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Chcmistrv: ｾ＠

Q. I.

a. l ｷｲｾ＠ ,;1ln·r n:-ds :• rL· <!: ppi.'d in I t .... 1 H C I and I ｾﾷＱ＠ H ｾ＠ 0 ｾ＠ . In \Vhk·il <:>f 1h'-· tWt) Ｚｾｯ［Ｎﾷｩ､ｳ＠ w i li ｾｨＧＭﾷ＠ ,; ｩｩｶｾｲ＠ rt)d,;

d•s,llh c und"'l ｾｾＮｭ､ＺＱｮｬ＠ ｾ＠ .. Ｉｮ､ｮｾｬｬＡﾷｨＧＧ＠ ｴＮｾＬ＼＠ . .'!'l

Ag + HN03 --7 Ag• +NO+ H20 then

Eo A:;lhc ce/J

Q. 2.

For 0.5 M H2S03 solution Ka1 = 1.8x 10-2 and Ka2 = 8.3x 10-5

Find the concentrations of H •, HSO::; and so:;- ?

Sol.

a.

b. N2 ＰＴ､ｩｳＬ［ｲｾ｣ｩＺｬｾｳ＠ ｷｩｾｨ＠ ＼ｾ＠ ｬＧｫｧＮｲ｣ｾ＠1 hi.' ｶＺＱｬｯｾ＠ t)f K p . ( i ｩｶｾｮ＠ 1<:>1:11

c. 1 .\·(.:.)lc llf ｮ［ｬｮｬｾｃｮ＠ ;;nd -1

ad<kd and tiH.' \'i.'Si-d

•

ＮｾｲＺｳｾｾｾ｢Ａｩｳｨ＠ Kx. Rd:nilm hi.'l\\'i.'i.'n Kx :Hh'l Kp :m11

T"' .\15 K

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••

h.

H 2S03 ｾ＠ H• + HSO;

Hso- ｾ＠ H. + so,_ 3 3

H2S03 ｾ＠ H• + HS03-

0.5 - ;r; ;r;

;r;, ｾ ｬＮ ｓｸ ＡＰＭ Ｒ＠ = --

0.5 - lC

;r;

Kal = 1.8 X J04

Ka, = 8.3 x w-5

or0.9 x 10-2 -1.8x10-2 x = x2 or x2 +1.8x 10-2 x-0.9 x 10-2 = 0

=> x2 + 0 018x-0.009 = 0

[so,_ [w] Value of x = [w] = [Hso; ]= 0.08625 mo/11 Ka, = ｾ ＸＰ ｟＠

3

= 8.3x 1o-s As [w ]= [HSo;] [so;-] CONC = Ka, = 8.3 x 1 o-s mo/11

N,O, 2N02 Total moles

t= eq 1-0.4= 0.6 ｾ＠ 0.4x2= 0.8 1.4

Ｈ ｾＩ Ｌ＠1.4

- (0.6) 1.4

0.8x 0.8 ｸｾ＠ =0.76 1.4 X 1.4 0.6

Also, K1

= Kx (P,.,..r) .. • = 0.76 (1) 1 = 0.76 atm

N1 + 3H1 -7 2NH3 ....

lMow 4 Mow 2 mow

(1 mow H, wjtout)

• '

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b.

What iS the order of the reaction With respect to 12 7 Also ｧｾｶ･＠ the total order

[12 ) Mollltr [CHpOCH3 ] Mollltr ｾ＠[H •] Mollltr Rate Mollltr sec

3xl0-3 2.5xl0-2 15xl0-3 2xl0-2

"'" '''"' '"" """"" ""'' "' "" "" '"""'" """""""' ;· :·; ';: :0" -i- --i- .. \) ' r-, a pho>l<•<k<'lr,>ll. t:oc freq"enev ,, ｾｩｶ･ｮ＠ bv the ,·xpre"i''" ( 2 n 11; ｬｨｾ＠ｷ｡ｶｾｨＮＺｮｧｴｨ＠ ｲｾｦ＠ ｾ＠

0 (2, ' . 6600 A ' 'Ill ' . .. .., • ＱＱＱＢｾ＠ ｰＡＧｨｬｬｦｾＺｾｾｾｾ｜ＩＱＱ＠ ｾＺ［＠ . w.l:ll w: h' l.h: v:l!H<-' <:>t ·n :

c.

SoL

32 (r·•2) =- 1312 x 2 KJ I mole to be same.

hl':" ｬｩＱｨｩｵＱｾｬ＠ l h\!'l ｣ｮＢｾｲｾｹ＠ :;hllUid be 6 ｾ＠Li •2

b. ｓｬｾ＠ ｬｬＧＺＢ､ｾﾷｲ＠ ｬｬｬＧｬｨｾ＠ rc:H.'IilHl \\".':".1:

(2xl0-2)= K [2.5xlo-2 ][L5xi0-3 ]K= 2xlo-

2

=533mor1 Isec-1

2.5 X 10-2 X 1.5 X 10-3

'K' value for second order of the reaction = mor1 I sec -1

c.

3. 3 x 108

15 ( I I ) c ( . ) -----:1::-0 = 3. 3 x I 0 - 2 - - 2 as v = - n "' 4 ｾＴＢ＠ orbit 6600 x 10- 2 n ;l,

• Q.4.

&b .. ,, ) A ,.,...nz, ) Nylon 6

Rearrangement

(' ｹｾ＠ ｽｴＩｬｾ＼ＮＧ＠ X :llll)llllXiiH<.'

b. lih:mify whidl <:>f 1h'-· ft)!lfm·ing ＮｾｩｶＧＭﾷｮ＠ ｾｬｈｬｾｰ＼Ｚ＾｜ｬｮ､ｳ＠ is l)pt:.;.·ai!y :lcliv'-·

iij1 . .;,·hlll':"l\ Ｎｾ＠ .. ｾｨｾｬｨｹｬ＠ ｰｾｮｬＮ＠ I. :l.dicnc

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SoL

a.

b.

Iii) ＮｾﾷｬｾｨＮＧｴｨｹｬ＠ J ·hydrf-:li.y pC'!'lliHhll

iili) ｾ＠ . .;;hl(ln> ｊＮｮｾｾﾷｬｨｹｬ＠ ｢ｭ｡ｮｾ＠

ｃｬｬｭﾷｾﾷｮＺ＠

iij

Ph-C = CH -?Ph- C- CH3

II 0

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C!

0!1 0 ｔＺｬｵｴ､ｭ･ﾷｩＯＮｾＧ＠ .,

Pr: ··· ( m CH · .. .i ＮＺＮｾﾷﾷｾｾＮＺﾷＮＺ＠ ··.) ｾＮＬﾷＺ＠ · Ｈｾ＠ . · C tl Ｚｾ＠ ................................. ｾ＠ ｐｾｬ＠ ... Ｏｾ＠ ·· <.:H , c. iij ;:;" ... Ｚｬ＼ｩｩｾ＠ .. ｾＮＺｽＬ＠

Q. ;,

a.

b.

Sol. "

a. ＧｦＡｬ｣ｾｾ｜ｉｓ＼Ｎ＠4 CH3

ＭｾｃｈＬＫ＠N CH3

2 -methyl propane

(Isobutane )

COOH

··Nilh ーｈｩＮＺＮﾷＺ［ｾ＠ lh;Hl ｩＱｾ＠ ｩｩＮ｜Ｉ｜ＮＧＱ｜ＮＧ｜ＮＧｬｲｩｾ＠ Ill\; III;, ｾｬｬＺｴｾｵｬＺｵ｣ｾ＠ :n I hi.'

lh)iHI h ｜ＮＧ＼Ｉ＼ｾＮｾｵｬＺｬ＠ h.'S :II :llllh'k E s pl:l in I his ｲｨｾｾｈｾｭｃｩｨＩｬｬＮ＠

rca\.'1 ｃＺｉｾｅｹ＠ ｗｾｬｨ＠ Br'2 in cs2and ＧｎｨｹＧｾ＠

(0)

CH 3

CH3 -C-OH

I CH3

Tertiary Butanol (C4H 100)

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0

II H2 N- (CH2 )

5- CH- C- NH- CH- (CH2 )

3 - COOH and

I I NH2

0

II

COOH

H 2N- (CH2 )5

- CH- NH- C- CH- (CH 2 )3

- COOH

Q. (>,

So1.

a. ｜ｾＮＺｨｹ＠ 1

b.

b.

Q. 7.

... ·

I I COOH NH2

r--·. ¥ 0

:: ＮＺｵｾ＠

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a.

b.

Sol.

b.

().&.

b.

i.'.

