Jee 2014 Booklet5 Hwt Integral Calculus 1

8/13/2019 Jee 2014 Booklet5 Hwt Integral Calculus 1

1/13

Wcfyhohefcr Nahssms

WON/Cetmjrha Nhanuaus-8 04 @ZV/Oht`mohtcns

FHVM 9 VCOM 9 >4 Oceutms OHRK^ 9 [ \\\ /84_ VM^V NLFM 9 CN-8 [8_

^VHRV VCOM 9 MEF VCOM 9 VCOM VHKME9 THRMEV^ CJEHV]RM 9

V`cs tmst nlethces h tltha lg 84 Lbimntcvm Vypm Xumstcles. Mhn` qumstcle nhrrcms 8 ohrk. V`mrm cs EL EMJHVCWM ohrkcej.

N`llsm t`m nlrrmnt hatmrehtcvm. Leay lem n`lcnm cs nlrrmnt. @lwmvmr, qumstcles ohrkmf wct` '*' ohy `hvm Olrm t`he Lem

nlrrmnt lptcle.

8.

8

8

e

e

e nls xfx

sce x

mquhas9

(H)

8

e

e

nls xN

sce x

(B)

8

e

e

sce xN

sce x

(N)

8

e

e

nls xN

sce x

(F)

esmn x the x N

*2. 2 > = 2 > =h b nthe x the x the x fx alj smn x . smn x . smn x K . V`me 9

(H) h,b,nhrm ce @.T. (B) h?b?n (N) hb+bn+nh? 4 (F) > > > 8 8 8>h b n h b n

>. Glr hey ehturha euobmr 8

> 2 22 > 7

t fxt t t t t

t , x x x x x cs 9

(H)

8

> 28 2 > 77 8

t

t t t tx x x Nt

(B) 28 2 > 77

tt t

x x x Nt

(N) 2

> 28

8

t t tx x x N

t

(F) Elem lg t`msm

6.2

2 >

8

xfx

x x

cs9

(H)2 288 2 8

2x x alj x x x N

(B)

2 282 8 2 82

x x alj x x x N

(N)2 22 8 2 8x x alj x x N

(F)2 22 8 2 8x x alj x x N

=.

28x

x

m xfx

nls xm

(H) xthe m x N (B) xnls xm (N) smn( )xm x N (F) xthe m x N

7.

2

8

8 x

xfx

x xm

cs 9

(H)8

8 8

x

x x

xmalj N

xm xm

(B)

8

8 8

x

x x

xmalj N

xm xm

(N)8 8

8

x

x x

xmalj N

xm xm

(F)

8 8

8

x

x x

xmalj N

xm xm

:.

2 8x

x x

m fx

m m cs 9

(H) 2 2 8xm m N (B) 82

x

x

malj N

m

(N)

8 8

2 2

x

x

m

alj N m

(F)

2

8

x

x

m

alj N m


2/13

Wcfyhohefcr Nahssms


0.

8

= 6fx

x x cs 9

(H) 8 6the x N (B) 82 6the x N (N) 8 6the x N (F) 82 6the x N

3. x xm smnx m . alj smnx the x fx cs 9(H) xm alj smn x the x N (B) xm alj smn x the x N

(N) x

m smn x N (F) xm alj smn x the x N

84.8 8

8 8

sce x nls xfx

sce x nls x

cs 9

(H) 82

2 8 8x sce x x x x N

(B) 8


(N) 82


(F) 8



3/13

Wcfyhohefcr Nahssms






nlrrmnt lptcle.

8. Cg 82 28 6

xx

xfx k sce N

, t`mekmquhas 9

(H) alj2 (B) 8/2

(N) 8/> (F)8

2alj

2. Cg>

> >

8 8

8 8 8

fx xk alj N

x x x

, t`mekmquhas 9

(H) alj2 (B) 8/2

(N) 8/> (F)8

2alj

>. Cg8

fxk x alj sce x nls x N

the x , t`mek

mquhas9

(H) alj2 (B) 8/2

(N) 8/> (F)8

2alj

6.

