8. f = {(-1, 2), (-3, 1), (-5, 6), (-4, 3)} - i.) ii)..

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1 இர மத ப பண கள வ ன க கள 1.கணங கள ம ச ப கள ம 1. A ={4, }, B = {2,4,6} C= {1,2,3,4,5,6 } i. A U (B C) ii. A \ (C \ B). 2.. i. (A B)' ii. A (BUC) iii. A U (B C) iv. A' B' v. A\ (B C) 3. A = { 1,4,9,16 } - B = { -1,2,-3,-4,5,6 } -?. f 1 = {(1,-1), (4, 2), (9,-3), (16,-4)} f 2 = {(1, 2), (4, 5), (9, -4), (16, 5)} f 3 = {(1,-4), (1,-1), (9,-3), (16,2)} 4. A = {1,2,3,4,5}, B = N f : A B f(x) = x² f -. 5.F = {(1, 3), (2, 5), (4, 7), (5, 9), (3, 11)},. 6.R = {(а, -2), (-5, b), (8, c), (d, -1) } abc,, d. 7. f = {(12, 2), (13, 3), (15, 3), (14, 2), (17,17)} 2,3. 8. f = {(-1, 2), (-3, 1), (-5, 6), (-4, 3)} - i.) ii).. 9. A C B A B A \ B.

2 2.எண ண யல 1. n - a n = a n-1 / n+2 n >1 n ε N 2. 20,19¼, 18½, t n n-?. 3. 4, 9, 14, ,120,115, ¼,22½, 21¾,... 3?. 6. 2/5,6/25, 18/125,. 7. 4,-2,-1,1,-1/2,. 8. 1/4, -1/2, 1,-2, ,2,4,8, a = 5, n = 30, l = 121 s n. 11. a = 5, r = 3, n = 12 s n

3 p = 171 1³ + 2³ + 3³ + +p³ =? ² + 2² + 3² ². 3. இயற கண தம x = 1/4 x = , /3, /3, -1/3 4. x³ + x² -7x -3 x x 3-2x 2 +7x-5 x x³ +x² -3x +5 x x³ - 6x² +11x - 6 x - 1.

4 8.... i. x 4-27a³x, ( x - 3a)² ii. m² -3m -18, m² +5m i. x³ + y³, x³ - y³, x 4 + x²y² + y 4 ii. 3(a-1), 2(a-1) 2, a 3-1 iii. (x+4) 2 (x-3) 3, (x-1) (x+4) (x-3) 2 iv. x²y + xy², x² + xy x+20 / 7x x 3-5x 2 / 3x 3 +2x x 2 +9 x / 3x 2 - x x x / x 2 + x+1 5. x 3-27 / x 2 +2x 3x+6 x+2 x a 3 +b 3 a 2 + b a 2 2ab+b 2 a-b 13.. x x 2 x+1 x x 2-36 / x 2-49 x+6 / x x 3 / x / 2-x 16.. (x-3) (x 2-5x +4) / (x-1) (x 2-2x+3) 17.. i. 4x 2 +20xy +25y 2 ii. 16x 2-24x+9 iii. 81x 4 y 6 z 8 / 64w 12 s 14

5 x 2 +8x+12=0 2. 2x 2-3x+4=0 3. x 2-11x+4=0 4. 2x 2 +5x+5=0 5. 4x 2-28x+49= x 2-6x+5=0 2. 3x 2-5x=0 3. 8x 2-25= (1). 3,4, (2). 7+ 3,7-3, (3). 3+ 7, x 2-5x+2=0 α, β. 1. α/β +β/α 2. α - β

6 4. அண கள 1. a ij = 2i-3j / A =[a ij ]. : 2. a ij = I - j / I + j 2 2 A =[a ij ]. 3. A = A T. 4. A = (A T ) T = A. 5.A = 3A.. 6. A = B = C = 2A + B?. 7. A = B = 6A - 3B-.?. 8..: = 9. x, y z. = 10. :: = 11. A =, A T (A T ) T. 12. A = -, A i) ii) iii) 14. அண ய ன பர க க லப ப ற த த ந ர.