SoL

;).

b.

v,.:hy NH 3 ｩｾ＠ mf:>r.:.· ｾｲｾｬｮ｢＠ h.: in water th:m pH 3 ﾷｾ＠

｜ｾＺ＠ hy BH 3 ､ｾｾｨＮｾｲｩｩＧＧＭＧｾ＠ htH BF3 ､ｦｻＧｾ＠ lh\l'?

rhc ｾＧｬｬＡｬｾｬＩｫＮ｜Ｚ＠ K [PtCl3C2H 4 ｝ｨＺｬｾ＠ Ｍｾ＠ ｾﾷＡｬｨ｜ｲｩｮＧＭﾷ＠ ｩｬｨ｜ｬｾｬｾ＠ hlHHkd (\) phu;num. \Vhv

ｾＮＩｐｐ＼ＧＺ＾ｓｾｉｩＮＧ＠ hl i.'lhi.'IH.' h:1v.:.- ｨｾｧＮｨｩＮＧｲ＠ bt)nd Ｚｾﾷｮｧｴｨ＿＠

.. . NH3 . . , .. 1 ... ｾ［ｴｮｬｾｻＧＡｬ＠ m ;:; Ｂｾｫｾ｜ＧｬｬＧｬｈｬ＠ u{'IH'-' ;;nd ＧＭﾷｫＮＮＺＺｬｬＧｬｬＡｬｃｾＺｈｾ｜ﾷ｣Ｎ＠ H l:l:' ｾＡｬ｣＠ ［［｢ｾｩｉｙ＠ 1\) Ａｬｹ､ｲＮ［ＬｬｾＢｾｮ＠ bll

ｩ｜ｨｲｾｳｰｨ＼Ｚ＾ｬＧｬｬｏｾ＠ ｾＡｴｈＧｾ＠ ｮｴｾｬ＠ ｾｨｲｾｷ＠ hyd n)g.:.·n b<:>nd ing.

BF3 ｾ［［＠ ｾｬ［［｢ｾＱｩｚｻＧ､＠ hy ｐｾｲＭ ｐｾｲ＠ h:h:k ｢ｬ｜ｬｨｈｮｾ＠ du{' hl \\'hi..::h lh{' Ｂｾｫ｜ＧｬｬＧｬｈｬ＠ ddil!.

ｾＺｈｩｾｬＺｻﾷ､Ｎ＠ ｂＺｬＮＺＮＭｫｴｾＨＩｾｈｩｩｮｧ＠ is •wt ｳ｣ｾｮ＠ in ｂｈＮｾ＠ du.:.- t<) which :1 ｾｈ｜ＧｴｾＡｱﾷｾ＠ in bridg·

•. I . n; - I ,. ' ! ' n; - ' I . ' . ' . 1·.u.:.·n'-· ［ｾ＠ ｾｾ＠ ｾ＠ ll!Wr ［ｾｾ［ＱＡｬｵ＠ ·.s l'-.'11 ｾｾｾｻＧ＠ l!nlm ｬ｜ｾ＠ {'lll;;nc ﾷｾ＠ pll•:lr;z··

PL ｾｨｬＡ＠ ､ｾＡ＼ｊｲｩｮｬＡ＠ lying ｴｾｰｰ＼Ｚ＾ｓｾｉｾＧ＠ H) :1 ｣ｸｰｬＡｲＺｩＮＧｈｾｻﾷｾ＠ ri.'puls:<:-ns. ｬｨｩｾ＠ ｾﾷ｡ｵＺ＠

II , Po?- . , No?- , .. : ﾷｾｙ＠ " ; ｬ｜ＱＱｾ＠ Ｂｾｸ＠ＱｾＱ＠ l'lll .. ｬｬｬＡｬｾ＠ m\ll ｾ＠ .>

Why B2 ｾＬ＠ ｰ［［ｲｾｵｾｬｾｾｾｮ｜ＮｾｬｩＮＮＺﾷ＠ bul c2 ｩｾ＠ !Wl'?

}:()f (! ｬｬｾﾷｾ｡ｨＮＺＮﾷ､ｲＺｬｩ＠ ｮ｣ｩｾＡｾ＠ｾｲｬｾｵｩｮＮｾ＠ 6 o > p

ｩｾ＠ ｨｩｾＡｬＮＺＮＭｲＮ＠ Y.:xpl:li!l 1h'-· ｾｬｬｩｮ＠ ｬｾｬＺｬｾｮＢｾｬｩｬＡ＠ Ａｬｾｬ｜ＱＬ＠

field.

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Q.9.

a.

b.

SoJ.

b.

Q. Ill.

a.

b.

Sol.

= J(4)(4 + 2) B.M = 4.8 B.M

.1.1 . . 1 . 1 • . •

1. , . PtC12 . lC' ＮＺＮﾷｮｾｰｮｾﾷＺ＠ ｨｬｦＡｬｾｵ＠ a lll :m ｡ｬｾｬｬｩｕ＠ 'ii.' ｾ｜ＩｕｾＡｨｬｕＡｬｵ＠ 1:'

AgN03 we get[Pt (NH3 ),]Cl2 and Ag2 [PtCJ,j

(CH3) 3 N p= 5.02D

F. ｜ｾＮＺ＠ hy ii. 2 ﾷｾｷｲ｣＠

Cr02-v.,.:hy ii. 4

. (SiH 3) 2 0 and .....

(C2HJ3 P ,u = 4.89 D

•h:lll Moo;-

3)2 O \d1ich ｾｩＭ ＺｈＩｾ｜Ｇ＠ ｢｡ｩＭｩｾﾷ＠ ;)Ht! why'.'

;)Ht! ｩｮｾﾷｮﾷ｡ｩＭｩｮｧＮ＠ I hi.' ｲ｣｡ｾﾷｾｬｶｾｬ＠ y ll r ｆｾ＠ . lli-1 ｴｾｘ＼Ｚ＾＠ hmi- <:>f Ｎ［Ｌﾷｨｭｭｨｾｭ＠ Ｚｬｲｾ＠ q·ry ｩＭｭＺＭｮＮｾｬｹ＠ ｴｾｸｩ､ｩｸｩｮｧＮＮ＠ TIH' ｭｴＩｩＭｾ＠ ｳｴ｡｢ｩｾﾷ＠ <:>sid:llilm ｳｴ｡ｴｾ＠ ()r \.'lmlm:um :i-

. · · . . Cr02- to ｾｯｲｭ＠ cr•3

1 ···I l I;. 1h li- rci-u hi- : n i-p<:>m:••h:<:>us ｲｾ､ｮｾﾷｮｴｭ＠ ()I 4 Jl . F ()f mll ｩｹ｢ｴｫｬｬｬｾｭ＠ ＨＫｾｉ＠ l j s1 ［Ｉｾ＼ＮＮＧ＠ is

ｵｮＮＮＺＺｬ｜ﾷｾｵｾｷｮＬ＠ ｾｮ＠ ｩＢＺｬｾｩ＠ 1. Moo;-

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h<:>nding. ｾｨｈＮＧ＠ hl 1hc ｰｮＮﾷＬ［ｾｾｈＮＧｩＮＧ＠ llf \':H.':Inl ｾＡﾷｲｾｲ｢Ｚｬ＼､ｳ＠ ｜｜ﾷｩｾｨ＠ Si. Th:s h<:O\\'i.'\'i.'r :s ｾｈｾｾ＠ ｰ＼Ｚ＾ｳｾｩｨｩｾﾷ＠ \\'ilh ｾ｡ｲｨ＼Ｚ＾ｮ＠ :n

CH3 - 0-CH3 ｾｨｮﾷ＠ hl ＼ｾｨｾｾｾｈＮＧｩＮＧ＠ llf d·Mhitai,; ｭ｡ｫＺｮＮｾ＠ h mlll'i.' h:ls:.;.·.

Physics:

Q. I.

SoL

<L ｈｾｾｷ＠ many ｰｩｈｾｈｾｮｩＭ llf ｜ｖＺｮﾷＮＺＺｫｮｧＮｾｨ＠ :l.-;';) 111:1 i-Jwnid s1rik.:: ｾｭ＠ :1 perf'-·.;,·1ly

:1 Ａｬｾ｡ｹ＠ l.'Xl.'l'l a ｲｬｷｾＢｾ＠ llf I (1\'·_)

b. C:m ｜｜Ｇ＼ｾｬｩＮＧｲ＠ he ｨＨｾｩｫ､＠ ｜｜ﾷｩｾｊｈｾｵｾ＠ ｨＧＭﾷ＼ｾｬｩｮＮｾﾷＮｾ＠

2h =-

a.

h.