2

8

2 2

2 > 8

8 28 6

x fxx x

k alj k thexx x

t`mek mquhas 9

(H) alj2 (B) 8/2

(N) 8/> (F)8

2alj

=. Cg

2

88

2mx m x

g xalj m .alj mfx alj N

x g x

t`me

4

8

x

g xacox

mquhas 9

(H) 4 (B) 8

(N) m (F) 8/m

7. 2 >

fx

x x cs 9

(H) > 8alj x N

(B)> 8

> 8

xalj N

x

(N) > 8alj x N

(F)> 8

> 8

xalj N

x

*:. Cg >

2

>8

x fxglj x n

x

t`me 9

(H) g x x (B) 8j x nls x

(N) 8g x sce x (F) j x x x

0. 2x xm fx

(H) 2 xm n (B)

28 2

x

m nalj

(N)

82

8

xm

nx

(F) Elem lg t`msm

3. 2

8 8 2 8

> 2 82 8

xfx g n

xx x

, t`meg(x) ?

(H)8

the x

(B) alj x

(N)8

sce x

(F) Elem lg t`msm

84. V`m vhaum lg x xm sce m fx cs 9(H) xnls m (B) xnls m

(N)8( )xnls m (F)

xsce m


4/13

Wcfyhohefcr Nahssms

WON/Cetmjrha Nhanuaus-8 7> @ZV/Oht`mohtcns

FHVM 9 VCOM 9 >4 Oceutms OHRK^ 9 [ \\\ /84_ VM^V NLFM 9 CN-8 [>_



N`llsm t`m nlrrmnt hatmrehtcvm. Leay lem n`lcnm cs nlrrmnt.

8. Cg xm thex aljnls x fx g x alj smnx n , t`merhejm lgg(x) cs 9

(H) R (B) 4R

(N) R

(F) Elem

2.

8 2

sce x sce xsce x nls xm nls x fx m n

sce x

, cg x bmalejstl 9

(H) R (B)>

2 26 6

e , e

(N)=

2 26 6

e , e

(F) Elem lg t`msm

>.2> xx m fx cs mquha tl 9

(H)22

8xx m

(B)228

82

xx m

(N) 2 28 8

2

xm x (F)

28xm

6. 82

8 8

8

x fx. nls g x n

x xx

, t`meg(x) ?

(H)2

2

8x

x

(B)

2

2

8x

x

(N)2

2

8 x

x

(F) Elem

=. nls x fx(H) 2 x sce x nls x n

(B) x sce x nls x n

(N) 2 x sce x nls x n (F) Elem lg

t`msm

7.

> 6

2 6

8

8

fx

x x cs mquha tl 9

(H)

8 6

6

88 N

x

(B)

8 66 8x N

(N)

8 6

6

88 N

x

(F)

8 6

6

88 N

x

:.8

x sce xfx

nls x

cs mquha tl 9

(H)2

xx the N (B)

2

xnlt N

(N) 8alj nls x N (F) alj x sce x N

0. Cg 82 28 6

xx

xfx K sce N

, t`me K cs mquha tl

9

(H) alj2 (B)8

22

alj

(N) 8

2(F) 8

2alj

3.8 2

2

8

8

the x x xm fx

x

cs mquha tl 9

(H)8

the xxm N

(B)

82 the xx m N

(N)88 the x

m Nx

(F) Elem lg t`msm

84. Cg j x fx j x ,t`me j x g x g x fx cs mquha tl 9

(H) j x g x j x g x N (B) j x g x N

(N) j x g x N (F) 2j x g x N


5/13

Wcfyhohefcr Nahssms






8. Cg

88 8

6 88

2

fx H B the g x N xscex sce x

the

, t`me 9

(H) 8 2 6 >

= = 8= 8=

the xH , B , g x

(B)

6 828 8

= 8= 8=

xthe

H , B , g x

(N) 2 2 6 8= = =

the xH , B , g x (F) 6 8

2 2 2= = 8= 8=

xthe

H , B , g x

2. 8 2

8 2 the x the x smn x fx cs mquha tl 9(H) alj smn x smn x the x N (B) alj nlsmn x smn x the x N

(N) alj smn x smn x the x N (F) alj smn x thex N

>. the x

fxsce x nls x cs mquha tl 9

(H) 2 the x N (B) 2 nlt x N (N)2

the xN (F) Elem lg t`msm

6.=

= == = =

x xx. . fx

cs mquha tl 9

(H)

