Govt Hr Sec School, Sowdhapuram, Namakkal – (Dt) (2014-15)

X– STD , MATHS (¸½¢¾õ)

MARCH-2012,2013,2014, JUNE– 2012,2013,2014, OCT- 2012,2013,2014,

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MATHS Important Public Questions-Chapterwise 2-Marks, 5-Marks,10 Marks :

2014 - 15

À¢Ã¢× -II (2 - MARKS) (Answer 10 Questions) [Qn No.30 Compulsory] [ 10 x 2 = 20 ]

[ Total No of Qns ,2 marks Qn : 108 ] [ 5 marks Qn : 88 ] [10 marks Qn : 23 ]

[ Total Qns : 219 ]

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[ 2 – MARK Questions ]

CH: I. ¸½í¸Ùõ , º¡÷Ò¸Ùõ : [2 – Qns]

I.¸½í¸û: {§¸ûÅ¢ ±ñ:16 }

1. A = {10,15,20,25,30,35,40,45,50} ,B = {1,5,10,15,20,30} ÁüÚõ

C={7,8,15,20,35,45,48} ±É¢ø A \ (B ∩ C) ¸¡ñ¸.[P.15,Ex.1.2 – (8)] [MAR-12]

2. A={4,6,7,8,9}, B = { 2,4,6 } ÁüÚõ C={ 1,2,3,4,5,6 } ±É¢ø A ∩ ( B U C ) ³ì

¸¡ñ¸. [P.11, Ex – 1.1 – (4)(ii)] [JUNE-12]

3. A = {4,6,7,8,9} ,B={2,4,6} ÁüÚõ C={1,2,3,4,5,6} ±É¢ø A∩(BUC) ¸¡ñ¸.

[ P.11, Ex1.1 – (4(ii))] [OCT-12,JUNE-12]

4. A = {4,6,7,8,9} ,B={2,4,6} ÁüÚõ C={1,2,3,4,5,6} ±É¢ø A⋃(B∩C) ¸¡ñ¸.

[ P.11, Ex1.1 – (4)(i)] [M’14]

5. U = {4,8,12,16,20,24,28} , A = {8,16,24} k‰W« B = {4,16,20,28} våš, (A∪ 𝐵)′

k‰W« (A∩ 𝐵)′ M»at‰iw¡ fh©f. [ P.15, Ex1.2 – (5)] [Jn’14]

6. (A∪ 𝐵)′ ¡F bt‹gl« tiuf. (C.Q) [OCT-13]

7. A ⊂ B våš, A ∩ B k‰W« A \ B M»at‰iw¡ fh©f. (bt‹gl¤ij¥ ga‹gL¤Jf). [ P.11, Ex1.1 – (2)] [Oct’14]

º¡÷Ò¸û: {§¸ûÅ¢ ±ñ:17} 1. X = { 1, 2 , 3 , 4 , 5 } , Y = { 1 , 3 , 5 , 7 , 9 } ±ý¸. X Ä¢ÕóÐ Y ì¸¡É ¯È×

{(1,1),(1,3),(3,5),(3,7),(5,7)} ±É ŨÃÂÚôÀ¢ý «Ð º¡÷Ò ¬ÌÁ¡ ±É ¬Ã¡ö¸. þø¨Ä

±É¢ø ¸¡Ã½õ ÜÚ :- [P.29 , EX - 1.4 4(iii)] [MAR’12]

2. 𝑓 = { (12 , 2), (13 , 3) ,(15 , 3),(14 , 2),(17 , 17)} ±ýÈ º¡÷À¢ø 2 ÁüÚõ 3

¬¸¢ÂÅüÈ¢ý Óý ¯Õ츨Çì ¸¡ñ¸. [P.29, Ex1.4 – (8)] [JUNE-12]

3.A ={1,4,9,16} Ä¢ÕóÐ B={-1,2,-3,-4,5,6} ìÌ f = {(1,-1),(4,2),(9,-3),(16,-4)} ±ýÀÐ ´Õ

º¡÷À¡ÌÁ¡? 𝑓 ±ýÀÐ º¡÷Ò ±É¢ø «¾ý ţò¨¾ì ¸¡ñ.[P.22 Eg.1.17] [OCT-12]

4. A= { l,m,n,o,2,3,4,7} ÁüÚõ B={2,5,3,-2,m,n,o,p} ¬¸¢ÂÅüÈ¢üÌ ¸½í¸Ç¢ý ¦ÅðÎ,

ÀâÁ¡üÚô ÀñÒ ¯¨¼ÂÐ ±ýÀ¨¾ ºÃ¢À¡÷ì¸×õ. [P.11, Ex – 1.1 – (6)][March-13]

5. R = { (a,-2),(-5,b),(8,c),(d,-1)} ±ýÀÐ ºÁÉ¢ º¡÷¨Àì ÌÈ¢ìÌõ ±É¢ø a,b,c ÁüÚõ d

¬¸¢ÂÅüÈ¢ý Á¾¢ôÒ¸¨Çì ¸¡ñ¸,[P.29, Ex.1.4 – (5), S.B:P.15 – 5)] [MAR’13][Compulsary Qn]

6. A = {1, 2, 3, 4} k‰W« B = {- 1, 2, 3, 4, 5, 6, 7, 9,10 ,11,12} v‹f. R = {(1, 3), (2, 6), (3, 10), (4, 9)} ⊆ A × B xU

cwÎ våš, R I xU rh®ò vd¡fh£Lf. mj‹ kÂ¥gf«, Jiz kÂ¥gf« k‰W« Å¢rf« M»adt‰iw¡

fh©f. [g¡f« : 21 , v.fh. 1.14] [OCT-13]

7. X = {1,2,3,4} என்க. 𝑓 = { (2 , 3), (1 , 4) ,(2 ,1),(3 , 2),(4 ,4)} என்ம உமவு X- யிருந்து X-க்கு

ஒரு சார்பாகுா? என ஆாய்க.உன் விடைக்கு ஏற்ம விரக்கம் தருக. [g¡f« : 22 , v.fh. 1.16(i)] [M-14]

8. º¡÷Ò ƒ : [ -3 , 7) ⟶ 𝑅 ¸£ú¸ñ¼Å¡Ú ŨÃÂÚì¸ôÀðÎûÇÐ.

𝑓 𝑥 = 4𝑥2 − 1 ; −3 ≤ 𝑥 < 2 3𝑥 − 2 ; 2 ≤ 𝑥 ≤ 42𝑥 − 3 ; 4 < 𝑥 ≤ 6

±É¢ø À¢ýÅÕÅÉÅü¨Èì ¸¡ñ¸:-

(i) 𝑓 5 + 𝑓 6 [P.30, Ex–1.4(15(i))] [June’14]

9. A = { 5, 6, 7, 8 }; B = { –11, 4, 7, –10,–7, –9,–13 } v‹f. f = {( x,y) : y = 3 - 2x, x ∈ A, y ∈ B }

vd tiuaW¡f¥g£LŸsJ våš f ‹ Å¢rf« fh©f [g¡f« : 29 , gæ‰Á 1.4 (10)] [Oct-14]

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CH: II. ¦Áö¦Âñ¸Ç¢ý ¦¾¡¼÷Å⨺¸Ùõ ¦¾¡¼÷¸Ùõ: {§¸ûÅ¢ ±ñ:17}

1. 5+11+17+... ... +95 ±ýÈ ÜðÎò¦¾¡¼Ã¢ý Üξ¨Äì ¸¡ñ¸ [P.53, ±.¸¡.-2.16][Á¡÷î-13]

2.13+2

3+3

3+ ... ... + n

3 = 36100 ±É¢ø 1+2+3+... ... +n ý Á¾¢ô¨Àì ¸¡ñ¸.

[P.66, ±.¸¡: 2.33-(ii)] [June-2013]

3. bjhl® tçiræšyhj rh®ò¡F xU vL¤J¡fh£L jUf. (C.Q) [OCT-13]

4). 4,9,14 ... ... ... என்ம கூட்டு ததாைர் வரிடசின் 17-வது உறுப்டபக் காண்க [g¡f« : 43, gæ‰Á 2.2 - (5)] [M-14]

5. 5 + 11 +17+ ... ... +95 v‹w T£L¤bjhlçš v¤jid cW¥òfŸ cŸsd ? (C.Q) (June-14)

6.ËtU« bjhl®fë‹ TLjiy¡ fh©f. 13

+23

+33

+… …+203

[g¡f« : 65, v.fh 2. 31 ] [Oct-14]

CH: III. þÂü¸½¢¾õ: {§¸ûÅ¢ ±ñ:18 («) 19} [1-Qn]

1) 3 , 4 ¬¸¢ÂÅü¨È ãÄí¸Ç¡¸ì¦¸¡ñ¼ þÕÀÊ ºÁýÀ¡ð¨¼ì ¸¡ñ¸.

[P. 119 Ex 3.18 , 2(i)] [JUNE-12](OCT’12)

2) 𝛼 ,𝛽 ±ýÀÉ 3x2

– 6x + 4 = 0 ±ýÛõ ºÁýÀ¡ðÊý ãÄí¸û ±É¢ø 𝛼2 + 𝛽2 ý Á¾¢ôÒì

¸¡ñ¸. [P.120, Ex 3.18 – (4)] [MAR’12]

3) ax2 -5x + c ±ýÈ þÕÀÊ ºÁýÀ¡ðÊý ãÄí¸Ç¢ý Üξø 10,ÁüÚõ ¦ÀÕì¸üÀÄý 10

±É¢ø a ÁüÚõ c ¬¸¢ÂÅüÈ¢ý Á¾¢ôÒ¸¨Çì ¸¡ñ¸. [P.116, ±.¸¡.-3.49][Á¡÷î-2013]

4) x = 1

4 ÁüÚõ x = -1 ±ýÈ âÂí¸¨Çì ¦¸¡ñ¼ þÕÀÊ ÀøÖÚôÒì §¸¡¨Å¨Âì

¸¡ñ¸. [P.85, ±.¸¡.-3.13] [ ƒ£ý – 2013 ]

5) ¾£÷ì¸ : 𝓍 + 1

𝑥 =

26

5 [P.85, ±.¸¡.-3.13] [Jn-13]

6. þÕ ¦¾¡¼÷ó¾ ´ü¨ÈôÀ¨¼ ±ñ¸Æ¢ý Üξø 20 ±Ç¢ø «ù¦Åñ¸¨Æì ¸¡ñ¸.(C.Q) [MAR’12]

7. Û.bgh.k fh©f. x2y+ xy

2 , x

2+ xy [g¡f« : 95, gæ‰Á 3.7 – (6)] [OCT-13]

8.Ô®¡f. 3x - 8

𝑥 = 2 [g¡f« : 108, gæ‰Á 3.14 - (v)] [OCT-13]

9. m2-3m-18 , m

2+5m+6 ஆகி ககாடவகரின் ீ.தபா.வ fh©f. [g¡f« : 93, gæ‰Á 3.6 – 2(iii)] [M-14]

10.7+ 3 ற்றும் 7+ 3 ஆகிவற்டம மூயங்கராகக் தகாண்ை இருபடிசன்பாடு ஒன்மிடன அடக்க:- [P.119 , ±.¸¡.-3.51] [M-14,Oct-14]

11.RU¡Ff :

𝑥2−4

𝑎2−1 ×

𝑎3−𝑎

𝑥3+2𝑥2 [C.Q] [June-2014]

12. bjhFKiw tF¤jiy¥ ga‹gL¤Â ËtUtdt‰¿‰F <Î k‰W« Û fh©f.

