Nfhzj;jpd; gug;igf; fhz;f. 4. (5,2) ,(3,-5) kw;Wk; (-5,-1) Mfpa Gs;spfis cr;rpfshf nfhz;l Kf;Nfhzj;jpd; gug;G fhz;f. 5. (-4,-5) ,(4,5) kw;Wk; (-1,-6) Mfpa Gs;spfis cr;rpfshf nfhz;l Kf;Nfhzj;jpd; gug;G fhz;f. 6. A(6>7)> B(-4>1) kw;Wk; C(a>-9) Mfpatw;iw Kidfshff; nfhz;l ∆ABC –d; gug;G 68 r.myFfs; vdpy;

a –d; kjpg;ig fhz;f.

7. (0,0),(4,a) ,(6,4) Mfpa Gs;spfis cr;rpfshff; nfhz;l Kf;Nfhzj;jpd; gug;G 17 r.myFfs; vdpy; a - d; kjpg;igf; fhz;f

8. (m,m),(4,5) ,(6,-1) Mfpa Gs;spfis cr;rpfshf nfhz;l Kf;Nfhzj;jpd; gug;G 9 r.myFfs; vdpy; m - d; kjpg;igf; fhz;f

9. A(2>3)> B(4>0) kw;Wk; C(6>-3) Mfpa Gs;spfs; xNu Neh;f;Nfhl;by; mike;Js;sd vd epUgp.

10. (4,3) ,(1,2) kw;Wk; (-2,1) vd;w Gs;spfs; xNu Neu;f;Nfhl;by; mikAk; Gs;spfsh vd Muha;f. 11. A(2>-5)> B(3>-4) kw;Wk; C(9>k) Mfpa Gs;spfs; xNu Nfhliktd vdpy; k –d; kjpg;G fhz;f.

12. (k,k), (2,3) kw;Wk; (4,-1) Mfpa Gs;spfs; xU Nfhliktd vdpy; k - d; kjpg;g fhz;f 13. (a>0)> (0>b) Mfpa Gs;spfis ,izf;Fk; Neh;f;Nfhl;Lj; Jz;bd; Nky; mike;Js;s VNjDk; xU

Gs;sp P(x,y) vdpy; + = 1 vd epWTf. ,q;F a,b ≠0.

14. A(h>0)> B(a>b) kw;Wk; C(o>k) Mfpa Gs;spfs; xNu Neh;f;Nfhl;by; mikAk; Gs;spfs; vdpy; + = 1 vd epWTf. ,q;F h,k ≠0.

15. (-4>-2)> (-3>-5)> (3>-2) kw;Wk; (2>3) Mfpatw;iw Kidfshff; nfhz;l ehw;fuj;jpd; gug;igf; fhz;f.

16. (6,9), (7,4), (4,2) kw;Wk; (3,7) Mfpatw;why; mikf;fg;gLk; ehw;fuj;jpd; gug;G fhz;f. 17. (-3,4), (-5,-6), (4,-1) kw;Wk; (1,2) Mfpa Gs;spfis cr;rpfshf nfhz;l ehw;fuj;jpd; gug;G fhz;f. 18. (-4,5), (0,7), (5,-5) kw;Wk; (-4,-2) Mfpa Gs;spfis cr;rpfshf nfhz;l ehw;fuj;jpd; gug;G fhz;f. 19. (6>7)> (2>-9) kw;Wk; (-4>1) Mfpad xU Kf;Nfhzj;jpd; Kidfs; vdpy; Kf;Nfhzj;jpd;

eLf;NfhLfspd; rha;Tfisf; fhz;f.

20. A(-5>7)> B(-4>-5) kw;Wk; C(4>5) Mfpad ∆ABC -d; Kidfs; vdpy; Kf;Nfhzj;jpd; Fj;Jauq;fspd; rha;Tfisf; fhz;f.

21. A(2>1)> B(-2>3) kw;Wk; C(4>5) Mfpad ∆ABC -d; cr;rpfs; vdpy; cr;rp A – apypUe;J tiuag;gLk; eLf;Nfhl;bd; rkd;ghl;ilf; fhz;f.

22. (2>2) vd;w Gs;sp topr;nry;tJk;> ntl;Lj;Jz;Lfspd; $Ljy; 9 MfTk; nfhz;l Neh;NfhLfspd; rkd;ghl;bidf; fhz;f.

23. 2x+y-3=0 , 5x+y-6=0 Mfpa Neh;NfhLfs; re;jpf;Fk; Gs;sp topahfTk;> (1>2)> (2>1)Mfpa Gs;spfis ,izf;Fk; Neh;Nfhl;bw;F ,izahfTk; cs;s Neh;Nfhl;bd; rkd;ghl;ilf; fhz;f.

24. 5x-6y=1 , 3x+2y+5=0 Mfpa Neh;NfhLfs; re;jpf;Fk; Gs;sp topahfTk;> 3x-5y+11=0 vd;w Neh;f;Nfhl;bw;F nrq;Fj;jhfTk; mikAk; Neh;Nfhl;bd; rkd;ghl;ilf; fhz;f.

25. 3x -y+9 = 0 , x +2y =4 Mfpa Neu;f;NfhLfs; re;jpf;Fk; Gs;spAld; 2x +y-4 = 0 , x -2y +3=0 Mfpa Neu;f;NfhLfs; ntl;Lk;; Gs;spia ,izf;Fk; Neu;f;Nfhl;bd; rkd;ghl;ilf; fhz;f.

26. ∆ABC -d; Kidfs; A(2>-4)> B(3>3)> C(-1>5) vdpy; B – apypUe;J tiuag;gLk; Fj;JNfhl;L topr;nry;Yk; Neh;f;Nfhl;bd; rkd;ghl;ilf; fhz;f.

27. ∆ABC -d; Kidfs; A(-4>-4)> B(8>4)> C(8>10) vdpy; A – apypUe;J tiuag;gLk; eLf;Nfhl;L topr;nry;Yk; Neh;f;Nfhl;bd; rkd;ghl;ilf; fhz;f.

28. xU tl;lj;jpd; ,U tpl;lq;fspd; rkd;ghLfs; x+2y=7 , 2x+y=8 kw;Wk; tl;lj;jpd; kPJ mike;Js;s xU Gs;sp (0>-2) vdpy;> ,t;tl;lj;jpd; Muj;ij fhz;f.

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6. tbtpay; ,U kjpg;ngz; tpdhf;fs;:

1. D kw;Wk; E Mfpa Gs;spfs; KiwNa∆ABC – d; gf;fq;fs; AB kw;Wk; AC–fspy; DE ∥ BC vd;wthW

cs;sd. NkYk;> AD=6 nr.kP>DB=9nr.kP kw;Wk; AE=8nr.kP vdpy;AC iaf; fhz;f. 2. D kw;Wk; E Mfpa Gs;spfs; KiwNa∆ABC – d; gf;fq;fs; AB kw;Wk; AC–fspy; DE ∥ BC vd;wthW

cs;sd. NkYk;> AD=4x-3 nr.kP>DB=3x-1nr.kPkw;Wk;AE=8x-7nr.kP kw;Wk;EC=5x-3vdpy; x iaf; fhz;f.

3. E kw;Wk; F vd;w Gs;spfs; KiwNa ∆PQR–d; gf;fq;fs; PQkw;Wk; PRMfpatw;wpd; kPJ mike;Js;sd. NkYk; PE=3.9 nr.kP>EQ=3nr.kP,PF=3.6 nr.kP kw;Wk; FR=2.4nr.kP vdpy; EF ∥ QR ia rhpghh;f;f.

4. ∆ABC – y; DE ∥ BC kw;Wk; = > AE = 3.7 nr.kPP vdpy;> EC – iaf; fhz;f.

5. ∆PQR– d; gf;fq;fs; PQ kw;Wk; PR fspd; kPJ mike;j Gs;spfs; S kw;Wk; T vd;f. NkYk; ST ∥ QR, PR = 5.6 nr.kP kw;Wk; = > vdpy;> PT – iaf; fhz;f.

6. ∆ ABC – y; ∠퐴 vd;w Nfhzj;jpd; cl;Gw ,U rkntl;b AD MdJ> gf;fk; BC –ia D –y; re;jpf;fpwJ. BD =2.5 nr.kP> AB =5 nr.kP kw;Wk; AC =4.2 nr.kP vdpy; DC ia fhz;f.

