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MODEL PAPER
g‘¶ … ½ K§Q>m
{df¶ … Applied Mathematics
A{YH$V‘ A§H$ … 30
H$moS> g§»¶m … 104
104
ZmoQ>…1
...
2
...
_________________________________
1
...
bter
...
bter
...
3x
Ho$ àgma ‘| x3 H$m JwUm§H$ h¡3
(1) 3
6
(2)
(log 3) 3
3
(3)
log (3) 3
6
(4)
(log 3) 3
6
CÎma (4)
3
...
ii
H$m H$mën{ZH$ ^mJ h¡(1) 0
(2) 1
(3) 2
(4) - 1
CÎma (1) 0
¶h ‘m°S>b nona {dÚm{W©¶m| Ho$ ‘mJ©Xe©Z Ho$ {b¶o Ed§ CZH$s V¡¶mar H$mo ñd¶§ naIZo Ho$ {b¶o {ZewëH$
CnbãY H$adm¶m J¶m h¡& àH$meH$ Bg ‘m°S>b nona go narjm ‘| àíZ AmZo H$s H$moB© ^r g§^mdZm 춳V
Zht H$aVm h¡& {dÚm{W©¶m| H$mo gbmh Xr OmVr h¡ {H$ do Q>o³ñQ> ~wH$ go Aܶ¶Z H$a|&
5
...
¶{X sin q = 24 hmo Am¡a q {ÛVr¶ MVwWmªe ‘| h¡, V~
25
sec q + tan q = ?
(1)
(2)
(3)
(4)
-3
-5
-7
-9
CÎma (3) - 7
7
...
bter
...
bter
...
¶{X
(1)
(2)
(3)
(4)
1+a 1
1
1 1 + b 1 = 0 , Vmo a-1 + b-1 + c-1
1
1 1+c
~am~a h¡-
1
-1
abc
BZ‘| go H$moB© Zht
CÎma (2) - 1
¶h ‘m°S>b nona {dÚm{W©¶m| Ho$ ‘mJ©Xe©Z Ho$ {b¶o Ed§ CZH$s V¡¶mar H$mo ñd¶§ naIZo Ho$ {b¶o {ZewëH$
CnbãY H$adm¶m J¶m h¡& àH$meH$ Bg ‘m°S>b nona go narjm ‘| àíZ AmZo H$s H$moB© ^r g§^mdZm 춳V
Zht H$aVm h¡& {dÚm{W©¶m| H$mo gbmh Xr OmVr h¡ {H$ do Q>o³ñQ> ~wH$ go Aܶ¶Z H$a|&
9
...
a
Ho$ {H$g ‘mZ Ho$ {bE g‘rH$aU {ZH$m¶
^a + 1h2 x ^a + 2h2 y - ^a + 3h3 = 0
^a + 1h x + ^a + 2h y - ^a + 3h = 0 ,
x + y - 1 = 0 g§JV h¡ (1) 1
(2) 0
(3) - 3
(4) - 2
CÎma (4) - 2
g‘rH$aU x3 - x - 5 = 0 H$m 1 d 2 Ho$ ~rM nhbr nwZamd¥{Îm Ho$
~mX ݶyQ>Z-a¡âgZ {d{Y go ‘yb hmoJm(1) 1
...
904
(3) 1
...
940
CÎma (1) 1
...
{gångZ Ho$ EH$-{VhmB© {Z¶‘ Ho$ Cn¶moJ go {ZåZ Am±H$‹S>m| Ho$ {bE
3
# f^x hdx H$m ‘mZ h¡1
x
:
1
1
...
5
3
¶h ‘m°S>b nona www
...
site na CnbãY h¡& www
...
site {H$gr ^r àH$ma
go Board of Technical Education, Rajasthan go gå~pÝYV Zht h¡ VWm
CgH$s A{YH¥$V do~gmBQ> Zht h¡&
f ^x h
(1)
(2)
(3)
(4)
:
2
...
4
2
...
8
3
55
...
1
5
...
975
CÎma (3) 5
...
¶{X {~ÝXþAm| ^x, 2h VWm ^3, 4h Ho$ ‘ܶ Xÿar 2 BH$mB© hmo, Vmo x
H$m ‘mZ hmoJm
(1) 2
(2) 1
(3) 3
(4) 4
CÎma (3) 3
13
...
erfm] c 2, 32- 1 m , b 1 , - 1 l VWm b2, - 1 l dmbo {Ì^wO H$m
2
2
2
bå~Ho$ÝÐ h¡(1) c 3 , 36- 3 m
2
(2) b2, - 1 l
2
(3) c 5 , 34- 2 m
4
(4) b 1 , - 1 l
2
2
CÎma (2) b 2, - 1 l
2
15
...
bter
...
bter
...
x - 2 = t2 , y = 2t
g‘rH$aU h¡ (1) y2 = 4x
(2) y2 = - 4x
(3) x2 = - 4y
(4) y2 = 4 ^x - 2h
17
...