(3x3 +4x

2 -10x + 6) ÷ (3x – 2) [g¡f« : 88, gæ‰Á 3.4 – 1(iii)] [Oct-14]

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CH: IV. «½¢¸û : {§¸ûÅ¢ ±ñ:20 & 21 («øÄÐ) 19 & 20} [2 – Qns]

1. A = 8 5 21 −3 4

±É¢ø 𝐴𝑇 ÁüÚõ 𝐴𝑇 T ¬¸¢ÂÅü¨Èì ¸¡ñ¸.[ P.131, Eg 4.5] [Jn-12,14,M-13]

2. 3 −25 1

4 1 2 7

±ýÈ «½¢¸Ç¢ý ¦ÀÕ츨Äì ¸¡ñ¸.[ P.144,Ex 4.3 - (2)-(ii)]

[June’12] [MAR-12]

3. A= 1 3 9 − 6

±É¢ø AI = IA = A ±ýÀ¨¾î ºÃ¢À¡÷ì¸.þíÌ I ±ýÀÐ Å⨺ 2

¯¨¼Â «ÄÌ «½¢. [P.142 Eg. 4.17] [OCT-12,M-14]

4. A = 4 −25 −9

, B = 8 2−1 −3

±É¢ø 6 A – 3 B ±ýÈ «½¢¨Âì ¸¡ñ¸.

[P.136 – Ex.4.2–(5)] [MAR-12]

5. A= 2 3−9 5

- 1 5

7 − 1 ±É¢ø A ý Üð¼ø §¿÷Á¡Ú «½¢¨Âì ¸¡ñ¸.

[P.136, Ex 4.2 – (3)] [OCT’12,13]

6. 30 ¯ÚôÒ¸û ¦¸¡ñ¼ «½¢ìÌ ±ùŨ¸ Å⨺¸û þÕì¸ þÂÖõ? [Àì.132, À¢üº¢ : 4.1- (5)] [ƒ£ý13]

7. A =(1 2 -1) , B = 214 ±É¢ø 𝐴𝐵 T – ¨Âì ¸¡ý¸. C.Q [ƒ£ý13]

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8. mâæ‹ bgU¡fš gy‹ fh©f : 6−3

2 −7 (C.Q) [OCT-13]

9. aij = 2𝑖 − 3𝑗 v‹w cW¥òfis¡ bfh©l, tçir 2 x 3 cŸs mâ A = [aij] – æidmik¡fΫ.

[g¡f« : 131 , v.fh. 4. 4] [M-14](Compulsary Question)

10. A = 3 25 1

, B = 8 −1 4 3

våš C = 2A+B v‹w mâia¡ fh©f

[Àì.136, À¢üº¢ : 4.2- (4)] [ƒ£ý14]

11. 2𝑥 + 5𝑥 − 3𝑦

= 6

13 våš, x k‰W« y - fë‹ Ô®Îfis¡ fh©f. [Àì.136, À¢üº¢ : 4.2- (2)] [m¡-14]

12. ËtUtdt‰¿‰F mâfë‹ bgU¡fš tiuaW¡f¥gLkhdhš, mt‰iw¡ fh©f.

2 9 −34 −1 0

= 4 2−6 7−2 1

[g¡f« : 144 , gæ‰Á 4.3] [m¡-14]

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CH: V. ¬Âò¦¾¡¨Ä ÅÊÅ¢Âø : {§¸ûÅ¢ ±ñ: 22 (or) 23} [1-Qn] 1. ´Õ Åð¼ò¾¢ý ¨ÁÂõ ( - 6 , 4 ) «ùÅð¼ò¾¢ý ´Õ Å¢ð¼ò¾¢ý ´Õ Ó¨É

¬¾¢ôÒûÇ¢ ±É¢ø, Áü¦È¡Õ ӨɨÂì ¸¡ñ¸. [ P.154, Ex – 5.1 (3)] [JUNE’12,14]

2. 5x – 2y - 9 = 0,ay + 2x – 11 = 0 ¬¸¢Â §¿÷째¡Î¸û ´ýÚ즸¡ýÚ ¦ºíÌòÐ

±É¢ø a - ý Á¾¢ô¨Àì ¸¡ñ¸. [P.176, À¢üº¢ :5.5–5, S.B:P.162][MARCH -2013]

3. (7,3), (6,1), (8,2) ÁüÚõ (P,4) ±ýÀÉ µ÷ þ¨½¸Ãò¾¢ý Å⨺ÀÊ «¨Áó¾ ¯îº¢¸û

±É¢ø P – ý Á¾¢ô¨Àì ¸¡ñ¸. [P.153 , Eg – 5.6] [JUNE’12]

4. º¡ö×째¡½õ 30 ͦ ¦¸¡ñ¼ ÁüÚõ (4,2),(3,1) ¬¸¢Â ÒûÇ¢¸¨Ç þ¨½ìÌõ

§¿÷째¡ðÎò ÐñÊý ¿ÎôÒûÇ¢ ÅƢøÖõ §¿÷째¡ðÊý ºÁýÀ¡ð¨¼ì

¸¡ñ¸. [ P.173 , Ex.5.4 – (7)] [OCT’12]

5) A(4,-6), B(3,-2) ÁüÚõ C(5,2) ¬¸¢ÂÅü¨È ¯îº¢¸Ç¡¸ì ¦¸¡ñ¼

Ó째¡½ò¾¢ý ¿Î째¡ðÎ ¨ÁÂõ ¸¡ñ¸. [P.153 Eg. 5.5] [OCT-12]

6.ÒûÇ¢ (1,3) ¨Â ¿Î째¡ðΨÁÂÁ¡¸ì ¦¸¡ñ¼ Ó째¡½ò¾¢ý þÕ Ó¨É¸û(-7,6) ÁüÚõ

(8,5) ±É¢ø Ó째¡½ò¾¢ý ãýÈ¡ÅРӨɨÂì ¸¡ñ¸.[Àì.154,À¢üº¢:5.1- (4)][Á¡÷î-12]

7. (6,7), B(-4, 1) ÁüÚõ C(a,-9) ¬¸¢ÂÅü¨È Өɸǡ¸ì ¦¸¡ñ¼ ∆ ABC – ý ÀÃôÒ

68 º.«Ä̸û ±É¢ø a –ý Á¾¢ô¨Àì ¸¡ñ¸. [P.158, ±.¸¡:5.9] [ƒ£ý13]

8. (-5,-2) ±ýÈ ÒûÇ¢ÅÆ¢ ¦ºøÅÐõ ¬Â «î͸ÙìÌ þ¨½Â¡ÉÐÁ¡É §¿÷째¡Î¸Ç¢ý

ºÁýÀ¡Î¸¨Çì ¸¡ñ¸. [P.170,±.¸¡:5.19] [ƒ£ý13]

9. rhŒÎ¡ nfhz« 45° k‰W« y-bt£L¤J©L

2

5 M»at‰iw¡ bfh©l ne®¡nfh£o‹ rk‹gh£il¡

fh©f. [g¡f« : 170 , v.fh. 5. 20] [OCT-13]

10. A(2 , 3), B(4 , 0) k‰W« C(6, -3) M»a òŸëfŸ xnu ne®¡nfh£oš mikªJŸsd vd ã%Ã.

[g¡f«: 158 , v.fh. 5. 10] [OCT-13]

11. (3,- 4) v‹w òŸë tê¢ bršY« k‰W« Ma m¢RfS¡F Ïizahf mikªj ne®¡nfhLfë‹

rk‹ghLfis¡ fh©f. [g¡f«: 170 , v.fh. 5. 19] [M-14] (Compulsary Question)

12. (-2,3) ±ýÈ ÒûÇ¢ÅÆ¢ ¦ºøÅÐõ º¡ö× 1

3 ¯¨¼ÂÐÁ¡É §¿÷째¡ðÊý

ºÁýÀ¡ð¨¼ì ¸¡ñ¸. [P.170,±.¸¡:5.21] [ƒ£ý14]

13. (–3, 5) k‰W« (4, –9) M»a òŸëfis Ïiz¡F« nfh£L¤ J©oid c£òwkhf 1 : 6 v‹w é»j¤Âš

Ãç¡F« òŸëæ‹ m¢R¤bjhiyÎfis¡fh©f? (C.Q) Model [g¡f«: 151 , v.fh. 5. 3] [Oct-14]

CH: VI. ÅÊÅ¢Âø : {§¸ûÅ¢ ±ñ: 23 (or) 24} [1-Qn]

1. ∆ ABC ø DE || BC ÁüÚõ 𝐴𝐷

𝐷𝐵 =

2

3 AE = 3.7 ¦º.Á£ ±É¢ø EC ³ì ¸¡ñ¸.

[JUNE-12,14] [Àì¸õ:187 (±.¸¡.6.1)]

A

D E

B C

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2.

A B

4344

P

T

À¼ò¾¢ø , TP ´Õ ¦¾¡Î§¸¡Î, A,B ±ýÀÉ Åð¼ò¾¢ý Á£ÐûÇ ÒûÇ¢¸û. ∠BTP=720 ÁüÚõ

∠ATB = 430 ±É¢ø ∠ABT - ³ì ¸¡ñ¸. [ P.203, Ex.6.3 -1] [MAR - 13](SCORE BOOK : P. 183)

3. ΔABC -ø ∠𝐴 ±ýÈ §¸¡½ò¾¢ý ¯ðÒÈ þÕºÁ ¦ÅðÊ AD ¬ÉÐ Àì¸õ BC ³

D-ø ºó¾¢ì¸¢ÈÐ.§ÁÖõ BD = 2.5 ¦º.Á£ ,AB=5 ¦º.Á£ ÁüÚõ AC=4.2 ¦º.Á£ ±É¢ø

DC ³ì ¸¡ñ¸. [P.189, Eg. 6.5] [MAR’12, OCT-12,13]

4. Q

M

10cm

N

12 cm O 6cm P

MP ±ýÀÐ ∆MNO – ø ∠M – ý ¦ÅÇ¢ôÒÈ þÕ ºÁ¦ÅðÊ. §ÁÖõ ÏJ NO – ý ¿£ðº¢Â¢¨É

P –ø ºó¾¢ì¸¢ÈÐ.MN = 10 ¦º.Á£, MO = 6 ¦º.Á£, NO = 12 ¦º.Á£ ±É¢ø

OP –¨Âì ¸¡ñ¸. [Àì¸õ:191,À¢üº¢ : 6.1 – (11)] (ƒ£ý – 13) [m¡-14] (compalsary Qn)

5. xU t£l¤Âš AB, CD v‹D« ÏU eh©fŸ x‹iwbah‹W c£òwkhf P-æš

bt£o¡ bfhŸ»‹wd.

(i) CP = 4 br.Û, AP = 8 br.Û., PB = 2 br.Û våš, PD-I¡ fh©f. [g¡f« : 203, gæ‰Á 6.3 - 2(i)] [M-14]

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CH: VII. Ó째¡½Å¢Âø : {§¸ûÅ¢ ±ñ: 24 &25 (or) 25 &26} [2-Qns]

1. sin 𝜃

cosec 𝜃+

cos 𝜃

sec 𝜃 = 1 ±ýÀ¨¾ ¿¢Ú׸. [P.208, Eg – 7.1] [JUNE’12]

2. 1−𝑠𝑖𝑛𝜃

1+𝑠𝑖𝑛𝜃 = sec𝜃 - tan𝜃 ±É ¿¢Ú׸. [P.214 , Ex 7.1 – 2 (iii)] [OCT’12][Jn-14]

3. 1sin2𝜃

− 1−sin2𝜃1−cos2𝜃

= 1 ±É ¿¢Ú׸. {C.Q} [March-2013]

4. cos 𝜃

sec 𝜃−tan 𝜃 = 1 + sin 𝜃 ±ýÈ Óü¦È¡Õ¨Á¨Â ¿¢Ú׸. [P.214,À¢üº¢ 7.1 – 2(iv)] [ƒ£ý13]

5. θ xU FW§nfhz« k‰W« sinθ = cos𝜃 våš tan2θ – 2cos2θ = 0 vd ã%áf. (C.Q) [OCT-13]

6.

