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7/27/2019 Jee 2014 Booklet6 Hwt Integral Calculus 2
1/15
Yb`yanak`br Ecassls
YNE/Bktlmrac Eaceucus-? 1:1 F]P-9/Natflnatbes
@APL 7 PBNL 7 0: Nbkutls NA_HU 7 X TTT /1:^ PLUP ED@L 7 BE-? X1^
UPA_P PBNL 7 LK@ PBNL 7 PBNL PAHLK7 ZA_LKPU UBMKAP\_L 7
Pfbs tlst edktabks a tdtac di 1: Dogletbvl Pypl Qulstbdks. Laef qulstbdk earrbls 1 narh. Pflrl bs KD KLMAPBYL narhbkm.
Efddsl tfl edrrlet actlrkatbvl. Dkcy dkl efdbel bs edrrlet.
1.
:< 0
`x
eds x
bs 7
(A) /? (O) /0
(E) /5 (@) /9
?. Clti7_ _ ak`m7_ _ ol edktbkudus iuketbdks.
Pflk tfl vacul di tfl bktlmrac
?
?
i x i x m x m x `x
(A) 1(O) :
(E)? ?
i i
(@)? ?
m m
5. Clt m (x) ol a iuketbdk satbsiybkm m x m x ak`
m (:) > 1 ak` i (x) ol a iuketbdk tfat
satbsibls ?i x m x x . Pflk tfl vacul di tfl
bktlmrac 1
:
i x m x `x bs 7
(A)=
0
l(O)
5
?
l
(E)?
5
? ?
ll (@)
?5
? ?
ll
0. Bi
?
1
l
l
`xB
cdm x ak`
?
?
1
xlB `x
x , tflk 7
(A) 1 ??B B (O) ? 1?B B
(E)1 ?
:B B (@)1 ?
:B B
7/27/2019 Jee 2014 Booklet6 Hwt Integral Calculus 2
2/15
Yb`yanak`br Ecassls
YNE/Bktlmrac Eaceucus-? 1:? F]P-9/Natflnatbes
@APL 7 PBNL 7 0: Nbkutls NA_HU 7 X TTT /1:^ PLUP ED@L 7 BE-? X?^
UPA_P PBNL 7 LK@ PBNL 7 PBNL PAHLK7 ZA_LKPU UBMKAP\_L 7
Pfbs tlst edktabks a tdtac di 1: Dogletbvl Pypl Qulstbdks. Laef qulstbdk earrbls 1 narh. Pflrl bs KD KLMAPBYL narhbkm.
Efddsl tfl edrrlet actlrkatbvl. Dkcy dkl efdbel bs edrrlet.
1.1
?
11
ltak x cdm x
`xx x
bs 7
(A)1
tak l (O) cdm tak l (E) 11
takl
(@)1
tak l
?.
?11
11 sbk x
sbk x `x
bs 7
(A)?
6
0
(O)
?6
0
(E)
?6
?
(@)
?6
?
5. 9
?1
:
sbk x ` x , wflrl {x} bs iraetbdkac part iuketbdk bs 7
(A) ?5 6 (O) ?5 6 (E) ?5 6
?
(@)
?5 6?
0. Pfl arla oduk`l` oy ? ?? 1y y x ak` bts vlrtbeac asynptdtls bs 7
(A)?
(O) (E) ? (@) 0
7/27/2019 Jee 2014 Booklet6 Hwt Integral Calculus 2
3/15
Yb`yanak`br Ecassls
YNE/Bktlmrac Eaceucus-? 1:5 F]P-9/Natflnatbes
2. ? 5
? 5 ?
:
x eds x `x
bs 7
(A)5
(O)
0
(E)
9
(@)
1?
1:. Bi 0
1
0i x `x
ak` 0
?
= =i x `x , tflk tfl vacul di ?