7. ∆ ABC – y; ∠퐴 vd;w Nfhzj;jpd; cl;Gw ,U rkntl;b AD MdJ> gf;fk; BC –ia D –y; re;jpf;fpwJ. AB =5.6 nr.kP> AC =6 nr.kP kw;Wk; DC =3 nr.kP vdpy; AC ia fhz;

8. ∆ ABC – y; ∠퐴 vd;w Nfhzj;jpd; cl;Gw ,U rkntl;b AD MdJ> gf;fk; BC –ia D –y; re;jpf;fpwJ. AB =x AC =x-2 kw;Wk; BD =x+2 , DC =x-1 vdpy; x- ia fhz;

9. ∆ ABC – y; ∠퐴 vd;w Nfhzj;jpd; ntspg;;Gw ,U rkntl;b MdJ BC –d; ePl;rpia E –y; re;jpf;fpwJ. AB =10 nr.kP> AC =6 nr.kP kw;Wk; BC =12 nr.kP vdpy; CE ia fhz;

10. glj;jpy; AP =3 nr.kP AR=4.5nr.kP AQ =6 nr.kP AB =5 nr.kP kw;Wk; AC =10 nr.kP vdpy; AD ia fhz;

11. gpjhfu]; Njw;wj;ij (ghe;jad;)vOJ. 12. njhLNfhL ehz; Njw;wj;ij vOJ. 13. xU tl;lj;jpy; AB> CD vd;Dk; ,U ehz;fs; xd;iwnahd;W cl;Gwkhf P –apy; ntl;b

nfhs;fpd;wd. NkYk; CP =4 nr.kP> AP =8 nr.kP kw;Wk; PB =2 nr.kP vdpy; PD iaf; fhz;. 14. xU tl;lj;jpy; AB> CD vd;Dk; ,U ehz;fs; xd;iwnahd;W cl;Gwkhf P –apy; ntl;b

nfhs;fpd;wd. NkYk; AP =12 nr.kP> AB =15 nr.kP kw;Wk; CP = PD vdpy; CD iaf; fhz;. 15. AB> CD vd;Dk; ,U ehz;fs; tl;lj;jpw;F ntspNa P –apy; ntl;bf; nfhs;fpd;wd. NkYk; AB = 4

nr.kP> BP = 5 nr.kP kw;Wk; PD = 3 nr.kP vdpy; CD iaf; fhz;f. 16. AB> CD vd;Dk; ,U ehz;fs; tl;lj;jpw;F ntspNa P –apy; ntl;bf; nfhs;fpd;wd. NkYk; BP = 3

nr.kP> CP = 6 nr.kP kw;Wk; CD = 2 nr.kP vdpy; AB iaf; fhz;f. 17. glj;jpy; x –d; kjpg;G fhz;f.

18. glj;jpy; x –d; kjpg;G fhz;f. 19. glj;jpy; TP xU njhLNfhL. A,B vd;gd tl;lj;jpd; kPJs;s Gs;spfs;. ∠퐵푇푃=72 kw;Wk; ∠ATB = 43 vdpy; ∠ABT If; fhz;f.


1. mbg;gil tpfpjrkj; Njw;wk; my;yJ Njy;]; Njw;wj;ij vOjp epWT. 2. mbg;gil tpfpjrkj; Njw;wj;jpd; kWjiyia vOjp epWT. 3. Nfhz ,Urkntl;bj; Njw;wj;ij vOjp ep&gp; (cl;Gwk; kl;Lk;) 4. Nfhz ,Urkntl;bj; Njw;wjpd; kWjiyia vOjp ep&gp; (cl;Gwk; kl;Lk;) 5. ABCD vd;w ehw;fuk;> mjd; vy;yh gf;fq;fSk; xU tl;lj;ij njhLkhW mike;Js;sJ. AB = 6

nr.kP> BC = 6.5 nr.kP kw;Wk; CD = 7 nr.kP vdpy;> AD – d; ePsj;ijf; fhz;f. 6. xU ,izfuj;jpd; vy;yh gf;fq;fSk; xU tl;lj;ij njhLkhdhy; mt;tpizfuk; xU rha;rJukhFk;

vd epWTf. 7. nrt;tfk; ABCD – d; cl;Gw Gs;sp O – tpypUe;J nrt;tfj;jpd; Kidfs; A, B, C, D

,izf;fg;gl;Ls;sd vdpy; OA2 + OC2 = OB2 + OD2 vd epWTf.

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8. ∆ABC – y; gf;fq;fs; AB kw;Wk; AC – apy; KiwNa P kw;Wk; Q vd;w Gs;spfs; cs;sd. AP = 3 nr.kP> PB = 6 nr.kP> AQ = 5 nr.kP kw;Wk; QC = 10 nr.kP vdpy; BC = 3 PQ vd epWTf.

9. A, B vd;gd ∆PQR – d; gf;fq;fs; PQ, PR – fspd; Nky; mike;j Gs;spfs; vd;f. NkYk; AB ∥ QR , AB = 3 nr.kP> PB = 2 nr.kP kw;Wk; PR = 6 nr.kP vdpy;> QR – d; ePsj;ijf; fhz;f.

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7. Kf;Nfhztpay;;;

,U kjpg;ngz; tpdhf;fs;:

1. + = 1 vd;w Kw;nwhUikia epWTf.

2. 푐표푠 휃 + 푠푒푐 휃 = 2 + 푠푖푛휃 Kw;nwhUikia MFkh.

3. 푠푒푐 휃+푐표푠푒푐 휃 = 푠푒푐 휃푐표푠푒푐 휃 vd;w Kw;nwhUikia epWTf.

4. = 푐표푠푒푐휃 − 푐표푡휃 vd;w Kw;nwhUikia epWTf.

5. = vd epWTf.

6. = 푠푒푐휃 − 푡푎푛휃 vd epWTf.

7. = 푐표푠푒푐휃 + 푐표푡휃 vd epWTf.

8. = 1 + 푠푖푛휃 vd epWTf.

9. √푠푒푐 휃+푐표푠푒푐 휃 = 푡푎푛휃 + 푐표푡휃 vd epWTf. 10. 푠푒푐휃(1 − 푠푖푛휃)(푠푒푐휃 + 푡푎푛휃) = 1 vd epWTf.

11. = 푡푎푛휃 vd;w Kw;nwhUikia epWTf.

12. = vd epWTf.

13. (푠푖푛 휃+푐표푠 휃) = 1 − 3푠푖푛 휃푐표푠 휃 vd epWTf.

14. 푥 = 5푠푖푛휃 , 푦 = 4푐표푠휃 vdpy; + = 1 vdf; fhl;Lf. 15. Rtupy; rha;j;J itf;fg;gl;l Xu; VzpahdJ jiuAld; 60o Nfhzj;ij Vw;gLj;JfpwJ.>

Vzpapd; mb Rtw;wpypUe;J 3.5 kP J}uj;jpy; cs;sJ vdpy;> Vzpapd; ePsj;ijf;fhz;f.

16. 30 kP ePsKs;s xU fk;gj;jpd; epoypd; ePsk; 10√3 kP. vdpy;> R+upadpd; Vw;wf; Nfhzj;jpd; (jiu kl;lj;jpypUe;J Vw;wf; Nfhzk;) mstpidf; fhz;f.

17. xU NfhGuj;jpd; mbapypUe;J30√3 kP. njhiytpy; epw;Fk;xU ghu;itahsu; mf;NfhGuj;jpd; cr;rpapid300 ; Vw;wf; Nfhzj;jpy; fhz;fpwhu;.jiu kl;lj;jpypUe;J mtUila fpilepiyg; ghu;itf;Nfhlbw;F cs;;s J}uk; 1.5 kP vdpy;> NfhGuj;jpd; cauj;ijf; fhz;f.

18. xU Rik Cu;jpapypUe;J Rikia ,wf;f VJthf 300 Vw;wf; Nfhzj;jpy; xU rha;Tj; jsk; cs;sJ. rha;Tj; jsj;jpd; cr;rp jiuapypUe;J 0.9 kP cauj;jpy cs;sJ vdpy;> rha;Tj; jsj;jpd; ePsk; ahJ.

19. 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;ij fhz;.

20. 40 nr.kP ePsKs;s xU CryhdJ> xU KO mistpd; NghJ> mjd; cr;rpapy; 600

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.

Ie;J kjpg;ngz; tpdhf;fs;: 1. Neu;f;Fj;jhd xU kuj;jpd; Nky;ghfk; fhw;wpdhy; Kwpe;J> mk;Kwpe;j gFjp fPNo

tpOe;Jtplhky;> kuj;jpd; cr;rp jiuAld; 300 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

2. 200 mb cauKs;s fyq;fiu tpsf;fj;jpd; cr;rpapypUe;J> mjd; fhg;ghsu; xU Njhzp kw;Wk; xU glF Mfpatw;iw ghu;f;fpwhu;. fyq;fiu tpsf;fj;jpd; mb> Njhzp> kw;Wk; glF

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Mfpatw;;iw ghh;f;fpwhh;. fyq;fiu tpsf;fj;jpd; mb> Njhzp> kw;Wk; xU glF Mfpad xNu jpirapy; xNu Neh;f;Nfhl;by; mikfpd;wd. Njhzp> kw;Wk; glF Mfpatw;wpd; ,wf;ff; Nfhzq;fs; KiwNa 450 kw;Wk; 300 vd;f. ,t;tpuz;Lk; ghJfhg;ghf ,Uf;f Ntz;Lnkdpy;> mitfSf;F ,ilg;gl;l J}uk; Fiwe;jJ 300 mbahf ,Uf;f Ntz;Lk;. ,ilntsp Fiwe;jhy; fhg;ghsu; vr;rupf;if xyp vOg;g Ntz;Lk;. mtu; vr;rupf;if xyp vOg;g Ntz;Lkh?.