1+𝑠𝑒𝑐𝜃

𝑠𝑒𝑐𝜃=

𝑠𝑖𝑛²𝜃

1−𝑐𝑜𝑠𝜃 vd ãWÎf [g¡f« : 212 , v.fh. 7. 10] [OCT-13]

7. ËtU« K‰bwhUikia ãWÎf. 𝑠𝑒𝑐2𝜃 + 𝑐𝑜𝑠𝑒𝑐2𝜃 = tanθ + cotθ [g¡f« : 214, gæ‰Á 7.1 - 2(v)] [M-14]

8. ËtU« K‰bwhUikfis ãWÎf.

sin 𝜃

cosec 𝜃+𝑐𝑜𝑡𝜃 = 1 - cosθ [g¡f« : 214, gæ‰Á 7.1 – 2 (viii)] [Oct-14]

9. ÍÅâø º¡öòÐ ¨Åì¸ôÀð¼ ´÷ ²½¢Â¡ÉÐ ¾¨ÃÔ¼ý 60 ͦ §¸¡½ò¨¾

²üÀÎòи¢ÈÐ.²½¢Â¢ý «ÊôÀ¡¸õ ÍÅüȢĢÕóÐ 3.5 Á£ àÃò¾¢ø ¯ûÇÐ

±É¢ø, ²½¢Â¢ý ¿£Çò¨¾ì ¸¡ñ¸. [ P.218 ±.¸¡:7.15] [4Á¡÷î-13,2-Á¡÷ì-«ì-12,ƒ£ý-14]

10. 30 Á£ ¿£ÇÓûÇ ´Õ ¸õÀò¾¢ý ¿¢ÆÄ¢ý ¿£Çõ 10 3 Á£ ±É¢ø ÝâÂÉ¢ý ²üÈì

§¸¡½ò¾¢ý (¾¨ÃÁð¼ò¾¢Ä¢ÕóÐ ²üÈì §¸¡½õ) «ÇÅ¢¨Éì ¸¡ñ¸.

[P.218,Eg – 7.16] [MAR’12,14]

11. ¯ÂÃõ 150 ¦º.Á£ ¯ûÇ ´Õ º¢ÚÁ¢ Å¢ÇìÌì ¸õÀò¾¢ý Óý ¿¢ýÈÅ¡Ú 150 3 ¦º.Á£

¿£ÇÓûÇ ¿¢Æ¨Ä ²üÀÎòи¢È¡û ±É¢ø, Å¢ÇìÌì ¸õÀò¾¢ý ¯îº¢Â¢ý ²üÈì

§¸¡½ò¨¾ì ¸¡ñ¸. [P.225, Ex – 7.2 (2)] [JUNE’12]

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12. 5 «Ê ¯ÂÃÓûÇ ´Õ º¢ÚÅý ´Õ རĢÕóÐ 100 «Ê àÃò¾¢ø ¿¢ýÚ «¾ý ¯îº¢¨Â

450 ²üÈì §¸¡½ò¾¢ø À¡÷ò¾¡ø རý ¯ÂÃõ ±ýÉ? [C.Q]

13. xU Rik C®ÂæèUªJ (truck) Rikia Ïw¡f VJthf 300

V‰w¡ nfhz¤Âš xU rhŒÎ¤ js« (ramp)

cŸsJ. rhŒÎ¤ js¤Â‹, c¢Á jiuæèUªJ 0.9 Û cau¤Âš cŸsJ våš, rhŒÎ¤ js¤Â‹ Ús«

ahJ? [g¡f« : 225, gæ‰Á 7.2 – (1 )] [Oct-14]

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CH: VIII. «ÇÅ¢Âø : {§¸ûÅ¢ ±ñ: 26 &27 (or) 27 &28} [2-Qns]

1. ´Õ ¯ûÇ£¼üÈ ¯Õ¨Ç¢ý ¯û ÁüÚõ ¦ÅÇ¢ ¬Ãí¸û Өȧ 12 ¦º.Á£

ÁüÚõ 18 ¦º.Á£ ±ý¸.§ÁÖõ «¾ý ¯ÂÃõ 14 ¦º.Á£ ±É¢ø , «ù×ըǢý

ŨÇÀÃôÒ ¸¡ñ¸. (𝜋 =22

7 ±ý¸) [P.234,Eg.8.5] [MAR-12]

2. ´Õ ¾¢ñÁìÜõÀ¢ý ¬Ãõ ÁüÚõ º¡ÔÂÃõ Өȧ 20 ¦ºÁ£ ÁüÚõ 29 ¦º.Á£

±É¢ø «ò¾¢ñÁìÜõÀ¢ý ¸É «Ç¨Åì ¸¡ñ¸. [P.250, Ex.8.2 – (9)] [MAR-12]

3. ´Õ ¾¢ñÁ §¿÷Åð¼ ÜõÀ¢ý ¬Ãõ ÁüÚõ ¯ÂÃõ 7 ¦º.Á£ ÁüÚõ 24 ¦º.Á£ ±É¢ø ,

«¾ý ŨÇÀÃô¨Àì ¸¡ñ¸. [P.241, Ex– 8.1 - (10)] [JUNE-12]

4. ´Õ ¾¢ñÁ ¯Õ¨Ç¢ý ¬Ãõ 14 ¦º.Á£,«¾ý ¯ÂÃõ 30 ¦º.Á£ ±É¢ø

«ù×ըǢý ¸É«Ç¨Åì ¸¡ñ¸. [ P.249 Ex.8.2-(i)] [OCT-12]

5. 8.4 ¦º.Á£ Å¢ð¼õ ¦¸¡ñ¼ ´Õ §¸¡ÇÅÊÅ ¾¢ñÁ ¯§Ä¡¸ ±È¢ÌñÊý

¸É«Ç¨Åì ¸¡ñ¸.( 𝜋 = 22

7 ) [P.248, [Àì-248 , ±.¸¡ : 8.17][Á¡÷î -13]

6. Өȧ 3 ¦º.Á£ ÁüÚõ 4 ¦º.Á£ ¬Ãí¸Ç¡¸ì ¦¸¡ñ¼ þÕ §¸¡Çí¸Ç¢ý ¸É

«Æ׸Ƣý Å¢¸¢¾ò¾¢¨Çì ¸¡ñ¸. (C.Q) [JUNE’12]

7. ´Õ ¾¢ñÁ §¿÷Åð¼ì ÜõÀ¢ý «ÊîÍüÈÇ× 236 ¦º.Á£ ÁüÚõ «¾ý º¡ÔÂÃõ 12 ¦º.Á£

±É¢ø «ìÜõÀ¢ý ŨÇÀÃô¨Àì ¸¡ñ¸. [P.241,À¢üº¢ 8.1-12,S.B:214-12][Mar-13,Jn- 13]

8. 62.37 ¸.¦º.Á£ ¸É «Ç× ¦¸¡ñ¼ ´Õ ¾¢ñÁ §¿÷Å𼠯ըǢý ¯ÂÃõ 4.5 ¦º.Á£

±É¢ø «ù×ըǢý ¬Ãò¨¾ì ¸¡ñ¸. [Àì¸õ:249,À¢üº¢:8.2 – (4)] [ƒ£ý13]

9. 98.56 r.br.Û òw¥gu¥ò bfh©l xU ©k¡ nfhs¤Â‹ Mu¤ij¡ fh©f.

[g¡f« : 241, gæ‰Á 8.1 – (16)] [OCT-13]

10. ku¤Âdhyhd xU ©k¡ T«Ã‹ mo¢R‰wsÎ 44 Û. k‰W« mj‹ cau« 12 Û våš m¤Â©k¡

T«Ã‹ fdmsit¡ fh©f. [g¡f« : 250, gæ‰Á 8.2 – (10 - model)][C.Q] [OCT-13]

11. xU ©k ne® t£l cUisæ‹ Mu« 14 br.Û k‰W« cau« 8 br.Û. våš, mj‹tisgu¥ò k‰W«

bkh¤j¥ òw¥gu¥ig¡ fh©f. [g¡f« : 240, gæ‰Á 8.1 – (1)] [M-14]

12) 4.2 Û é£lKŸs miu¡nfhs tot¤ bjh£oæš ãu¥g¥gL« Úç‹ fdmsit è£lçš fh©f.(C.Q)(M’14)

13. 14 br.Û g¡f msÎ bfh©l xU fd¢rJu¤Âš ÏUªJ äf¥bgça (Û¥bgU fdmsΟs) nfhs«

bt£obaL¡f¥gL»wJ våš , m¡nfhs¤Â‹ fdmsÎ fh©f. [g¡f« : 250, gæ‰Á 8.2 – (19)] [Model- Jn-14]

14. xU ©k miu¡nfhs¤Â‹ bkh¤j òw¥gu¥ò 675r r.br.Û våš mj‹ tisgu¥ig¡fh©f.

[g¡f« : 240, v.fh 8.10 ] [Jn-14] (Compulsary Qn)

15. xU ©k ne® t£l cUisæ‹ bkh¤j¥ òw¥gu¥ò 231 r. br.Û. mj‹ tisgu¥ò bkh¤j òw¥gu¥Ãš

_‹¿š Ïu©L g§F våš, mj‹ Mu« k‰W« cau¤ij¡ fh©f. [g¡f« : 240, gæ‰Á 8.1 – (5)] [Jn-14](compalsary)]

16) 14 Û MHKŸs xU »z‰¿‹ Mu« 5 Û. xU rJu Û£lU¡F %.2 Åj« m¡»z‰¿‹ c£òw¢ Rt‰¿‰F Ábk©£ ór

MF« bryéid¡ fh©f. [g¡f« : 232, v.fh : 8.1 (modal)] [Oct-14](C.Q)]

17) 21 br.Û MuKŸs xU t£l¤ÂèUªJ 1200

ika¡ nfhz« bfh©l xU t£l¡nfhz¥gFÂia

bt£obaL¤J, mj‹ Mu§fis x‹¿iz¤J xU T«gh¡»dhš,»il¡F« T«Ã‹ tisgu¥ig¡

fh©f (𝜋 =22

7). [g¡f« : 237, v.fh : 8.8] [Oct-14] (Compalsary Qn)]

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CH: XI. ÒûǢ¢Âø : {§¸ûÅ¢ ±ñ: 28 } [1-Qn] 1. 43,24,38,56,22,39,45 ¬¸¢Â ÒûÇ¢ Å¢ÅÃí¸Ç¢ý Å£îÍ ÁüÚõ Å£îÍì ¦¸Ø

¸¡ñ¸. [P.293, Eg.11.1] [MAR-12]

2. ËtU« kÂ¥òfS¡F Å¢R k‰W« Å¢R¡ bfG fh©f. 59, 46, 30, 23, 27, 40, 52, 35, 29.

[g¡f« : 308, gæ‰Á 11.1-(Ï) ] [m¡-14]

www.Padasalai.Net

3. ´Õ ÒûÇ¢ Å¢ÅÃò¦¾¡ÌôÀ¢ý Á£ô¦ÀÕ Á¾¢ôÒ 7.44 ÁüÚõ «¾ý Å£îÍ 2.26

±É¢ø, «ò¦¾¡ÌôÀ¢ý Á£îº¢Ú Á¾¢ô¨Àì ¸¡ñ¸.[P.294 , Eg 11.3] [OCT-12]

4. 50 «Ç׸Ǣø Á¢¸ô¦Àâ Á¾¢ôÒ 3.84 ¸¢.¸¢., «¾ý Å£îÍ 0.46 ¸¢.¸¢., ±É¢ø

«ÅüÈ¢ý Á£îº¢Ú Á¾¢ô¨Àì ¸¡ñ¸.[P.308,Ex.11.1-(3),(SB.273-3) MARCH-13]

5. ´Õ ÒûǢŢÅÃò¾¢ý Á¡ÚÀ¡ðÎì¦¸Ø 57 ÁüÚõ ¾¢ð¼Å¢Äì¸õ 6.84 ±É¢ø, «¾ý

ÜðÎîºÃ¡ºÃ¢¨Â측ñ¸. [P.309, Ex – 11.1 (17)] {JUNE’12,13}

6. Kjš 13 Ïaš v©fë‹ Â£l éy¡f¤ij¡ fz¡»Lf. [g¡f« : 308, gæ‰Á 11.1 – (5)] [OCT-13]

7. Kjš 10 Ïaš v©fë‹ Â£l éy¡f¤ij¡ fh©f. [g¡f« : 300, v.fh. 11.11 ] [M-14]

CH – XII : ¿¢¸ú¾¸× {§¸ûÅ¢ ±ñ: 29 } [1-Qn]

1. Ó¾ø þÕÀÐ þÂø ±ñ¸Ç¢Ä¢ÕóÐ ´Õ ÓØ ±ñ ºÁÅ¡öôÒ Ó¨È¢ø

§¾÷ó¦¾Îì¸ôÀθ¢ÈÐ. «ó¾ ±ñ ´Õ À¸¡ ±ñ½¡¸ þÕôÀ¾ü¸¡É ¿¢¸úò¾¸Å¢¨Éì

¸¡ñ¸. [P.317 , Eg – 12.3] [MAR’12]

2. 35 ¦À¡Õð¸û «¼í¸¢Â ¦¾¡ÌôÒ ´ýÈ¢ø 7 ¦À¡Õð¸û ̨ÈÀ¡Î¨¼ÂÉ.