=

>

=

=

x

Nalj

(B) = >== =x

alj N (N)

==

>

=

=

x

Nalj

(F) Elem lg t`msm

=. Cg8

8 2

xfx the h b

sce x

, t`me 9

(H)6

h , b R

(B)6

h , b R

(N)=

6h , b R

(F) Elem lg t`msm

7. g x j x g x j x fx cs mquha tl 9

(H)

g x

j x (B) g x j x g x j x

(N) g x j x g x j x (F) g x j x g x j x

:. Cg 26 7 3 63 6

x xx

x x

m mfx Hx B alj m N

m m

, t`me 9

(H)> >=

42 >7

H , B , N (B)>= >

>7 2H , B , N R

(N)> >=

2 >7H , B , N R (F) Elem lg t`msm


6/13

Wcfyhohefcr Nahssms


0.

22

> > 8

xfx

x x x

cs mquha tl 9

(H)

88

> > 8

xthe

x

(B)

82

> > 8

xthe

x

(N)82

> 8

xthe

x

(F) Elem lg t`msm

3. V`m vhaum lg t`m cetmjrha2

6

8

8

xfx

x

cs mquha tl 9

(H)8 2

the x N (B)

288 8

2 2

xthe

x

(N)2

2

8 2 8

2 2 2 8

x xalj N

x x

(F) Elem lg t`msm

84. Cg ra x omhesalj alj alj. . . .x, t`m alj bmcej rmpmhtmfrtcoms, t`me 8

2 > rx a x a x a x . . . a x fx

cs mquha tl 9

(H) 8ra x N (B) 8

8

ra x

Nr

(N) ra x N (F) Elem lg t`msm


7/13

Wcfyhohefcr Nahssms

WON/Cetmjrha Nhanuaus-8 7= @ZV/Oht`mohtcns

FHVM 9 VCOM 9 >4 Oceutms OHRK^ 9 [ \\\ /84_ VM^V NLFM 9 CN-8 [=_




nlrrmnt lptcle.

8.

>

>

8xfx

x x

cs mquha tl 9

(H) 2 88x alj x alj x the x N (B) 2 88 82

x alj x alj x the x N

(N) 2 88 82

x alj x alj x the x N (F) Elem lg t`msm

2.

8

8e

fxx x

cs mquha tl 9

(H)8

8

e

e

xalj N

e x

(B)

88 e

e

xalj

e x

(N)8

e

e

xalj N

x

(F) Elem lg t`msm

>.x

hfx

x cs mquha tl 9

(H)x

hN

alj h (B)

2 x

hN

alj h (N) 2 xh . alj h N (F) Elem lg t`msm

*6. Cg 8

= 6 2

fx xHthe B the N

nls x

, t`me 9

(H) H ? 8 (B)2

>H (N)

8

>B (F)

2

>B

*=. V`m vhaum lg t`m cetmjrha

8

8

alj x alj xfx

x x

cs 9

(H) 2 28 8

8 82 2

alj x alj x alj x alj x N

(B) 2 2

8 8alj x alj x alj x . alj x N

(N)

28 8

82

alj N x

(F) Elem lg t`msm

7. Cg 8

2 2

28 8

8

x the xfx x g x Halj x x N

x

t`me 9

(H) 8 8g x the x, H (B) 8 8g x the x, H

(N) 82 8g x the x, H (F) 82 8g x the x, H


8/13

Wcfyhohefcr Nahssms


:. Cg 28

8 8x alj fx g x .alj x j x . x Hx Nx

, t`me 9

(H) 282

g x x (B) j x alj x (N) H? 8 (F) Elem lg t`msm

*0. Cg 8 28

xx

x

xmfx g x m alj j x N

m

, t`me 9

(H) 8g x x (B) 8 8

8 8

x

x

mj x

m

(N)

8 8

8 8

x

x

mj x

m

(F) 2 2g x x

3. V`m vhaum lg> =

2 6

nls x nls xfx

sce x sce x

cs 9

(H) 87sce x the sce x N (B) 8

2sce x sce x N

(N) 8 82 7sce x sce x the sce x N

(F) 8 82 =sce x sce x the sce x N

*84. Cg

8 8

2 2

8

28 6

xfx H the x B the N

x x

, t`me 9

(H)8

>H (B)