3. xU NfhGuj;jpd; mbapypUe;J xU Fd;wpd; cr;rpapd; Vw;wf;Nfhzk; 600 vd;f. Fd;wpd; mbapypUe;J NfhGuj;jpd; cr;rpapd; Vw;wf;Nfhzk; 300kw;Wk; NfhGuj;jpd; cauk; 50kP. vdpy;> Fd;wpd; cauj;ijf; fhz;f.

4. 60 kP cauKs;s xU NfhGuj;jpypUe;J xU fl;blj;jpd; cr;rp kw;Wk; mb Mfpatw;wpd; ,wf;f Nfhzq;fs; KiwNa 300> kw;Wk; 600 vdpy;;>fl;blj;jpd; cauj;ijf; fhz;f.

5. 40 kP cauKs;s xU NfhGuj;jpd;; cr;rp kw;Wk; mb Mfpatw;wpypUe;J xU fyq;fiu tpsf;fpd; cr;rpapd; Vw;wf; Nfhzq;fs; KiwNa 300> kw;Wk; 600 vdpy;;> fyq;fiu tpsf;fj;jpd;; cauj;ijf; fhz;f. NkYk;> fyq;fiu tpsf;fpd; cr;rpapypUe;J NfhGuj;jpd; mbf;F cs;s J}uj;ijAk; fhz;f.

6. xU nrq;Fj;jhd RtUk;> xU NfhGuKk; xU Fwpg;gpl;l ,ilntspapy; cs;sd. NfhGuj;jpd; cr;rpapypUe;J ghu;f;Fk;NghJ> Rtw;wpd; cr;rp kw;Wk; mb Mfpatw;wpd; ,wf;ff; Nfhzq;fs; KiwNa 450 kw;Wk;; 600 MFk;. NfhGuj;jpd; cauk; 90 kP. vdpy; Rtw;wpd; cauj;ijf;

fhz;f.(√3 =1.732) 7. xU fl;blj;jpd; Nky; xU nfhbf;fk;gk; epw;fpwJ. jiuapYs;s xU Gs;spapypUe;J

nfhbf;fk;gj;jpd; cr;rp kw;Wk; mb Mfpatw;wpd; Vw;wf;Nfhzq;fs; KiwNa 600 kw;Wk;; 450

vd;f. NkYk; nfhbf; fk;gj;jpd; cauk; 10kP vdpy;> fl;blj;jpd; cauj;ijf; fhz;f. (√3 =1.732)

8. xd;Wf;nfhd;W Neu; vjpuhf cs;s ,U kuq;fspd; kPJ A,B vd;w ,U fhf;iffs; 15kP. kw;Wk; 10kP. cauq;fspy; mku;e;Jf;nfhz;bUf;fpd;wd. mit jiuapypUf;Fk; xU tilapid KiwNa 450 kw;Wk;; 600 ,wf;ff; Nfhzj;jpy; ghu;f;fpd;wd. mit xNu Neuj;jpy; fpsk;gpf; Fiwthd ePsKs;s ghijapy; rkNtfj;jpy; gwe;J > mt;tilia vL;f;f Kaw;r;rpj;jhy; ve;j gwit ntw;wp ngWk;?

9. 700 kP. cauhj;jpy; gwe;Jf; nfhz;bUf;Fk; xU ntwypfhg;lupy; ,Ue;J xUtu; Xu; Mw;wpd; ,U fiufspy; Nenujpuhf cs;s ,U nghUl;fis 300> 450 ,wf;ff;Nfhzq;fspy; fhz;fpwhu;

vdpy;> Mw;wpd; mfyj;ijf; fhz;f. (√3 =1.732) 10. tFg;giwapy; mku;e;Jf;nfhz;bUf;Fk; xU khztd; fUk;gyifapy; fpilepiyg; ghu;itf;

Nfhl;bypUe;J 1.5 kP. cauj;jpy; cs;s Xtpaj;ij 300 Vw;wf; Nfhzj;jpy; fhz;fpwhd;. Xtpak; mtDf;Fj; njspthf njupahjjhy; Neuhff; fUk;gyifia Nehf;fp efu;e;J kPz;Lk; me;j Xtpaj;jij 450 Vw;wf;Nfhzj;jpy; njspthff; fhz;fpwhd; vdpy;> mtd; efu;e;j J}uj;ijf; fhz;f.

11. xU rpWtd;; 30 kP cauKs;s fl;blj;jpw;F vjpNu Fwpg;gl;l J}uj;j;py; epw;fpwhd;. mtDilaf; fpilepiyg; ghu;itf;NfhL jiu kl;lj;jpypUe;J 1.5 kP. cauj;jpy; cs;sJ. mtd; fl;blj;ij Nehf;fp ele;J nry;Yk;NghJ> mf;fl;blj;jpd; cr;rpapd; Vw;wf;Nfhzk; 300 ypUe;J 600 Mf cau;fpwJ. mtd; fl;blj;ij Nehf;fp ele;J nrd;wj; J}uj;ijf; fhz;f.

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8. mstpay; ,U kjpg;ngz; tpdhf;fs;:

1. xU jpz;k Neu; tl;l cUisapd; Muk; 7 nr.kP.kw;Wk; cauk; 20 nr.kP.vdpy; mjd; tisgug;G kw;Wk; nkhj;j gug;G fhz;f.

2. xU jpz;k Neu; tl;l cUisapd; nkhj;jg; Gwg;gug;G 880 r.nr.kP. kw;Wk; mjd; Muk; 10 nr.kP.

vdpy;> mt;TUisapd; tisgug;igf; fhz;f. 휋 =

3. xU jpz;k Neu; tl;l cUisapd; nkhj;jg; Gwg;gug;G 660 r.nr.kP. kw;Wk; mjd; tpl;lk; 14 nr.kP. vdpy;> mt;TUisapd; cauj;ijAk;> tisgug;igf; fhz;f.

4. ,uz;L Neu;tl;l cUisapd; Muq;fspd; tpfpjk; 3:2 vd;f. mjd; cauq;fspd; tpfpjk; 5:3 vdpy;> mtw;wpd; tisgug;Gfspd; tpfpjk; fhz;f.

5. xU jpz;k Neu; tl;l cUisapd; tisgug;G kw;Wk; mbr;Rw;wsT KiwNa 4400 r.nr.kP. kw;Wk; 110 nr.kP. vdpy; mt;TUisapd; cauj;ijAk;> tpl;lj;ijAk; fhz;f.

6. xU cs;sPlw;w cUisapd; cs; kw;Wk; ntsp Muq;fs; KiwNa 12nr.kP.kw;Wk; 18nr.kP vd;f. NkYk;>mjd;; cauk;14nr.kP.vdpy; mt;TUisapd; tisgug;G kw;Wk;nkhj;jg;Gwg;gug;igf;fhz;f.휋 =

7. xU cs;sPlw;w cUisapd; ntsg;Gw tisgug;G 540 π r.nr.kP.; mjd; cs; tpl;lk;; 16 nr.kP. kw;Wk; cauk; 15 nr.kP. vdpy; mf;Fohapd; nkhj;jg; Gwg;gug;igf; fhz;f.

8. xU jpz;k Neu;tl;lf; $k;gpd; Muk; kw;Wk; rhAuk; KiwNa 35nr.kP> 37 nr.kP vdpy; mjd; tisgug;G kw;Wk; nkhj;jg; Gwg;gug;igf; fhz;f.

9. xU jpz;k Neu;tl;lf; $k;gpd; Muk; kw;Wk; cauk; KiwNa 7 nr.kP kw;Wk; 24 nr.kP vdpy; mjd; tisgug;G kw;Wk; nkhj;jg; Gwg;gug;igf; fhz;f.

10. xU jpz;k Neh; tl;l cUisapd; Muk; 14 nr.kP kw;Wk; cauk; 8 nr.kP vdpy;> mjd; tisgug;igf; fhz;f.

11. xU jpz;k Neu;tl;lf; $k;gpd;; cr;rpf;Nfhzk; kw;Wk; Muk; KiwNa 600 kw;Wk; 15 nr.kP vdpy; mjd; cauk; kw;Wk; rhAauk; fhz;f.

12. xU jpz;k Neu;tl;lf; $k;gpd;; mbr;Rw;wsT 236 nr.kP kw;Wk; mjd; rhAauk; 12 nr.kP vdpy; mjd; tisgug;ig fhz;f.

13. new;Ftpaiy kioapypUe;J ghJfhf;f fpj;jhd; Jzpahy; kpfr;rupahf %lg;gLfpwJ vdpy; Njitahd fpj;jhd; Jzpapd; gug;igf; fhz;f.