«ò¦¾¡ÌôÀ¢Ä¢ÕóÐ ´Õ ¦À¡Õû ºÁÅ¡öôÒ Ó¨È¢ø §¾÷ó¦¾ÎìÌõ §À¡Ð «Ð

̨ÈÀ¡¼üÈ ¦À¡ÕÇ¡¸ þÕôÀ¾üì¸¡É ¿¢¸úò¾¸× ¡Р? [P.317, Eg – 12.4] [JUNE’12]

3. ´Õ º£Ã¡É À¸¨¼ þÃñÎ Ó¨È ¯Õð¼ôÀθ¢ÈÐ.Ó¸ ±ñ¸Ç¢ý Üξø 9

¸¢¨¼ì¸ô ¦ÀÚžü¸¡É ¿¢¸ú¾¸× ¸¡ñ¸. [P.322,Ex – 12.1 (2)] [OCT’12,14]

4. ¿ýÌ ¸¨ÄòÐ «Î츢 ¨Åì¸ôÀð¼ 52 º£ðθ¨Çì ¦¸¡ñ¼ º£ðÎì ¸ðÊÄ¢ÕóÐ

ºÁÅ¡öôÒ Ó¨È¢ø ´Õ º£ðÎ ±Îì¸ôÀθ¢ÈÐ. «ó¾ º£ðÎ Š¤À¼¡¸¤Å¡ (Spade)

«øÄÐ þạš¸§Å¡ (King) þÕôÀ¾ü¸¡É ¿¢¸ú¾¸Å¢¨Éì ¸¡ñ¸.

[Àì¸õ: 329,À¢üº¢:12.2-(10)] [ƒ£ý–13]

5. e‹F fiy¤J it¡f¥g£l 52 Ó£Lfis¡ bfh©l Ó£L¡ f£oèUªJ rkthŒ¥ò¢ nrhjid

Kiwæš xU Ó£L vL¡f¥gL»wJ. mªj¢ Ó£L ËtUtdthf ÏU¡f ãfœjfÎfis¡ fh©f.

(i) fU¥ò Ïuhrh (ii) °ngL fh®L [g¡f« : 318 , v.fh. 12. 6] [OCT-13]

6. _‹W gfilfŸ xnu neu¤Âš cU£l¥gL«nghJ, _‹W gfilfëY« xnu v©»il¥gj‰fhd

ãfœ¢Áæ‹ ãfœ¤jféid¡ fh©f. . [g¡f« : 323, gæ‰Á 12.1 – (14)] [M-14]

7. 20 Ó£Lfëš 1 Kjš 20 tiuÍŸs KG v©fŸ F¿¡f¥g£LŸsd. rkthŒ¥ò Kiwæš xU Ó£L

vL¡f¥gL»‹wJ. m›thW vL¡f¥g£l Ó£oYŸs v© 4-‹ kl§fhf ÏU¡f ãfœjfÎ fh©f.

[g¡f« : 323, gæ‰Á 12.1 – (12)] [É‹-14]

(((((((((((((((((((((((((((((((((((((((((((((((((((((((()))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

X – STD , MATHS (¸½¢¾õ) À¢Ã¢× -III (5 – MARKS) (Answer 9 Questions ) [ Qn No.45 Compulsory] [ 9 x 5 = 45 ]

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CH: I. ¸½í¸Ùõ , º¡÷Ò¸Ùõ : [2 – Qns] {§¸ûÅ¢ ±ñ: 31 & 32} [2 – Qns]

I - ¸½í¸û: {§¸ûÅ¢ ±ñ:31}

1. U = { -2 ,-1, 0 ,1, 2 , 3 ... , 10 } , A = { -2 , 2 , 3 , 4 , 5 } ÁüÚõ B = {1,3,5,8,9} ±ý¸.

Ë Á¡÷¸É¢ý ¸½ ¿¢ÃôÀ¢ Å¢¾¢¸¨Çî ºÃ¢À¡÷ì¸×õ. [ P.14, Eg.1.9] [MAR-12]

2. ¦ÅýÀ¼í¸¨Çô ÀÂýÀÎò¾¢ A \ (B ∩ C) = (A \ B) U (A \ C) என்னும் டி-ார்கனின் கண வித்திாச

விதிிடன சரிபார்க்கவும் [P.13,Eg 1.8] [JUNE-12] [ OCT-12],[M-14]

3. ¦ÅýÀ¼í¸¨Çô ÀÂýÀÎò¾¢ A \ (B ∪ C) = (A \ B) ∩ (A \ C) என்னும் டி-ார்கனின் கண வித்திாச விதிிடன சரிபார்க்கவும் [P.15, gæ‰Á 1.2 - 9(iv)] [JUNE-14]

4. ´Õ ¿¸Ãò¾¢ø 85% §À÷ ¬í¸¢Ä ¦Á¡Æ¢, 40% §À÷ ¾Á¢ú ¦Á¡Æ¢ ÁüÚõ 20% §À÷ þó¾¢

¦Á¡Æ¢ §À͸¢È¡÷¸û. 42% §À÷ ¾Á¢Øõ ¬í¸¢ÄÓõ,23% §À÷ ¾Á¢Øõ þó¾¢Ôõ ÁüÚõ 10%

§À÷ ¬í¸¢ÄÓõ þó¾¢Ôõ §À͸¢È¡÷¸û ±É¢ø ,ãýÚ ¦Á¡Æ¢¸¨ÇÔõ §Àºò

¦¾Ã¢ó¾Å÷¸Ç¢ý º¾Å£¾ò¨¾ì ¸¡ñ¸. [Àì¸õ: 18, À¢üº¢ : 1.3 –(6)] [ƒ¥ý – 13]

www.Padasalai.Net

5. 170 tho¡ifahs®fëš 115 ng® bjhiy¡fh£ÁiaÍ«, 110 ng® thbdhèiaÍ« k‰W« 130 ng®

g¤Âç¡iffisÍ« ga‹gL¤Â»wh®fŸ v‹gij xU és«guãWtd« f©l¿ªjJ. nkY«, 85ng®

bjhiy¡fh£Á k‰W« g¤Âç¡ifiaÍ«, 75 ng® bjhiy¡fh£Á k‰W« thbdhèiaÍ«, 95 ng® thbdhè

k‰W« g¤Âç¡ifiaÍ«, 70 ng® _‹¿idÍ« ga‹gL¤J»wh®fŸ vdΫ f©l¿ªjJ. bt‹gl¤Âš

étu§fis¢ F¿¤J, ËtUtdt‰iw¡ fh©f. [g¡f« : 18, gæ‰Á 1.3 – (7)] [OCT-13]

(i) thbdhèia k£L« ga‹gL¤Jgt®fë‹ v©â¡if.

(ii) bjhiy¡fh£Áia k£L« ga‹gL¤Jgt®fë‹ v©â¡if.

(iii)bjhiy¡fh£Á k‰W« g¤Âç¡iffis¥ ga‹gL¤Â, thbdhèia¥ ga‹gL¤jhjt®fë‹ v©â¡if.

II-º¡÷Ò¸û: {§¸ûÅ¢ ±ñ:32}

1. A = { 0 , 1 , 2 , 3 } ÁüÚõ B= {1 , 3 , 5 , 7 , 9} ±ýÀÉ þÕ ¸½í¸û ±ý¸.

𝑓 : A → 𝐵 ±ýÛõ º¡÷Ò 𝑓 𝑥 = 2𝓍 + 1 ±Éì ¦¸¡Îì¸ôÀðÎûÇÐ. þ÷À¢¨É

i) Åâ¨ºî §º¡Ê¸Ç¢ý ¸½õ

ii) «ð¼Å¨½

iii) «õÒì ÌÈ¢ôÀ¼õ

iv) ŨÃÀ¼õ ¬¸¢ÂÅüÈ¡ø ÌÈ¢ì¸. [P.25, ±.¸¡: 1.20] [JUNE-12,MARCH-13]

2. A= { 4,6,8,10 } ÁüÚõ B = { 3,4,5,6,7 } ±ý¸. 𝑓 : A → 𝐵 ±ýÀÐ 𝑓 𝑥 = 1

2 𝓍 + 1

±É ŨÃÂÚì¸ôÀðÎûÇÐ. º¡÷Ò 𝑓 ³

(i) «õÒìÌÈ¢ À¼õ

(ii) Åâ¨ºî §º¡Ê¸Ç¢ý ¸½õ

(iii) «ð¼Å¨½ ¬¸¢ÂÅüÈ¢ý ãÄõ ÌÈ¢ì¸×õ,[P.30 Ex1.4 –(14)] [OCT-12]

3. A = { 6, 9, 15, 18, 21 }; B = { 1, 2, 4, 5, 6 } k‰W« f : A ⟶ B v‹gJ f(x) = 𝑥−3

3 vd

tiuaW¡f¥g£oU¥Ã‹ rh®ò f –I : (m) m«ò¡F¿ gl« (M) tçir¢ nrhofë‹ fz«

(Ï) m£ltiz (<) tiugl« M»at‰¿‹ _y« F¿¡fΫ.[g¡f« : 30, gæ‰Á 1.4 – (13)] [{É‹-14]

4. º¡÷Ò ƒ : [ -3 , 7) ⟶ 𝑅 ¸£ú¸ñ¼Å¡Ú ŨÃÂÚì¸ôÀðÎûÇÐ.

𝑓 𝑥 = 4𝑥2 − 1 ; −3 ≤ 𝑥 < 2 3𝑥 − 2 ; 2 ≤ 𝑥 ≤ 42𝑥 − 3 ; 4 < 𝑥 ≤ 6

±É¢ø À¢ýÅÕÅÉÅü¨Èì ¸¡ñ¸:-[P.30,Ex – 1.4(15)] [MAR’12]

(i) 𝑓 5 + 𝑓 6 (ii) 𝑓 1 − 𝑓(−3) (iii) 𝑓 −2 − 𝑓 4 (iv) 𝑓 3 + 𝑓 −1

2𝑓 6 − 𝑓 1

5. X = { 1, 2, 3, 4, 5 }, Y = { 1, 3, 5, 7, 9 } v‹f. X-èUªJ Y-¡fhd cwÎfŸ ÑnH bfhL¡f¥g£LŸsd.

Ït‰¿š vit rh®ghF«? c‹ éil¡fhd jFªj fhuz« jUf. nkY«, mit rh®ò våš, v›tif¢

rh®ghF«? [g¡f« : 29, gæ‰Á 1.4 – (4)] [OCT-13]

(i) R1 = {( x, y) | y = x + 2, x ∈ X , y ∈ Y }

(ii) R2 = { (1, 1), (2, 1), (3, 3), (4, 3), (5, 5) }

(iii) R3 = { (1, 1), (1, 3), (3, 5), (3, 7), (5, 7) }

(iv) R4 = { (1, 3), (2, 5), (4, 7), (5, 9), (3, 1) } 6. rh®ò ƒ : [ 1 , 6) ⟶ ℝ MdJ ËtUkhW tiuaW¡f¥g£LŸsJ .

