Page 1 Admission Tech বাংলাদেশ কৃষি...

1 Admission Tech

<n�� 1C"i-t 1_S� M�f.cf"'TJ ,�� .p;qf3i��

I � 91;f) "'ifl: =>�-::> 9.; �- '<1S _

01 . <£l� � � -s �'5 «>fF�""'f �� I <.QiC� 2 °/o <£l<f� 3 '1/c, � �"C<5'f1 I � 'S � '<"I�� 'c� Sf I t.{I c.q, � �<Of ��i'B'��?® 4�"o ® 6°/<, © 8°/c. @ 12'1/o

et¾fl C 14iAffvij Ei- -= � mv2

. /\.Ek __ L\rn ., 2 Av .. 2 + -, x _3_ 8 . . Ei.. na .. v I 00 - I 00 I 00

02. A, ii <£l�'- c � �-nu <£)� � �'6-unr � ra�rrr.:�""

@ A.(B x C) @ /�.l3.Ci!'A/4i A f»«.el A. B <£1�� C h;-.ef.u

� X.(r� x C) · o1

03. s ,...,. 3 t 3 + 3t 5l.dll-:l_>ilC's¥

� <£l"'?f C<f'S'f � <.!I� �?@9 @ 15

i§/41 C 11t9,;e1 v � :;t ( S)

.·. �\ (s) = t2 + 3 -� (��+

04. <£l� <1'>9Tif "Q,� F =

@4J @ 16J

- > ->F. r

661C�; 4s

@26

/,

r"2.:: ' . .,,.\

OS. ::::!:::,.�1.>(Tr"lk..,_.._ 7 x 10 7 m I

_!t.{'"'""'i� @ 6 .02 � ® I 1 .6 x I 0·'1ns 1

© 15.8x 10",ns 1 <1.:D 19.52x IO"'n,s 1

WciZ8.i EW!Li.{,a :::I � Ve a- - / 2 Cl: M E,ij,.� A r:pv'l'V:YJ �,�� •

. "-.j ..._ � � I 2 X 6.67 :x IO 1 I X I .9 X ! or, -- 6.02 X I o·'rns I "-J 7x 107

06. <.!I�� C..,..i.i1:t..•-, <£l�'.. 2 x 10 1 1 N m··2 -'!tv'- �Cf""t"q; r<!lfwf'2--�=<11C"=>� "=>IC-SBl �"-.,f:r lm � � I mm :e:t>tlR!_"=> �=i:l�

�<5��31��7 ® IOJ ® I03J

�°"�J @) I 0 7 J

� ... � tWNet -r�<!>I� = � Y�/.!

I 2 x IO 1 1 x 1 x ( I :x 1 0 3)2

2 �-------�-----� -� I os J

1 Admission Tech

1 Admission Tech

07. �' �9'1 600�911ft"�.31"1-1S� ,� I· 12. 1/1� � �'1 lfOOf �of'll'J '<3 �� Cl;'lt�

_!_2J)OJ "I �'1 <m �<It_ '5191..._� �'1 � � 'll� O.Sm 1/l<lt. 0.05m I�� ,

I '5T"I � '5T"flftil!1 �? �� l!ll C'lftil! � � � �?® i50K- @273K ©300K ©330K ®0.21rn @0.27m ©0.54m @l.OOm

llf A Ed .Qi�= Ii,.., f!!?Jf]l)ivel L � fo + D x r,. o.s + 4 x 0.05

�--...J--�Qz T2 � --'----- D+fc 4 �0.05 '(' � _Ii.Qi_ 600 X 300 _ = (0.5 ·l 0.04) "' 0.54 nl

.... ,, « l, . . Ti·· 01 - 1200

- ISO K 13.� 'lit� �W<l> � 1.08 IQ<I� �-) 08. 10-6C l!l<lt_ 2 x 10·6c � � 'lll'tlfA � � �.!1'<1<111.005 � Jt )l'flfITT i!oTtCi'ftil C<I� ""5?

