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 (@) :