14. xU Neu;tl;lf; $k;gpd; MuKk; rhAauKk; 3:5 vd;w tpfpjj;jpy; cs;sd. mf;$k;gpd; tisgug;G 60 π r.nr.kP vdpy; mjd; nkhj;jg;;gug;igf; fhz;f.

15. xU jpz;k miuf;Nfhsj;jpd; nkhj;j Gwg;gug;G 675π r.nr.kP vdpy; mjd; tisgug;igf; fhz;f. 16. 98.56 r.nr.kP Gwg;gug;G nfhz;l xU jpz;k Nfhsj;jpd; Muj;ijf;fhz;f. 17. xU jpz;k miuf;Nfhsj;jpd; tisgug;G 2772r.nr.kP vdpy;mjd;nkhj;jGwg;gug;ig fhz; 18. xU cs;sPlw;w miuf;Nfhsj;jpd; ntsp Muk; kw;Wk cs; Muk; KiwNa 4.2 nr.kP kw;Wk; 2.1 nr.kP

vdpy; mjd; tisgug;G kw;Wk; nkhj;jg; Gwg;gug;igf; fhz;f 19. miuNfhs tbtpyhd Nkw;$iuapd; cl;Gw tisgug;gpw;F tz;zk; G+r Ntz;bAs;sJ. mjd; cl;Gw

mbr;Rw;wsT 17.6kP vdpy;>xU rJu kPl;lUf;F &.5 tPjk; MFk; nkhj;j nrytpidf; fhz;f. 20. Neu; tl;l cUisapd; tisgug;G 704 r.nr.kP kw;Wk; mjd; cauk; 8 nr.kP vdpy; mt;TUisapd;

fd msit ypl;lupy; fhz;f. 21. xU jpz;k cUisapd; Muk; 14 nr.kP kw;Wk; mjd; cauk; 30 nr.kP vdpy; mt;TUisapd; fd

msit fhz;f. 22. ,uz;L Neu;tl;l cUisapd; Muq;fspd; tpfpjk; 2:3 vd;f. mjd; cauq;fspd; tpfpjk; 5:3 vdpy;>

mtw;wpd; fd msTfspd;; tpfpjk; fhz;f. 23. xU cUisapd; Muk; kw;Wk; cauj;jpd; tpfpjk; 2:3 .NkYk; mjd; fd msT 4400 f.nr.kP vdpy;

mt;TUisapd; Muj;ijf; fhz;f. 24. 66 nr.kP X 12 nr.kP. vDk; msT nfhz;l xU cNyhf jfl;bid 12 nr.kP. cauKs;s xU

cUisahf khw;wpdhy; fpilf;Fk; cUisapd; fd msitf; fhz;f. 25. xU Neu;tl;lf; $k;gpd;; fd msT 216π f.nr.kP kw;Wk; mf;$k;gpd; Muk; 9 nr.kP vdpy; mjd;

cauj;ijf; fhz;f. 26. xU jpz;kf; $k;gpd; Muk; kw;Wk; rhAauk; KiwNa 20 nr.kP kw;Wk; 29 nr.kP vdpy; mj;jpz;k

$k;gpd; fd msitf; fhz;f. 27. kuj;jpdhyhd xUjpz;k $k;gpd; mbr;Rw;wsT 44kP kw;Wk; mjd; cauk; 12kP mj;jpz;k $k;gpd; fd

msitf; fhz;f 28. xU Neu;tl;lf; $k;gpd;; fd msT 216 π f.nr.kP kw;Wk; mf;$k;gpd; Muk; 9 nr.kP vdpy; mjd;

cauj;ijf; fhz;f. 29. xU cs;sPlw;w Nfhsj;jpd; cs; kw;Wk; ntsp Muq;fs; KiwNa 12 nr.kP kw;Wk; 10 nr.kP vdpy;

mf;Nfhsj;jpd; fd msitf; fhz;f. 30. xU miu Nfhsj;jpd; fd msT 1152 π f.nr.kP vdpy;> mjd; tisgug;Gf;; fhz;f.

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31. 20 nr.kP gf;f msT nfhz;l xU fd rJuj;jpy; ,Ue;J ntl;bnaLf;fg;gLk; kpfg;ngupa $k;gpd; fd msitf; fhz;f.


1. xU cs;sPlw;w ,Uk;Gf; Fohapd; ePsk;;; 28 nr.kP mjd; ntsp kw;Wk; cs; tpl;lq;fs; KiwNa 8

nr.kP.kw;Wk; 6 nr.kP vdpy; ,Uk;Gf; Fohapd; fd mstpidf; fhz;f. NkYk;; 1 f.nr.kP. ,Uk;gpd;

vil 7 fpuhk; vdpy; mf;Fohapd; viliaf; fhz;f. 휋 =

2. xU jpz;k cUisapd; mbg;gf;fg; gug;G kw;Wk; fd msT KiwNa 13.86 r.nr.kP. kw;Wk; 69..3 f.nr.kP. mjd; cauk; kw;Wk; tisgug;igf; fhz;f.

3. xU ,ilf;fz;l tbtpyhd thspapd; Nkw;Gw Muk; 15 nr.kP. mbg;gf;fj;jpd; Muk; 8 nr.kP. NkYk;>

Mok; 63 nr.kP vdpy; thspapd; nfhs;ssitf; fhz;f. 휋 =

4. xU ghj;jpuk; ,ilf;fz;l tbtpy; cs;sJ. mjd; Nkw;Gw Muk; kw;Wk; cauk; KiwNa 8 nr.kP.

kw;Wk; 14nr.kP vd;f. mg;ghj;jpuj;jpd; fd msT f.nr.kP vdpy; mbg;gf;fj;jpYs;s tl;lj;jpd;

Muj;jpidf;fhz;f. 5. xU Neu; tl;lf; $k;gpd; ,ilf;fz;lj;jpd; ,UGwKk; mike;j tl;l tpspk;Gfspd; Rw;wsTfs;

KiwNa 44 nr.kP.kw;Wk; 8.4π nr.kP vd;f. mjd; cauk; 14 nr.kP vdpy; mt;tpilf;fz;lj;jpd; fd msitf; fhz;f.

6. xU jpz;k kug;nghk;ik miuf;Nfhsj;jpd; Nky; $k;G itj;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 jahupf;f gad;gLj;jg;gl;l kuj;jpd; fd msT fhz;f.

7. xU tpisahl;L gk;gukhdJ $k;gpd;kPJ miuf;Nfhsk; ,ize;j tbtpy; cs;sJ. miuf;Nfhsj;jpd; tpl;lk; 3.6 nr.kP. kw;Wk; gk;guj;jpd; nkhj;j cauk; 4.2 nr.kP. vdpy;> mjd; nkhj;j Gwg;gug;igf; fhz;f.

8. xU Nfhg;igahdJ miuf;Nfhsj;jpd; kPJ cUis ,ize;j tbtpy; cs;sJ. cUisg; gFjpapd; cauk; 8 nr.kP. kw;Wk; Nfhg;igapd; nkhj;j cauk; 11.5 nr.kP. vdpy; mf;Nfhg;igapd; nkhj;j Gwg;gug;igf;; fhz;f.

9. xU fd cUtkhdJ miuf;Nfhsj;jpd; kPJ cUis ,ize;j tbtpy; cs;sJ. cUisg;gFjpapd; tpl;lk;; kw;Wk; nkhj;j cauk; 21 nr.kP. kw;Wk 25.5 nr.kP.; vdpy; mjd; fd msitf; fhz;f

10. xU ru;f;f]; $lhukhdJ cUisapd; kPJ $k;G mike;jhw;Nghd;w tbtpYs;sJ. $lhuj;jpd; nkhj;j cauk; 49 kP. mjd; mbg;gf;f tpl;lk; 42 kP.> cUis ghfj;jpd; cauk; 21kP. NkYk; 1r.kP. fpj;jhd; Jzpapd; tpiy &.12.50 vdpy; mf;$lhuk; mikf;fj; Njitahd fpj;jhd; Jzpapd;

tpiyiaf; fzf;fpLf 휋 =

11. xU kUe;J Fg;gpahdJ cUisapd; ,UGwKk; miuf;Nfhsk;; mike;jJ Nghd;w tbtpy; cs;sJ. mjd; nkhj;j ePsk; 14 kp.kP. cUisapd; tpl;lk; 5 kp.kP. khj;jpiuf; Fg;gpapd; Gwg;gug;G fhz;f.

12. xU $lhukhdJ cUisapd; kPJ $k;G mike;jhw;Nghd;w tbtpYs;sJ. $lhuj;jpd; nkhj;j cauk; 13.5 kP. mjd; tpl;lk; 28kP.> NkYk;> cUis ghfj;jpd; cauk; 3kP. $lhuj;jpd; nkhj;j Gwg;gug;igf; fhz;f.

