= tpj;aghujp nkl;hpf;nky;epiyg;gs;sp · 12.12.2018 · 2 30. n=5 p 2 6 ,, €3,5 , 4,4 , 5,3^ , 6,...

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= tpj;aghujp nkl;hpf;Nky;epiyg;gs;sp , rf;fuhk;ghisak;. 99655 – 31727 . 1

= tpj;aghujp nkl;hpf;Nky;epiyg;gs;sp rf;fuhk;ghisak;> mfuk;(mQ;ry;)> vyr;rpg;ghisak;> jpUr;nrq;NfhL(tl;lk;)> ehkf;fy; (khtl;lk;)-637 202.

miyNgrp : 99655-31727> 94432-31727

miuahz;Lg; nghJj;Njh;T – brk;gh; 2018 tFg;G: 12 Njjp: 14.12.2018

ghlk; : fzpjk; kjpg;ngz;fs; : 90

gphpT – I tp.vz; tpilf;Fwpg;G kjpg;ngz;

1. b) f(x) = x2 1

2. a)(6,6) 1

3. c)k≠-4 1

4. c) xU jsk; mikahjit 1

5. b)-1 1

6. b)2 1

7. b)33 1

8. d) ( )p p 1

9. c)

1 21

3 410

10. c) 40 1

11. a) cosx 1

12. a)65 1

13. c)100

3 1

14. a) 3

15. a)48 1

16. c) 25

51 1

17. d)-tanx 1

18. b) 3 1

19. c)(z,.) 1

20. b)256 1

gphpT – II

21. 6 12 6

1 2 1

4 8 4

6 12 6

~ 0 0 0

0 0 0

( ) 1A

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= tpj;aghujp nkl;hpf;Nky;epiyg;gs;sp , rf;fuhk;ghisak;. 99655 – 31727 . 2

22. [ a b

b c

c a

]=0

2[ a

c]=0

[ a

c]=0

23. 11

n=4

24. 2 4y ax 2 3600y x

64 16

36 9x

25. ( ) sinf

'( ) 1 cosf

cos 1 (0,2 )

khWepiy vz; = epiy vz;fs; =(,)

26. 3 2( ) 2 5 4f x x x x 2'( ) 6 10f x x x

''( ) 12 10f x x ''( ) 0f x ,x=-5/6

,ilntsp ''( ) 12 10f x x

FopT / FtpT

fPo; Nehf;fp FopT

Nky; Nehf;fp FtpT

27. Let =

Let , =-1/300

3 999 10-0.0033

3 999 9.9967

28. 11 1 1 4

20 0

(sin (sin )

41I

4 2

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= tpj;aghujp nkl;hpf;Nky;epiyg;gs;sp , rf;fuhk;ghisak;. 99655 – 31727 . 3

29.

p q ~

T T T F

T F F T

F T T F

F F T F

30. n=5

3,5 , 4,4 , 5,32 6 , 2 , , 6,P

36p ,

36q

31( 0) 5

36p X C

531

gphpT – III

31. 2 4

21 7 8

18 6 4

AdjA

22( 28 48) (84 14) 4(126 126)A

400 40 60

360 60

32. 1a b c

1a b c

2 2 2

2 . 2 . 2 . 1a b c a b b c c a

1 1 1

2 . 2 . ( ) 2 ( ). 12 3 6

a b bm a b m a b a

1 2 . 1a b

2 . 0a b

a b

33.

x d; kjpg;Gfs;:

34. 2 6a 2 4b

2 2

2a b

ae aa

3 2x 5 0y

Ftpaq;fs ( 3 2,5) &( 3 2,5)

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= tpj;aghujp nkl;hpf;Nky;epiyg;gs;sp , rf;fuhk;ghisak;. 99655 – 31727 . 4

35.

36. x = cost , y = sint, z =t.

;

37. rpwg;G rkd;ghL; :

nghJj;jPh;T =

38. Njw;wk;:

ep&gzk; : (i)

(ii) * ) b

∴ . d; Neh;khW

∴

39.