V•/IH'n ｮｊｈｾｨｬｈ＠ ｩｮｾﾷｩ､ｾｭ＠ <:>II IH'I'f.;.·cllv rdk'-'lin£ snrf:l\.'i.'t::l "h<W•' J' •• ｾ＠ ｾ＠

L'-·t n p!·wh\IH ｩｮｾｩ､ＧＭﾷｮＱ＠ p.:.·r ｩＭＢｾＮ［ＬﾷＮ［Ｌｾｮ､＠ th.:.·n fllre.:.· ＧＭＧｸＢｾｲｬｬＮＧ､Ｎ＠

6 6 X ]Q-34 ＴＳＹＱＰｾ＠

10= 2xnx 439x 10-9 So,n = 2 x6.6x 10-3• = ＴＳＹｸｬｯｾﾷＳｳ＠ = 3.325x1027

132

On ｩｮｾﾷｲＮＺＮﾷ［［ｩＭｩｮｾ＠ pr'-·s:;ur.:.· ＮＺＮｾｮｨｬ＠ t\ '-' f;rO,l'' ﾷＺｮｾ＠ a pr.;,':>i-urc ｾﾷｬＧｬ｜ｫＮＺＮﾷｲ＠ ｾＢ＠ ｨＮＺＮｾｩｬｩｮｾ＠ l)lli!lt ｩｾ＠ dc-·v:ncd. ｾｩｭｩ｢ｲｴｹ＠ｾＩｉｉ＠ ､ｾＧＭﾷｲｾＺＱｳＺｮＮｾ＠ ｰｲｩＮＧｩＭｩＭｕｲｾ＠ :n :l \ 'i.'l ｾﾷＨ＠ 'lin? . ·:ncr ｩｾｳ＠ ｬｨｬｾＡｩｮｧＮ＠ ｰｾｾＺｮＱ＠ w:n he ｉＨｈ｜ﾷＮＺＺｲｾ､＠ and w:11l.·r \\'ill ｢ｩＮﾷＮｾｩｮ＠ ＨＨＬｾ＠

bl\il ＬｯＬＺＺｴｨＮＺＮｾｭ＠ Ｚ＾ｵｰｰＱｹ［ｮｾＮ＠

(). 2.

1 ＺｬｾＭｵｲｲ｜ＮＧｉｈ＠ ｰＺｬＺＧｾｃｩＭ ｲｮｭｾ＠ ｕｬＮﾷｾ｡ｬｩ｜ＧｬＮＧ＠ h\ f'll:'iti\'l.' ｴＮＺＮｲｭｾＡｬＺｬＱ＠ ｜ｾｦ＠ ｴｬｨｾ＠ b:Ht<.•ry ｬｨｬｬ＼ＮＧＡｬｬｾ［［Ｑ＠ ､ｩｲｦｬＮＧｉＧｃＧｕｾＢｾ＠

l:nc ＮＺＮﾷＱｾｬｦ｡ｮ､＠ int.:.·ma! ｲＮ［ＬﾷＺ［ｾｩＭｴＺＱｮｾＢｾ＠ ll(thc ｨ｡ｴｬＢｾｬＩＧＮ＠

ｲ｡ｾＡＺｵｳ＠ ｾＨｊ＠ <.'m :HHI m<:>1:1.;,·m ＨＬｾｦ＠ :ni.·ni:l ｬｌｾｾ＠ ｫＮｾ＠ m1 ｾｩＭ Ui-l.·d h:> h:mg ﾷｾｾｫｧ＠ m:lSi- w:1h the heir

I r th1:; ｩＮＺＮｾ｡､＠ ｾＬ＠ l'l.'ka:;l.·d ｴｨ｜Ｌｾｮ＠ ｾﾷＺｬｫｵｬＺｬｫｾ＠ Ｚｬｾ｜ＮＧ｜ＮｾｬＮ［ＮＭｲＺｕｩｬｈｬ＠ Ｎ［ＬｾＨ＠ ｴｬｨｾ＠ bhl<.'k.

ｴｾＪｩｦＱ＠

® I

Ｒｫｾｯﾷ＠"

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Sol.

a. Jn first .:.·aM:. cd l is ＨＧＧｨｍｾｩ ｴｴ ｾ＠ ｓ｜ｾＮ＠ V"' E ··· lr ｾ＠

I] = F. + 4 ·, ..... (il ｾＭﾷ ＮｯｯＭＱ ＮＱＭＭＭ

TR=la a

T=0.32x ( )2 20 X J0- 2

(ii)

Fitting the value of Tin (i ) 2 g -032

a_. = 2a . (i) 400 x JO

2 g -0·32

(a) 2 (a); 2 g =lOa; a= 2 g = 2m I sec1

0.04 10

Q.3. • . . . ·- ._ r = 5 13

a ｭ＼ＭｮｯｾｴｯｲＮｵ｣＠ ｾＰＱＺＺＮ＠ n\lto ol S.fh."'i"HIC ｲｩＺＧ＾ｾｬ＠

t:1blc o( th\· fo!towin!l-

S I W 00(; = 000(; X 0! X z;f'" = t{3 z;f" = 'A ｰＮ［Ｑ［Ｎ｜｜ｕＮ｜｜ｴｾｰ＠ ｴｬｾＮＢｾｰＮＺＮＱＮ｜＠ ｾｕｬＧｾｦｬＺ＠ 1.1.1ftf\> ,'ip Jll . ＮＺ［ＱｾＭｾｬＧｴﾷＧﾷＧ＠ ."HLt ·q

. ,,,,,, ·" •r . , ······-r·· .. : -.l,<. ｰｨｬＬｾ＠ m:q; ＮＺｾｾｬｨｬｬ＠ . . ｾＺ＠. 1:-. ｜ＮＮＬｾ｜Ｇｉ＠ If. ·: ＬＧＬＢｾｉｬｬＧ＠ ｉｉＧｾ＠ｾＭｾｾｬｬＧｬＧｬｬＧ＠ r,,." " '1 ' .... '''"" """"''""'"' ｾＧ＠.. "" ""' ' ' '" .. ,

.. .. ,,, "" ,. ,, ''".. .. ' ' ,1,\l.:llll)\jll ｾｬｩｬＩ＠ .:. ·. ｾﾷ｜ＬＬｉｉ｜ｾ＠ " ｊＮＺｬｾｬｾｕｬｾｬ＠ ＮＺＱｾＮＱＱＧＱ＠ .· i + "'"''''I'·'" ＧﾷＧＢＧＧＧＧＧｩ＾ｾｬｬ＠. · .>.10, '"' , , ''I ·'"I,.,, . ｾＧ＠ｳＮＧＮＮＺＧｬｾｬＧ＠

1

• · :' • J.:ll: ·'' u, • , i " 1''

1

" 1 ,, ' ' ｬｦｬｾｬ＠ . ' .. ·' ,.... . ' ' .

.... , ' .. ' '"" ,,. .. .. ' '"""" ' ... .. :'ISJ,'.\U' \'"'·. ·: ' ... q,> :m; '·'"P 'I .,J ｾ＠., ., i

·q

.b •. pU."'U:'I(HH ,..! , i . ' ｊＮｬｬﾷｬｾﾷＧ＠ .... '\ '\ ; . ｾＬ＠ •. ｊｬｾｬ＠ .n:.'FmN Ｇｂｾ＠.. )

,U . .WJ _.(U,)IJR:\_'

ＬＢＧＬＧＩｊｬＧｾｬ＠

· .. ﾷＺｩｦＬＺＬＢ＾ｾｬＬＢ＾＠ ﾷｾＢｾｬ､ｷＺ＠ ﾷｾｵｮ［ｵｾｾｬｾｬｾｗ＠ Jl;fnifuv

,">ill ｾＭＢ＾ｾＡｊｉＺＧ＠ ｉｾ＠ If:"'! If.\\ ljl!·''- ｴ｜ＡＬｾｾｕｾＧ＠

Ａｾ＠ ｾｾ＠ a;s v Ｇｦｈｭｴｈｾ＠ W\)JJ u;

Ｇｬｾ＠

ﾷｬＺＡ［ｊｾＢｵＺ＠ }<.' ［ｵｾｕＮｉｬｈｾ＠ pm; ,":lNJ ﾷｾｮｨｊ＼ＮＧｉ＠

l!li ｾＮｗｩｦ＠ ｾＮｾｐＡ＠ au;••l' ［［ｾﾷｾﾷＧＧｬｬｬｬｬｾｪ＠ .:llt; ..1 ｬｾ＠ ｾｾＭｾ＠ ｾｩｬＬＢｩ｜＠ · Ｎｾ＠

·pun<.Hfi

vu•hlJii' ｾｱ［＠ ］ＭｾｾＡＮＱＱＺＧ＠ pm! I! W<.'.:J ｰＮＧｩｦＮＢｉ［ｉＮＺｉｐｾＡ＠ ＱＭｾｾＢｦｴｦ｜ｬ＠

I Ｎｾｬｾ＠ p.1,"1thi ｬｾｬｬ＠ \\ ＮＨｦｰ［ｬｬｩ｜ＬＩｚＡＮｉｬｬｬｾ＠ ＧｦｯＧｬｱＮ｜ｬｾ｡［＠ S! ＬＧｩｈｾｬ､ＮＡＡｬ［＠ U\:' ·q

ｪ｜ｬＬｾ＠ pm; ｾＢＺＢＧｎｊ＠ Ｌ｡ＺＬＢ＾ｪＬｾｲｬｩｬ＠ ｕＮＺｬｾＮ｜｜［ｾｱ＠ ｾＢＺＢＧｕｾＮｉＮＺｬｪｊＡｐ＠ ,">ip.:l;!.l,"i\ '\j

'l<tS

·t- ·o

I t l ..... . .. ..... I 0 I I I 0 () () () ),, H V

［ｬｾ＠ ｱＱＺｾ＠ I(IHJ J.