13. 7 nr.kP tpl;lKs;s xU cUis tbt Kfitapy; rpwpjsT jz;zPu; cs;sJ. mjpy; xt;nthd;Wk;; 1.4 nr.kP tpl;lKs;s rpy Nfhs tbt gspq;F fw;fs; Nghlg;gLfpd;wd. jz;zPupd; cauk; 5.6 nr.kP. mjpfupf;f vj;jid gspq;F fw;fis Nghl Ntz;Lk;.

14. rpwpjsT jz;zPu; epug;gg;gl;l 12 nr.kP tpl;lKs;s xU cUis tbt ghj;jpuj;jpy;; 6 nr.kP. tpl;lKs;s xU jpz;k Nfhsj;jpid KOtJkhf %o;fr; nra;jhy; ghj;jpuj;jpy; cau;e;j ePu;kl;lj;jpd; cauj;ij fhz;f.

15. 5 nr.kP cs; tl;l MuKk; 24 nr.kP cauKk; nfhz;l $k;G tbt ghj;jpuj;jpy; KO mstpy; jz;zPu; cs;sJ. ,j;jz;zPuhdJ 10 nr.kP. cs; MuKs;s cUis tbt fhyp ghj;jpuj;jpw;F khw;wg;gLk; NghJ mg;ghj;jpuj;jpy; cs;s jz;zPu; kl;lj;jpd; cauj;ijf; fhz;f.

16. 4.4nr.kP ePsKk; 2kP mfyKk; nfhz;l xU fdr; nrt;tf tbtj; njhl;bapy; kioePu; Nrfupf;fg;gLfpwJ. ,j;njhl;bapy; 4nr.kP. cauj;jpw;F Nrfupf;fg;gl;l kio ePuhdJ 40 nr.kP MuKs;s cUis tbt fhyp ghj;jpuj;jpw;F khw;wg;gLk; NghJ mg;ghj;jpuj;jpy; cs;s jz;zPu; kl;lj;jpd; cauj;ijf; fhz;f.

17. 8 nr.kP tpl;lKk; 12 nr.kP cauKk; nfhz;l xU Neu; tl;l jpz;k tbt ,Uk;G $k;ghdJ cUf;fg;gl;L 4 kp.kP MuKs;s jpz;kf; Nfhs tbt Fz;Lfshf thu;f;fg;gl;lhy; fpilf;Fk; Nfhs tbt Fz;Lfspd; vz;zpf;if fhz;f.

18. 12 nr.kP tpl;lKk; 15 nr.kP cauKk; nfhz;l xU Neu; tl;l cUis KOtJk; gdpf;$opdhy; (ice cream) epug;gg;gl;Ls;sJ .,g;gdpf;$ohdJ 6 nr..kP tpl;lKk;> 12 nr..kP cauKk; nfhz;l Nkw;Gwk;

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miuf;Nfhsk; ,ize;j tbtpyike;j $k;gpy; epug;gg;gLfpwJ. vj;jid $k;Gfspy; gdpf;$opid KOtJkhf epug;gyhk;?..

19. fspkz;zpid gad;gLj;jp xU khztd; 48 nr.kP cauKk;> 12 nr.kP MuKk; nfhz;l Neu; tl;l jpz;kf; $k;igr; nra;jhu;. mf;$k;ig kw;nwhU khztu; xU jpz;k Nfhskhf khw;wpdhu;. mt;thW mikf;fg;gl;l Gjpa Nfhsj;jpd; Muj;ijf; fhz;f.

20. 18 nr.kP MuKs;s jpz;k cNyhf NfhskhdJ cUf;fg;gl;L %d;W rpwpa ntt;NtW msTs;s Nfhsq;fshf thu;f;fg;gLfpwJ. mt;thW thu;f;fg;gl;l ,uz;L jpz;k Nfhsq;fspd; Muq;fs; KiwNa 2 nr.kP kw;Wk; 12 nr.kP vdpy; %d;whtJ Nfhsj;jpd; Muj;ijf; fhz;f.

21. 24 nr.kP MuKs;s jpz;k cNyhf NfhskhdJ cUf;fg;gl;L 1.2 kp.kP MuKs;s rPuhd cUis fk;gpahf khw;wg;gl;lhy; fk;gpapd; ePsj;ijf; fhz;f.

22. xU cs;sPlw;w cUis tbt Fohapd; ePsk; 40 nr.kP > mjd; cs; kw;Wk; ntsp Muq;fs; KiwNa 4 nr.kP kw;Wk; 12 nr.kP . mt;Ts;Plw;w cUis Foha; cUf;fg;gl;L 20 nr.kP ePsKs;s jpz;k cUisahf khw;wg; gl;lhy; fpilf;Fk; Gjpa cUisapd; Muj;ijf; fhz;f.

23. kzyhy; epug;gg;gl;l xU cUis tbt thspapd; cauk; 32 nr.kP kw;Wk; Muk; 18 nr.kP. mk;kzy; KOtJk; jiuapy; xU Neu;tl;l $k;G tbtpy; nfhl;lg;gLfpwJ. mt;thW nfhl;lg;gl;l kzw;$k;gpd; cauk; 24 nr.kP vdpy; mf;$k;gpd; Muk; kw;Wk; rhAauk; fhz;f.

24. 14 kP tpl;lKk; 20 kP MoKk; cs;s xU fpzW cUis tbtpy; ntl;lg;gLfpwJ. mt;thW ntl;Lk;NghJ Njhz;bnaLf;fg;gl;l kz; rPuhf gug;gg;gl;L 20kP X 14kP; msTfspy; mbg;gf;fk; nfhz;l xU Nkilahf mikf;fg;gl;lhy;> mk;Nkilapd; cauk; fhz;f.

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9.nra;Kiw tbtpay;

1. 3.2 nr.kP MuKs;s xU tl;lk; tiue;J mt;tl;lj;jpd; Nky; VNjDk; xU Gs;spia Fwpf;f. tl;lj;jpd; ikaj;ij gad;gLj;jp mg;Gs;sp topNa njhLNfhL tiuf.

2. 4.2 nr.kP MuKs;s xU tl;lk; tiuf. mt;tl;lj;jpd; Nky; P vd;w VNjDk; xU Gs;spia Fwpf;f. mg;Gs;sp topNa njhLNfhL tiuf.( tl;lj;jpd; ikaj;ij gad;gLj;Jf)

3. 3.2 nr.kP MuKs;s xU tl;lk; tiuf. mt;tl;lj;jpd; Nky; P vd;w VNjDk; xU Gs;spia Fwpf;f. njhLNfhL – ehz; Njw;wj;ijg; gad;gLj;jp mg;Gs;sp topNa njhLNfhL tiuf.

4. 4.8 nr.kP MuKs;s xU tl;lk; tiuf. mt;tl;lj;jpd; Nky; P vd;w VNjDk; xU Gs;spia Fwpf;f. njhLNfhL – ehz; Njw;wj;ijg; gad;gLj;jp mg;Gs;sp topNa njhLNfhL tiuf.

5. 3 nr.kP MuKs;s xU tl;lk; tiue;J mjd; ikaj;jpypUe;J 7 nr.kP njhiytpy; xU Gs;spia Fwpf;f. mg;Gs;spapypUe;J tl;lj;jpw;F njhLNfhLfs; tiue;J mjd; ePsq;fis fzf;fpLf.

6. 6 nr.kP MuKs;s xU tl;lk; tiue;J mjd; ikaj;jpypUe;J 10 nr.kP njhiytpy; xU Gs;spia Fwpf;f. mg;Gs;spapypUe;J tl;lj;jpw;F njhLNfhLfs; tiue;J mjd; ePsq;fis fzf;fpLf.

7. 10 nr.kP tpl;lKs;s xU tl;lk; tiue;J mjd; ikaj;jpypUe;J 13 nr.kP njhiytpy; P vd;w Gs;spia Fwpf;f. mg;Gs;spapypUe;J tl;lj;jpw;F PA kw;Wk; PB vd;w njhLNfhLfs; tiue;J mjd; ePsq;fis fzf;fpLf.

8. 3 nr.kP MuKs;s xU tl;lk; tiue;J mjd; ikaj;jpypUe;J 9 nr.kP njhiytpy; xU Gs;spiaf; Fwpf;f. mg;Gs;spapypUe;J tl;lj;jpw;F njhLNfhLfs; tiue;J> mjd; ePsq;fis fzf;fpLf.

9. AB = 6 nr.kP ∠C = 40° kw;Wk; cr;rp C - apypUe;J AB – f;F tiuag;gl;l Fj;Jf;Nfhl;bd; ePsk; 4.2 nr.kP nfhz;l ∆ ABC tiuf.

10. PQ = 6 nr.kP ∠푅 = 60° kw;Wk; cr;rp R - apypUe;J PQ – f;F tiuag;gl;l Fj;Jf;Nfhl;bd; ePsk; 4 nr.kP nfhz;l ∆ PQR tiuf.

11. PQ = 4 nr.kP ∠푅 = 25° kw;Wk; cr;rp R - apypUe;J PQ – f;F tiuag;gl;l Fj;Jf;Nfhl;bd; ePsk; 4.5 nr.kP nfhz;l ∆ PQR tiuf.

