66

†bvqvLvjx miKvwi gwnjv K‡jR, †bvqvLvjx welq †KvW : 2 6 6

mgq25 wgwbU D”PZi MwYZ wØZxq cÎ eûwbe©vPwb Afxÿv c~Y©gvb25
[we‡kl `ªóe¨ : mieivnK…Z eûwbe©vPwb Afxÿvi DËic‡Î cÖ‡kœi µwgK b¤^‡ii wecix‡Z cÖ`Ë eY©msewjZ e„Ëmg~n n‡Z mwVK/ m‡e©vrK…ó Dˇii e„ËwU ej c‡q›U Kjg
Øviv m¤ú~Y© fivU Ki| cÖwZwU cÖ‡kœi gvb 1| cÖkc
œ ‡Î †Kv‡bv cÖKvi `vM/wPý †`Iqv hv‡e bv|]
1. 3  5i Gi Av¸©‡g›U KZ? 10. (x) = 2 tan1 x n‡j 18. †Kv‡bv we›`y‡Z wµqviZ 10 N I 6N ej `ywUi
5 5 4x AšÍM©Z †Kv‡bv KZ n‡j jwä 2 19N n‡e?
K   tan1 L   + tan1 i. (x) = tan 1
3 3 1 + x2 K 30 L 60
5 5
M  tan1
3
N  tan 1
( )

3 ii. (x) = sin1
2x
1 + x2
M 90 N 120
19. `yBwU mgvb e‡ji jwäi eM© Zv‡`i
1 1  x2
2. 1 + sin   i cos 
Gi ev¯Íe Ask wb‡Pi iii. (x) = cos1 ¸Yd‡ji wZb¸Y n‡j ej؇qi AšÍM©Z
1 + x2
†KvbwU? wb‡Pi †KvbwU mwVK? †KvY KZ?
1 K 30 L 60
K
2
L2 K i I ii L i I iii
M 90 N 120
cos   cos  M ii I iii N i, ii I iii
M N  wb‡Pi Z‡_¨i Av‡jv‡K 20 I 21 bs cÖ‡kœi
2 + 2 sin  2 + 2 sin  11. sin  = sin  n‡j mvaviY mgvavb wb‡Pi
DËi `vI :
 wb‡Pi Z‡_¨i Av‡jv‡K 3 I 4 bs cÖ‡kœi †KvbwU?
12 kg I 8 kg IR‡bi `ywU mgvšÍivj ej
DËi `vI : 
20 cm e¨eav‡b wµqv K‡i|
n
2 K  = (2n + 1) L  = n + ( 1) 
2
Z= GKwU RwUj msL¨v|
4 + 3i  20. ejØq wem`„k mgvšÍivj n‡j e„nËi ej
3. Gi AbyeÜx RwUj msL¨v †KvbwU? M  = n +  N  = (4n + 1)
z 2 †_‡K jwäi cÖ‡qvM we›`yi `~iZ¡ KZ?
K
2
L
2 12. n GKwU c~Y©msL¨v n‡j 2 sin 2x = 1 K 40 cm L 30 cm
4  3i 4  3i M 20 cm N 10 cm
mgxKi‡Yi mvaviY mgvavb †KvbwU?
2 2
M
25
(4 + 3i) N  (4 + 3i)
25  n  21. ejØq m`„k mgvšÍivj n‡q hw` ci¯úi
K n + L + ( 1)n
4. | z | = KZ?
12 2 12 wµqv we›`yi Ae¯’vb cwieZ©b K‡i Zvn‡j
25 2 M n 

N n + ( 1)n
 jwäi miY KZ?
K L 12 6
2 5 K 2 cm L 4 cm
2 2 13. KwbK x2 = 8y Gi Dr‡Kw›`ªKZv KZ? M 8 cm N 12 cm
M N
25 5 K e=0 L e=1
22. †Kv‡bv we›`y‡Z wµqviZ P, 2P Ges 3P
5. 2x2  mx + 2 = 0 mgxKi‡Yi g~jØq RwUj M 0<e<1 N e>1
GKK ejÎq wµqv K‡i mvg¨ve¯’v m„wó
n‡e hLb 14. 4x  y + 2 = 0 mij‡iLvwU y2 = 32x
K‡i| 1g `ywU e‡ji AšÍfz©³ †KvY KZ?
K m>4 L 4<m<4 cive„ˇK ¯úk© Ki‡j ¯úk©we›`y KZ? K 30 L 60
M m<4 N m4
6. x2  4x + 1 = 0 mgxKi‡Yi g~jØq m, n
K (12 4) L (4 12) M 90
23. GKwU †bŠKv 8m s1 †e‡M †mvRvmywR GKwU
N 120

n‡j m3 + n3 Gi gvb KZ? M (1, 8) N (8, 1)

b`x cvwo w`‡Z cv‡i| hw` †mÖv‡Zi †eM
K 52 L 75 x2 y2
15. y = 3x + k †iLvwU 4 + 3 = 1 Dce„‡Ëi 6 m s1 nq, Z‡e †bŠKvi †eM KZ?
M 1692 N 1764
¯úk©K n‡j k Gi gvb KZ? K 2 m s1 L 2 7 m s1
7. 2x3  9x2 + 14x  5 = 0 mgxKi‡Yi `ywU 1 1
M 10 m s N 14 m s
1 K± 13 L± 15
g~j 2  i I 2 n‡j Aci g~j KZ? 24. GKwU ey‡jU †Kv‡bv †`qv‡j 4 Bw XzKvi
M ±6 N ± 39
K 2+i L 2i 16. 16x2  25y2 = 400 Awae„‡Ëi AmxgZ‡Ui ci †eM A‡a©K nvivq| ey‡jUwU †`qv‡ji
M 2+i N 2i
mgxKiY wb‡Pi †KvbwU? wfZi Avi KZ Bw XzK‡e?
8. x2 + mx + 3 = 0 mgxKi‡Yi GKwU g~j 2 n‡j 4 5 K
3
L
4
3 K x=± y L x=± y 4 3
i. Aci g~j 5 4
2 8
4 5 M N3
7 M y=± x N y=± x 3
ii. m Gi gvb 5 4
2 x2 y2 25. u Avw`‡e‡M Avbyf‚wg‡Ki mv‡_  †Kv‡Y
1 17. 
25 16
= 1 Awae„‡Ëi
wbwÿß e¯‘i
iii. g~j؇qi AšÍi
2
i. AbyeÜx A‡ÿi ˆ`N©¨ 8 wePiYKvj
u sin 
wb‡Pi †KvbwU mwVK? i.
g
20
K i I ii L i I iii ii. wbqvgK †iLvi mgxKiY y = ± u2
41 ii. e„nËg cvjøv
M ii I iii N i, ii I iii 32
g
iii. Dc‡Kw›`ªK j‡¤^i ˆ`N©¨ u2 sin2 
9. sin1 x + cos1 x = KZ? 5 iii. me©vwaK D”PZv
2g
K

L
 wb‡Pi †KvbwU mwVK?
6 4 wb‡Pi †KvbwU mwVK?
K i I ii L i I iii
  K i I ii L i I iii
M N M ii I iii N i, ii I iii
3 2 M ii I iii N i, ii I iii