ＦＢＫｖ］ｾＫｉｾ］Ｈｾ＠ ｾＩ］ｊ＠ﾷｵ［ｴｾｰ＠ .... ［ＭｾＮＺＮｾ＠ )\) ｾＭＢﾷＱｊｦｩＬＢｰ＠

f :\tUll ｾｬＺｬｪ＠ ｬｾ＠ ｬｾＤ＠ ﾷｾＢｕｪｬｯＮＧＮＺ＠ ｨｬｾｬｩｮ［ＬＢ＠ ｗﾷｾ＠ Ｚ｜ｰｘｾｬｬＡｦ＠ ＬＢ＾Ｌ｜｜ｑｾ＠ 111;;"1 ＺＧＱ［ｾ＠ ＢＡｬｾｬｬｬｬ｜Ａﾷｬｈｈｈｾｉ＠ ｾＭｾｕｾＤ＠ ﾷＬＮＺｩｩﾷｊＬＢ＾ｾｉｾＢ＠ ｾＮｗｩｦｬｈＺＬｬ＠ ＮＺｬｰｄＮＺｬｦｬｾｕｉ＠

1: If,"! If.\\ li! ｾ＠ .. ·:1;,\'. ｉｕＬＢ＾ｰｕＬＢ＾､ｾＢｰﾷｵＺ＠ }\l ｊｾＢｴｦｬｾｬｮｩｬ＠ ｾｱ［＠ ｾＡ＠ U.h'(:'.:l.:l.lj j\l ＮＺＭｾＮＺＮｩ［ＧＮＺＭｰ＠ ,">iiJ. £ f ﾣＯｾ］ＭＫ｛］ＭＫ｛］ａＮ＠

<': <':

·q

'\!

woJ ·aJe ;wexa· MMM

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\'. v,.:h;l.;,· ｶ､ｬｬｾｩｬｹ＠ Ｚ､ｬｬｕｾ＠ IH.)riZll!'ll;;1 Vx , .. llhj m.:i- L\.'llhc ｡ｮｾｫ＠ ｮｾ［ｨｫ＠ by ｬｬｨＮｾ｣ｾｬ＠ ··Nith \·.;,·nk;ll d<.)Wnward ;s

V, 100m Is Then tan 8 = - = = I f 2 8 = tan -l (II 2)

8 V, 200m Is '

d.

Q. ;,

Sol.

a. ｲｮＩｮｾ＠ :11<.;bk, ;l nld ii. ｨｩｮｾ｣､＠ a:;shln;,:n in 1hc ｅｾｵｲ｣Ｎ＠

｡｜ﾷｾﾷＧＭﾷｨＺｲＺｈｽｴｭ＠ ｲｾｦ＠ \.'i.'llli.'r t)f ma:;i-.

b.

I I a=mg-

2

5 I t:.T ::::}- =-- ::::} 5 X I 00 = ..!. t:, T X 100

2 T 500 2 T

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SoL

b. /\ ｾｾｬｮ､ｴｾｴｩｮｾ＠ \.'0:.)11\.' ii. ｧＮｾｮﾷｮ＠ ｾｨＺＱｲｾ｣＠ ＨｾＮ＠

pf:>imS I) f ＮＺＬＧＨｬｾｨＺＧＮｾ＠

h

'ij, ..... _,_ .... 4 ........ .

a. l Thi.' ｭ｡ｧｮｾｴＡｾ＠ ｦｾ｣ｽ､＠ :11 ､ＺＬ［ｾＺｈｈＮＧ＠ •

b.

l'•ll dy ｬｬＺｮｾｴｨ＠ dF "' ｾＨｩｹｂ＠

(r. t) (r.t) li'd li' Total fore{! F = ! B dy i = ! ｾｾＡｙ＠ - ｾ ＱＰ

Ｑ＠

[log y J: • 1;

14,li x+l 14,li [ I] F = -log --=-log I+-210 X 210 X

ｾ＠ .. a= _q_ so,q= a .4.m·2

. . ＴｾﾷＲ＠Ch;H'l!,\.' dCUi-il\' ｾｲＮｬ＠

ｓｩｮ･ｾＮｾ＠ ｰ､ｦＦＮＮｴｩ＼ｾｬ＠ 1Ul snrt:!l#r.ny \.'dlld\1\.'Wr is .:.'(lUSianl

.kq -=constant

I or a oc-

r r

a. Eqo:Hhm f,u· tWI) w:l\'i.'S is ｧＮｩｶｾｮ＠ a,;

Yl =a sin (a.t + "'1),y2 =a= sin (a.t+ ..1)1- 1· ' 1 · · 1 ,. ＧｾＧ＠ Y"2 1 :•mr ｾｴｵｻｈＧ＠ :ul( t;mc pcr:.o:.)t ,),

rcsuhant w;wc (il'•c:; 110:.)1 ｾｨﾷｭｾ｣＠ th.;,·n ｾＺＱｫｵｬＺｵ｣＠ Ｈｾ＠ - ｾＩ＠

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Sol.

b.

Q,l\,

b.

!' ind p<>l<'llli:ll :u di"'""''' x. wher,·: < x < R .

Let ¢ = ¢.. 1ft:, and resul tan t amplitude A = a

A2 =a 2 +a 2 +2aacos(tA Ｍﾢ Ｒ Ｉｾ｡Ｒ＠ =2a2 +2a2

cos (¢.. - ¢2) = - ｾ＠ 1 e, (¢1 - 1ft:,) = 120°

0

3300 A h:. : m.-:(knl llll ｭｾｾＺｬｬ＠ ｷｲｦＺｾｯ［Ｎﾷｾﾷ＠ ｲｾｦ＠ ｷｲｾｲｫ＠ fun<.' I :<:on

: ｾﾷｮｫＧｲ＠ :n ｵﾷＮｭｮﾷｾｮ［ＧＭﾷ＠ ｭ＼ｾｾｾｾｾﾷｬｩＮ［Ｎﾷ＠ ｦＺｾﾷｾ､＠ 6·7 X l0-6 Tan<! mm ｩｮ＼ｾ＠ ｣ｩＺﾷｾｮＡ｡ｲ＠ p:Hh

Ｇｉｾｌ＠ (' ｾＭｴ｡ｨＮｾ＠ ｾｨＺＱｲｾｃＧ＠ l\f ｾﾷＺｾﾷｾＧｈＧｬ｜ｬｬ＠ ｲｮｬｾｬｾ＠ lhC" ｾｨﾷｾＡＧｬ＠ d:u:e

md ｭ｡ｧｮｾﾷＱｩＮ［Ｌ＠ ｦＺｾﾷＡ､＠ Ｚｰｲｬｩｾ､＠ ｡ｾｭｳｩＭ ｰＺｭｵＺＱＺｧＮｮ｣Ｑｩｾﾷ＠ Ｌ［ｵｨｳｬ｡ｮＮ［Ｌﾷｾﾷ＠ ＺＱｲｾ＠ Ｑｲｩｰｩｾ､Ｎ＠ ｾｨｷＮＺ＠ 1:1:Hl)' 1i1:1cs

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= (he)= (6.63 X 10-34

X 3108

) = 6 X I o-19 J A 3. 3 X 10-7

.j2m (KE) )2 X 9.1 x W31 X (2 X 10-19

) Now r = 0 5 = -'---------''-;----'-

' eB e X 6 7 X I o-6

e= 6 X ＱＰＭｾｓ＠ 12

( )

= -X I o-19 coloumb =I 79 X 10-19 c (approll)

6.7 x 1 ｯｾ＠ ..!. 6 7 2

B /OC-

T

().9.

a. r-.,\.ll ｾＧｬＧ［ｬｳ＠ m & !'l ｨＺＱ｜ﾷｩｮｾ＠ ｾＰ＠ llln!S :111d 15 HlniS ｮＺＺｾｰ＠ ... ｾＭＮＮﾷＧｴＭＭｬＢＺ＼ＮＮＧ＠ I' · h' ＧＭﾷ｡､ｾ＠ lllh-::r. \\/h<..'ll ｾＺ｜＠ ｾﾷｵｲｲＭＺＺｭ＠:s ｲＮＺｉｓｩＮｩｬｬｾ＠ ｬｨｮｬｮｾｨ＠ Cf:>il m. ｾｨｬＮﾷｮ＠ nux linh·d :n 1.8 X l0-4 ｜ｾＮ＠ ｾﾷ＠ Ｉｾｲ＠ ｲｾＺﾷ＠ lum. lf ·';\ ｾＧｉｕｔｬＮＧｬｬｬ＠ :s paSi-<..'d

ｬｨｮｬｵｾｨ＠ Ｎ［ＬﾷｾＩｩｬ＠ n ｾｨＭＺＺｮＬ＠ ｾﾷＺＱｫｵｬＺｵＧＭﾷ＠ 111 ... ｾ＠ iiux Enk ... ｾ､＠

Sol.

a.