1
i x `x
bs 7
(A) < (O) 0 (E) 5 (@) 5
7/27/2019 Jee 2014 Booklet6 Hwt Integral Calculus 2
4/15
Yb`yanak`br Ecassls
YNE/Bktlmrac Eaceucus-? 1:0 F]P-9/Natflnatbes
@APL 7 PBNL 7 0: Nbkutls NA_HU 7 X TTT /1:^ PLUP ED@L 7 BE-? X5^
UPA_P PBNL 7 LK@ PBNL 7 PBNL PAHLK7 ZA_LKPU UBMKAP\_L 7
Pfbs tlst edktabks a tdtac di 1: Dogletbvl Pypl Qulstbdks. Laef qulstbdk earrbls 1 narh. Pflrl bs KD KLMAPBYL narhbkm.
Efddsl tfl edrrlet actlrkatbvl. Dkcy dkl efdbel bs edrrlet.
1.
1 ? bs 7(A) 1 (O) ? (E) 5/? (@) 1/?
?.
?
0 0
:
x sbk x eds x`x
sbk x eds x
(A)?
5?
(O)
?
6
(E)
?
19
(@)
19
5.?
:1
x sbk x`x
eds x
(A)0
(O)
?
0
(E)
?
?
(@)
?
0. Bi ?
15 ?
x
m x t m t `t x
, tflk ?m bs 7
(A)1
?(O)
5
0(E) 1 (@)
5
?
7/27/2019 Jee 2014 Booklet6 Hwt Integral Calculus 2
7/15
Yb`yanak`br Ecassls
YNE/Bktlmrac Eaceucus-? 1:= F]P-9/Natflnatbes
2. Clt
1
5 5
11
5 5
:1
kk
r
kk
k r
`x, Z cbn
x k
/
tflkcdm Zbs 7
(A) ? 1cdm (O) ? 5 5cdm (E) ? ?cdm (@) 0 5 ?cdm
1:.
?
:
1 5
1 ?
sbk x`x
sbk x
bs 7
(A)?
(O)
6
(E) 1 (@)
1
?
7/27/2019 Jee 2014 Booklet6 Hwt Integral Calculus 2
8/15
Yb`yanak`br Ecassls
YNE/Bktlmrac Eaceucus-? 1:6 F]P-9/Natflnatbes
@APL 7 PBNL 7 0: Nbkutls NA_HU 7 X TTT /1:^ PLUP ED@L 7 BE-? X < (O) 9O (E) E> 5 (@) O> 9
*0. Bi5 0 5
1 1 ?
1 ? 5
: : 1
? ? ?x x xB `x, B `x, B `x , ak`0
?
0
1
?xB `x, tflk 7
(A) ? 1B B (O) 5 0B B (E) 0 5B B (@) 1 ?B B
* : (O)?
A O
(E) A O (@)0
A O
9. Clt ?
? 1 5 1
5 ? 1
x , xi x
x , x
ak`
?
0 = < :
< = :
x , xm x
x x , x
. Pflk vacul di
?
?
m i x `x
lquacs 7
(A) : (O) 1:1/1? (E) 1221/9 (@) 1221/1?
=.
1
?: 1
xxl`x
x
(A)?
l(O)
11
?l
(E)
1?
?l
(@) Kdkl di tflsl
6. ?
? 0
?sbk x sbk x sbk x eds x x
/
/bs lquac td 7
(A)0
1 :, tflk
5
1 5i x `x /
(A) 0/5 (O) 6/5 (E) 1/5 (@) Kdkl
7/27/2019 Jee 2014 Booklet6 Hwt Integral Calculus 2
10/15
Yb`yanak`br Ecassls
YNE/Bktlmrac Eaceucus-? 11: F]P-9/Natflnatbes
@APL 7 PBNL 7 0: Nbkutls NA_HU 7 X TTT /1:^ PLUP ED@L 7 BE-? X9^
UPA_P PBNL 7 LK@ PBNL 7 PBNL PAHLK7 ZA_LKPU UBMKAP\_L 7
Pfbs tlst edktabks a tdtac di 1: Dogletbvl Pypl Qulstbdks. Laef qulstbdk earrbls 1 narh. Pflrl bs KD KLMAPBYL narhbkm.
Efddsl tfl edrrlet actlrkatbvl. Dkcy dkl efdbel bs edrrlet.
1.
0
?0 1
`x
sle x sbkx
/
/
(A) /0 (O) /?(E) (@) ?
?. Arla ednndk td tfl ebrecl? ?
90x y ak` tfl
paraodca?