� 10cm "{Cl!� 1 'lll'tlfA � �ttll'I� .� ® 0.88 x 103ms·: @2.08 x 108ms 1

��-�'-�"fU�? ©2.88 x I08ms 1 ©3.25 x 108ms 1

&e.-

®4.14cm @4.86cm RJ oflitve!© 6.21cm © 8.32cm ��

= _c<1_c<>=IC_"l

=P-=-=

ll=

c",;:"='�

RI A ilMi C, "):l) 'l!t� IO cm =(3 0

10'}--�.A-__ \2 X 10.. �'lf nJ'\11irrdl'lf

Q1 '-y--) '-y--)ql X 10-X

,,,.,,.,, E - I I 0-6 ,,,..,,. E .. I 2 X !0"6

"'"'"'· ·1 ----,-- "'"'' ·2 ·---� · 4ne0 x· 4nec(IO-x) �. E 1 - E2 = 0 :. E 1 = E2

�'lf!t.-1-�=-'-�4ne0 x 4ne0 (10-x)"

::::) .; = � ::::) l = __ji_ x· (10-x) x 10-x

:. x = 4.14cm 09. 200 mt� Ill� �Jl61'151Ciilfii'rilt.1BI�;,,:t1::ii�i:uj�"

® 1.11 n

i©2.s2 n .'2

�t:/. �

I= =-S-xl ;

, u · ).

6 S 10 S � 20 ::::) I �� 9S = 2 S = 2.22 Q

IO. d � �

IO""C °''"' 9.11 , 11T''kg

t�� r��1/�mff�)l'f-i ? ..,....

®9.23 x 10·2'Am2 @9.23 x 10 22 Arn1

\ ©9.23 X 10·20Am2 @9.23��10"16Arn2

•--r---_.. I •• 0"J'/4:R A fl)ltH � � µ = C; / t>' � : 4mn

;,._I') ._ l.6x I0'19x6.3x 10:14 _,8 81 ,024A 2I 'I . X, nt o 4x3.1416x9.11x!O' ' 11. 400 � <ll<li1t � � � tl"l115 8mH l!l<ft

•� 5 X 10..JA � l�"ll'Clf)' ��"1ml<t�m1@10 5Wb @10 7Wb ©10 9Wb @10 11 Wb

Bl B ,-.,1 E = ��q> :. dq> "' �I

= 8 X 10 3 X 5 X IO 3 = 10 7 Wb400

®� 4

@-:;-.) .)

RI D tloifel Ill�, w�I� � �. ,µg -�. gµ, "% <1l!flrn1 m, wflg X gµ, X ,!lw = I

9 2 . l 4 ::::) 8 X

J X ,µ, = ::::) 1Jlw = J

17.� Cl'fC"! �'-� �t. � "lm't'l � 5.5 x1011 kWh I�� 15ml �'llt<t <1>'5?®12 kg @20kg ©22kg @25kg

� C flofve! E - mci .� 5.5 x I 011 x I 03 x 3600. m = 5.5 x I 0 14 x 3600 � 22k . .

(3 X 108)2 g 18. � '519f'lffilll � '<3 ll>Uli\4J�{; � \!1<15'� �"�.

ml � <15'i!Prtll?®-40° • @-30° ©-20° @ IO°

� A � f _ F - 32 . � = X 32�--IW-...J�l:J· m::;:.=, 5 9 .. S 9 ::::) (9x-5x) =-160 :. x =- 40°

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1 Admission Tech

19.�� J,jl,i�iGICiHI et= 0.98 Ill�� Ir.= 1.SmA � 18 26.2NHJ + 3Cu0 � N2 + 3Cu + 3H:O f&lmf NIIJ

® 30µA . @ 40�tA © 50µA

!l?ij A l!IWel a " !( - - · If

@60µA

lc '·(0.98 X l.5 X 10 3)� 1.47 X 10 'A.!.-c.;. 18 =(IE -le)= 1.5 x 10 3- 1.47 x I0"3

'"" 3 x IO -S " 30µA • � lffull-fflll<! �7

� [\1L 1T 1 ] @[ML2T 1)� (Mt.'"r2 · @ (ML3T3]