7 15. A = B =, AB BA.. 5.ஆயத த ல வட வ யல 1. (3,0), (-1,4). 2. A (4,-6), B (3,-2) C (5,2). 3. (1,-1), (-5,3). 4. (1,3), (2,7) (12,-1). 5. (-6,4),. 6. (1,3) - (-7,6) (8,5). 7. A (6,7), B (-4,1) C (a,-9) ABC a-.

8 8. A (2,3), B (4,0) C (6,-3). 9. (4,3), (1,2) (-2,1). 10. ( k,-1), (2,1) (4,5) k / (3,-2) (-1,4) (3,-2) (7,2). 17. (2,-4) y- 2/ (-2,3), 1 / (-1,1), (2,-4). 21. x- 2 / 3 y- 3 / y- 4.

9 23. 4x-2 y+1=0 y-. x y =0 y (1,2), (-2,5), (3,6). 27. x- 2 y x- -1 / 3 y- 3 / x+3y-15=0 x, y x-y+16=0 x, y x+2y- x y 32. x+ y x 12=0, = =0, 2 -y+5= x+4y-6= x=5 y x+2 y+1=0, 3 x+6 y+2= x- y x y 5 +7=0, = y / 2 = x - p ax y., +5 =3 a x-2 y+9=0, ay+2 x-11=0 a வட வ யல

10 1. ABC - DE BC AD / DB =2 / 3, AE = 3.7 EC-. 2. PQR- PQ PR- S T. ST QR PS / SQ = 3 / 5 PT-., PR = ABC - A AD-, BC- D-.. BD=2.5, AB = 5 AC=4.2 DC- 4. ABC - A BC- E -. AB =10, AC = 6 BC=12 CE-. 5. ABC - DE BC AD= 6, DB = 9 AE=8 AC ABC - DE BC AD= 8, AB = 12 AE= 12 CE AP = 3, AR = 4.5, AQ =6 AE=12 AD-. 8. AD ABC - A, BC- D-. i. BD = 2, AB = 5, DC = 3 AC-. i i. AB = 5.6, AC = 6 DC, = 3 BC-. 9. AD ABC - A. i. AB = 4, AC =6, BD = 1.6 CD= 2.4 i i. AB = 6, AC =8 BD, = 1.5 CD= 3.

11 10. A, B PQR- PQ PR-. AB QR, AB = 3, PB = 2 PR= 6 QR ABC- AB AC- P Q. AP = 3, PB = 6, AQ =5 QC= 10 BC = 3 PQ. 12. ABC- 6, 4, 9 ABC PQR PQR- 35 PQR-?. 13. DE BC AD / BD = 3 / 5 i. ADE - / ABC- i i. BCED- / ABC-. 7. ம க க ணவ யல

12 1. Sinθ / cosecθ + cosθ /secθ = Ö 1-cosθ / 1+cosθ = cosec θ - cot θ. 3.Sec 2 θ + cosec 2 θ = Sec 2 θ cosec 2 θ. 4. Sinθ / 1- cosθ = cosec θ + cot θ. 5.Ö 1- Sinθ / 1+ Sinθ = sec θ - tan θ. 6.Cosθ / sec θ - tan θ = 1+ Sinθ. 7.Ö Sec 2 θ + cosec 2 θ = tan θ + cot θ. 8.Sinθ / cosec θ + cot θ = 1-cosθ. 9.sec θ (1- Sinθ) (sec θ + tan θ) = ,. (.) , Ö ?.

13 Ö 3, , , :2. 5: , ,

14 : , :3. 5: , ப ள ள ய யல

15 1. 43,24,38,56,22,39, ,46,30,23,27,40,52,35, Ö ந கழ தகவ 1..?. 2..?.

16 3..? ?. 5.? ?. 7.,?. 8. A B. P(A) = 3 / 5, P(B) = 1 / 5 P(AUB)-. 9. A B. P(A) = 1 / 4, P(B) = 2 / 5 P(AUB) = 1 / 2 P(A B)-. 10.A B. P(A) = 1 / 2, P(B) =7 / 10 P(AUB) = 1 i. P(A B) ii P(A'UB'). Prepared by S.LAKSHMI, M.SC,M.ED, M.Phil B.T ASST MATHS GOVT.GIRLS HR.SEC.SCHOOL CHIDAMBARAM CUDDALORE DT.

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