1?y x bs lquac td 7
(A) 19 0 55
(O) 19 6 55
(E) 19 0 5
5
(@) Kdkl di tflsl
5. Pfl arla oduk`l` oy tfl eurvls ?y x ak`
??
1y
x
bs 7
(A) 5 5
5
(O)
5 ?5
(E) 5 ?
9
(@) Kdkl di tflsl
0. Pfl arla lkecdsl` oltwllk tfl eurvlsy> tak x, takmlkt
`rawk td bt at0
x
ak` :y bs 7
(A) 0 1
0
cdm (O)
0 1?
cdm
(E) 0 1
0
cdm (@) Kdkl di tflsl
? ak`x> 0 bs 7
(A) 0 5 ? ? 5cdm (O) 6 5 0 ? 5cdm
(E) 6 5 0 ? 5cdm (@) 0 5 ? ? 5cdm
9.1
1
:sbk x`x
(A) 1?
(O) 1
?
(E) 1 (@) Kdkl
=. Pfl vacul di 0
:x `x , wflrl {} `lkdtls tfl
iraetbdkac part dixbs 7
(A) 19/5 (O) ?
7/27/2019 Jee 2014 Booklet6 Hwt Integral Calculus 2
11/15
Yb`yanak`br Ecassls
YNE/Bktlmrac Eaceucus-? 111 F]P-9/Natflnatbes
@APL 7 PBNL 7 0: Nbkutls NA_HU 7 X TTT /1:^ PLUP ED@L 7 BE-? X=^
UPA_P PBNL 7 LK@ PBNL 7 PBNL PAHLK7 ZA_LKPU UBMKAP\_L 7
Pfbs tlst edktabks a tdtac di 1: Dogletbvl Pypl Qulstbdks. Laef qulstbdk earrbls 1 narh. Pflrl bs KD KLMAPBYL narhbkm.
Efddsl tfl edrrlet actlrkatbvl. Dkcy dkl efdbel bs edrrlet.
1.
? ?1 ?
1 ?
1 1?
1 1
x x`x
x x
/
/
(A) 5 (O) 5
1 1?
eds
(E) 5 1 1eds (@) Kdkl di tflsl
?. Arla bkecu`l` oltwllk tfl paraodcas?
0y ax ak`?
0x ay bs lquac td 7
(A)?
65a (O)
?
195a
(E)
?0
5
a(@) Kdkl di tflsl
5. Arla oduk`l` oy ?1 6y x y x | | , &x-axbs bs lquac td7
(A)
?< ? 9
?
(O)
? 5< ? 9 0 ? 9
? ?0
(E) ? 5
< ? 9 0 ? 9
0 ?0
(@) Kdkl di tflsl
0. Pfl arla di tfl snacclr rlmbdk oduk`l` oy tfl
ebrecl ? ? 1x y ak` tfl cbkls |y| >x+ 1 bs 7
(A) ?
0
(O)
??
(E) ?
?
(@) Kdkl di tflsl
M.B.I., a W , tflk 7
(A)
??
1aB
B
(O) 1 1B aB
(E) 1 ?1B a B (@) ? 1B aB
7/27/2019 Jee 2014 Booklet6 Hwt Integral Calculus 2
12/15
Yb`yanak`br Ecassls
YNE/Bktlmrac Eaceucus-? 11? F]P-9/Natflnatbes
@APL 7 PBNL 7 0: Nbkutls NA_HU 7 X TTT /1:^ PLUP ED@L 7 BE-? X6^
UPA_P PBNL 7 LK@ PBNL 7 PBNL PAHLK7 ZA_LKPU UBMKAP\_L 7
Pfbs tlst edktabks a tdtac di 1: Dogletbvl Pypl Qulstbdks. Laef qulstbdk earrbls 1 narh. Pflrl bs KD KLMAPBYL narhbkm.
Efddsl tfl edrrlet actlrkatbvl. Dkcy dkl efdbel bs edrrlet.
1. Arla oduk`l` oy tfl eurvls 1 :y x y | |, ak`
?x | | bs mbvlk oy 7
(A) < (O) 0
(E) 2/? (@) Kdkl
?. Pfl arla oduk`l` oy tfl eurvls?
