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Physics AIEEE Solution (26 - 04 - 09)

e See- See - O e e e e e ee e e

e be ebe e w ee

1. Statement 1 : e le P e e w e by ele el

e le eee e e P

Statement 2 : e e w e by e e bje l le l ze

Sol. See- See- b e e b See- e e el See-

2.

e be l b eey e le b e le M; e

ee le e e:

A B C+ + C A B + + D E F+ + F D E , + + wee e eey elee? I w e e?

Sol. A B C+ + le B e

F D E + + le B e

3. j w e e ee le e e V ee e

e e I e e be w by :

Sol.

4. e l w belw e we w P e e

we

O

Set # A

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Sol.

5. I ee e lee e ely e ele le ee le

e e e w e llw e e w e ?

Sol.2

x Asin tT

=

A2 2 tv cosT T

=

2 2 2

2 2

2 2

4 A 4 tv cosT T

=

2

2

4 2 ta Asin

T T

=

4 2 2

2 2 2

2 2

16 cos 4 t4 v A

T T

=

4

2 2

4

16 A 2 ta sin

T T

=

4

2 2 2 2

2

16 2 ta T A .sin

T T

=

S42 2 2 2 2

2

16a T 4 v A const.T

+ = =

2aT const. 4

x= =

2 24 A 2 t 4 A 2 t

aT 2 v sin cosT T T T

+ = +

24 A 2 t 2 tcos sin

T T T

=

2aT Acos T.cos t

A sin t

=

Note : Both 1 and 2 are correct, but option 1 is a function of time period and option 2 is independent of

unit of time.

6. I eee w e e bje e e e e e le

e e ee je e le e e bje bewee e bje e e

e e e e e e le le e e le e w e

le e le 5 w e - ee e eeel e P e

e P wll be:

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Sol.1 1 1

v u f =

1 1 1

u v f=

1 f v

u fv=

2fv f (v f f ) f u f

v f v f v f

+= = =

2fu f

v f+ =

7. le l w eely b zl e I

l ee I ee e e :

Sol. h sin (1 sin )2 2 2

= + = +

2

21 m. mg. h2 3

=

2 2

6g

8. Le 4Q

P(r) r R

=

be e e ey b l ee l e P

e e ee e

e ee e ee e e ele el :

Sol. 4Q

P(r) .r R

=

r 2

40

Qrq 4 r dr.

R=

4 4

4 4

4Q r Qr q .

R 4 R= =

4 2

4 2 4

0 0

1 Qr Qr E .4 R r 4 R = =

9. e e e = = ye le el lle Ie e

wll be be e :

Sol. e lwe eey eee b ee

10 . Oe ee 8 / e ey e / W e eey

e e el ?

Sol.4

2 3

N kgP 8 10 , 4

m m= =

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5KE PV

2= PV =

PV =m

RTM

PM m

RT V= =

45 1KE 8 102 4

= 4KE 5 10 J=

e See- See - O e e e e e ee e e

e be ebe e w ee

11. Statement 1 : e eee eeee ee lly e =

+ e ee

we e 5 we eee ee 7 7 le = 5 /

Statement 2 : =

+ l ly we e e e eee ll =

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19 . der rbber b reey rm e = m rz e pe me e dr

ebe d e w e pe y e

Te e ey me d e e me w be:

Sol.1

vg ve is downward direction.

t

= = +

1 1 1 1t 2t t t= =

(d)

20 . re ped e e ppe rer re re ped e e er w

e I e e elel e ze e / el:

Sol.

2

2 2

Qq 2 Q0

d 2d+ =

Qq 2

2

=

Q2 2

q=

21 . l ell b y e e e e e e e ey-e e

eee l e le e b e be ebe by w e llw?

Sol.d kA dT

dt dx

=

dT ( dx)

I we e e -e e ell be

22 . e l yll ee e 2

.3

e by l y e e

e e e w e e

e e le w e l y ze l e wll e :

Sol2

sin sin3

=

2sin(90 ) 1 1

3 =

3cos cos30

2 = =

30 = P

2 1sin sin 30

3 3 = =

1 1sin

3

=

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23 . ee we el le e eee + ey ee e be ebe be e e e wll be:

Sol.A B C

f 1 f f 1 +

Se & w be pe e e d & w be pe e e

& w be pe we eS w be pe e e der mm we d re pe mey

ee pe e eery e be reey =

Note : in some books it is written 2 but is not corresponding to absolute maxima.