(i)

ii)

40. ( ) sinf x x =,ul;ilr;rhh;G

2 2

sin 2 sinxdx xdx

= 2

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= tpj;aghujp nkl;hpf;Nky;epiyg;gs;sp , rf;fuhk;ghisak;. 99655 – 31727 . 5

gphpT – IV

41. (a) )

vdpy; vz;zpf;ifaw;w jPH;T cilaJ. xU 2x2 rpw;whzpf;NfhitahdJ

G+r;rpakw;w ,Ug;gjhy; ,j;njhFg;ghdJ; ,U rkd;ghLfshf ,Ue;J xU rkd;ghLlhf khw;w Ntz;Lk;.

,q;F

fpNukh; tpjpg;gb

jPh;tHdJ

(b) 3 3

tanx y

f ux y

n=2 vd;gJ rkg;gbj;jhd gb rhh;G.

A++yhpd; Njw;wk; 2f f

x y fx y

(tan ) (tan ) 2x u y u fx y

2 2sec sec 2 tan

u ux u y u u

x y

sin 2u u

x y ux y

42. (a) tiug;glk;

(A-B) =sin(A-B)

sin(A-B)

(b) ntf;lh; tbtk;::

, and

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= tpj;aghujp nkl;hpf;Nky;epiyg;gs;sp , rf;fuhk;ghisak;. 99655 – 31727 . 6

fhh;brpad; tbtk;:

and

43. (a) tiuglk;

gutisaj;jpd; rkd;ghL

B(6, -4) vd;w Gs;sp topNa nry;tjhy;

(6)2= -4a(-4) ⇒ ⇒

⇒

vwpNfhzk;

(b) tiuglk; :

= 6

ghijapd; epakg;ghij:

44. (a)

‘ as

‘ ’rha;T

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= tpj;aghujp nkl;hpf;Nky;epiyg;gs;sp , rf;fuhk;ghisak;. 99655 – 31727 . 7

ntl;Lj;Jz;Lfspd; $Ljy; =

(b)

nrt;tfj;jpd; gug;G

ePsk; = mfyk; =

vdNt ,U xU rJuk; MFk;.

45. (a) tiuglk; 4y

2 = 9x and 3x

2 =16y are and .

Njitahd gug;G =

R.A.

rJu myFfs;.

(b)

= c

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= tpj;aghujp nkl;hpf;Nky;epiyg;gs;sp , rf;fuhk;ghisak;. 99655 – 31727 . 8

rkd;ghL (1) kw;Wk; (2)

⇒

46. (a)

Let

(b) t Neuj;jpy; NjePhpd; ntg;gepiy T vd;f.

since S =15 ⇒ ⇒

= 85

t = 5, T = 60 ⇒ ⇒

⇒

t = 10, T

47.

(a) nfa;yp; ml;;ltiz

Let

i)milg;G tpjp: ml;ltizapypUe;J milg;G tpjp cz;ik.

(ii)Nrh;g;G tpjp:. kl;L ngUf;fy; 8 d; fPo; Nrh;g;G tpjp cz;ik.

(iii) rkdp tpjp:

e=[1]

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= tpj;aghujp nkl;hpf;Nky;epiyg;gs;sp , rf;fuhk;ghisak;. 99655 – 31727 . 9

(iv) Neh;khW tpjp: d; Neh;khW

d; Neh;khW

xU Fyk; MFk;.

(v) ghpkhw;W tpjp: ml;ltizapypUe;J milg;G tpjp cz;ik.

xU vg{ypad; Fyk; MFk;..

(b) 1 24

i cis

2 2

2(1 ) 4

( ) ( )6 6

cisi

cis cis

= 642 2 .ii

e e

3 2

122 2i

=5 5

2 2 cos sin12 12

fzpjj;Jiw = tpj;aghujp nkl;hpf;Nky;epiyg;gs;sp

rf;fuhk;ghisak;> mfuk;(mQ;ry;)> vyr;rpg;ghisak;> jpUr;nrq;NfhL(tl;lk;)> ehkf;fy; (khtl;lk;)-637 202.

miyNgrp : 99655-31727> 94432-31727 Cell : 8667482750, 9842512985, 9976318384

***********

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