𝑓 𝑥 = 1 + 𝑥 ; 1 ≤ 𝑥 < 2 2𝑥 − 1 ; 2 ≤ 𝑥 < 4

3𝑥2 − 10 ; 4 ≤ 𝑥 < 6

( Here , [1 , 6) = { x ∈ R : 1 ≤ x < 6})

(m) 𝑓 5 (M) 𝑓 3 (Ï) 𝑓 1 (<) 𝑓 2 − 𝑓 4 (c) 2𝑓 5 − 3 𝑓 1

M»at‰¿‹ kÂ¥òfis¡ fh©f. [g¡f« : 28, v.fh 1.22] [M-14]

7. rh®ò f : [ 1 , 6) ⟶ ℝ Ñœ¡ f©lthW tiuaW¡f¥g£LŸsJ.

𝑓 𝑥 = 𝑥2 + 2𝑥 + 1 ; −7 ≤ 𝑥 < −5 𝑥 + 5 ; −5 ≤ 𝑥 ≤ 2𝑥 − 1 ; 2 < 𝑥 < 6

ËtUtdt‰iw¡ fh©f. (i) 2 f (- 4) + 3 f (2) (iii) 4𝑓 −3 +2𝑓(4)

𝑓 −6 − 3𝑓(1) [g¡f« : 31, gæ‰Á 1.4-(16)] [Oct-14]

www.Padasalai.Net

CH: II. ¦Áö¦Âñ¸Ç¢ý ¦¾¡¼÷Å⨺¸Ùõ ¦¾¡¼÷¸Ùõ: {§¸ûÅ¢ ±ñ:33} 1) 6 + 66 + 666 +................... ±Ûõ ¦¾¡¼Ã¢ø Ó¾ø n ¯ÚôҸǢý Üξø ¸¡ñ¸.

[ g¡f« - 59 , Eg - 2.27 ] [OCT’12 , Á¡÷î-2013]

2. 7 + 77 + 777 +… … bjhlçš n cW¥òfë‹ TLjš fh©f. [g¡f« : 60, gæ‰Á 2.5 - 8(i)] [M-14]

3) 300 ìÌõ 500 ìÌõ þ¨¼§ÂÔûÇ 11 ¬ø ÅÌÀÎõ «¨ÉòÐ þÂø ±ñ¸Ç¢ý

Üð¼üÀÄý ¸¡ñ¸. [P.56, Ex – 2.4(10)] [JUNE’12]

4) 12 ¦º.Á£, 13 ¦º.Á£, ... ..., 23 ¦º.Á£ ¬¸¢ÂÅü¨È Өȧ Àì¸ «Ç׸ǡ¸ì ¦¸¡ñ¼

12 ºÐÃí¸Ç¢ý ¦Á¡ò¾ô ÀÃôÀÇ× ¸¡ñ¸. [P.67, Ex – 2.6(5)] [JUNE’12]

5) 11 br.Û, 12 br.Û, 13 br.Û, g, 24 br.Û M»adt‰iw Kiwna g¡f msÎfshf¡ bfh©l 14 rJu§fë‹

bkh¤j¥ gu¥ò fh©f. [g¡f« : 66 , v.fh. 2. 34] [M-14]

6. xU njh£l¡fhu® rçtf toéš Rt® x‹¿id mik¡f £läL»wh®. rçtf¤Â‹ Ú©l Kjš tçir¡F

97 br§f‰fŸ njit¥gL»wJ. Ëò x›bthU tçiræ‹ ÏUòwK« Ïu©ou©L br§f‰fŸ Fiwthf

it¡f nt©L«. m›totik¥Ãš 25 tçirfëU¥Ã‹, mt® th§f nt©oa br§f‰fë‹ v©â¡if

v¤jid? [g¡f« : 56, gæ‰Á 2.4 – (20)] [OCT-13]

7. ËtU« bjhlç‹ TLjiy¡ fh©f.113 + 12

3 + 13

3+… … … + 28

3 [g¡f« : 65 , v.fh. 2. 31(ii)] [OCT-13]

8. xU bgU¡F¤ bjhlç‹ Kjš n, 2n k‰W« 3n M»a cW¥òfë‹ TLjšfŸ Kiwna S1 ,S 2k‰W« S3

våš, S1( S3- S2)= (S2- S1)2

vd ãWÎf. [g¡f« : 61, gæ‰Á 2.5-(12)] [M-14] (Compulsory Qn)

9. 8 Mš tFgL« mid¤J _‹¿y¡f Ïaš v©fë‹ TLjš fh©f. [g¡f« : 55, gæ‰Á 2.4-(8)modal] [Oct-14]

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CH: III. þÂü¸½¢¾õ: {§¸ûÅ¢ ±ñ:34 ,35 («) 35,36} [2-Qns]

1. ¸¡Ã½¢ôÀÎòи : 2x3 - 3x

2 - 3x + 2 [P.89, Eg.3.17] [MAR-12]

2. ¸¡Ã½¢ôÀÎòи : x3 – 3x

2 – 10x + 24 [P.90, Eg 3.18]

3. ¸¡Ã½¢ôÀÎòи : x3 – 5x2

– 2x + 24 [P.90, Ex:3.5 – (1)-xii)(SB.Page 75-xii)] [Á¡÷î-13][ƒ£ý14]

(or) x3 -5x

2 -2x +24 ±ýÈ ÀøÖÚôÒì §¸¡¨Å¨Âì ¸¡Ã½¢ôÀÎòи. [P.90 Ex.3.5 -1 (xii)] [«ì-12]

4. ¸¡Ã½¢ôÀÎòи : x3 +13x

2 +32x + 20 [P.90, Ex:3.5 – (1)-vi)] (ƒ¥ý–13)]

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5. x4 – 6x3 +19x2 –30x + 25 – ý Å÷ì¸ãÄò¨¾ì ¸¡ñ¸. [Àì¸õ:105, ±¸¡: 3.34] [ƒ¥ý-13]

6. x4 – 10x3 +37x2 –60x + 36 – ý Å÷ì¸ãÄò¨¾ì ¸¡ñ¸. [Àì¸õ:105, ±¸¡: 3.33] [ƒ¥ý-14]

7. x4 – 4x3 +10x2 –ax + b ´Õ ÓØ Å÷ì¸õ ±É¢ø a , b ¬¸¢ÂÅüÈ¢ý Á¾¢ôÒ¸¨Çì ¸¡ñ¸.

[P.106, Ex.3.13 – (2)(ii)] [MAR-12]

8. 4x4 – 12x3 + 37x2 + ax + b ¬ÉÐ ´Õ ÓØ Å÷ì¸õ ±É¢ø a , b –¢ý Á¾¢ôÒ¸¨Çì

¸¡ñ¸. [P.106 Ex 3.13 – 2(i)] [JUNE-12]

9. 4x4 + 8x3 + 8x2 +4x + 1 ±ýÈ ÀøÖÚôÒ §¸¡¨Å¢ý Å÷ì¸ ãÄõ ¸¡ñ.

[P.106 Ex 3.13 – I (ii)] [OCT-12]

10. m - nx + 28x2

+ 12x3 + 9x

4 MdJ xU KG t®¡f« våš, m, n M»at‰¿‹ kÂ¥òfis¡ fh©f.

[g¡f« : 105 , v.fh. 3. 35] [OCT-13 ,14]

11. 𝛼, 𝛽 v‹gd 3x2

- 6x + 4 = 0 v‹D« rk‹gh£o‹ _y§fŸ våš, 𝛼2 + 𝛽2 -‹ kÂ¥ò¡ fh©f.

[g¡f« : 120, gæ‰Á 3.18 – (4)] [OCT-13]

12. 3x2 - 6x + 1

= 0 v‹w rk‹gh£o‹ _y§fŸ 𝛼 , 𝛽 våš, Ñœ¡fhQ« _y§fis¡ bfh©l rk‹ghLfismik¡f :

(m)

1

𝛼,

1

𝛽 (M) 𝛼2𝛽 , 𝛽2𝛼 (Ï) 2𝛼+𝛽, 2𝛽 + 𝛼 [g¡f« : 120, gæ‰Á 3.18 – (8)] [ É‹-14]

13. 11 bg‹ÁšfŸ k‰W« 3 mê¥gh‹fë‹ bkh¤j éiy %. 50. nkY«, 8 bg‹ÁšfŸ k‰W« 3

mê¥gh‹fë‹ bkh¤j éiy %. 38 våš, xU bg‹Áš k‰W« xU mê¥gh‹ éiyia¡ fh©f.

[g¡f« : 74 , v.fh. 3.2] [OCT-13](Compulsory Qn)

www.Padasalai.Net

14. mirt‰w Úçš xU ÏaªÂu¥gl»‹ ntf« kâ¡F 15 ».Û. v‹f. m¥glF Únuh£l¤Â‹ Âiræš 30 ».Û

öu« br‹W, ÃwF v®¤ Âiræš ÂU«Ã 4 kâ 30 ãäl§fëš Û©L« òw¥g£l Ïl¤Â‰F ÂU«Ã

tªjhš Úç‹ ntf¤ij¡ fh©f. [g¡f« : 113, gæ‰Á 3.16 – (6)] [M-14]

15.RU¡Ff

𝑎2−16

𝑎3−8 x

2𝑎2− 3𝑎−2

2𝑎2+9𝑎+4 ÷

3𝑎2− 11𝑎−4

𝑎2+2𝑎+4 [C.Q – S.B , P-388-(7)] [M-14]

16. α k‰W« β v‹gd 3x2- 4x+ 1=0 v‹D« rk‹gh£o‹ _y§fŸ våš,

𝛼2

𝛽 k‰W«

𝛽2

𝛼 M»at‰iw

_y§fshf¡ bfh©l ÏUgo¢ rk‹gh£oid mik¡f.[g¡f« : 119, v.fh 3.52] [M-14](Compulsory Qn)

17. Óuhd ntf¤Âš xU bjhl® t©oahdJ (train) 90 ».Û öu¤ij¡ flªjJ.mjDila ntf«

kâ¡F 15 ».Û mÂfç¡f¥g£oUªjhš, gaz« brŒÍ« neu« 30 ãäl§fŸ FiwªÂU¡F« våš,

bjhl® t©oæ‹ Óuhd ntf« fh©f. .[g¡f« : 113, v.fh 3.16] [Oct-14](Compulsory Qn)

@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@

CH : IV. «½¢¸û : {§¸ûÅ¢ ±ñ:37 («) 38} @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@

1. A = 1 −12 3

±É¢ø A2 – 4A + 5I2 = 0 ±É ¿¢Ú׸.[P.144,Ex 4.3-(6)][M-12,13] [June’12,13] [OCT-12]

2. A = 5 27 3

ÁüÚõ B = 2 −1−1 1

±É¢ø (𝐴𝐵)𝑇 = 𝐵𝑇𝐴𝑇 ±ýÀ¨¾ ºÃ¢À¡÷ì¸×õ.

[P.144 Ex.4.3 – 9] [m¡nlhg®-12,14] [É‹ - 14]

3. 𝑥2𝑦2

+3 2𝑥−𝑦

= −94 ±É¢ø x ÁüÚõ y ±ýɦÅýÚ ¾£÷ì¸ :-

[Àì.136,À¢üº¢ 4.2-(8)(SB:Page.127][MARCH-2013]

4. A = 1 87 2

våš, A2 - 3A - 54I = O vd ãWÎf. (C.Q) [OCT-13]

5. A = 3 2−1 4

, B = −2 56 7

k‰W« C = 1 1−5 3

våš, A(B + C) = AB + AC

v‹gij rç¥gh®¡fΫ. [g¡f« : 141, v.fh 4.16 ] [M-14]

********************************************************************************************************************

CH: V. ¬Âò¦¾¡¨Ä ÅÊÅ¢Âø : {§¸ûÅ¢ ±ñ: 38 & 39} [2-Qns]

********************************************************************************** 1.ÒûÇ¢¸û (6 , 9) , (7 , 4), (4 , 2) ÁüÚõ (3 , 7) ¬¸¢ÂÅü¨È Өɸǡ¸ì ¦¸¡ñ¼

¿¡ü¸Ãò¾¢ý ÀÃôÒì ¸¡ñ¸: [P.159,Ex 5.2 – 5(i)] [MAR-12]

2. (-4,5), (0,7), (5,-5) ÁüÚõ (-4,-2) ¬¸¢Â ÒûÇ¢¸¨Ç Өɸǡ¸ì ¦¸¡ñ¼

¿¡ü¸Ãò¾¢ý ÀÃôÀÇ× ¸¡ñ¸. [P.159 Ex.5.2 – 5-(iii)] [OCT-12] (ƒ¥ý–13)]

3. (-4, -2), (-3, -5), (3, -2) k‰W« (2, 3) M»a òŸëfis Kidfshf¡ bfh©l eh‰fu¤Â‹ gu¥ig¡

fh©f. [g¡f« : 158, v.fh 5.12 ] [M-14]

4. (-3, 4), (-5, -6), (4, -1) k‰W« (1, 2) M»a Kidfis¡ bfh©l eh‰fu¤Â‹ gu¥ig¡ fh©f.

