· 2018/2/10 · gFjp –, my;y J 2. y =x-p k‰W« ax+5=3y v‹gd Ïiz våš, a-‹ kÂ¥ig¡...
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Transcript of · 2018/2/10 · gFjp –, my;y J 2. y =x-p k‰W« ax+5=3y v‹gd Ïiz våš, a-‹ kÂ¥ig¡...
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gFjp – M
II. VNjDk; 10 tpdhf;fSf;F tpilasp : [ tpdh 30 f;F fl;lhakhf tpilaspf;fTk; ] 10 X 2 = 24
^A \ Bh+ ^A \Ch
, 0
, 0
vD«nghJ
vD«nghJx
x x
x x 1
$=
-) ,
{ (x,y ) | y = |x |, x ! R } v‹w cwÎ, rh®ig tiuaW¡»wjh? mj‹ Å¢rf« fh©f.
m¡fofhu« v¤jid Kiw xè vG¥ò«?
x
2 2 x
83
-+
-
16. A,B k‰W«C M»a _‹W fz§fS¡F bt‹gl§fŸ tiuf.
y
x
x
3 y
6 2
31 4=
-
y
1 x
3
2
3 0
0
9
0
0c m c m= c m våš, x k‰W« y-fë‹ kÂ¥òfis¡ fh©f.
18. xU fofhu« xU kâ¡F xU Kiw, 2 kâ¡F ÏU Kiw, 3 kâ¡F _‹W Kiw v‹wthW, bjhl®ªJ rçahf x›bthU kâ¡F« xè vG¥ò« våš, xU ehëš
19. xU v© k‰bwhU v©â‹ _‹W kl§ifél 2 mÂf«. Á¿a v©â‹4 kl§fhdJ bgça v©izél 5 mÂf« våš, m›bt©fis¡ fh©f.
20. vëa toéš RU¡Ff. x
21. ԮΠfh© : c m e o+
x22.
23. ËtU« òŸëfŸ xnu ne®¡nfh£oš mikÍ« òŸëfsh vd
MuhŒf. (-2, -), (-6, -2) k‰W« (-2, 2)
2sin i1 -
1 + cosi11. =
(A) cosi (B) tani
(C) coti (D) coseci
12. xU ©k miu¡nfhs¤Â‹ é£l« 2 br.Û våš mj‹ bkh¤j òw¥gu¥ò
©k nfhs¤Â‹ tisgu¥ò 24 br.Û.2 mªj nfhs¤ij Ïu©L miu¡nfhs§fshf¥
Ãç¤jhš »il¡F« miu¡nfhs§fëš x‹¿‹ bkh¤j¥ òw¥gu¥ò
(A) 12 br.Û 2 (B) 8 br.Û 2 (C) 16 br.Û 2 (D) 18 br.Û 2
(A) 12 br.Û 2 (B) 12r br.Û 2 (C) 4r br.Û 2 (D) 3r br.Û 2.
13. xU
14. n cW¥òfŸ bfh©l vªj xU v©fë‹ bjhF¥Ã‰F« (Rx) - x =
(A) nx (B) (n- 2)x (C) (n- 1)x (D) 0
fœ¢Áæ‹ ãfœjfÎ p våš, ËtUtdt‰¿š p vij ãiwÎ brŒÍ«
(A) 0 1 p 1 1 0 # p 1 1 (D) 0 1 p # 1
15. A v‹w ã
(B) 0 # p # 1 (C)
10. AB, CD v‹gd xU t£l¤Â‹ ÏU eh©fŸ. mit Ú£l¥gL«nghJ P-š
rªÂ¡»‹wd k‰W« AB = 5 br.Û, AP = 8 br.Û, CD = 2 br.Û våš, PD =
(A) 12 br.Û (B) 5 br.Û (C) 6 br.Û (D) 4 br.Û
17.
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gFjp – ,
my;yJ
2. y= x- p k‰W« ax+ 5= 3y v‹gd Ïiz våš, a -‹ kÂ¥ig¡ fh©f.
31. A= {x ; x v‹gJ 42 -‹ gfh¡ fhuâ}, B = {x ;5 1 x # 12, x ! N} k‰W«
C= {1,4,5,6} våš, A , ^B , Ch= ^A , Bh, C v‹gij rçgh®¡fΫ.
bjçªjt®fë‹ rjÅj¤Âid¡ fh©f.
32. xU efu¤Âš 85% ng® jäœ bkhê, 40% ng® M§»y bkhê k‰W« 20% ng® Ϫ bkhê ngR»wh®fŸ. 32% ng® jäG« M§»yK«, 13% ng® jäG« ϪÂÍ« k‰W« 10% ng® M§»yK« ϪÂÍ« ngR»wh®fŸ våš, _‹W bkhêfisÍ« ngr¤
mfy¤ij 2 br.Û mÂfç¤jhš, br›tf¤Â‹ gu¥ò 33 r. br. Û mÂfç¡F« våš, br›tf¤Â‹ gu¥ig¡ fh©f.
x - 7x+ 6 3
III. VNjDk; 9 tpdhf;fSf;F tpilasp : [ tpdh 45 fl;lhakhf tpilaspf;fTk; ] 9 X 5 = 45
26.
25. ehz; Njw;wk; tiuaiw nra;f.
KfN; fhzk ; ABC xU rkgff; KfN; fhzk ; vdpy ; sin A, cos B, tan C
kjpgG; fisf; fhzf; .
jf£o‹ Mu§fis Ïiz¤J xU T«ò cUth¡f¥gL»wJ våš, m¡T«Ã‹ Mu¤ij¡ fh©f.