Now, flux through coil m; 10¢,. =MI.; ＱＰｾＮＬ＠ = 13.5x to-• x 3; ¢,. = 40.5 x 10-5 Wb

V = = = ,/90000 = 300 m Is ｾＶＰ＠

4 X 10-3

4

'

Let nV = 375 ..... (i) and (n + 1) ｾ＠ 450 ... (ii) 2/ 21

Q. !II.

Subtract (i) from (ii), we get ((n + 1)n) ｾ＠ 450-375; 300 = 75, I= 2m 2/ 2/

Mass per length= 4 x 10-3; m = 4 x 10-3; m= l x 4 x 10-3 = 2 x4 x 10-3 = 8x 10-3 kg I

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St>f.

·· · · 6 j./F I < I \" I '• . . I . I . I . ' II r·· I . ( ［ｬｰＺｬｾｮ［ｭｾＮ［Ｌﾷ＠ lll ｾＺ［＠ .;,• ｬ［ｈﾷｾ｜ＮｾｬＮ＠ 'Y (, : ＬＬ［ｵｾＺｲｹＮ＠ ［ｾｬｬｗ＠ ［ｉｾＺ［＠ ｃｬ｜ｬｬｩｈＮＧｾｉｻＧｾ＠ \nil aH u\.'hlr .:.)1 ｾｭ＠ · . ·;nt ｾﾷｵｲｲ｜ＮＧｉｈ＠ m

ind\1\.'h:>r whi.'ll l/3ril t)f ｬ､ｬ＼ｾｬ＠ ｾｮＮ［Ｌﾷｲｾｹ＠ is ｭ｡ｾｮｾｴＺｾＮ＠

b. An ｬｬｨＮｫｾﾷｴ＠ is ｴｨｾｷＮＮＺｮ＠ Ｌﾷｾｲｩ［Ｎ［Ｎ［［ｈｹ＠ upw:H·d \\·i1h ｾｬ｜ｬｾｬｾ＠ ｾｾＩｾＮ［Ｌﾷ､Ｎ＠ h cr.:.)s:;c:' ＱＱｈＩｩｭｾ＠ p, (l ｷｨｩｾｨ＠ ;;r.;,• ｾＮ［Ｌﾷｰ［［ｲ｡ｬ｜ＮＧ､＠ by h

b.

121 -6 -6 =-CV =-x6x10 x36=108x10 J 2 2

And magnetic energy=]_ total energy,::::}]_ LI2 = ]_ x 108 x 10-6

3 2 3

l= ｦｾｸＱＰＸｸＱＰＭ Ｖ＠ = V3L

2 X 108 X 10-6

3x5x10-3

ｴ］Ｒｾ＠p 1}-----g- t = 2 . f! q ' g

= j7

52

x 10-3 = 169 x 10-3 A

• '

Biology:

a. ｃｹｬｦＺ［ｫｾｫｨｬＡｬ＠

b. PhyH)l .;,·ha:n

c. ｓｾＺｮ｣ｲｾｨｾ＠

<!.

ｾﾷＮ＠ • ｃｹｾ＼ＺＭｰｬＺｳｭ＠ ()f l.'\lk:••}llt:.;.· ｜ＮＧｩＮＧｾｬＮ＠

Supllllrl t<J ｾｨｾ＠ ｾｾ＠ H

Chi.:.)nlphy H

:\ ndwrs ｾｨｾ＠ .;,·hl<:>mphy 1! :Ht)! .. ＮＭｾｮｫ＠ im() 1 hi.' Hp:d pari ll r thy! akt):d mcmbr:m'-·.

c. ｌｬｬｾＺｬｬｩｬｬｕ＠ ｅｾｮ｢ｲｹｬｬ＠ :;:1\.'

}:uncli()n ｓＧＭﾷＮ［ＬﾷｲＧＭﾷＱｩｮｾ＠ ｜ＮＧｬｾｾﾷｭ＼Ｚ＾ｬＺｬ｜ＮＧｬｩ｣＼ｾｮｹ＠ Ｚｨﾷｾｩｶｾ＠ ｷ｢ｾｾＺｭ｣ｩＮＧ＠ ft)r aur:•.;.·1ing. p<:>lkn lnhi.' :111il ｦＨＩｲｭｩｮＮｾ＠ ｾＧＭﾷ＼ｈ＠ ft)r p<:>lkn

111 h.;,· ､ｾｾｾ＠ ｨ｡ｲｾ｣Ｎ＠

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-.t. ltlt.':llitlO PhltlCm

Funclit.m ｔｲｩＡｈＺ･ＮｬＧｬＧｬＨＧＺｕｾＧｬｬｬｾ＠ i'f ｾＩｬｵｩｾＮＺ＠

r. Lttc:ui,,n {'hrtltnC.:>tHnc

ｬ Ｚ ｬｈｈＮＧｉｩｩｬｾｬ＠ Ｚ｜ｈＺｴｩＮＧｉ ＱＱｾＱｌＧｉＱＱ＠ ｴＮｾ ｦ＠ ::.pindk f'ihn:•,:.,

Q.l.

( tl)

(C)

ｗｨｾｬ＠ is: ｾ ｨｴＮ｜ＧﾷＧＧＧＧ＠ in ､ｩＺｴＮｾｲｾｮｮ＠ ＨｾｬｩＧ Ａ＠

｜ｎ ｨｾ ｴｬ＠ an.· (P't ant! ((})'.t

• Ｍｩｬｬ ｬ｜Ｇ ｴＺＧＬＩｬ ＧＬ ｬ ｾｬ ｬＡ ｬ＠

"''""'' ,_,_, ｾ ｬ ｬＡｬｪｾ｜Ｍｊ ｬｬＮｩＨＬＧｴｬｬ＠

＼ＮＧ Ｑ ｜ＧＱ｜ＡＱ＾Ｇｾ Ｚ＠ "'"'

Whkh tyr.c ,,f .. wui,'

(';h·c ont' ｲＮＺＭ｡ｾｯｯＮ＠

. ｾＮＮ［Ｚ ＱＺＡＱＱＱＧＮＧ＠ ｾｎ Ａ ﾷＮＢｾＧ＠ｾＦ Ｎ ＺＭｾＯ＠ .... ［Ｚｾｾ＠ ... , .. ;!

N('ls:tc-.:-: il') = ｦｫｴＨＧｮＮＧＺＺｴｾＧＭｳＺｴＺ＠ (f); = ａｾｩｮ｣ｴ｣＠

b. T; ·J'hat-(o.'. ｩｾｩ＠ i.'tlll2r. (b' Tail fibre

.... . :\t\i.\lftltW uJ<. twul.:. Ht,dy '". ihc f•\'tll.: ｩｾ＠ i 1\\'..:"l'h.·d.

d. Epigytu.Hl::. ill\Vcr ... • .. ｾ＠ .. Cuntrbil:t\.' (':h:. t\Sif.' t':t.:.'i.'ih'

Wh:u ｩｾ＠ this. ty('{" ,,, fit,wcr c:tllcd':

(i in: ＮＺＭｸ｡ｭｰｫｾ＠ ｾｦ＠ Alt.'h n,,wcr:

(.'. v <·xi nary ,,)r .. ｾＮＺＮﾷＺ［＠ ｣ＮＺＺｮ､ｾＮＬｾ＠ imbrh:al..:" ' .: Ｎｾ＠ .. Stl)'!tht.•at'L (j r:nn. Cnlh\lari:t. L'h.: .