2

>B (N)

8

>H (F)

8

7B


9/13

Wcfyhohefcr Nahssms

WON/Cetmjrha Nhanuaus-8 7: @ZV/Oht`mohtcns





8. V`m vhaum lg

> 2smnxm . smn x sce x nls x sce x sce xnls x fx cs9(H) 2smn xm smn x smn x the x N (B)

smn xm N

(N) smn xm smn x the x N (F) Elem lg t`msm

2.0 0

2 28 2

sce x nls xfx

sce xnls x

(H)

82

2sce x (B)

82

2sce x

(N)8

2sce x (F) 2sce x

>. V`m vhaum lg

2

22 2 2

hx bfx

x n x hx b

cs 9

(H)8

bhxxsce k

n

(B)

22

8bhx

xsce k n

(N)8

bhx

xnls k n

(F)

2

28

bhx

xnls k n

6. Cg 26 7 3 63 6

x xx

x x

m mfx Hx B alj m N

m m

, t`me H?

(H)>

2

(B)>=

>7

(N)>

2(F)

>=

>7

=.

>8

8fx

x x

\\\\\\\\\\.

(H)

>

>

8 8

>

xalj N

x

(B)

>

>

8

> 8

xalj N

x

(N)

>

>

8xalj N

x

(F)

>

> 8

xalj N

x

7.2

88

2 8

fx H alj x N

x x

glr 8x , t`meH ? \\\\\\\\\.

(H) 8 (B) 8

(N) 2 (F) 2:. V`m hetc-fmrcvhtcvm lg 2xg x m w`lsm jrhp` phssms

t`rluj` t`m plcet (4, >) cs \\\\\\\\\.

(H)2> xm (B) 26 8xm

(N)22 8

xm (F) Elem lg t`msm

0. Cgg (x) cs t`m hetc-fmrcvhtcvm lg 8the x sun` t`ht t`m

nurvm y g x phssms t`rluj` t`m plcet (4, 2), t`me

g(x) ? \\\\\\\\\\\.

(H)8 8

2x the x x the x

(B)8 8 2x the x x the x

(N) 8 2x the x

(F) Elem lg t`msm

3.28

x

x

m fx

m

(H) 8 xsce m N (B) 8 xnls m N

(N) 8 2 xsce m N (F) 8 2 xnls m N

84.

2

8

2

xxm fx

x

(H)8

xm

Nx

(B)2

xm

Nx

(N)

2

8

xm

Nx

(F)

2

2

xm

Nx


10/13

Wcfyhohefcr Nahssms


FHVM 9 VCOM 9 >4 Oceutms OHRK^ 9 [ \\\ /84_ VM^V NLFM 9 CN-8 [:_




8.

>

2

x xm fxx

\\\\\\\\\\\\\.

(H) 2

xmN

x

(B)

2

2

xmN

x

(N)

>2

xm

Nx

(F) Elem lg t`msm

2. Cg2

8

8> 62

x H

fx alj ,x Bx x

t`me 9

(H) H ? 7, B ? : (B) H ? :, B ? 7

(N) H ? 7, B ? 86 (F) H ? 86, B ? 7

>. V`m vhaum lg2

2

8

8

x

x

mfx

m

cs 9

(H) x xalj m m N (B)

x xalj m m N

(N) x xalj m m N (F) Elem lg t`msm

6. V`m hetc-fmrcvhtcvm lg 2xg x m w`lsm jrhp` phssms

t`rluj` t`m plcet (4, >) cs 9

(H)22

xm (B) 22 8

xm

(N)2 2xm (F) 2

8 =

2 2

xm

=. V`m hetc-fmrcvhtcvm lg 8g x the x w`lsm jrhp`

phssms t`rluj` t`m plcet (4, 2) cs 9

(H)8 2x the x x

(B)8

2the x x

(N) 88 2x the x x

(F) Elem lg t`msm

7. 8 22 2x

x x

fxHthe m N

m m

, t`me H ?