��<rot? @ Catalyst ® Oxidizing agent © Reducing agent @ Substituting agent _...,._.,,,..,....,.. -3 0 f!Pil C lfplvtj2Nll3 , 2Cu0 -> N2 � 3Cu t 3Hz() �wt��<! -lt�-3 C� � C"ml O � I � ��'Pit� � Core>� � NI !3 mmr:; <l1 Reducing agent

27. <!l'll! filttll � so � � etr<ll'tol �<>rtf.r� "ilt>tf.it<>ll � �?® 5 ppb @ 5cf.i,�b © l 00 ppb @ 500 ·

� = � X ��<!='Sil X �·I X �'I IP1l s]liwef I ppb � I µgL" 1;:i.4i\ (WJ "' fMLT 2] x [L]: [ML2T 2J I 28. HCI '(J NaOH � IS

l!"lro · 7

:1.�� 1% '1% ?l!i11 WI, I A.fii�� 61 � � �'5 �� ll �? I © ��;ffe. - ""®,nos $)440s ©450s @460s N.ll: � l!lf-rs '(J , . � RN� ftljAfliiveJl!l��l% qf��llifl:t� �--ill �coJ (Wi<.'-� .l32 �6 � !wi ! 29. C<fi!'I l!T"�

::. ·{it �ll � ll� .128Hz •.!Flt 3841-!z I @ Pb , 'llm1 IITT'117

� �Wl:f ®il:tt'it>1'Jil �"'IT-:5 � ��?

@1:3

-t5.7°C � y Ill� m�1.3© 1.66

©3:1 @9:1

_...._ __ 1v · · ·· � fs/ =(/vJ '0 79= �d'':f) . .:,.:� .. 1�1.35=> · ef

=:�

1

/n (0.5) ��- -ll� 'lfl� � �\!R� 1rR 0.1 mm � � �

��MP ,:, "ll'l<'fl�? @0.0001111 @O.OOlm ©0.0lrn @O.lm Ill 8 f&i!yej '5lf.m: 10 X 0.1 � '"� �Sf11 �=>T.!!�ISit<ti!�=0.001 rn 1

25. � 1fJl'l �'tll �S! ll� 25 ms-•, 30ms-1 <!l��35ms-1; '51m "lj_i! � �sf-�st "'57® 17.ms 1 @30ms 1©30.3ms 1 @90.3ms 1

B[cJl!fu1W='1c'!� c{ +c/

.,, '1(25)2 + (3�)z + (35), ., 30.3 ms I

©Ti • @Hg m-X: C 2 �<@.ITT! Kp "<l Kc lll"if "lfCIIJ ffl�

@KP.,, KcRT

i.!:=��K�c(�Jr!J,1')2 @Kp =· KcR

Ive Kp ,., K,(RT) \n 1!11/lr,I, /\n 2 I - I'-"!!!""'-''--'------:. Kp = K.,(RT)

I • \?fJTClflf.r!rt "!�<! Cffl !'jq'f �� <ffi � 7 ®� ;;1�Ql:i @�1fll Gl!i!T� ©� @�t

1?11�@ 2Nll3 � llg1l: -> NH,[Hg�l;I I NH,I

(� <:Sl�8C'.';>Of) � �m�� w4w:iaor �

32. C4iM! ��<fil pl I "lfli'! 5 cQfc<> � C� 7 �'t51 11' <!lil��l!ITT"?@2v-1 @20 �<! © 100 ti'l @200 �'I � C fflowel pH �� 5, [H.] - 10 spl 111-.r,; 7, I 11 • l � IO 7

10 5:. pH o.!!1Pl7�-Wf 9ITTi To7 == I 00 �'I

33. �R Clllf$ Fehling !;<ft<lll � � � �\?i�:�<f �7® RCI 11X @ (CH,)2CO © RCI 12CHO @ RCH20H el. C lfoJvcJ RCH2CII .; 2Cu(OH)i + NaOH -> RCH1COO a+ Cu20.,. 1120 ·