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ｾｾＮ＠

b.

<'.

ｾＮｴ＠

<'.

s. :<.

i ｾｾＩ＠

ｾｨＺﾷ＠

ii.')

ｾ｣ｏ＠

io.')

a.

b.

<'.

<'.

r· .. ｾｾｾ＠t·ll:·i<md .. ·r

\\' ｨｾＺｬｾ＠

s II II ［ｬｴｬＧＮ｜ﾷｾﾷＺﾷ＠ｾＮＺｬｵｾｬＺ｜ｲ､＠

f'lant l)Jan•nnuion

ｰＬ｟ｾｾｾ＠ ｾＮＺＱ＠ :l':".Y,i lt;;1

( ·twi:•n<kr Ｚ｜ＺｾｩＺｫ＠

\.Vhc:•l ｲＭｳＺＬｾｾｬ＠

ｓｵｮｦＧｩｴｬＧＮ｜ﾷｾﾷｲ＠ ｈＺｬｾ＼､＠

ｾﾷＱ＠ ｵｾｾＺ＠ rei r:li.'o.'l:li." ｩｽ＼ｾｲｩｩＮﾷｾＺｬ＠

ｓｬｩｾｬｾｾ＠ ｉｾｈＧ＾ｾｉｉ､ｾ＠ :md ｲｾｭｾｩ＠

( \;Hhh;m :l:HJ h yp<W ｉｾｗＮＺｉ＠ ｩｕｾｬｾ＠

B ＱｴｬｫＮｾｩｩＮＧ＼､＠ ｾｾｾ｡ｧＺＱＱ＠ ＨｩｩＮＧ＼ｾｬ＠ ｩＨｾｮ＠ a:lt

Siliqu:l

Candt•x

l:! ｬｾＮｨＧｾｬｾｬﾷＢｾ＠ :J ｬＺｾＢｵＬＺ［ｽ＠ Wll.:, p;llll\:.1,,) \:,,i;:'.:\i l:\l

ＺＺＧｾＢＺＭＮＮﾷＬＧ＼ＮｬｬＡＡ＠ ｵＮＧﾷＧｾｾｾｴ＠ ｾｐｊＧＧﾷＧＧ＠ ﾷＧｴｱ｜Ｚｾ［ｮＬＺ＠ ltl!·" qm:jq ｾＢｬｴｬ＠ l!;

ｌｾＡ［＠ ｾｾＢＮＧ＠ · ｾ＠ ｾ［Ａ［＠ lp; ﾷ｣ｾ［＠ ｾＭＢＩ＠ ·q)

11 .. '1:1 ;pu\l,">,:.J

)\l If

Ｍｾｾ｜ＩＱＱＮＢＱ Ｌ＠

ｬｨＧｾｾ｜［ｦｦｾｬＨｬＡｬｬＮＩ＠ ｾ［［Ｎｾ［＠

ｬｬＧＧＡｬＬＢｬｬｦｾＺＧｉｈＺｊ＠ J. ( ［Ｎｾ［＠

ｬｨＧｾｈＺｾｉＺＮＺＮＬＧＩＺＧｕ｜ＺＮＱＮＱＮ＠ ( ';

ｾｾｾＺｾｾｾｾｾｬＺＮｉｊ＠ ＡｾﾷｰｾｮＺＺ［ｯ＠ i ＮｾＡ［＠

,':'l:;<.l!J,':'UI:J J. ＬＺＮｾＮＱｾＢ＠ ｜ｾｾｾ＠ ｾ＠ ｾ［［［＠

ｾｬｬ｜ＮＺＬＧ､ＨＩ＠ ( ｾＡ＠ i

II"IIUIIII<t.)

,:; Ill

｜ｾ＠ ｐｾｕ＠ l:,, ｾＢｬＺｾｬｬＺ＠

11 'l!ll! a:.'! ｬｴ＼Ｎｬ＼ＮｈｾｉＡＬＧ＠ ｰｾｦｦ｜ＺＬＬ＠

.. \j'l\q ｊＬＢｬＨｾ＠ \\ ,'{P J ll I II,''Hi.Hp;.; H.'

-:;pf."!.: li.ll\.:_; ).:l' 1111.1 \)1 ,'U(I

uou r. ［Ｌｾ＠ 11du.uu :·1

·;;·," W.1l\,".:d

·-:;n,-,1

··:i ＱＺｾＱＺ＠ ·') ·' ＡｕＭＢｩｾ＠ I l'-:;1'; .'.:1: ｾｊﾷＢﾷＧＧＧＧｾｬＺ＠ fp;if P·'HI:,, ,;.;,'.\>.llf)

ﾷｾ］ＧｾＢｉｬｬ＠ ＢﾷＧｐｾ］ＧｾＢｕ＠ ·dn,, ｾＢｬｴｬ＠ .. h' ﾷＧ］ＧＱＺｾ＠ ﾷＧｾｦｬｬｬＺ＠ :'J,">.,nl!,l ＬＺＮｰｾｉｾｉＮＢｊ＠

·'i!U•"J fHII; ＧＡｬＧｾｾｬｩｬ｜＠ ,'IF .:1:,'U ＮＢＢｾＮｗ＠ ＮＱﾷＢﾷＧﾷＬ［ＬｾＱＮＺ＠ Ｇｬ｡ＺｴＮｾ＠ ·:;.;,11•\).:;3

ｾＢｾｬｬｕＺＮＨｬ＠ ｾｾｾ＠ ＼ＮｨＺＢｾ＠ ｾＢｬｦｬＮｗ＠ ｉｬｬＺＮ｜ｾ＠ ＮＺｾＱＡＱＡＡ＠ ＬＺＮｾｰ＠ II'' ｾｬＡＮＺＮ＼Ｎｾｱ＠ ,">.:.l:

-:;J," \\\)IJ

• ｰ［Ｌｈｾﾷｾｉﾷ｜＠ ｰｭｾ＠ q;.PI:f ｾＮＧ［Ｎｉ＠

l"llutl\l(t.)

IIUHllll.) fHH; f· llli.Hlill,, ﾷＢｬｾｩ＠ ｾｰｬｱﾷｾ＠ '>; '()