24 . e e w e ele e y bee /9 wee = e ele e y e

e e e e e e e :

Sol

2g R h g

9g ' R g / 9

+ = = =

h

1 3R

+ = h 2R=

25 . w we e e e e el e e e le Hwee we -el e

we -el e I e le we ee by ly e w e eee e we by e e ?

Sol.

=

=

= 1

x=

= ?2

x=

FLy

A=

S 2F

y A

2

21 2 2

2 12 2

1 2 1

F F AF F 3 F

A A A

= = =

2F 9F=

26 . I eee e le e ee be ee e 9 e le ely

e w e e ee le I e lle e le l--eee =5

e e le e e :

Sol. e le = 5

Le =s (1/2)

n 30

=

11'

60

=

= e e

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27 .

e L = H e ee

= = e ee bey e V w e e e el ee e bey elble He w S

le = e el L e :

Sol. = e L = H

=

= =

2R 2=

Rt

L0

v v e

=

0v 12 volt=

2R tLv 12e

=

32 105t400v 12e 12e v

= =

Directions: e be 8 9 e be e llw w le el e

e e e yle w e P-

28 . e be el e w e e :

Sol. PV =

B A B AW P(V V ) nR(T T )= =

[ ]2 R 500 300=

W 400R=

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29 . e w e e :

Sol. I Iel Pe

1

e

2

PW nRTlog

P=

2e

1

PnRTlogP

= =

e2R 300log 2=

600R 0.6932 415.9200R= =

DAW 414R =

30 . e e w e e e yle :

Sol. W

=

W

=

W

= C

BC e

B

PW nRT log

P=

2

e e

1 102 R log 2R log

2 100

= = =

= 9 5 = 9

W

=

l W = 7

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CHEMISTRY AIEEE SOLUTION (26 - 04 - 09)

31 . Kw e ey l L e + e w e llw

ee e ?

ee e le ze e L III e b eely e

b e ze L III eee eel w e be

L III e eelly lle

L III ye e ly b e

Sol. (c) e eee e ele L III e eelly le

32 . l w e w el ee HSO

w e w y ell w

e e l w:

HOH b HHO H

O H

H

OOH

Sol. (d) y ell e e ee

H SO2 42 5 3 3 2 5 2C H OH CH COOH CH COOC H H O + +

33 . e e b 3 3(CH )C, CCl H CH H5 2CH e e ee bly :

H

5

2CH > 3CCl > H C > H CH b H CH > 3CCl > H5 2CH > H C

3CCl > H5 2CH > H CH > H C H C > H CH >H5 2CH > 3CCl

Sol. (c) I3CCl

26 5C H C H

ee ee

I3CCl e e elle bewee b l ee e ee l well l e elee-

e

I6 5 2C H CH ee e elle bewee b b b le eleee

e le

Hee3CCl e ble 6 5 2C H CH

3 2 3 3(CH ) CH (CH ) CH

stability

>

I e le +I ee b

34 . e lee eb eel e :

ee b -eyl ee -bee -eyl--bee

Sol. (c)

a

bC C

a

b

b

ye lele w w ee bly be b w eel e

35 . I w e llw ee e eee ly e ey we ?

O

< SO

< SO

< PbO

: e we

b H < Hl < H < HI : e e

H

< PH

< H

< SbH

: e b e

< < O < : e z ely

Set # A

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Sol. (c) I ye e ly H SbH

by eee e ee ze el le

36 . e j be e el w ye b e :

bez b lylleye lyl l

Sol. (c) Klbe e

OH

+ NaOH2 + CO2

OH

COOH

Salicylic acid

heating

underpressure

37 . W e llw ee e e y ?

I bee e Wl e

b Me ely leble e e be ely

Ue ee el l lel lye be e

ly adsorption( H ) lw e

Sol. (a)

38 . W e llw e w e KOH e eleye ?