27. 180c ika¡ nfhzK« 21 br.Û. MuK« bfh©l t£lnfhz toéyhd ÏU«ò¤
2/ = 1530 våš, khWgh£L¡ bfGit¡ fz¡»Lf.28. n = 10, x = 12 k‰W« x
fh©f.2 2 2 2
29. Kjš ÏUgJ Ïaš v©fëèUªJ xU KG v© rkthŒ¥ò Kiwæš
nj®ªbjL¡f¥gL»wJ. mªj v© xU gfh v©zhf ÏU¥gj‰fhd
ãfœjféid¡
30. m) ËtU« K‰bwhUikfis ãWÎf. i+ i = i i sec cosec sec cosec
våš, m¡T«Ã‹ tisgu¥ig¡ fh©f.
M) xU ©k ne® t£l¡ T«Ã‹ mo¢R‰wsÎ 236 br.Û . k‰W« mj‹ rhÍau« 12 br.Û
p, q, kwW; k ; r MtJ cWgGf; s ; KiwNa a, b , c vdpy ; (q − r)a + (r − p)b + ( p − q)c = 0
vd ep&gp. ( xU $l;Lj;njhlh; )
A k‰W« B
2
4
5
= 1 3 6
-f p = ^ - h v‹w mâfS¡F (AB) B AT T T= v‹gij
rç¥gh®¡f.
33. 400-¡F« 600-¡F« ÏilnaÍŸs 11 Mš tFgL« mid¤J Ïaš v©fë‹
T£l‰gy‹ fh©f.
35. xU br›tf¤Â‹ Ús¤ij 2 br. Û mÂfç¤J mfy¤ij 2 br.Û Fiw¤jhš, mj‹ gu¥ò 28 r. br.Û Fiw»wJ. Ús¤ij 1 br.Û Fiw¤J
36. fhuâ¥gL¤Jf:
38. 3ABC -‹ KidfŸ A(2, 1), B(6, –1), C(4, 11) v‹f. A-æèUªJ tiua¥gL«
F¤J¡nfh£o‹ rk‹gh£il¡ fh©f.
39. ngsjpad ; Njww; k ; vOjp epWTf.
24.
34.
37.
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x+
, Q = x y
y
+ våš,
P Q P Q
Q1 2
- 2 2-
-
k‰W« t£l¤Â‹ ÛJ mikªJŸs xU òŸë (0, -2) våš, Ï›t£l¤Â‹Mu¤ij fh©f.
gFjp – <
xt;nthU tpdhtpYk; cs;s ,uz;L khw;W tpdhf;fspypUe;J xU tpdhitj; Njh;e;njLj;J ,U
tpdhf;fSf;Fk; tpilaspf;fTk;. 2 X 10 = 20
br.Û., BC = 6 br.Û. k‰W« AD = 4.2 br.Û. msÎfŸ bfh©l
2
= -‹ tiugl« tiuªJ, mjid¥ ga‹gL¤Â x 4x 5 02- - = v‹w
rk‹gh£il¤ Ô®¡fΫ.
40 ».Û. ntf¤Âš brš»wJ. Ïj‰Fça öu-fhy bjhl®Ã‰fhd tiugl« tiuf. Ïij¥ ga‹gL¤Â 3 kâneu¤Âš Ï¥ngUªJ gaâ¤j¤
my;yJ
nfhë‹ V‰w¡ nfhz§fŸ Kiwna 30c k‰W«
60c vd cŸsd. m›éU ãiya§fŸ, bra‰if¡nfhŸ M»a Ïit _‹W« xnu br§F¤J¤ js¤Âš mik»‹wd. ÏU ãiya§fS¡F« Ïilna cŸs öu« 4000 ».Û våš, bra‰if¡nfhS¡F«, óä¡F« Ïilna cŸs öu¤ij¡ fh©f. ( 3 = 1.732 )
m¢bra‰if¡ 40. xU bra‰if¡ nfhS¡F xnu Âiræš óäæš mikªJŸs ÏU f£L¥gh£L
ãiya§fëèUªJ
41. 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.
»il¡F« nfhs tot F©Lfë‹ v©â¡ifia¡ fh©f.
42. 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
x 70 74 78 82 86 90
f 1 3 5 7 8 12
43. ËtU« òŸë étu¤Â‰fhd £l éy¡f« fh©f.
54
32
73 v‹f. A k‰W« B ÏUtU« nr®ªJ ԮΠfh©gj‰fhd ãfœjfÎ
158 .
B k‰W« C ÏUtU« nr®ªJ ԮΠfh©gj‰fhd ãfœjfÎ 72 . A k‰W« C ÏUtU«
nr®ªJ ԮΠfhz ãfœjfÎ 3512 , _tU« nr®ªJ ԮΠfhz ãfœjfÎ
358 våš,
ahnuD« xUt® m›édhé‹ Ô®Î fh©gj‰fhd ãfœjféid¡ fh©f.
44. A, B, C M»nah® xU édhé‰F¤ ԮΠfh©gj‰fhd ãfœjfÎfŸ Kiwna
, ,
45. m) P = I¡ fh©f.x y
my;yJ
M) xU t£l¤Â‹ ÏU é£l§fë‹ rk‹ghLfŸ x + 2y = 7 , 2x + y = 8
M) AB = 6 br.Û., AC = 7
t£l eh‰fu« ABCD tiuf.
47. m) xU ngUªJ kâ¡F
M) y x
.
my;yJ
46. m) 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.
öu¤ij¡ f©LÃo.
III.
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