. ＬＺＮＺＮｾ＠ .. 1! :'111.1," )'' lil.:.l:d

,'.\ ｩｗＺｏＬＧｾＢＧ＠ ｉｾＧｈＺｰＡ＠ p11 1;.1 ｜ｾｾｾｈｅ＠ V .:ll ｾｾｾｐＡ＠ fHII;.l

ｾｬｬｾｫｈｾＮｊ｜ＮＩ＠ .(q ーｾＺＧｬ［ＮｬＺＬｬ＠ ｾＢｬｩ｜ＺＬＺＮｾＡＱｾ＠ ｴ｜ＺｾＱＡＱＱＩ＠ \i ｾ［＠ lf

!SIU tllftl.\\ ＱＮｾ［＠

ＧｉｾＧｾＡ＠ 11;.1!) ｩｾｉｾＨｾｕｩｬ｜ｾｱ＠

P·'tfl:,, ｾ［＠ ｕ｜ｬｕｾＢｉｾｉ｜ｬｬＡＬＧｾｦ､＠ ｾＢｉｕＮ＠ · ... ｮ］Ｍｾ［［＠ ｾ｜ｩｊ＠

U! ｬＡｬｬＡ｡Ｚｰ［ＮｷｮＮＢＺＢｾｬＺ＠ .:;n;; \ll ｾＢＢｐ＠ t·'·'·'t ＺＧｬＡｬｦ､ＬＬＮＺｾ＠

1:! ＮＢｾＡＮＱ＠ .'IF ｱＱｾｳＮ＠ ｾｵＺｾｾｾ｡ＺＵＮｾＮＺＮ｜＠ _1\) ｡ｾＵＡﾷＧＮ｜＾Ｎ＠

l!lnl ｊｾＢ､＠ ｾｉｕ［Ｌ＼Ｎ｜ＱｭＺ＠ I!; ＬＺＮｾ｜ＺＬＢ＾ＬＺＬＱＱＡ［＠ ｰｭｾ＠ ｬｾＡｬＺｬｴＧ＠ ｦｾ｜ｬ｜ｬｊ＠

llWI ｾｾＱＺ､＠ ｾＮＧｰｾＬＬｾｩｾＮＧ､＠ ＧｬｾＱＺｰＱＺＮ［＠ ｦ［ＮＢＢｾｰ［ＬｾＡｴｦﾷｬＺｬｬＮ｜＠

tiO! 1 H ｊｾｊＡ＠ uft 1t Ul f I! ;,!'i:OI<t!H

'\;;q.:.<.Hfdll':l

. ;;· ·' I! IS!i.l ＡｾＮｮ［ｬｬﾷＢ＼ＮｴｗＬＢＡﾷＺＺ［＠ Ｈｾ＠ Ａｾｱ＠

. ＮＺ［Ａｾｬｬ｜＠ p.'W,'':i,".:d,\; -:;! ＮＺＮＱＮ｜｜［ＬｾｬＺ＠ •'ti:U:,':I ＧＱＱＮＢＢｾＡＺＱＱ［Ｑｾ＠

ｾＢＱｾＱＱＡ］Ｇ＠ ｜ｾ＠ .1\q .\jUll ｐｾＢｉｕＬＺＮｾ＠ ... ＮＺＮ＼Ｎｬｾｊ＠ ｾＮＺＮ｜Ｚ＠ :'.I,:.·'"'U

ﾷＢｉｉ［ｌＮｾ＠ ﾷＮＧＮＺﾷＧｬｬｦＧｾＮＬｬ［Ａ＠ ｰＮＧ､ＨｾｱＭＺ［＠ du,, 1: ＱＱ［ｱＺＺｾＮ｜＾Ｎ＠

ｐｾＢｬｩｬｬｴﾷＧｬＡＬＧ＠ ,:; ｾＢＺＧｬｵｾＮＧ］ＧｾＢｊ｜ｬｬｩｕＡ＠ ｾｴｬｬｩｌ｜｜＠ ·,,u:.C'

ｰｾｬｬ＼Ｎｬｊ｜｜ＬＢｾ＠ 11; Ｌ［ＮｾＮＧＮ｜＾Ｎｬｬｌｾ＠ ·'t1:u: Jll

(p:•

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a. ｩｾ＠ h: i'tlphtw:• ｨ＼ｾｳ＠ ｨｲｾＺｨ＠ ..................................................................... :•nd .

b. ih ·• ＮＺ｜ＬｬｾＺｬｬ＠ ic ｰｩｾｵｈｾ＠ ｾｾｲ＠ .. ｾ＠ .................................................................. i ｐｾｾ､ＬｫＧｴＧｨ＠ ＺＺ［Ｌ｟ｾ＠ ·•

and .................................................................... ｾ＠ Ｚ｜［ｬｾｨｬｾｰ＠ .. ·t:l: ﾷｾ＠

... ic ｾ＠ ｐｬＺｬｾｬ［＠ h .. ﾷｾｾｲｩｮｾ＠ h,,lh ﾷｾＬｾｾｫ＠ Ｚｬｾｈｉ＠ ＨＬﾷｬｾｬＺｬｫ＠ ｦｬｲＩ［Ｌ｜ﾷＬ｟ｾｲｾ＠ ［ｾ＠ '-':l11<-'d ...

､［ｾﾷｬｾＺＧＬＧｬｬｬ＠

Ｚｫｾｷ＠ .. ﾷｴｾ＠ tl( dh' sa:l:'-' pl:l;li is c<dkd ..

d. . ................................... ｨＺｬｾＮ＠

a. ｩＧｾｬｨＧｬｬＺｬＺｗｰｩｷｲｾﾷｾＭ Vivip:l:)·

b. i\.:l:l':":>ik:l. Ｈ［［ＧＭｨｨｍｾｬｩＺｬ＠

\'. ｩ｜ＮﾷＱｬｬＺｷｾﾷｾﾷ＠ ｩｬｬｬｬｾＮ＠ ( ＩｯＮﾷｩ［ｲｾ［ｷｾＺｬ［ｮｹ＠

d. ｣ｹｾﾷＺｬｾＮ＠ ｣ｬ｜ｲｾ､ｬＨＩｩ､＠ r()();

(). 1.

b.

SoL •

;\. ｩ｜ＮＺｬｵｾＺ｜ｾ［ｬＬｮ＠ c:1n ｢ｾ＠ d .. ﾷｾﾷｩｮｾ､＠ ;\5 .......................................................................................... '·:l':"i:ni,,n.

b. Mmat:tli:O k:His ill "'\f:>lu:ill:l Ｈｾｲ＠ ............................................................... tl( ｡ＮｾＧＭＧｬｨＧＮ＠'· Ｈｩｾｮｾｾ＠ ｾｘｰＺＧ＼ＮＧＵｾ＠ .. ·d ＨＩｾｬｬｹ＠ ｩｾｬ＠ ｬｨＧｉｾｈＩｉｙＮｾＨＩｾｉｾ＠ ｾＱＺＱＱ＠ .. ｾ＠ :l':"<-' .. .

d. ｜｜ＺｾｨＧｬｬ＠ ｨｲｾＺｨ＠ a!kk::. ＼ＧＺ＾Ｈ｡ｾ＠ .. ﾷｾＬＬ｟ﾷ＠ ＺｬＺﾷｾﾷ＠ ｯＮＧｬ｜ｐｉ｜Ｇｳｳｾﾷ､＠ i1 :s.

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..... Ｈｩｾｮ｣Ｌ＠ \;,:hich ｩｾ＠ ｮｾｦＡ［ｩ＠ ｦｲｾｱｵ｣ｮｬ＠ ｩｾ＠ .............................................. }YPC.

Sol.

a. S\1ddcn h .. ﾷｲｩｾＺｨｨＺ＠

b. ｎｾ｜［Ｌﾷ＠ ｡ｬｬ･ｬ･ｾ＠

ｾＮ＠ ｒｾｾﾷＧＭﾷｳＬ［＠ ｩｶｾ＠

d. C ｬｬｾｨ｜ｬｾｬ＠ in:uH.'<..'

Q.9.

Sol.

b.

<.

;;. ( •• ＬｮｨＮｾｬ＠ ,,nd :\ ll,lrd

b. S()l' ( h:} ... ＺｬｬｬｬｾｬＧＭＮＧｬＺｬｕＺｉＺ＠

l I J I) S I'Bl:h.'h

c. fhlrlh\\'id:. lndu\'l;,)n llr ＱＱＬＩ｜｜ＧＢｾｲｩｮｾ＠

( olumn ... l

• ivj('!'("

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ih.l

ih.l

ｔＬｾ［ＺｬｬｬｬｬｬｬＺｬｨＺｲ＠ ＬｾＨ＠ pbnl ;p.: ... ·i,_·; (llll:l;,! ia <m ＺＱｲｾﾷＺＱ＠

ｾｬｭｾ［＠ ｩ｡ｾｬｾＺＺＮ＠ ; 1 Ｇｾ＠ ｾｬＩｲＺｬＮ＠

Uabhat

;\. ｣ﾷｲ｣ﾷｾＭ ( •L: ｾＺｬｾｾｾｨＺｬｮｾｴ＠ ｾｾＨｾ＠ ＮＺｮｩｬｮｬｬｬｾ＠ ｬ｜Ｇｩ［Ｌｾ＠ .. ﾷｾ＠

b. ｔｨＱｾｮＺｴｬｬｮｬｰＱｾ［ｮＮ＠ Epi;l:1::1y.

ﾷｾﾷＬＬＩｬｬｬｬＧＭＧ＠ Ｎｾ･ＮｬＭＮＱＱＮ｟ﾷＮＮＬ＠ \\ I';H:l \\ lu.:h .l "I

ｾｉｬｬ［Ｎｾ＠ ＺＧｾＱＧＱ｜ＩｾｨｨＮＺＬﾷＮ＠

-·

:. ;'\·i,_•h,_• Ｚﾷｾﾷｰｲ＠ .. ﾷＺＺｾﾷＺｵ［＠ Dtll ll:lly ［ｾｨＧ＠ ｰｩ＼ｾ＠ .. ﾷｾﾷ｜｜＠ h,_•r,_· :l:l

·. ＬＩｲｾＺｬｮ［ＺＺＮｾｬｾ＠ li\ .. ｾｾ＠ h·:l; 1h .. ｾ＠ ran.;:_,·,)!· ..:•,ndi;;l\n::. ｾｭＬｾ＠

. ;\';-..,)111\·,_· qealni,_·; \\ i:ili:l \\ hi .. ·h :l ＺＺｰｾﾷｬﾷｩ＠ .. ·:- ,_•:nl ｾＺＮｬｲＧ［Ｑ｜ﾷｾﾷ＠

ｾｉｬｬ［ＮＡ＠ ＺＧｾＱＧＱ｜ＩｾｨｬＮＮＺＬﾷＮ＠

\ · ｴＧｾ＼ﾷｴ［ＮＬｴｩｯｮ＠

· ｔｹｰｾｾ＠ l\f pi:uH::. ｾﾷＬＩＮＺｬｾｨｬ＠ in ;\n ｾｾｲ＠ .. ｾｾｾ＠ ｬＧＬＩｾｬｾｬｩ［ﾷＺｬ［ｾ＠ lh,·

ｶＬ｟ﾷＮｾＬ｟ﾷｬＨｾｬｩＬＩｩｬ＠ ;,l( lh,_• :11\':1 ｾﾷ＠ .. ｾﾷﾷ＠ ｘｾﾷＺﾷ［Ｌｬｰｨｹｬｩｬﾷ＠ ｜ﾷｾﾷｾｾＧｻ［ｈＺｴｬｄ＠ ｩｾ＠