12. mbgf;fk; BC = 5.5 nr.kP ∠A = 60° kw;Wk; cr;rp A - apypUe;J tiuag;gl;l eLf;NfhL AM – d; ePsk; 4.5 nr.kP nfhz;l ∆ ABC tiuf.

13. ∆ ABC -apy; BC = 5 nr.kP ∠A = 45° kw;Wk; cr;rp A - apypUe;J BC f;F tiuag;gl;l eLf;Nfhl;bd; ePsk; 4 nr.kP nfhz;l ∆ ABC tiuf.

14. BC = 5 nr.kP ∠BAC = 40° kw;Wk; cr;rp A - apypUe;J BC – f;F tiuag;gl;l eLf;Nfhl;bd; ePsk; 6 nr.kP vd;w msTfs; nfhz;l ∆ ABC tiuf. NkYk; cr;rp A - apypUe;J tiuag;gl;l Fj;Jf; Nfhl;bd; ePsk; fhz;f.

15. AB = 6 nr.kP> AC = 7 nr.kP> BC = 6 nr.kP kw;Wk; AD = 4.2 nr.kP msTfs; nfhz;l tl;l ehw;fuk; ABCD tiuf.

16. AB = 6 nr.kP> AD = 4.8 nr.kP> BD = 8 nr.kP kw;Wk; CD = 5.5 nr.kP msTfs; nfhz;l tl;l ehw;fuk; ABCD tiuf.

17. PQ = 4 nr.kP> QR = 6 nr.kP> PR = 7.5 nr.kP kw;Wk; QS = 7 nr.kP msTfs; nfhz;l tl;l ehw;fuk; PQRS tiuf.

18. AB = 6 nr.kP> BC = 5.5 nr.kP> ∠ABC = 80° kw;Wk; AD = 4.5 nr.kP msTfs; nfhz;l tl;l ehw;fuk; ABCD tiuf.

19. EF = 5.2 nr.kP> ∠GEF = 50°, FG = 6 nr.kP> kw;Wk; ∠EGH = 40° ; vd;w msTfs; nfhz;l tl;l ehw;fuk; EFGH tiuf.

20. PQ = 4 nr.kP> ∠P = 100°, ∠PQS = 40° ; kw;Wk; ∠SQR= 70° ; vd;w msTfs; nfhz;l tl;l ehw;fuk; PQRS tiuf.

21. AB = 5.8 nr.kP> ∠ABD = 35° , AD = 4.2 nr.kP kw;Wk; AB ∥ CD vd;w msTfs; nfhz;l tl;l ehw;fuk; ABCD tiuf.

22. AB = 5.5 nr.kP> ∠ABC = 50°, ∠BAC = 60°, kw;Wk; ∠ACD = 30° ;; vd;w msTfs; nfhz;l tl;l ehw;fuk; ABCD tiuf.

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10. tiuglq;fs; vitNaDk; xd;wDf;F kl;Lk; tpilasp. (10 kjpg;ngz;fs;)

1. y=2x2-x+3 – d; tiuglk; tiuf. 2. x2-2x-3=0 – ia tiuglk; %yk; jPh;f;f. 3. 2x2+x-6=0 – ia tiuglk; %yk; jPh;f;f. 4. (x-5)(x-1)=0 – ia tiuglk; %yk; jPh;f;f. 5. y=2x2 - d; tiuglk; tiue;J mjpypUe;J 2x2+x-6=0 vd;w rkd;ghl;il jPh;f;f. 6. y=2x2+x-6 - d; tiuglk; tiue;J mjpypUe;J 2x2+x-10=0 vd;w rkd;ghl;il jPh;f;f. 7. y=x2+2x-3 - d; tiuglk; tiue;J mjpypUe;J x2-x-6=0 vd;w rkd;ghl;il jPh;f;f. 8. y=x2+3x+2 - d; tiuglk; tiue;J mjpypUe;J x2+2x+4=0 vd;w rkd;ghl;il jPh;f;f. 9. y=x2-x-8 - d; tiuglk; tiue;J mjpypUe;J x2 - 2x-15=0 vd;w rkd;ghl;il jPh;f;f. 10. y=x2+x-12 - d; tiuglk; tiue;J mjpypUe;J x2 + 2x+2=0 vd;w rkd;ghl;il jPh;f;f. 11. y=x2 - d; tiuglk; tiue;J mjpypUe;J x2 -4x-5=0 vd;w rkd;ghl;il jPh;f;f. 12. fPo;f;fhZk; ml;ltizf;F jFe;j tiuglk; tiue;J khwpfspd; khWghl;Lj; jd;ikiaf; fhz;.

x 2 3 5 8 10

y 8 12 20 32 40

NkYk; x=4 vdpy; y – d; kjpg;igf; fhz;f. 13. thq;fg;gl;l Nehl;Lg; Gj;jfq;fspd; vz;zpf;if kw;Wk; mjw;fhd tpiy tptuk; jug;gl;Ls;sJ.

Nehl;Lg; Gj;jfq;fspd; vz;zpf;if x 2 4 6 8 10 12

tpiy &y 30 60 90 120 150 180

,jw;fhd tiuglk; tiue;J mjd; %yk; (i) VO Nehl;LGj;jfq;fspd; tpiyiaf; fhz;f. (ii) & 165 - f;F thq;fg;gLk; Nehl;Lg; Gj;jfq;fspd; vz;zpf;iff; fhz;f.

14. fPo;f;fhZk; ml;ltizf;F jFe;j tiuglk; tiue;J> mjd; %yk; (i) x = 4 vdpy; y – d; kjpg;igf; fhz;f. (ii) y =12 vdpy; x – d; kjpg;igf; fhz;f.

15. 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;ifiaf; fhz;f.

16. xy = 20, x,y >0 vd;gjd; tiuglk; tiuf. mij gad;gLj;jp (i) x = 5 vdpy; y – d; kjpg;igAk; (ii) y =10 vdpy; x – d; kjpg;igAk; fhz;f.

17. xU tq;fp %j;jf;Fbkfdpd; 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; a) & 650 itg;Gj; njhiff;F fpilf;Fk; tl;b kw;Wk; b) & 45 tl;bahf fpilf;f tq;fpapy; nrYj;jg;gl Ntz;ba itg;Gj;njhif Mfpatdtw;iwf; fhz;f

18. xU NgUe;J 40fp;.kP Ntfj;jpy; nry;fpwJ.,jw;Fhpa J}u-fhy njhlh;gpw;fhd tiuglk; tiuf. ,ijg; gad;gLj;jp 3 kzpNeuj;jpy; ,g;NgUe;J gazpj;jj; J}uj;ijf; fz;Lgpb.

19. 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 a) tpfpjrk khwpypiaf; fhz;f. b) 3 ypl;lh; ghypd; tpiyiaf; fhz;f.

20. xU kpjp tz;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;jpid flf;f vLj;Jf; nfhz;l Neuk; Mfpatdtw;iwg; gw;wpa tptuq;fs; (Ntf - fhy) gpd;tUk; ml;ltizapy; nfhLf;fg;gl;Ls;sd.

x 1 3 5 7 8

y 2 6 10 14 16

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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;gl;l J}uj;ij 40 kzp Neuj;jpy; flf;f ve;j Ntfj;jpy; gazpf;f Ntz;Lk;.

Ntfk; (fp.kP / kzp) x 2 4 6 10 12

Neuk; (kzpapy;) y 60 30 20 12 10

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11. Gs;spapay; ,U kjpg;ngz; tpdhf;fs;:

1. 43,24,38,56,22,39,45 vd;w tptuq;fspd; tPr;R kw;Wk; tPr;Rf;nfO fhz;f. 2. 59,46,30,23,27,40,52,35,29 vd;w tptuq;fspd; tPr;R kw;Wk; tPr;Rf;nfO fhz;f. 3. xU 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. 4. xU Gs;sp tptuj;jpd; kPr;rpW kjpg;G 12 kw;Wk; mjd; tPr;R 59 vdpy;> mj;njhFg;gpd; kPg;ngU

kjpg;igf;fhz;f. 5. xU tptuj;njhFg;gpd; kPg;ngU kjpg;G 3.84 fp.fp. kw;Wk; mjd; tPr;R 0.46 fp.fp vdpy;> mj;njhFg;gpd;

kPr;rpW kjpg;igf;fhz;f.

6. Kjy; n ,ay; vz;fspd; jpl;l tpyf;fk; vd epWTf..

7. Kjy; 10 ,ay; vz;fspd; jpl;l tpyf;fk; fhz;f. 8. Kjy; 13 ,ay; vz;fspd; jpl;l tpyf;fk; fhz;f. 9. fz;lwpe;j Gs;sp tptuj;njhFg;gpYs;s 20 kjpg;Gfspd; jpl;l tpyf;fk; √5 vd;f. gs;sp tptuj;jpd;

xt;nthU kjpg;igAk; 2 My; ngUf;fpdhy;fpilf;Fk; GjpaGs;sp tptuq;fspd; jpl;ltpyf;fk; kw;Wk; tpyf;f tu;f;f ruhrup fhz;f.