H

Ol b H

H

l H

l H

l H

Hl

Sol. (d) HH

Cl

Cl

+ KOH H

H

OH

OH+ Kl

H

H

OH

OH 2H O 3CH CHO

39 . I ele vg w peed f / w uy f 5% ey w w e

p f e ele be led = kg f ele e

= 9 kg

5 b 5 9 d 8

Sol. (c) 5600 5 10 = = = /e

h

4

34

31 2

6.6 10x

9.1 10 3 10 4 3.14

= 9

40 . I fuel ell el ued fuel d yge g ued dze Te e

3 2 2 2CH OH( ) 3 /2O (g) CO (g) 2H O( )+ + 98 K dd Gbb eege f f f O

O d O

g e 7 d 9 kJ l epevely If dd elpy f bu f

el 7 kJ l effey f e fuel ell wll be :

8 % b 87 % 9% d 97 %

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Sol. (d)| G |

100H

= Tedy effey

G = { } { }394.4 2(237.2) 166.2

= 7 kJ

702.6100 %726 = = 97 % = 97 %

41 . Tw lud X d Y f del lu K vpu peue f e lu g l f X d l

f Y 55 g e e epeue f l f Y fue dded lu vpu peue f e

lu ee by g Vpu peue g f X d Y e pue e wll be epevely :

d b d d d 5 d

Sol. (c)A A B BP P X P X= +

AP = f g

BP

= f g

42 . Te lf lfe ped f f de el e 9 ue Te e eued f e ple f 99%

f e el e wll be lg = :

ue b ue ue d ue

Sol. (c)0.693 2.303 100

log6.93 t 1

=

=

43 . Gve: 0 03 2Fe FeFe Fe

E 0.36V,E 0.439V+ += = Te vlue f dd elede pel f e ge

3 2(aq)Fe e Fe (aq)

+ ++ wll be

7 V b 85 V 77 V d 7 V

Sol. (c) Fe+ e + Fe = V

Fe Fe+ + e = + 9

G

= G

+ G

F

=

F

+ F

= [ ] + [ 9] = 77 V

44 . O e b f e fllwg eel d : (aq)( fG H 0)+ =

O l + + O ; = 57 kJ

g +1

2O

g

O l ; = 8 kJ

Te vlue f elpy f f f O 5 :

88 kJ b 888 kJ + 888 kJ d 5 kJ

Sol. (b) = 888 kJ

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45 . ppe ylle f w u ell leg f p W e du f ppe ?

8 p b 7 p 57 p d 8 p

Sol. (b)a

r2 2

= = 7 p

46 . W f e fllwg pl e ?

3 3[CO(NH ) Cl]

+ b 23 2[CO(en)(NH ) ]

+

32 4[CO(H O) (en)

+ d 32 3 2[CO(en) (NH ) ]

+

Sol. (c) f f ple wll be plly ve wle e

47 . Sld NO

gdully dlved M N

O

lu w e f + wll

pepe beg f ? Kp

f O

= 5 9 :

5 M b 5 5 M 8 8 M d 8 7 M

Sol. (b) Q > kp

5 9 = [+]

[+] = 5 5

48 . W e f e fllwg e f Xe pud notfeble ?

Xe O

+ F XeF+

O

b Xe F

+ O Xe + Xe O

+ F + 5 O

Xe F

+ O Xe + F + O

d Xe F

+ RbF Rb [XeF7]

Sol. (a)

49 . Ug MO ey ped w f e fllwg pee e e bd leg ?

22O + b 2O+ 2O d22O

Sol. (a) Species Bond order

O

+

O

+ 5

O 5

O

d de f O+ lge bd leg le

50 . I e w e elee w f e fllwg e e ?

I dd e l d e e ze d e l w by ee elee pleeb I e ge d e e el w b e d f plee

I e ge d e f e f fve elee S M ll e d d ele e ued

f bdg

d Oe e 5 fgu eeeded e edey vlve ll e d ele bdg deee

Sol. (b) Lw d e e b bu ge d e elee e d ue d ge

d e ey f ple

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51 . lule e wveleg ee ed w p vg

M f p = 7 7 kg d = J :

b 5 d

Sol. (b)

34

27 3

h 6.63 10m

mv 1.67 10 10

= =

=

52 . by lud lu peped by g -epe d el W e f e fllwg ee e

egdg e bevu f e lu ?