[g¡f« : 159, gæ‰Á 5.2 ] [Oct-14]

5) A(2,1), B(-2,3), C(4,5) ±ýÀÉ ∆𝐴𝐵𝐶 ¢ý ¯îº¢¸û. ¯îº¢ A - ¢ĢÕóРŨÃÂôÀÎõ

¿Î째¡ðÊý ºÁýÀ¡ð¨¼ì ¸¡ñ¸. [P.171, Eg – 5.23] [MAR’12]

6. ∆𝐴𝐵𝐶 ¢ý Өɸû A(2,1), B(6,-1), C(4,11) ±ý¸.A ¢ĢÕóРŨÃÂôÀÎõ

ÌòÐ째¡ðÊý ºÁýÀ¡ð¨¼ì ¸¡ý¸. [ P.176, Eg – 5.29] [JUNE -12 ,14 ]

7. (3, 4), (-1, 2) v‹w òŸëfis Ïiz¡F« ne®¡nfh£L¤J©o‹ ika¡F¤J¡nfh£o‹

(Perpendicular bisector) rk‹gh£il¡ fh©f. [g¡f« : 176, gæ‰Á 5.5 – (10)] [M-14]

8. (2, - 5) , (3, - 4) k‰W« (9, k) M»a òŸëfŸ xU nfhliktd våš, k-‹ kÂ¥ig¡ fh©f.

[g¡f« : 159, gæ‰Á 5.2 – 4(ii)] [OCT-13]

9. (-2, -1), (4, 0), (3, 3) k‰W« (-3, 2) M»a òŸëfis tçirahf vL¤J¡bfh©L rhŒéid¥

ga‹gL¤Â mit X® Ïizfu¤ij mik¡F« vd¡ fh£Lf. [g¡f« : 164 , v.fh. 5.17] [OCT-13]

10. ∆ABC-‹ KidfŸ A(1, 8), B(-2, 4), C(8, -5). nkY«, M, N v‹gd Kiwna AB,AC Ït‰¿‹ eL¥òŸëfŸ

våš, MN-‹ rhŒit¡ fh©f. Ïij¡ bfh©L MN k‰W« BC M»a ne®¡nfhLfŸ Ïiz vd¡ fh£Lf.

[g¡f« : 165, gæ‰Á 5.3 – (12)] [OCT-14] (Compalsary Qn)

www.Padasalai.Net

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

CH: VI. ÅÊÅ¢Âø : {§¸ûÅ¢ ±ñ: 39 (or) 40}

vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv

1.À¢¾¡¸ÃŠ ¤¾üÈò¨¾ ±Ø¾¢ ¿¢Ú׸.[Àì.198,¤¾üÈõ:6.5] [Á¡÷î-2013]

2.«ÊôÀ¨¼ Å¢¸¢¾ºÁò §¾üÈò¨¾ ±Ø¾¢ ¿¢Ú׸. [Àì.182 – §¾üÈõ: 6.1] (ƒ¥ý–13),[M-14,Oct-14]

3) ABCD ±ýÈ ¿¡ü¸Ãò¾¢ø ∠ 𝐵 ÁüÚõ ∠D ¬¸¢ÂÅüÈ¢ý þÕ ºÁ¦Åðʸû AC ³ E ¢ø

¦Åðθ¢ýÈÉ ±É¢ø, 𝐴𝐵

𝐵𝐶 =

𝐴𝐷

𝐷𝐶 ±É ¿¢Ú׸. [P.191 , Ex.6.1 – (12) ] [OCT’12]

4. nfhz ÏU rkbt£o¤ nj‰w¤ij vGÂ ãWÎf:- [g¡f« : 185, nj‰w« 6.3 ] [OCT-13]

5. br›tf« ABCD-‹ c£òw òŸë O-éèUªJ br›tf¤Â‹ KidfŸ A, B, C, DÏiz¡f¥g£LŸsd

våš, OA2+ OC

2= OB

2+ OD

2 vd ãWÎf. [g¡f« : 203, gæ‰Á 6.3 – (7) ] [É‹ - 14]

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

CH: VII. Ó째¡½Å¢Âø : {§¸ûÅ¢ ±ñ: 40 (or) 41(or) 42} [1 – Qn]

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

1. (sin𝜃 + 𝐜𝐨𝐬𝐞𝐜𝜽)2 + (𝐜𝐨𝐬 𝜽 + 𝐬𝐞𝐜 𝜽)2 = 7+ tan2𝜃 + cot

2𝜃 ±É ¿¢Ú׸.

[g¡f« : 210, ±.¸¡ 7.6] [Á¡÷î-13]

2. tan θ + sin 𝜃 = m, tan 𝜃 - sin 𝜃 = n k‰W« m ≠ n våš, m2 - n

2 = 4 𝑚𝑛 vd¡ fh£Lf.

[g¡f« : 213 , v.fh. 7.12] [OCT-13]

3) 40 Á£ ¯ÂÃÓûÇ ´Õ §¸¡ÒÃò¾¢ý ¯îº¢ ÁüÚõ «Ê ¬¸¢ÂÅüȢĢÕóÐ ´Õ ¸Äí¸¨Ã

Å¢Ç츢ý ¯îº¢Â¢ý ²üÈì §¸¡½í¸û Өȧ 300 ÁüÚõ 60

0 ±É¢ø, ¸Äí¸¨Ã

Å¢Ç츢ý ¯ÂÃò¨¾ì ¸¡ñ¸. ¸Äí¸¨Ã Å¢Ç츢ý ¯îº¢Â¢Ä¢ÕóÐ §¸¡ÒÃò¾¢ý «ÊìÌ

¯ûÇ àÃò¨¾Ôõ ¸¡ñ¸. P.227, Ex – 7.2(17)] [JUNE’12]

4. §¿÷ìÌò¾¡É ´Õ ÁÃò¾¢ý §ÁøÀ¡¸õ ¸¡üȢɡø ÓÈ¢óÐ , «õÓÈ¢ó¾ À̾¢ ¸£§Æ

Å¢ØóÐÅ¢¼¡Áø, ÁÃò¾¢ý ¯îº¢ ¾¨ÃÔ¼ý 300 §¸¡½ò¨¾ ²üÀÎòи¢ÈÐ.ÁÃò¾¢ý

¯îº¢ «¾ý «Ê¢ĢÕóÐ 30 Á£ ¦¾¡¨ÄÅ¢ø ¾¨Ã¨Âò ¦¾¡Î¸¢ÈÐ ±É¢ø, ÁÃò¾¢ý

ÓØ ¯ÂÃò¨¾ì ¸¡ñ¸. [P.219 , ±.¸¡: 7.18 ] [Oct -12] [June-14]

5).ÅÌôÀ¨È¢ø «Á÷óÐ ¦¸¡ñÊÕìÌõ ´Õ Á¡½Åý ¸ÕõÀĨ¸Â¢ø ¸¢¨¼¿¢¨Ä À¡÷¨Åì

§¸¡ðÊÄ¢ÕóÐ 1.5 Á£ ¯ÂÃò¾¢ø ¯ûÇ µÅ¢Âò¨¾ 300 ²üÈì §¸¡½ò¾¢ø ¸¡ñ¸¢È¡ý.

µÅ¢Âõ «ÅÛìÌ ¦¾Ç¢Å¡¸ò ¦¾Ã¢Â¡¾¾¡ø §¿Ã¡¸ ¸ÕõÀĨ¸¨Â §¿¡ì¸¢ ¿¸÷óÐ Á£ñÎõ

«ó¾ µÅ¢Âò¨¾ 450 ²üÈ째¡½ò¾¢ø ¦¾Ç¢Å¡¸ì ¸¡ñ¸¢È¡ý ±É¢ø, «Åý ¿¸÷ó¾

àÃò¨¾ì¸¡ñ¸. [P.226,EX.7.2-(10)(SB.P.202-10)][MAR’2013]

6.500 Û cau¤Âš gwªJ¡ bfh©oU¡F« xU bAèfh¥lçèUªJ xUt® X® M‰¿‹ ÏU fiufëš

nebuÂuhf cŸs ÏU bghU£fis 300

, 450

Ïw¡f¡ nfhz§fëš fh©»wh® våš, M‰¿‹

mfy¤ij¡ fh©f. ( 3 = 1.732 ) [g¡f« : 226, gæ‰Á 7.2 – (8)] [M-14](Qn Model) 700 ¡F gÂyhf 500 bfhL¡f¥g£LŸsJ)

7.xU nfhòu¤Â‹ moæèUªJ xU F‹¿‹ c¢Áæ‹ V‰w¡nfhz« 60

0

v‹f. F‹¿‹ moæèUªJ

nfhòu¤Â‹ c¢Áæ‹ V‰w¡nfhz« 300

k‰W« nfhòu¤Â‹ cau« 50 Û våš, F‹¿‹ cau¤ij¡

fh©f. [g¡f« : 220 , v.fh. 7.20] [OCT-14]

www.Padasalai.Net

==============================================================================

CH: VIII. «ÇÅ¢Âø : {§¸ûÅ¢ ±ñ: 41 & 42 (or) 42 & 45 (Com.Sum)} [2-Qns]

=======================================================

1. ´Õ þ¨¼ì¸ñ¼ ÅÊÅ¢Ä¡É Å¡Ç¢Â¢ý §ÁüÒÈ ÁüÚõ «ÊôÒÈ ¬Ãí¸û ӨȧÂ

15 ¦º.Á£ ÁüÚõ 8 ¦º.Á£ . §ÁÖõ ¬Æõ 63 ¦º,Á£ ±É¢ø , «¾ý ¦¸¡ûÇǨŠĢð¼Ã¢ø

¸¡ñ¸. ¸.( 𝜋 = 22

7 ) [P.246,±.¸¡:8.16] [MARCH-13]

2. xU ne®t£l¡ T«Ã‹ Ïil¡f©l¤Â‹ ÏUòwK« mikªj t£l éë«òfë‹ R‰wsÎfŸ

Kiwna 44 br.Û k‰W« 8.4r br.Û v‹f. mj‹ cau« 1 4 br.Û våš, m›éil¡f©l¤Â‹

fdmsit¡ fh©f. [g¡f« : 250, gæ‰Á 8.2 – (12)] [M-14]

3. xU gh¤Âu« Ïil¡f©l« toéš cŸsJ. mj‹ nk‰òw Mu« k‰W« cau« Kiwna 8 br.Û k‰W«

14 br.Û v‹f. m¥gh¤Âu¤Â‹ fdmsÎ

5676

3 f.br.Û våš, mo¥g¡f¤ÂYŸs t£l¤Â‹

Mu¤Âid¡ fh©f. [g¡f« : 250, gæ‰Á 8.2 – (11)] [OCT-13]