¶{X A{Vnadb¶ H$s {Z¶Vm x + 2y = 1, Zm{^ ^2, 1h VWm
CËHo$ÝÐVm 2 hmo, Vmo CgH$m g‘rH$aU hmoJm (1) x2 - 16xy - 11y2 + 12x + 6y + 21 = 0
(2) 3x2 + 16xy + 15y2 - 4x - 14y - 1 = 0
(3) x2 + 16xy + 11y2 - 12x - 6y + 21 = 0
(4) BZ‘| go H$moB© Zht
CÎma (1) x2 - 16xy - 11y2 - 12x + 6y + 21 = 0
¶h ‘m°S>b nona {dÚm{W©¶m| Ho$ ‘mJ©Xe©Z Ho$ {b¶o Ed§ CZH$s V¡¶mar H$mo ñd¶§ naIZo Ho$ {b¶o {ZewëH$
CnbãY H$adm¶m J¶m h¡& àH$meH$ Bg ‘m°S>b nona go narjm ‘| àíZ AmZo H$s H$moB© ^r g§^mdZm 춳V
Zht H$aVm h¡& {dÚm{W©¶m| H$mo gbmh Xr OmVr h¡ {H$ do Q>o³ñQ> ~wH$ go Aܶ¶Z H$a|&
19
...
3
2
lim x + x - 2
x " 1 sin ^x - 1h
(1)
(2)
(3)
(4)
CÎma (1) ;- p , 7p E
6 6
H$m ‘mZ hmoJm-
2
3
4
5
CÎma (4) 5
21
...
bter
...
bter
...
cot-1 6 cos 2x @
2
(1)
3
1
(2)
3
(3)
(4)
H$m x = p na AdH$bO h¡6
3
6
CÎma (1)
23
...
¶{X EH$ JmobmH$ma Jwã~mao H$m Ma ì¶mg 3x + 9 hmo, Vmo x Ho$ gmnoj
2
CgHo$ Am¶VZ ‘| n[adV©Z H$s Xa hmoJr(1) 27p ^2x + 3h2
(2) 27p ^2x + 3h2
16
(3) 27p ^2x + 3h2
8
(4) BZ‘| go H$moB© Zht
CÎma (3) 27p ^2x + 3h2
8
¶h ‘m°S>b nona {dÚm{W©¶m| Ho$ ‘mJ©Xe©Z Ho$ {b¶o Ed§ CZH$s V¡¶mar H$mo ñd¶§ naIZo Ho$ {b¶o {ZewëH$
CnbãY H$adm¶m J¶m h¡& àH$meH$ Bg ‘m°S>b nona go narjm ‘| àíZ AmZo H$s H$moB© ^r g§^mdZm 춳V
Zht H$aVm h¡& {dÚm{W©¶m| H$mo gbmh Xr OmVr h¡ {H$ do Q>o³ñQ> ~wH$ go Aܶ¶Z H$a|&
25
...
#e
(1)
(2)
(3)
(4)
x
cos e x dx =
x
2 sin e x
sin e x
2 cos e x
- 2 sin e x
CÎma (1) 2 sin e
27
...
bter
...
bter
...
dy
AdH$b g‘rH$aU dx = ex - y + x2 e-y H$m hb h¡3
(1) ey = ex + x + c
3
(2) ey = ex + 2x + c
(3) ey = ex + x3 + c
(4) y = ex + c
3
CÎma (1) ey = ex + x + c
3
29
...
a # b 2 + ^a $ b h2 =
(1) ^a # a h $ ^b # bh
(2) ^a $ a h^b $ bh
(3) ^a # bh ^a $ bh
(4) 2 ^a $ bh^a $ bh
CÎma (2) ^a $ a h^b $ b h
*******
¶h ‘m°S>b nona {dÚm{W©¶m| Ho$ ‘mJ©Xe©Z Ho$ {b¶o Ed§ CZH$s V¡¶mar H$mo ñd¶§ naIZo Ho$ {b¶o {ZewëH$
CnbãY H$adm¶m J¶m h¡& àH$meH$ Bg ‘m°S>b nona go narjm ‘| àíZ AmZo H$s H$moB© ^r g§^mdZm 춳V
Zht H$aVm h¡& {dÚm{W©¶m| H$mo gbmh Xr OmVr h¡ {H$ do Q>o³ñQ> ~wH$ go Aܶ¶Z H$a|&