(H)8

2(B) 8

(N) 2 (F) 6

:. Amt 8 > >xg x alj hef G x bm cts hetc-fmrcvhtcvmw`cn` hssuoms t`m vhaum : glr x? 2. V`m vhaum lgxglr

w`cn` t`m nurvmG(x) nuts t`mx-hxcs cs 9

(H) 4 (B) 8

(N) 2 (F) >

0. Cg 2

8

8g x

nls x the x

, t`me cts hetc-fmrcvhtcvmG(x)

shtcsgycejG(4) ? 6 cs 9

(H) 8 6the x (B) > 22

8>

thex

(N)

2 8 8the x (F) Elem lg t`msm

3. Cg 2 2

8

6 > =g x

nls x sce x

hef cts hetc-fmrcvhtcvm

88

>G x the j x N t`mej(x) ?

(H) >thex (B) 2 thex

(N) 2thex (F) Elem lg t`msm

84. Cg the x

g xsce x.nls x

hef G(x) cs cts hetc-fmrcvhtcvm

shtcsgycej 7

6

G

, t`meG(x) ?

(H) 2 8thex (B) 2 >the x

(N) 2 2thex (F) Elem lg t`msm


11/13

Wcfyhohefcr Nahssms






8. V`m vhaum lg6 2= 6

fx

x x cs 9

(H)8 88 8

> 2 2

xthe x the N

(B)8 8> 2

> 2

x xthe the N

(N)8 88 8

> 7 2

xthe x the N

(F)8 88 8

> 7 2

xthe x the N

2. V`m guentclegw`lsm jrhp` phssms t`rluj`:

4>

,

hef

w`lsm fmrcvhtcvm cs 28x x cs jcvme by 9

(H) > 2

28 8 :>

g x x

(B) 8>

72

g x sce x

(N)

> 228 8 0

>g x x

(F) > 2

22 8 0>

g x x

>.

6 8fx

x x cs mquha tl9

(H)6

6

8 8

6

xalj N

x

(B)6

6

8

6 8

xalj N

x

(N) 68 86

alj x N (F) Elem lg t`msm

6. 2

> 6 2

8

2 2 8

x fx

x x x

cs mquha tl 9

(H)6 2

2

2 2 8x xN

x

(B)6 2

>

2 2 8x xN

x

(N)6 22 2 8x x

Nx

(F)

6 2

2

2 2 8

2

x xN

x

=. Cg playelochas T hef X shtcsgy

> 8 8 2x nls x x sce x fx Tnls x X sce x (cjelrm t`m nlesthet lg cetmjrhtcle) t`me 9

(H) > 2T x (B) 2X x

(N) > 8T x (F) > 8X x

7.2

7

sce xfx

nls x cs h 9(H) Tlayelocha lg fmjrmm = cesce x

(B) Tlayelocha lg fmjrmm 6 cethe x

(N) Tlayelocha lg fmjrmm = cethe x

(F) Tlayelocha lg fmjrmm = cenls x

:. Cg ct cs kelwe t`ht ht t`m plcetx? 8 twl hetc-fmrcvhtcvms lg

xg x m fcggmr by 2, t`m fcggmrmenm lg t`msm hetc-

fmrcvhtcvms ht 844x cs 9

(H)844m (B) 844

(N) 2 (F) Elem lg t`msm

0. Cg 8 2

x sce x xfx g x . the N

nls x

, t`me 9

(H) 2g x x (B) g x x

(N) 8g x nls x (F) Elem lg t`msm

3. Cg 6 >the xfx k the x the x g x , t`me 9

(H)2

>k (B) 2

(N) g x x N

(F)

6

>k

84. Cg t`m hetc-fmrcvhtcvm lg>

6 2 8

x x

x x

m m

m m

cs x xg m m N

t`me g x cs mquha tl 9

(H) scex (B)8

nls x

(N)8

the x

(F) the x


12/13

Wcfyhohefcr Nahssms






8. Cg> 2

6 =6 =

nls x sce xfx Hx B alj sce x nls x N

sce x nls x

,t`me 9

(H)2> 8

68 68H , B (B)

2> 2

68 68H , B

(N)88 2

2> 2>H , B (F)