4. ´Õ ܼ¡ÃÁ¡ÉÐ ¯Õ¨Ç¢ýÁ£Ð ÜõÒ þ¨½ó¾ ÅÊÅ¢ø ¯ûÇÐ.ܼ¡Ãò¾¢ý ¦Á¡ò¾

¯ÂÃõ 13.5 Á£ ÁüÚõ «ÊôÒÈò¾¢ý Å¢ð¼õ 28 Á£ . §ÁÖõ ¯Õ¨Ç À¡¸ò¾¢ý

¯ÂÃõ 3 Á£ ±É¢ø ܼ¡Ãò¾¢ý ¦Á¡ò¾ ÒÈôÀÃô¨À측ñ¸.[P.255, Ex – 8.3(4)] [MAR’12,13]

5) 14 Á£ Å¢ð¼Óõ ÁüÚõ 20 Á£ ¬ÆÓûÇ ´Õ ¸¢½Ú ¯Õ¨Ç ÅÊÅ¢ø ¦Åð¼ôÀθ¢ÈÐ,

«ùÅ¡Ú ¦Åð¼ôÀÎõ§À¡Ð §¾¡ñʦÂÎì¸ôÀð¼ Áñ º£Ã¡¸ ÀÃôÀôÀðÎ

20 Á£ x 14 Á£ «Ç׸Ǣø «ÊÀì¸Á¡¸ì ¦¸¡ñ¼ ´Õ §Á¨¼Â¡¸ «¨Áì¸ôÀð¼¡ø,

«õ§Á¨¼Â¢ý ¯ÂÃõ ¸¡ñ¸. [P.256, À¢üº¢ : 8.3(17)] [JUNE’12,13(Compalsary Qn)]

6. §¿÷Åð¼ì ÜõÒ ÅÊÅ¢ø ÌÅ¢ì¸ôÀð¼ ¦¿üÌÅ¢ÂÄ¢ý Å¢ð¼õ 4.2 Á£ , ÁüÚõ

¯ÂÃõ 2.8 Á£ ±ý¸. þó¾ ¦¿üÌÅ¢Â¨Ä Á¨Æ¢ĢÕóÐ À¡Ð¸¡ì¸ ¸¢ò¾¡ý н¢Â¡ø

Á¢¸îºÃ¢Â¡¸ ã¼ôÀθ¢ÈÐ ±É¢ø, §¾¨ÅÂ¡É ¸¢ò¾¡ý н¢Â¢ý ÀÃô¨Àì ¸¡ñ¸.

[P.241-(13)] [MAR’12, Oct-14]

7. fëk©iz¥ ga‹gL¤Â xU khzt‹ 48 br.Û cauK« 12 br.Û MuK« bfh©l ne® t£l©k¡

T«ig¢ brŒjh®. m¡T«ig k‰bwhU khzt® xU ©k¡ nfhskhf kh‰¿dh®. m›thW kh‰w¥g£l

òÂa nfhs¤Â‹ Mu¤ij¡ fh©f. [g¡f«-255,gæ‰Á – 8.3 (5)][m¡-12, kh®¢-14,É‹ -14]

8. 120 ¦º.Á£ ¿£ÇÓõ, 84 ¦º.Á£ Å¢ð¼Óõ ¦¸¡ñ¼ ´Õ º¡¨Ä¨Â ºÁôÀÎòÐõ

¯Õ¨Ç¨Âì ¦¸¡ñÎ ´Õ Å¢¨Ç¡ðÎò¾¢¼ø ºÁôÀÎò¾ôÀθ¢ÈÐ.

Å¢¨Ç¡ðÎò¾¢¼¨Ä ºÁôÀÎò¾ þù×Õ¨Ç 500 ÓØî ÍüÚ¸û ÍÆÄ §ÅýÎõ.

Å¢¨Ç¡ðÎò¾¢¼¨Ä ºÁôÀÎò¾ ´Õ º.Á£ð¼ÕìÌ 75 ¨Àº¡ Å£¾õ,¾¢¼¨Äî

ºÁôÀÎò¾ ¬Ìõ ¦ºÄ¨Åì ¸¡ñ¸:(𝜋 = 22

7 ) [Àì¸õ:233,±.¸¡:8.4] [ƒ¥ý-13]

9. 8 br.Û é£lK« 12 br.Û cauK« bfh©l xU ne® t£l ©k ÏU«ò¡ T«ghdJ cU¡f¥g£L 4 ä.Û MuKŸs

©k¡nfhs tot F©Lfshf th®¡f¥g£lhš »il¡F« nfhs tot F©Lfë‹ v©â¡ifia¡ fh©f.

[g¡f«-256,gæ‰Á – 8.3 - (13)][m¡-14]

***********************************************************************************************************

CH: XI. ÒûǢ¢Âø : {§¸ûÅ¢ ±ñ: 43 } [1-Qn]

*************************************************************************************************

1) 10 , 20 , 15 , 8 , 3 , 4 ±ýÈ ÒûǢŢÅÃí¸Ç¢ý ¾¢ð¼Å¢Äì¸ò¨¾ì ¸¡ñ¸.

[ P.308, Ex 11.1- 6(i)] [JUNE-12]

2) 38, 40, 34, 31, 28, 26, 34 ±ýÈ ÒûÇ¢ Å¢ÅÃí¸ÙìÌ ¾¢ð¼Å¢Äì¸õ ¸¡ñ¸.

[P.308, Ex. 11.1 - 6(2)] [OCT-12]

3. À¢ýÅÕõ Á¾¢ôҸǢý Á¡ÚÀ¡ðÎì ¦¸Ø¨Åì ¸½ì¸¢Î¸.

20 ,18 ,32 ,24 ,26 [ Àì¸õ: 304,±.¸¡:11.17 (model sum) [ƒ¥ý -13]

4.´Õ ÀûǢ¢ÖûÇ 200 Á¡½Å÷¸û ´Õ Òò¾¸ì ¸ñ¸¡ðº¢Â¢ø Å¡í¸¢Â Òò¾¸í¸Ç¢ý

±ñ½¢ì¨¸¨Â ÀüȢ ŢÅÃõ ¸£ú측Ïõ «ð¼Å¨½Â¢ø ¦¸¡Îì¸ôÀðÎûÇÐ.þ¾üÌ

¾¢ð¼ Å¢Äì¸õ ¸¡ñ¸.[P.308, Ex 11.1 – (8)] [MAR-12]

Òò¾¸í¸Ç¢ý

±ñ½¢ì¨¸

0

1

2

3

4

Á¡½Å÷¸Ç¢ý

±ñ½¢ì¨¸

35

64

68

18

15

www.Padasalai.Net

5. cyf¡ fhšgªJ ngh£ofëš 71 K‹dâ Åu®fŸ mo¤j nfhšfë‹ v©â¡ifæ‹ étu§fŸ

ËtU« m£ltizæš bfhL¡f¥g£LŸsJ. Ï›étu¤Â‹ £l éy¡f« fh©f.

[g¡f« : 302 , v.fh. 11.15] [OCT-13]

ÃçÎ

Ïilbtë

0-10 10-20 20-30 30-40 40-50 50-60 60-70

ãfœbt©fŸ 8 12 17 14 9 7 4

6. Ñœ¡f©l m£ltizæš bfhL¡f¥g£LŸs òŸë étu¤Â‹ £l éy¡f¤ij¡ fz¡»Lf.

[g¡f« : 308, gæ‰Á 11.1 – (7)] [M-14]

7. xU tF¥Ã‰F el¤j¥g£l bghJ m¿Î¤nj®éš bkh¤j kÂ¥bg©fŸ 40-¡F, 6 khzt®fŸ bg‰w

kÂ¥bg©fŸ 20, 14, 16, 30, 21 k‰W« 25. Ï¥òŸë étu¤Â‹ £l éy¡f« fh©f.

[g¡f« : 295, v.fh 11.5][Jn-14,Oct-14]

*********************************************************************************************************************

CH – XII : ¿¢¸ú¾¸× {§¸ûÅ¢ ±ñ: 44 } [1-Qn]

************************************************************************************************* 1. ´Õ ¨À¢ø 10 ¦Åû¨Ç , 5 ¸ÕôÒ, 3 À, ÁüÚõ 2 º¢ÅôÒ ¿¢ÈôÀóиû

¯ûÇÉ.ºÁÅ¡öôÒ Ó¨È¢ø §¾÷ó¦¾Îì¸ôÀÎõ ´Õ ÀóÐ ¦Åû¨Ç «øÄÐ ¸ÕôÒ

«øÄÐ À ¿¢ÈÁ¡¸ þÕôÀ¾üì¸¡É ¿¢¸úò¾¸Å¢¨½ì ¸¡ñ¸.

( JUNE - 2012, OCT’12 , MAR’12) [ P.328 - Eg.12.18 ]

2. ´Õ À¸¨¼ þÕÓ¨È ¯Õð¼ôÀθ¢ÈÐ.̨Èó¾Ð ´Õ ¯Õð¼Ä¢Ä¡ÅÐ ±ñ 5

¸¢¨¼ôÀ¾ü¸¡É ¿¢¸ú¾¸Å¢¨Éì ¸¡ñ¸.[Àì.325- ±.¸¡: 12.13] [Á¡÷î-13]

3) 52 º£ðθû ¦¸¡ñ¼ ´Õ º£ðÎì ¸ðÊÄ¢ÕóÐ ºÁÅ¡öôÒ Ó¨È¢ø ´Õ º£ðÎ

±Îì¸ôÀÎõ ¤À¡Ð «îº£ðÎ ´Õ þạ (King) «øÄÐ ´Õ †¡÷ð (Heart) «øÄÐ

´Õ º¢ÅôÒ ¿¢Èî º£ð¼¡¸ì ¸¢¨¼ôÀ¾ü¸¡É ¿¢¸ú¾¸Å¢¨Éì ¸¡ñ¸.

[Àì¸õ: 327, ±.¸¡ :12.17] [ƒ£ý–13]

4. e‹F fiy¤J mL¡» it¡f¥g£l 52 Ó£Lfis¡ bfh©l Ó£L¡ f£oèUªJ rkthŒ¥ò Kiwæš

xU Ó£L vL¡f¥gL»wJ. mªj¢ Ó£L °nglhfnth (Spade) mšyJ Ïuhrhthfnth (King) ÏU¥gj‰fhd

ãfœjféid¡ fh©f. [g¡f« : 329, gæ‰Á 12.2 – (10)][Jn-13]

5. xU òÂa k»œÎªJ (car) mjDila totik¥Ã‰fhf éUJ bgW« ãfœjfÎ 0.25 v‹f. Áwªj

Kiwæš vçbghUŸ ga‹gh£o‰fhd éUJ bgW« ãfœjfÎ 0.35 k‰W« ÏU éUJfS«

bgWtj‰fhd ãfœjfÎ 0.15 våš, m«k»œÎªJ [g¡f« : 329, gæ‰Á 12.2 – (14)] [OCT-13]

(i) FiwªjJ VjhtJ xU éUJ bgWjš

(ii) xnu xU éUJ k£L« bgWjš M»a ãfœ¢ÁfS¡fhd ãfœjfÎfis¡ fh©f.

6. ÏU Óuhd gfilfŸ xU Kiw cU£l¥gL»‹wd. Ñœ¡fhQ« ãfœ¢ÁfS¡fhd ãfœ¤jféid¡

fh©f. (m) Kf v©fë‹ TLjš 8 Mf ÏU¤jš(M) Kf v©fŸ xnu v©fshf (doublet) ÏU¤jš

(Ï) Kf v©fë‹ TLjš 8-I él mÂfkhf ÏU¤jš. [g¡f« : 317, v.fh 12.5] [M-14]

7.xU gfil ÏUKiw cU£l¥gL»wJ. Kjyhtjhf cU£l¥gL«nghJ xUÏu£il¥gil v© »il¤jš mšyJ

m›éU cU£lèš Kf v©fë‹ TLjš 8 Mf ÏU¤jš vD« ãfœ¢Áæ‹ ãfœjfit¡ fh©f.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

CH: IX –¦ºöÓ¨È ÅÊÅ¢Âø,geometry, [10– MARK ]{§¸ûÅ¢ ±ñ:46« (or) ¬}

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!