10. xU Gs;sp tptuj;jpy; 30 kjpg;Gfspd; $l;l ruhrup kw;Wk; jpl;l tpyf;fk; KiwNa 18 kw;Wk; 3 MFk;. mtw;wpd; $l;Lj;njhifiaAk;> NkYk; mtw;wpd; tu;f;fq;fspd; $l;Lj;njhifiaAk; fhz;f.

11. xU Gs;sp tptuj;jpy; 100 kjpg;Gfspd; $l;l ruhrup kw;Wk; jpl;l tpyf;fk; KiwNa 48 kw;Wk; 10 MFk;. mtw;wpd; $l;Lj;njhifiaAk;> NkYk; mtw;wpd; tu;f;fq;fspd; $l;Lj;njhifiaAk; fhz;f.

12. xU Gs;sptptuj;jpd; khWghl;Lf;nfO 57 kw;Wk; jpl;l tpyf;fk; 6.84 vdpy; mjd; $l;L ruhrupiaf; fhz;f.

13. xU FOtpy; Ngu; cs;sdu;> mtu;fspd; cauq;fspd; $l;Lr; ruhrup 163.8 nr.kP. kw;Wk; khWghl;Lf;nfO 3.2 vdpy;> mtu;fSila cauq;fspd; jpl;ltpyf;fk; fhz;f.

14. n=10, 푥̅ = 12, x2= 1530 vdpy; jpl;ltpyf;fk; fhz;f. 15. x = 99, n=9, (x-10)2= 79 vdpy; x2 kw;Wk; (x-x)2 I fhz;f.

Ie;J kjpg;ngz; tpdhf;fs;: 1. 10 khzth;fs; fzpjj; Njh;tpy; ngw;w kjpg;ngz;fs; gpd;tUkhW> 80>70>50>90>60>100>60>30.80>40.

,k;kjpg;GfSf;F jpl;l tpyf;fk; fhz;f. 2. xU tFg;gpw;F elj;jg;gl;l nghJ mwpTj;Nju;tpy; nkhj;j kjpg;ngz;fs; 40 f;F khztu;fs; ngw;w

kjpg;ngz;fs; 20,14,16,30,21 kw;Wk; 25 vdpy; ,k;kjpg;Gfspd; jp;l;l tpyf;fk; fhz;f. 3. 62,58,53,50,63,52,55 Mfpa kjpg;GfSf;F jpl;l tpyf;fk; fhz;f. 4. 10> 20> 15> 8> 3> 4 Mfpa kjpg;GfSf;F jpl;l tpyf;fk; fhz;f. 5. 3,5,6,7 Mfpa kjpg;GfSf;F jpl;l tpyf;fk; fhz;f.xt;nthU kjpg;GlDk; 4 If; $l;l filf;Fk; Gjpa

kjpg;GfSf;F jpl;l tpyf;fk; fhz;f. 6. 40,42,48 Mfpa kjpg;GfSf;F jpl;l tpyf;fk; fhz;f.xt;nthU kjpg;Gk; 3 My; ngUf;fg;gLgk;NghJ

Gjpa kjpg;GfSf;F jpl;l tpyf;fk; fhz;f. 7. fzpj tpdhb tpdhg; Nghl;bapy; 48 khzth;fs; ngw;w kjpg;ngz;fs; gpd;tUk; ml;ltizapy;

jug;gl;Ls;sd.

kjpg;ngz;fs; x 6 7 8 9 10 11 12 epfo;ntz;fs; f 3 6 9 13 8 5 4

,t;tptuj;jpw;fhd jpl;l tpyf;fj;ij fzf;fpLf. 8. gpd;tUk; ml;ltizapy; jug;gl;Ls;s Gs;sp tptuj;jpw;fhd tpyf;f th;f;fr; ruhrhpia fzf;fpLf.

x 70 74 78 82 86 90 f 1 3 5 7 8 12

9. fPo;f;fz;l ml;ltizapy; jug;gl;Ls;s Gs;sp tptuj;jpw;fhd jpl;l tpyf;fj;ij fzf;fpLf.

x 3 8 13 18 23 f 7 10 15 10 8

10. cyf fhy;ge;J Nghl;bfspy; 71 Kd;dzp tPuh;fs; mbj;j Nfhy;fspd; vz;zpf;ifapd; tptuq;fs;; gpd;tUk; ml;ltizapy; jug;gl;Ls;sd. ,t;tptuj;jpw;fhd jpl;l tpyf;fj;ij fzf;fpLf.

gpupT ,ilntsp 0 -10 10-20 20-30 30-40 40-50 50-60 60-70 epfo;ntz;fs; 8 12 17 14 9 7 4

11. xU ghjrhhp FWf;F ghijia flf;f rpyh; vLj;Jf;nfhz;l Neu tptuk; gpd;tUk; ml;ltizapy; jug;gl;Ls;sJ. ,t;tptuj;jpw;fhd jpl;l tpyf;fk; kw;Wk; tpyf;fth;f;f ruhrhpia fzf;fpLf.

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Neuk; (tpdhbapy;) 5-10 10-15 15-20 20-25 25-30 egh;fspd; vz;zpf;if 4 8 15 12 11

12. tPl;L cupikahsu;fs; 45 Ngu; mtu;fSila njUtpd; “ gRikr; R+oy;” jpl;lj;jpw;fhf epjp mspj;jdu;. tR+ypf;fg;gl;l epjpj;njhif tptuk; gpd;tUkhW:

njhif 0-20 20-40 40-60 60-80 80-100

tPl;L cupikahsu;fspd;; vz;zpf;if

2 7 12 19 5

13. gpd;tUk; kjpg;Gfspd; khWg;ghl;Lf; nfOit fhz;f. 20> 18> 32> 24> 26. 14. ∑푥 = 99, n = 9 kw;Wk; ∑(푥 − 10)2 = 79 vdpy;> ∑ 푥2 kw;Wk; ∑(x-푥̅)2 Mfpatw;iw fhz;f. 15. xU Gs;sp tptuj; njhFg;gpy; ∑ 푥 = 35, n = 5 kw;Wk; ∑(푥 − 9)2 = 82 vdpy;> ∑푥2 kw;Wk; ∑(x-푥̅)2

Mfpatw;iw fhz;f. 16. xU Gs;sp tptuj;jpy; 30 kjpg;Gfspd; $l;Lr; ruhrhp kw;Wk; jpl;l tpyf;fk; KiwNa 18 kw;Wk; 3

MFk;. mtw;wpd; $l;Lj;njhifiaAk;> NkYk; mtw;wpd; th;f;fq;fspd; $l;Lj;njhifiaAk; fhz;f.

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12.epfo;jfT ,U kjpg;ngz; tpdhf;fs;:

1. rktha;g;Gr; Nrhjidapy; Nju;e;njLf;fg;gl;l xU nel;lhz;by; (leap year), 53 nts;spf;fpoikfs; ,Ug;gjw;fhd epfo;jfT fhz;f.

2. rktha;g;Gr; Nrhjidapy; Nju;e;njLf;fg;gl;l xU nel;lhz;by; (leap year); 52 nts;spf;fpoikfs; kl;LNk ,Ug;gjw;fhd epfo;jfT fhz;f.

3. rktha;g;Gr; Nrhjidapy; Nju;e;njLf;fg;gl;l xU rhjhuz Mz;by; (non leap year), 53 nts;spf;fpoikfs;,Ug;gjw;fhd epfo;jfT fhz;f.

4. Kjy; ,UgJ ,ay; vz;fsp;y; xU vz; rktha;g;G Kiwapy; Nju;njLf;fg;gLfpwJ. me;j vz; xU gfh vz;zhf ,Ug;gjw;fhd epfo;jfT fhz;f.

5. 35 nghUl;fs; mlq;fpa njhFg;G xd;wpy; 7 nghUl;fs; FiwghLilad . mj;njhFg;gpypUe;J xU nghUs; rktha;g;G Kiwapy; Nju;njLf;fg;gLfpwJ mJ Fiwaw;w nghUshf ,Ug;gjw;fhd epfo;jfT fhz;f.

6. xU tFg;gpYs;s 35 khztu;fspy; 20 Ngu; Mz;fs; kw;Wk; 15 ngu; ngz;fs;.rktha;g;G Kiwapy; xU khztu; Nju;njLf;fg;gLfpwhu; vdpy; gpd;tUk; epfo;r;rpapd; epfo;jfT fhz;f.(i) khztdhf ,Uj;jy; (ii) khztpahf ,Uj;jy;.

7. xU Fwpg;gpl;l ehspy; kiotUtjw;fhd epfo;jfT 0.76. mf;Fwpg;gpl;l ehspy; kio tuhky; ,Ug;gjw;fhd epfo;jfT fhz;f.