Te lu fed del lu

b Te lu -del wg +ve dev f Rul Lw

Te lu -del wg Ve dev f Rul Lw

d -epe w + ve dev wle el w ve dev f Rul Lw

Sol. (b)

53 . Te ube f eee pble f pud f e leul ful =OMe

b d

Sol. (c)

OH

CH3

CH CH CH Me

: = f duble bd Geel

: = f l b pl

Tl ee e :

54 . Te IUP e f epee :

eylbue b -deylppe eylppe d -deylbue

Sol. (b) CH3 C

CH3

CH3

CH32 1

deyl ppe

55 . Te e epeeg e e de f du :

L+ > e+ > N+ > Mg+ b N+ > L+ > Mg+ > e+

L+ > N+ > Mg+ > e+ d Mg+ > e+ > L+ > N+

Sol. (b)

56 . Te w ful gup pee ypl byde e :

O d OO b O d OO > = O d O d O d O

Sol. (c,d)

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57 . Te bd d eegy f F F

kJ l wee f F F

55 kJ l Te e

e f ge F bd d eegy ped f F :

lle ze f - ped f -

b ge bd bewee d F F

ped bewee d F F

gf p - p e bewee d F F

wee ee pbly f u e

bewee d F F

d lwe degee f p-p e bewee d F F

bewee d F F

Sol. (d)

58 . I zz e gve belwOH

222Ph CHO Ph CH OH Ph CO

+i i

e lwe ep :

e k f : OH

e byl gup

b e fe f ydde e byl gup

e b f p f e byl gup

d e dep f P O

Sol. (b) Re ulepl dd d ee e fe f ydde uleple wll be e e deeg

ep

59 . W f e fllwg p epee lkge e ?

[u N

] [P l

] d [P N

] [ul

]

b [Pd P P

NS

] d [Pd P P

SN

]

[O N

5NO

]SO

d [ON

5SO

] NO

d [P l

N

]

d [P

N

] l

Sol. (b) I f e N e d e wle ed ulpe e d e

60 . u-N ye ubbe plye f :

2 2

Cl |H C CH C CH= = d = =

b = =

d

5

=

= N d

= =

d = N d

2 2

3

H C CH C CH |CH

= =

Sol. (c)

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Mathematics AIEEE Solution (26 - 04 - 09)

Directions : Que ube 5 e e - Re ype ue f ee ue

w ee :

Statement - 1 (Assertion ) d Statement - 2 (Reason).

f ee ue l fu leve e ly e f w e e we

Yu ve ele e e e

31. Statement - 1 : ~ p ~ euvle p

Statement - 2 : ~ p ~ ulgy

See - ue See - ue; See - e epl f See -

b See - ue See - fle

See - fle See - ue

d See - ue See - ue ;

See - e epl f See -

Sol. ~ p ~

p

1 2

(1) (2) (3) (4) (5) (6)

~ ~ ( )p q q p q s p q s p q

T T F F T T

T F T T F F

F T F T F F

F F T F T T

F lu 5 &

euvle ee ee - ue

f lu 5 ~ p ~ ulgy ee ee - fle

See - ue See - fle

32 . Le be

Statement - 1 : dj dj = ;

Statement - 2 : |dj | = | |



See - fle See - ue


See - e epl f See -

Sol. We kw

dj = | | I | dj | = | | |dj | = | |

Nw pu = dj dj dj dj = | dj | I dj dj = | | I

dj dj =(| | )

| |

A AA

A I

= djdj =

Set # B

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33 . Le f = +

Statement - 1 : Te e { : f = f } = { }

Statement - 2 : f bje



See - fle See - ued See - ue See - ue ;

See - e epl f See -

Sol. f = +

See -: Te e { : f = f} = { }

we kw lu e f f = f e lu e f f =

Tu lvg f = = d =

S lu e { }

e fu e-e e bjeve

See - ue See - ue

34. Statement - 1 : Te ve f f eve ul ube

2 1

4

n

Statement - 2 : Te u f f ul ube ( 1)

2

n n +d e u f ue f f ul ube

( 1)(2 1)

6

n n n+ +



See - fle See - ue


See - e epl f See -

Sol. Me = +

S D =

2

1

(2 ( 1))n

r

r n

n

=

+ SD =

2 1

3

n

V = SD =1

3

n ee ee - fle

35 . Le f = | | d g =

Statement - 1 : gf dffeeble = d devve uu p

Statement - 2 : gf we dffeeble =



See - fle See - ue


See - e epl f See -

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P ee =

1 0 1

P(1)P(1)

[ e ee wll be w e]

Ge P < P

el [ ] P b P le P

( P

38 . e e e bewee e le y = e e = y

:

2 3

8b

3 2

5

3

4

3 2

8

Sol. Le y y

be e e bl = y

Ge le y = +

eee e w 21 1( , ) 1

11

2y y

dy

dx y

= =

1

1

2y = 21

p y , y

y = x +1

0x

-e 1 1

,4 2

p

e le

1 11

3 3 24 2

82 4 2

+= =

39 . Le e le2 1 2

3 5 2

x y z += =

le e le + y z + = e , el :

7 b 5 5 5 5 7

Sol. Se e le2 1 2

3 5 2

x y z += =

le e le + y + =

S 5 = =

+ + + = 5 + = = 7

40 . ee el ee e el y e be elee e

w el e y lwy e le e e be ee :

le 5 b le 75 b le 75 b le

le le 5

Sol. wy ele el le =6

4

6.515

2.1c = =

wy ele y y = 31 3c =

wy e el Se y be le = 4 24=

l ee = 5 = 8 le

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41 . I bl b1

,4

B n p =

e bbly le e e ee el 9

10 e

ee :

10 10

1

log 4 log 3+ b 10 10

9

log 4 log 3 10 10

4

log 4 log 3 10 10

1

log 4 log 3

Sol. = = =0

0

3 11

4 4

n

nc

=3

14

n

e 9

10

3 91

4 10

n

1 3

10 4

n

3/ 4

1log

10

3/ 4log 10n ;

10

10

log 103

log4

n ;10 10

1log 4 log 3

n

42 . e le + y + = + + + y + = e eel le :

ely e le b ely w le e w le le

Sol. I ly ble we b le e llel

S + = 2 2

2

( 1)

( 1)

p

p

++

+ + + = + + = =

43 . I e ee e = = e :

= b = = =

Sol. by e =

44 . el le = + 5 + e

Rb e-e b e-e R

ee e-e R e-e b R

Sol. = + 5 + ; = + 5 >

Hee e-e R

45 . e eel e w eee e ly e 21

c xy c e= wee

e by

y = yy b yy = y yy = y y = y

Sol. 21

c x y c e=

2

1 2

c xy c c e = 2y c y =

2 y c y =

yy y

y

=

yy = y

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46 . Le b be b + I

1 1

1 1

1 1

+

+

+

a a a

b b b

c c c+

( ) ( ) ( )2 1

1 1 1

1 1 1

1 1 1+ +

+ +

+

n n n

a b c

a b c

a b c= e e le

:

y ee ee b y ee y ee ze

Sol.( )

1 1 1 1 1

1 1 1 1 1 1 0

1 1

+ + +

+ + + =

+

n

a a a a b c

b b b a b c

c c c a b c

by w l

( )

1 1 1 1

1 1 1 1 1 0

1 1 1 1

+ +

+ + + =

+ +

n

a a a a a a

b b b b b b

c c c c c c

ly ble we ee

47 . e ee le we ( )2 128 62

+nn e by 9 :

b 7 8

Sol. 2 2 18 62 +n n

( ) ( )2 1

64 62+

n n

( ) ( )2 1

63 1 63 1+

+ n n

( ) ( )2 1

1 63 1 63+

+ + n n

2

1 21 63 63 ... 63 + + + +

n n n n

nC C C +2 1 2 1 2 2 1 3 2 1 2 1

1 2 3 2 11 63 63 63 ... 63+ + + + ++ + +

n n n n n

nC C C C

( ) ( )2 1 2 11 1 2 22 63 63 ....+ + + + + + n n n nC C C C

O by 9 ee 7

48 . Le y be l ee by 2 2 cot 1 0 =x x x x y e ( )' 1y el :

b l l

Sol. = 2 2 cot 1 0 =x x x x y

= y = y =2

[ ] ( )2

2

.2 1 log 2cot 1 log

2. cos

+ +

=

x x

x

x x y x xdy

dx x ec y

=

[ ]21 2 1 log1 2 02

+ =

dy

dx

12

2= =

dy

dx

49 . I e e e 2 0+ + =bx cx a be y e ll el le e ee

2 2 23 6 2+ +b x bcx c :

le b b ee b le b ee b

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Sol. we e e e b + + = be y e

b < < bS le ee

/ =

2 2 2 2

2

36 4 3 2

4 3

b c b c

b

=

2 2

221212 =

c b cb

e le ee ee b

50 . e y e ee 2 3 42 6 10 14

1 ....3 3 3 3

+ + + + + :

b

Sol. (a) Le S = 2 3 42 6 10 14

....3 3 3 3

+ + + +

2 3 4

2 3 4

2 6 10....