ﾷｵＮＺＮ＾Ａｬｩｾｵ＠ f;u!i.l\>!.1.,,1p ＨｾＮＱ＠ ｰＮＺｯ､ｾＩｬＮＺｯＮＬ［ＭＮｰ＠ ＨｬｱｊｾＩ＠ ｰｾｵｮＺｳＮＮＭＺ［Ｎ［ＬＱ＠ ｾＮＺ［ＭＮＤﾷＬＱｩｩｶ＠ ﾷｾＱ＠ •()

ﾷＮＺｏＬｬｕＬＧｕ｢［ＭＮｾ＠ J\> S.:Op.l\> U! ｾＮＱｩＮｉＱ［Ｑｓ＠ ﾷｳｮＮＺｏｕｾ＠ ·sn;-.lll:l:l ＬＧＮｗｾｉ＠ .:OII;lf.:\:\ pmr n:H .,,

ﾷｾｵｮｴ＠ ＮＨｬｾｊ＠ .i! ｾｬｪｾ＠ _Ill ｾﾷＧＮＬ＠ ［ｗｬｬｩＮｾｾＮＧｬｊ､ｾﾷ｜Ｑ＠ .. \ 1 U\l lll ｾｬｩｬｬｬ＠ ｾｱ＠ ｬｾｉＮｈｬＮＬｾｬｰＮｮ［Ｚﾷｬ＠ pm; q,;:,,1.11;1 s ·p

ﾷＨｲ［ｰｾｷ｡［･ｵ［＠ ｳＭ［ｾｲｆｾ＠ ｬｬｾ＠ ＧｩＱｾＱｬＧｾｴＮｈｉｉＡｉｬＧｾｱ＠ n;u ｰｭｾ＠ ［ＭＮｾ･ｬｌＧ｜Ｚ｜＠ ·,,

ｾＧＺ＾･ｴﾷＧ＠ \>1 Ｍ［ｦｩｾｬｬＧｩﾷｈｉ＠ ｵＮＺＮ＾［､ＮｨｾＮＬｾ＠ ;-.i!lf.\\ ｩｾｐＮＱＧＺ＾ｬｬＡ＠ ｓＧＺ＾ｬｾｩﾷＧ＠ tH ｾｩｩｾｬｬ｜ｾＬＩｱ＠ ;-.;-.q ..;;.:011\>fl ﾷｳｮｴｈｉ｜＾ＧＺ＾Ａｴｾｕ＠ .'.n: ｵＮＺＮ＾［､ＮｬｴｾＮＬｾ＠ plH: ＮＱＮＢｾｴｊ＠

ﾷＮｊ｜ＮｕＮＢｾｕＮｉｬｾｌ｜＠ ｰ［ｊｾＢｕ［ｉＺｈ＠ ｾＮｗｴｬ＠ ＧＺ＾ｊＬＧｬｬｾｬｴＧ＠ ＮｾｮｬｾＮ｜｜＠ Ｎ｜ＮｮＮＺｯｾｵｾｵ＠ .. \-; p;jp\;.i ':>l:lj II':>!J.H!lS:

ﾷｬｈｬＡＧＺ＾ｾｪｾｬｩｾｭ［ｊｬ＠ ｰｵｾｨｬＧＺ＾＠ .Ill ｊｾｐｈＧ＠ ｾｬｪｬ＠ u: ｬｩｾＢｐＺｾＧＺ＾ｬｬ＠ ＮＧｬｬｾｾ＠ .. ｾｾｭＺｾ＠ ﾷｾﾷＢｾｐＡＧＺ＾ｾ｜ｬ＠ .n;.'l f ＮＢＱＮ｜ｬＺｬｾ＠ ｾ｜｜ｬｬｕｾｱＧ＠

,·.uall.\lfd J!.:Olfl ｊｴｾ＠ ｾＮＺｏＮ｜ＡｈｮｕＮＱＧＺ＾［ＢＱｓ､ＮＺｏｊ＠ Ｎ｜ｾ＠ ,\H: ':>I

ﾷＮｾ＠

·p

i.l'l fiu.:.>!,1i.l Ｎ｜［ＭＮｾｾｾ＠ ｳＭ［ｾｲＡＬＺｏｬｦＮＧＡｬｦﾷＧＧ＠ "}\> .(lll:m ·"l'H ·q

［ＢＱＡｾＮＱ｜ｬＮＺＧＭＧＺ＾ｬＺ＠ pm; ＮｾｕｾｘｬｬｊＧＡＮｉＮ｜､＠ ｾＱＡＱＱﾷＧ｜＠ ｬｩｾｕＮｉｉ［ｉＡﾷＧ＠ ｾｴｱｬｬｬｬｬＧＺ＾＠ u;.: 1; ='.

':>! t ｬＺｾｵＡ＠ 111; ｾｆﾷｾｾｉ＠ :"i\ ·\!

ｾｾｳｾｉｊｉ［ｾｳ＠ ·n;u ·w.hl.\\ljtn;:·l ﾷﾷｾｴ｜ＡｴｬＺＢｩ｜＠

':>ieu;!lH: ＱＢＱｾＱｾＺ｜｜ｬｬｩｬｴｾｽ＠ }\> U\() 'tl '()

·;-.u!Jflll! ｰＮＱＱＮＩＮＱＬＬｾＮＬＬ＠ .:o.u; ｰｾＮＬｾｾ＠

ｪ｜ｬｴｾｰｾｾｩ＠ Jt' ＢｾＢＺＧｬｬｊＧｊｾＢﾷＧｏ＠ P.l

V ｬｩｾｕｈ｡ＡＮＺ｜＠ ＨｾＮＱ＠

ｾｊｬＮ｜｜ｬｬＮｬｾ＠ ｰＮｾｾｕｬＺｾｾｊ＠ li.\\\ltl':> q ｾｈＡＮｉ＠

ｾｐﾷＢｬｕｦｩ＠ ｊｴｾ＠ ｰｵｾｾ＠ ＮＱＱｩｾｊＮＩｪｽｬ｜ｕ［＠ S:\\lllf':> .:0 (!!.1

ｾｊｬＮ｜｜ｬｬＮｬｾ＠ ＮｾｬＮｾｪ､ｾｬｈｬ［Ｂｬ＠ ＧＺ＾Ｎ｜ｾｬｬｬｾＧＺ＾＠ 1; (!.1

ｉｕＮｾｰｴｬｾＢ､ｾＢｐ＠ ｾｾＡｐ＠ ｾＢｊ｜Ａ＠ ｉｉｉｾｐﾷＧ｜＠ plil: 111.''·\l.:iJ.) (\!) 'II)S

\\\>fl 1 .• :0.1

i.lli.hU;; .:Olfl .(q 11.\\\HIS jHI.).U .1111 ＧＺ＾ｾ＠ ｬｩｾｬｬＺ｜｜＠ 1.1;.1

Sll\S.n;,:o ＧｩＱｾＱｾＨＩ［ＢｬＮＩｊ＠ .. (q ＮＱｕ［ＢｉｾｴｗｾＮＺｏ＠ .. 1.1!}} ｰ［Ｍ［ｾｲｱ＠ . ,,

ｰＮｾｾｾｾＢｬ＠ ｾｱ＠ t)l W.'l!Jlllli ｬｾｬ｜ｬｴｊｬｾＮ｜｜＠ ＩＮｾｾｰ＠ p;':>\!q ｐﾷＢｾＮＡ＠ ·q

Ｌｴｾ＠ ....,..__

• --- ·.::::;::;1 ' ) ＮＭＭＭＺＺＮｾｾｾ＠ .. -----" .

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1.1;p ［ＭＮｾ［ＭＮＱｕｷＮＺＮ＾ＮＺｯ＠ llll 1<1.1:-t ·e

ＮｾＮＺＭＭＡｾｾｾ＠ .. \(p;(13(, ｾ､ｾｨｬＣ＠ ｾＢﾷＢｾＮｈｕＮ＠ ·n ·o

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ｾ＿ＺＧＺ＠ Ｎｾﾥｾﾷ＠ ＮｾＮＺ［ﾷＬ＠ l•>:: ［ｾ＠ .. ｾ［＠ .:>:s ＺｾｴＺ＠ ;::

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