? 1 1 :x
y x x , l y ak` dr`bkatls 1x ak`x> 1 bs 7
(A) ?5 ? 5
5
l l
l
(O)
? 1ll
(E) ?5 ? 5
5
l l (@) Kdkl di tflsl
5. Clt tfl ebrecl ? ? 0x y `bvb`l tfl arla oduk`l` oy
takmlkt ak` kdrnac at 1 5, ak`x-axbs bkA1 ak` A?.PflkA1/A?>
(A)
5 5
(O)
5 5
(E)
5 5
(@) Kdkl di tflsl
0. Pfl vacul di
?
:1
/`x
edt x
bs lquac td 7
(A) (O) ?/
(E) 0/ (@) 5/
7/27/2019 Jee 2014 Booklet6 Hwt Integral Calculus 2
13/15
Yb`yanak`br Ecassls
YNE/Bktlmrac Eaceucus-? 115 F]P-9/Natflnatbes
@APL 7 PBNL 7 0: Nbkutls NA_HU 7 X TTT /1:^ PLUP ED@L 7 BE-? X2^
UPA_P PBNL 7 LK@ PBNL 7 PBNL PAHLK7 ZA_LKPU UBMKAP\_L 7
Pfbs tlst edktabks a tdtac di 1: Dogletbvl Pypl Qulstbdks. Laef qulstbdk earrbls 1 narh. Pflrl bs KD KLMAPBYL narhbkm.
Efddsl tfl edrrlet actlrkatbvl. Dkcy dkl efdbel bs edrrlet.
1. Clt i ol a plrbd`be edktbkudus iuketbdk wbtf plrbd`
:P . Bi :
P
B i x `x , tflk tfl vacul di
0 0
1
0
5
P
B i x `x
bs 7
(A) B (O) ?B
(E) 5B (@) 0B
?. Pfl vacul di?? 1
:
xx `x
, wflrl Xx^ bs tfl mrlatlst
bktlmlr clss tfak dr lquac tdx bs 7
(A) ? (O) 6/5
(E) 0 (@) Kdkl di tflsl
5. Pfl arla oduk`l` oy tfl eurvls?
7/27/2019 Jee 2014 Booklet6 Hwt Integral Calculus 2
14/15
Yb`yanak`br Ecassls
YNE/Bktlmrac Eaceucus-? 110 F]P-9/Natflnatbes
@APL 7 PBNL 7 0: Nbkutls NA_HU 7 X TTT /1:^ PLUP ED@L 7 BE-? X1:^
UPA_P PBNL 7 LK@ PBNL 7 PBNL PAHLK7 ZA_LKPU UBMKAP\_L 7
Pfbs tlst edktabks a tdtac di 1: Dogletbvl Pypl Qulstbdks. Laef qulstbdk earrbls 1 narh. Pflrl bs KD KLMAPBYL narhbkm.
Efddsl tfl edrrlet actlrkatbvl. Dkcy dkl efdbel bs edrrlet.
1. Pfl vacul di tfl bktlmrac
0
:5 ?
/
sbkx edsx`x
sbk x
bs 7
(A) cdm(?) (O) cdm(5) (E)1
0cdm(5) (@)
1
6cdm(5)
?. Pfl arla di tfl pcakl ibmurl oduk`l` oy tfl bktlrvac < 9/ di tfl x-axbs, tfl mrapf di tfl iuketbdk y eds x ak` tfl
slmnlkt sd tfl strabmft cbkls < 9x / ak` x bs 7
(A) 5/? (O)
7/27/2019 Jee 2014 Booklet6 Hwt Integral Calculus 2
15/15
Yb`yanak`br Ecassls
YNE/Bktlmrac Eaceucus-? 11< F]P-9/Natflnatbes
2. Pfl vacul di? ?
5 5 5 5 5 5
1 ?
1 ?
k
kcbn ..........
k k k kbs 7
(A)1
5(O)
1?
5cdm (E)
15
?cdm (@)
15
5cdm
1:. Bi ?1
:x i x ix
idr acc : tflk
sle
eds
x _ ~ i x `x
>
(A) ?sbk (O) 1 (E) sle eds (@) :