3 3 3 3

2 2 4 4 4........

3 3 3 3 3

= + + +

= + + + +

S

S

2 3 4

2 2 4 4 4......

3 3 3 3 3

= + + + + S

4

2 2 913 3

13

= +

S

2

3S=

2 4 3

3 9 2+

2 4

3 3=S

S =4 3

23 2 = Hee 2 3

2 6 101 .....

3 3 3+ + + + = S + =

51 . e je e e ee e e eeely e e e e e

e :

6 3 2

, ,5 5 5

b

6 3 2, ,

7 7 7

6 3 2, ,

7 7 7

Sol. lely6 3 2

, ,7 7 7

52 . Le A B ee e ee

A : cos cos cos 0+ + =

B : sin sin sin 0+ + =

I ( ) ( ) ( )3

cos cos cos2

+ + = e :

A le B e b b A B e e

b A B e le A e B le

Sol. Le = + b = + = + + b + =

( ) ( ) ( )cos sin cos sin cos sin + + + + +i i i =

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cos cos cos + + = = sin sin sin+ +

( )2

cos cos cos+ + + ( )2

sin sin sin+ + =

+ ( ) ( ) ( )( )cos cos cos + + =

( ) ( ) ( )3

cos cos cos2

+ + =

53 . Oe e elee 5 e be 9 e e bbly e e

e elee e 8 e e ee ze el :

1

7b

5

14

1

50

1

14

Sol. S : { 5 7 8 9 }

S =

: {8}

=

( )( )n E 1

P E = =n(S) 14

54 . ee e e e - el e le e e e

y e e e e e e el 1

3 e e ee

e le e :

5

,04

b5

,02

5

,03

Sol. lely le le ee e ee wll be ee l

I P y

1

3=

PA

PB

2 29 = PA PB

( ) ( )2 22 29 1 1 + = + + x y x y

2 2 5 10 02

+ + = x y x 5/

55 . I e e e e be + + + e e 55 e e el :

b

Sol. ( )101 100 / 2 101101

+ = dx = + 5

S e = | 5| + |9| + |8| + + || + | | + | | + + | 5|

= 5 5

Me e = 55 =50 51

101

d

=

56 . e elle 2 24 4+ =x y be ele le w e e e w be

e elle e e e e e e elle :

2 212 16+ =x y b 2 24 48 48+ =x y 2 24 64 48+ =x y 2 216 16+ =x y

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Sol.

2 2

14 1

+ =x y

( )2,1

( )4,0O

ee ele

le e ee elle

wll y e e2 2

21

16+ =

x y

b

2

4 11

16+ =

b

2 4

3=b

e elle2 23

116 4

+ =x y

2 212 16+ =x y

57 . I4

2 =Zz

e e le | Z | el :

5 1+ b 2 2+ 3 1+

Sol.4

2 =zz

4 4| |

| | z z

z z | z |

4

| |

22 4 0 z z

( ) ( )1 5 1 5 0 + + z z

1 5,1 5 + z

max1 5= +z

58 . I P e e ee e le + y + + 7y + 5 = + y + + y =

e ee le P :

ll ee e le b ll ee w le

ely e le ll le

Sol. 2 2x 3 7 2 5 0+ + + + = y x y p

2 2 2x 2 2 0+ + + = y x y p

ee le

( )2 2 2 2 2x 3 7 2 5 2 2 0+ + + + + + + + =y x y p x y x y p e

+ + +7 + 5 + + + + =

2

2 7

6

+=

p

p

ee ll le ee = 6, 6

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59 . I , , u v w e -l e e el be e e ely

[ ]3 u p v p w [ ]

pv w qu [ ]2

w qv qu = l :

ely w le b e w b ll le

ll le ely e le

Sol. we e [ ] 0 u v w

[ ] [ ] [ ]2 2

3 2 0 + =

p u v w pq u v w q u v w

[ ]( )2 23 2 0 + = u v w p pq q

ly ble we 2 23 2 0 + = p pq q ly ble we

= =

60 . [ ]0

cot x dx

wee [ . ] ee e ee ee el :

b 2

2

Sol. I = [ ]0

cot x dx

I = [ ]0

cot x dx

by ( ) ( )0 0

= a a

f x dx f a x dx

[] = []

Hee I = [ ]( )0

cot 1 x dx

I = [ ]0 0

cot 1 x dx dx

I = 2

= I

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