= 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,...
TRANSCRIPT
= tpj;aghujp nkl;hpf;Nky;epiyg;gs;sp , rf;fuhk;ghisak;. 99655 – 31727 . 1
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ghlk; : fzpjk; kjpg;ngz;fs; : 90
gphpT – I tp.vz; tpilf;Fwpg;G kjpg;ngz;
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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
1
10. c) 40 1
11. a) cosx 1
12. a)65 1
13. c)100
3 1
14. a) 3
1
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
A
6 12 6
~ 0 0 0
0 0 0
( ) 1A
1
1
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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
b
c]=0
[ a
b
c]=0
1
1
23. 11
1
ni
i
1n
i
n=4
1
1
24. 2 4y ax 2 3600y x
1
64 16
36 9x
1
1
25. ( ) sinf
'( ) 1 cosf
cos 1 (0,2 )
khWepiy vz; = epiy vz;fs; =(,)
1
1
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
1
1
27. Let =
Let , =-1/300
3 999 10-0.0033
3 999 9.9967
1
1
28. 11 1 1 4
20 0
(sin (sin )
41I
x
=
41
4 2
=4
64
1
1
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29.
p q ~
T T T F
T F F T
F T T F
F F T F
2
30. n=5
3,5 , 4,4 , 5,32 6 , 2 , , 6,P
5
36p ,
31
36q
5
0
31( 0) 5
36p X C
=
531
36
1
1
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
6
1
1
1
32. 1a b c
2
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
1
1
1
33.
x d; kjpg;Gfs;:
1
1
1
34. 2 6a 2 4b
2 2
2a b
ae aa
3 2x 5 0y
Ftpaq;fs ( 3 2,5) &( 3 2,5)
1
1
1
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= tpj;aghujp nkl;hpf;Nky;epiyg;gs;sp , rf;fuhk;ghisak;. 99655 – 31727 . 4
35.
1
2
36. x = cost , y = sint, z =t.
;
;
1
1
1
37. rpwg;G rkd;ghL; :
nghJj;jPh;T =
1
1
1
38. Njw;wk;:
ep&gzk; : (i)
(ii) * ) b
∴ . d; Neh;khW
∴
1
1
1
39.
(i)
ii)
1
1
1
40. ( ) sinf x x =,ul;ilr;rhh;G
2 2
0
2
sin 2 sinxdx xdx
= 2
1
1
1
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gphpT – IV
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1
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(A-B) =sin(A-B)
sin(A-B)
1
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, and
1
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= tpj;aghujp nkl;hpf;Nky;epiyg;gs;sp , rf;fuhk;ghisak;. 99655 – 31727 . 6
fhh;brpad; tbtk;:
and
2
1
43. (a) tiuglk;
gutisaj;jpd; rkd;ghL
B(6, -4) vd;w Gs;sp topNa nry;tjhy;
(6)2= -4a(-4) ⇒ ⇒
⇒
vwpNfhzk;
1
1
1
1
1
(b) tiuglk; :
= 6
=
ghijapd; epakg;ghij:
1
1
1
2
44. (a)
‘ as
‘ ’rha;T
1
2
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= tpj;aghujp nkl;hpf;Nky;epiyg;gs;sp , rf;fuhk;ghisak;. 99655 – 31727 . 7
ntl;Lj;Jz;Lfspd; $Ljy; =
1
1
(b)
,
nrt;tfj;jpd; gug;G
&
ePsk; = mfyk; =
vdNt ,U xU rJuk; MFk;.
1
1
1
1
1
45. (a) tiuglk; 4y
2 = 9x and 3x
2 =16y are and .
Njitahd gug;G =
R.A.
rJu myFfs;.
1
2
1
1
(b)
= c
= c
= c
=
2
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= tpj;aghujp nkl;hpf;Nky;epiyg;gs;sp , rf;fuhk;ghisak;. 99655 – 31727 . 8
rkd;ghL (1) kw;Wk; (2)
⇒
2
1
46. (a)
Let
1
2
2
(b) t Neuj;jpy; NjePhpd; ntg;gepiy T vd;f.
since S =15 ⇒ ⇒
= 85
t = 5, T = 60 ⇒ ⇒
⇒
t = 10, T
1
1
1
2
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]
2
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
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;..
1
1
(b) 1 24
i cis
2 2
2(1 ) 4
( ) ( )6 6
cisi
cis cis
= 642 2 .ii
e e
=
3 2
122 2i
e
=
5
122 2i
e
=5 5
2 2 cos sin12 12
i
1
2
1
1
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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