8. xU rktha;g;Gr; Nrhjidapy; xUepfo;r;rp A vd;f. mjd; epug;G epfo;r;rp 퐴̅ vd;f. P(A) : P(퐴̅) = 7:12 vdpy; P(A) If; fhz;f.

9. 1ypUe;J 100 tiuapyhd vz;fs; Fwpf;fgg;l;l rPl;Lfspy; xU rPl;L vLf;f> mJ 10 –My; tFgLk; vz;zhf ,Uf;f epfo;jfT vd;d.

10. 12 ey;y Kl;ilfSld;; 3 mOfpa Kl;ilfs; fye;J ,Ue;jd. xU ey;y Kl;ilia vLg;gjw;fhd epfo;jfT vd;d.

11. ,U ehzaq;fs; xNu Neuj;jpy; Rz;Lk; Nrhjidapy; mjpf gl;rkhf xU jiy tpOk; epfor;rpapd; epfo;jfT vd;d

12. ,U gfilfs; xUKiw cUl;lg;gLfpd;wd. Kf vz;fis nfhz;L mikf;fg;gLk; <upyf;f vz; 3 –My; tFgLk; vz;zhf ,Uf;f epfo;jfT fhz;f.

13. xU rPuhd gfil ,uz;L Kiw cUl;lg;gLfpwJ. Kf vz;fspd; $Ljy; 9 vdg; ngWtjw;F epfo;jfT fhz;f.

14. ,U gfilfs; xUKiw cUl;lg;gLfpd;wd. Kf vz;fspd; ngUf;fw;gyd; gfh vz;zhf ,Uf;f epfo;jfT fhz;f

15. %d;W gfilfs;; xNu Neuj;jpy; cUl;lg;gLk; NghJ ,U gfilfspYk; xNu vz; tpOk; epfor;rpapd; epfo;jfT fhz;f.

16. 3,5,7 Mfpa vz;fis ,yf;fq;fshf nfhz;L xU ,uz;byf;f vz; mikf;fg;gLfpwJ. mt;ntz; 57 ngupajhf ,Uf;f epfo;jfT fhz;f.(xNu ,yf;fk; kPz;Lk; kPz;Lk; tuf;$lhJ)

17. A,B ,uz;L epfo;rpfspy; P(A)= 1/2 P(B)= 7/10 kw;Wk; P(AUB)=1vdpy; (i) P(AB) (ii) P(AIBI) iaf; fhz;f

18. A,B,C vd;gd xd;iw xd;W tpyf;Fk; kw;Wk; epiwT nra; epfo;rpfs; vd;f. NkYk;>

P(B)= P(A) kw;Wk; P(C)=

P(B) vdpy; P(A) itf; fhz;f.


1. xU rPuhd gfil xUKiw cUl;lg;gLfpwJ. gpd;tUk; epfo;r;rpfSf;fhd epfo;jfTfisf; fhz;f. (i) vz; 4 fpilj;jy; (ii) xU ,ul;ilg;gil vz; fpilj;jy; (iii) 6 – d; gfh fhuzpfs; fpilj;jy; (iv) 4 – ia tplg; nghpa vz; fpilj;jy;.

2. xU rPuhd ehzak; ,uz;L Kiw cUl;lg;gLfpwJ. fPo;f;fhZk; epfo;r;rpfSf;fhd epfo;jfTfisf; fhz;f. (i) ,U jiyfs; fpilj;jy; (ii) Fiwe;jJ xU jiy fpilj;jy; (iii) xU G+ kl;Lk; fpilj;jy;

3. ,U rPuhd gfilfs; xUKiw cUl;lg;gLfpwJ. gpd;tUk; epfo;r;rpfSf;fhd epfo;jfTfisf; 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 – ia tpl mjpfkhf ,Uj;jy;

4. 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;tUtdthf ,Uf;f epfo;jfTfisf; fhz;f. (i) ,uhrh (ii) fUg;G ,uhrh (iii) ];NgL (iv) lakz;l;

5. 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;tUtdthf ,Uf;f epfo;jfTfisf; fhz;f.

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(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

6. 1 Kjy; 100 tiuapyhd KO vz;fspypUe;J rktha;g;G Kiwapy; Njh;e;njLf;fg;gLk; vz; (i) xU KO th;f;fkhf ,Uf;f (ii) KO fdkhf ,y;yhky; ,Uf;f Mfpatw;wpd; epfo;jfTfis fhz;f.

7. xU ngl;bapy; 4 gr;ir 5 eyk; kw;Wk; 3 rptg;G epw ge;Jfs; cs;sd. Rk tha;g;G Kiwapy; xU ge;ij Njh;e;njLf;f mJ (i) rptg;G epw ge;jhf ,Uf;f (ii) gr;ir epw ge;jhf ,y;yhky; ,Uf;f Mfpatw;wpd; epfo;jfTfis fhz;f.

8. 20 rPl;Lfspy; 1 Kjy; 20 tiuAs;s KO vz;fs; Fwpf;fg;gl;Ls;sd. rktha;g;G Kiwapy; xU rPl;L vLf;fg;gLfpd;wJ. mt;thW vLf;fg;gl;l rPl;bYs;s vz; (i) 4 – d; klq;fhf ,Uf;f (ii) 6 – d; klq;fhf ,y;yhky; ,Uf;f Mfpa epfo;r;rpfspd; epfo;jfTfis fhz;f.

9. %d;W ehzaq;fs; xNu Neuj;jpy; Rz;lg;gLfpd;wd. rhpahf ,U G+f;fs; my;yJ Fiwe;jgl;rk; xU jiyahtJ fpilf;Fk; epfo;r;rpapd; epfo;jftpidf; fhz;f.

10. xU gfil ,UKiw cUl;lg;gLfpwJ. Fiwe;jJ xU cUl;lypyhtJ vz; 5 fpilg;gjw;fhd epfo;jftpidf; fhz;f.

11. xU khztpf;F kUj;Jtf; fy;Y}hpapy; Nrh;f;if fpilg;gjw;fhd epfo;jfT 0.16 vd;f. nghwpapay; fy;Y}hpapy; Nrh;f;if fpilg;gjw;fhd epfo;jfT 0.24 kw;Wk; ,U fy;Y}hpfspYk; Nrh;f;if fpilg;gjw;fhd epfo;jfT 0.11 vdpy;> (i) kUj;Jtk; kw;Wk; nghwpapay; fy;Y}hpfspy; VNjDk; xU fy;Y}hpapy; Nrh;f;if fpilg;gjw;fhd epfo;jfT fhz;f. (ii) kUj;Jtf; fy;Y}papy; kl;LNkh my;yJ nghwpapay; fy;Y}hpapy; kl;LNkh Nrh;f;if fpilg;gjw;fhd epfo;jfT fhz;f.

12. “ENTERTAINMENT” vd;w nrhy;ypYs;s vOj;JfspypUe;J rktha;g;G Kiwapy; xU vOj;ijj; Njh;T nra;a> mt;ntOj;J Mq;fpy capnuOj;jhfNth my;yJ vOj;J T MfNth ,Ug;gjw;fhd epfo;jftpidf; fhz;f.

13. xU gfil ,UKiw cUl;lg;gLfpwJ. Kjyhtjhf cUl;g;gLk; NghJ xU ,ul;ilg;gil vz; fpilj;jy; my;yJ mt;tpU cUl;lypy; Kf vz;fspd; $Ljy; 8 Mf ,Uj;jy; vDk; epfo;r;rpapd; epfo;jftpidf; fhz;f.

14. 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 ];NglhfNth my;yJ ,uhrhthfNth ,Ug;gjw;;fhd epfo;jftpidf; fhz;f.

15. xU igapy; 10 nts;is> 6 rptg;G kw;Wk; 10 fUg;G epwg; ge;Jfs; cs;sd. rk tha;g;G Kiwapy;xU ge;jpid vLf;Fk; NghJ mJ nts;is my;yJ rptg;Gepwg; ge;jhf,Ug;gjw;;fhd epfo;jftpid fhz;f.

16. A, B, C MfpNahh; xU tpdhtpw;Fj; jPh;T fhz;gjw;fhd epfo;jfTfs; KiwNa > > vd;f. A

kw;Wk; B ,UtUk; Nrh;e;J jPh;T fhz;gjw;fhd epfo;jfT > B kw;Wk; C ,UtUk; Nrh;e;J jPh;T

fhz;gjw;fhd epfo;jfT > A kw;Wk; C ,UtUk; Nrh;e;J jPh;T fhz;gjw;fhd epfo;jfT > %tUk;

Nrh;e;J jPh;T fhz;gjw;fhd epfo;jfT > vdpy; ahNuDk; xUth; mt;tpdhtpd; jPh;T fhz;gjw;fhd

epfo;jftpidf; fhz;f.

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Tamil Nadu Trb Tet Tnpsc Class 10 Maths Question Bank for Centum Tamil Medium Download - Sslc Study Materials