82 2

2> 2>H , B

2. Cg 2g x fx nls x N , t`me g x

(H) sce x (B) sce x

x

(N) 2nls x (F) Elem lg t`msm

>. Cg t`m hetc-fmrcvhtcvm lg> 2

8

x xcs 8H x N t`me

H?(H) 2 (B) 8(N) > (F) 6

6. Cg 2nlsmn x fx g j x N , t`me 9

(H) Rhejm lg 4j x , (B) Flohce lg 4g x ,

(N) 2j x nls mn x

(F) 8

g xx

glr haa 4x ,

=. Cg 86 62sce x

fx the g x N nls x sce x

, t`me 9

(H) 2g x x (B) g x nls x

(N) g x sce x (F) 2

g x the x

7.

6

8 22 6 2

8

8

xfx

x x x

cs mquha tl 9

(H)6 2 8x x

Nx

(B)

2

6 2 8

xN

x x

(N) > 2

6 2 8x x x N (F)6 2 8x x

Nx

:. Cg

2

8

22

8

8

x fxthe x j x k

x

, t`me j x

(H)8

2

xthe

(B)2

8

8x

(N)

28

2 8x (F) Elem lg t`msm

0. Cg 2 822

6 026 0

xfx xk alj x x the N

x x

,

t`me t`m vhaum lgkcs 9

(H)8

2(B) 8

(N) 2 (F) Elem lg t`msm

3.8 2

2

8

8

the x x xm fx

x

cs mquha tl 9

(H)

8

28

the xmN

x

(B)

8

28

the xxmN

x

(N)8

the xx . m N

(F) Elem lg t`msm

84. Cg 22 >

fxglj x N

x x

, t`me 9

(H) 82 >

8:

xg x sce x, j x

(B) 8 2 >

8:

x

g x the x, j x

(N) 82 >

8:

xg x sce x, j x

(F) Elem lg t`msm


13/13

Wcfyhohefcr Nahssms






8.6 8

nls x

fxnlt x the x

cs mquha tl 9

(H) 8

62

nls x N

(B) 8

66

nls x N

(N) 8

22

sce x N

(F) Elem lg t`msm

2. V`m vhaum lg= 6

fx

nls x cs 9

(H)88 8

> >the the x N

(B)88 8

> > 2

xthe the N

(N)82 8

> >the the x N

(F)82 8

> > 2

xthe the N

>. V`m vhaum lg nlsx fx

scex nls x cs 9

(H)

2

2

xalj scex nlsx N

(B) 8

2x alj sce x nls x N

(N) 2alj sce x nls x x N

(F) Elem lg t`msm

6. Cg

8 8

2 2 28 6

fx xk the x the N

x x

, t`me 9

(H)2

>k (B)

2

>

(N)2

>k

(F)

8

7

=. Cg 228

xg xx

hef j x sce x ,

t`me glj x nls xfx cs 9(H) 8sce x the sce x N

(B) 8nls x the nls x N

(N) 82sce x the sce x N (F) Elem lg t`msm

7. 8

mxalj m fxx cs mquha tl 9

(H) 8m malj alj x N

(B) 8m malj alj mx N

(N) 8m malj alj x N

(F) 8m malj alj x N

:. V`m vhaum lg

> 2smn xm . smn x sce x nlsx sce x sce x . nlsx fx cs 9(H) smn xm smn x the x N

(B) 2smn xm smn x smn x . the x N

(N) 2smn xm smn x the x N (F) Elem lg t`msm

0. Amtghefjbm twl playelochas t`me

g x . j x g x . j x fx

cs mquha tl (cjelrcej t`m nlesthet lg cetmjrhtcle) 9(H)

g x

j x (B) g x . j x g x j x

(N) g x j x g x j x

(F) g x . j x g x j x

3. Amt 8 2xg x m x x fx . V`megfmnrmhsms ce t`mcetmrvha 9

(H) 2, (B) 2 8,

(N) (8, 2) (F) 2,

84. Cg 2

8

28

sce xfx x k the O the x N

sce x

, t`me 9

(H)8

2O (B)

8

2K

(N)8

2O

(F)

8

2K

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Jee 2014 Booklet5 Hwt Integral Calculus 1