I .¦¾¡Î§¸¡Î Ũþø: (PracticalGeometry)

1. 3 ¦º.Á£ ¬ÃÓûÇ Åð¼ò¾¢ý ¨ÁÂò¾¢Ä¢ÕóÐ 9 ¦º.Á£ ¦¾¡¨ÄÅ¢ø ´Õ ÒûÇ¢¨Âì

ÌÈ¢ì¸. «ôÒûǢ¢ø þÕóÐ Åð¼ò¾¢üÌ þÕ ¦¾¡Î§¸¡Î¸û ŨÃóÐ ,

«ÅüÈ¢ý ¿£Çò¨¾ì ¸½ì¸¢Î¸. [P.265, À¢üº¢ : 9.1 – (5)] [JUNE-12,13] [Oct -12,13]

2. 3 br.Û MuKŸs t£l« tiuf. t£l¤Â‹ ika¤ÂèUªJ 7 br.Û. bjhiyéš xU òŸëia¡

F¿¤J, m¥òŸëæèUªJ t£l¤Â‰F bjhLnfhLfŸ tiuf. nkY« bjhLnfhLfë‹ Ús¤ij

msªJ vGJf. [g¡f« : 264, v.fh 9.3] [M-14]

x 3 8 13 18 23

y 7 10 15 10 8

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3. 10 br.Û é£lKŸs xU t£l« tiuf. t£l¤Â‹ ika¤ÂèUªJ 13 br.Û. bjhiyéš P v‹w

òŸëia¡ F¿¤J m¥òŸëæèUªJ t£l¤Â‰F PA k‰W« PB v‹w bjhLnfhLfŸ tiuªJ

mj‹ Ús§fis fz¡»Lf. [g¡f« : 265, gæ‰Á 9.1-(3)] [É‹-14]

4) 6 br.Û MuKŸs xU t£l« tiuªJ mj‹ ika¤ÂèUªJ 10 br.Û bjhiyéYŸs xU òŸëia¡ F¿¡f.

m¥òŸëæèUªJ t£l¤Â‰F bjhLnfhLfŸ tiuªJ mj‹ Ús§fis fz¡»Lf.

[g¡f« : 265, gæ‰Á 9.1-(4)] [m¡-14]

II. Åð¼ ¿¡ü¸Ãõ Ũþø: :(PracticalGeometry)

1. AB = 6 ¦º.Á£ , AD = 4.8 ¦º.Á£, BD = 8 ¦º.Á£ ÁüÚõ CD = 5.5 ¦º.Á£ ±ýÈ

«Ç׸û ¦¸¡ñ¼Å𼿡ü¸Ãõ ABCD Ũø. [P.277, Ex 9.3 – (2)] [MAR-12,OCT-13]

2. PQ = 4 ¦º.Á£ , QR = 6 ¦º.Á£ , PR = 7.5 ¦º.Á£ ÁüÚõ QS = 7 ¦º.Á£ «Ç׸û ¦¸¡ñ¼

Åð¼ ¿¡ü¸Ãõ PQRS Ũø. [P.272, Eg 9.8] [OCT-12]

3. PQ = 5.5 ¦º.Á£ , QR = 4.5 ¦º.Á£ , ∠PQR = 450 ÁüÚõ PS = 3 ¦º.Á£ ¬¸¢Â «Ç׸û

¦¸¡ñ¼ Åð¼ ¿¡ü¸Ãõ PQRS Ũø. [P.277, Ex 9.3 – (3),SB:P.246-3] [MAR - 13]

4. AB = 7 br.Û., ∠A = 800, AD = 4.5 br.Û. k‰W« BC = 5 br.Û. v‹w msÎfŸ bfh©l

t£l eh‰fu« ABCD tiuf. [g¡f« : 277, gæ‰Á 9.3-(4)] [M-14,Oct-14]

**********************************************************************************************************************************

II. Ó째¡½õ Ũþø:(PracticalGeometry)

1. «ÊôÀì¸õ BC = 5.5¦º.Á£ ,∠A = 600 ÁüÚõ ¯îº¢ S ¢ĢÕóРŨÃÂôÀð¼

¿Î째¡Î AM –ý ¿£Çõ 4.5 ¦º.Á£ ¦¸¡ñ¼ Δ ABC Ũø.

[Àì¸õ:268,±.¸¡:-9.5] [MARCH – 12]

2. ΔABC ø, BC = 5 ¦º.Á£, ∠A = 450 ÁüÚõ ¯îº¢ A ¢ĢÕóÐ BC –ìÌ

ŨÃÂôÀð¼ ¿Î째¡ðÊý ¿£Çõ 4 ¦º.Á£ ±É þÕìÌõÀÊ ΔABC Ũø.

[Àì¸õ:270, À¢üº¢ :9.2 –(4)] [June – 12]

3. AB = 6 ¦º.Á£, ∠C= 400 ÁüÚõ ¯îº¢ C ¢ĢÕóÐ AB –ìÌ Å¨ÃÂôÀð¼ ÌòÐ째¡ðÊý

¿£Çõ 4.2 ¦º.Á£ ¦¸¡ñ¼ ΔABC Ũø.

[Àì¸õ:267, À¢üº¢ 9.4] [March–13, June-13,14]

CH – X : ŨÃÀ¼í¸û, graph ; [ 10 – MARK Qns ] {§¸ûÅ¢ ±ñ: 47 « (or) ¬ }

I.º¢ÈôÒ Å¨ÃÀ¼í¸û

1.

x

1

3

5

7

8

y

2

6

10

14

16

§Áü¸ñ¼ «ð¼Å¨½Â¢ø ¯ûÇ Å¢ÅÃò¾¢üÌ Å¨ÃÀ¼õ ŨÃóÐ «¾ý ãÄõ

i) x = 4 ±É¢ø y ý Á¾¢ô¨Àì ¸¡ñ¸. [SCORE BOOK P.269 – 3]

ii) y = 12 ±É¢ø x ý Á¾¢ô¨Àì ¸¡ñ¸. [P.291,Ex 10.2 – (3)] [MAR-12,13] [JUNE-12]

2. xy = 20 , x , y > 0 ±ýÀ¾ý ŨÃÀ¼õ Ũø. «¾¨Éô ÀÂýÀÎò¾¢ x = 5 ±É¢ø

y ý Á¾¢ô¨ÀÔõ, y = 10 ±É¢ø x ý Á¾¢ô¨ÀÔõ ¸¡ñ¸. [P.291, 10.2(5)] [OCT-12]

3. ´Õ §ÀÕóÐ Á½¢ìÌ 40 ¸¢.Á£ §Å¸ò¾¢ø ¦ºø¸¢ÈÐ. þ¾üÌȢ àÃ-¸¡Ä Ýò¾¢Ãõ ±Ø¾¢ ¦¾¡¼÷Ò¨¼Â

ŨÃÀ¼õ Ũø. þ¨¾ô ÀÂýÀÎò¾¢ 3 Á½¢ §¿Ãò¾¢ø þô§ÀÕóÐ À½¢ò¾ àÃò¨¾ì ¸¡ñ¸.

[ P. 290, À¢üº¢:10.2 – (1)] [JUNE-13,14]

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4. xU t§», _¤j¡Fokfå‹ it¥ò¤ bjhif¡F 10% jåt£o jU»wJ. it¥ò¤ bjhif¡F«

mj‰F X® M©L¡F¡ »il¡F« t£o¡F« Ïilnaahd bjhl®Ãid¡fh£l xU tiugl« tiuf.

mj‹ _y«, [g¡f« : 289 , v.fh. 10.9] [OCT-13]

(i) %. 650 it¥ò¤ bjhif¡F¡ »il¡F« t£o k‰W«

(ii) %. 45 t£oahf¡ »il¡f t§»æš brY¤j¥gl nt©oa it¥ò¤ bjhif M»adt‰iw¡ fh©f.

5. xU è£l® ghè‹ éiy % 15 v‹f. ghè‹ msΡF« éiy¡F« cŸs¤ bjhl®Ãid¡ fh£L« tiugl«

tiuf. mjid¥ ga‹gL¤Â, (i) é»jrk kh¿èia¡ fh©f.

(ii) 3 è£l® ghè‹ éiyia¡ fh©f. [g¡f« : 291, gæ‰Á 10.2-(4)] [M-14]

xU äÂt©o X£Lgt® A v‹w Ïl¤ÂèUªJ B v‹w Ïl¤Â‰F xU Óuhd ntf¤Âš xnu têæš

bt›ntW eh£fëš gaz« brŒ»wh®. mt® gaz« brŒj ntf«, m¤öu¤Âid¡ fl¡f vL¤J¡

bfh©l neu« M»adt‰iw¥ g‰¿a étu§fŸ (ntf-fhy) ËtU« m£ltizæš

bfhL¡f¥g£LŸsd.

ntf«(».Û. /kâ ) (x) 2 4 6 10 12

neu« (kâæš) (y) 60 30 20 12 10

ntf - fhy tiugl« tiuªJ mÂèUªJ,

(i) mt® kâ¡F 5 ».Û ntf¤Âš br‹whš öu¤ij¡ fl¡f MF« gaz neu«

(ii) mt® Ï¡F¿¥Ã£l öu¤ij 40 kâneu¤Âš fl¡f vªj ntf¤Âš gaâ¡f nt©L« M»adt‰iw¡

fh©f. [g¡f« : 288 , v.fh. 10.8] [OCT-14]

II.ÏUgo¡ nfhitfë‹ tiugl§fŸ (Quadratic Graphs)

1. ŨÃÀ¼õ ãÄõ ¾£÷ì¸ : 2x2 + x – 6 = 0 [ P.284, ±.¸¡ : 10.4] [Á¡÷î-2013]

2. ŨÃÀ¼õ ãÄõ ¾£÷ì¸ : x2 _

2x – 3 = 0 [ P.283, ±.¸¡ : 10.3] [ƒ¥ý-2013]

3. tiugl« _y« Ô®¡f : x2 -3x -10 =0 [g¡f« : 287, gæ‰Á 10.1 – (2) (ii)] [OCT-14]

4. Y = x2 + 2x – 3 þý ŨÃÀ¼õ ŨÃóÐ, «¾¨Éô ÀÂýÀÎò¾¢ x

2 – x – 6 = 0 ±ýÈ

ºÁýÀ¡ðÊý ãÄí¸¨Çì ¸¡ñ¸.(«øÄÐ) Y = x2 + 2x – 3 þý ŨÃÀ¼õ ŨÃóÐ,

«¾¨Éô ÀÂýÀÎò¾¢ x2 – x – 6 = 0 ±ýÈ ºÁýÀ¡ð¨¼ò ¾£÷ì¸×õ.

[P.287 – Ex – 10.1(4)] [MAR’12] [OCT’12]

5. y = 2x2 - x + 3 tiugl« tiuf. [g¡f« : 287, gæ‰Á 10.1 – 1-(iv)] [OCT-13]

6. y = 2x2 -ý ŨÃÀ¼ò¨¾ ŨÃóÐ, «¾¢Ä¢ÕóÐ 2x

2 + x - 6=0 ±ýÈ

ºÁýÀ¡ð¨¼ò ¾£÷ì¸×õ. [ P.285, ±.¸¡ : 10.5] [Á¡÷î-2014]

7. y = x2 +3x + 2 Ï‹ tiugl« tiuf. mij¥ ga‹gL¤Â x

2 +2x + 4 = 0 v‹w rk‹gh£il¤ Ô®¡fΫ.

[g¡f« : 286, v.fh10.6] [É‹ -14]

{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}

Å¡úòиټý,

” ¦º.¦ºøÅõ MSc.,MPhil.,BEd.,PGDCA.,

À𼾡â ¬º¢Ã¢Â÷ (¸½¢¾õ), «.§Á,¿¢.ÀûÇ¢. ¦ºª¾¡ÒÃõ, ¾¢Õî¦ºí§¸¡Î Åð¼õ, ¿¡Áì¸ø Á¡Åð¼õ.

2014 - 15 Email : selvamssh@gmail.com

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