�co<1cf

34. ;;Iii �� lf � �r,i�� f<II �<! �"I ®nst �� 7®62kJ @72kJ ©�� @�� m�

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1 Admission Tech

35. O.SM HNOJ <.!l'll 'i!1J:!l �'1 C� I 00 mL 0.1 M HNOJ

a-�<t � � <l"5 ml.�� m?®20 @50 ©80 @90 f22j C iliiv� 1 v,"' S2 V2

_ V : I 00 x 0.1 .,, ?O I => I 0.5 - m,

:. ffl �cmR (100-20)-· 80 mL 36. � � q� '1f?i,rn1�i:1"1 � �r

® HCI + K2Cr201 @ H2SO, ·t K2Cr201

© H2CO,.,. K2Cr201 @ HNO; +- K2Cr201 mn; 37.��'1l'!l(?

44. 25°C '5'19fl!Ti4tll �� '1Wiil � � �?® 10 7 @ 10 14

© 107 @ 10"

IE! nf;lfte! 25°C 1?>1'�P.l [ 11'] <l (OH ] � 10·7 '<l 10 7

:. ft�� lif'JlOH J � 10 7 X JO 7

'-' 10 II

45.��'11'il��?@� @ �"Qlll '51"� '5l°"'$;��© C'l"fflTll � @ �'!!Tll ..,.�

e C l!ISlve! � �� M �: �.� (NaCl).�. �. '-'R'" i

46. � C411"5fJJ.C>I �t �� m-:ittz;>wn� �?@KMnO, @K2Cr201 @� @� 1 • .,© (COOHh @ Na2CO;

i © c�<>IT� �.; @� RJ A PJ �� Tm "!"ifq/" "'1''[?( a2C0,.

1

tp;j n 11,tt� �. H2C20,.2H20, Na2C204, K2Cr20, �t �<'i i) �t .,l.;�.:;6,,..,.-<!lf-!-S I l.!l�l?.'!T <!Jr.ii� ��-cm (-'Tr�� I

I 38. Cffl C11'1� ��<ml 7 ii) ,,c,:.'7-;t

® aOH @ NI 12-NH, I iii) �W-��

(0 Li/\1114 @IINO; riml); iv)�39.��ffl��ll"!.P!t1/Jt�? I .v) �- �::a7!1:'."tt

@UV @JR ©y-ray @X-rn) . � -?�"!T'�"f�

lrljcfiJvtl Clfl�'l!tl!JC��?

� -r,;w� @) � ,;-� �V I 10 -·380nm c. � @!sf.i

��-----·"''��s$m-��?

�-Rav__ @;,q-�� ®��t.; y-Ray ©'lf�ml � @'li�� i �A:

-i:pc-��!il �l!J y- � '15i!' 49. 250 mL :!!'W'I � � Na1COJ ��'5 �<!5'til '31

�?'>tt�I c-4fil I[·.· I � �,{ �?

I ® 1 s.25g ® 14.sog

40. �I'!·$��.,_..._,,,....,_,-== '1ffl� � © 13 25g @12.25g ,..,, /217)'::cv P;fi] C flotve! W · SMV ½ x 106 x 0.250

@· �/\ � ��..f'5! ©� �� 1 @�ct mn: :. W"' 13.25 g

41. c� ro�rtt � '<l l.!l� �"C'ITT �l!:t �� 7 @ I ICOOH @ HCHO © Cl !,CHO @ CH3COOH fJPll A llilvg HCOOI I l!l 15/llo"!ffl,!i_�ll>� (-CHO)�<I� d'� ( COOH) �� iS� � HCOOH 15/Jl,-'IN,��iS '<l <am� �'1 � I

42. 49g H2S04 500 mL �Cf� � �� ,111<11Rsfili: � m1

@0.5M @ I.OM © I.SM

MMisliil&.tl W ... SMV�� I 000

:. S- Wx 1000"' 49x !000� I OM

MV 98 x 500 .

@2.0M

43. � �f,iis '<l � � � �� 1l'R �7® -55.22 kJ1mol @-55.37 kJ/mol

I ©·-57.17 kJlmol @•-68.60 kJ/mol mrc;

so. ffl 'lll<fJCll '<m'l-�'1 �,mr �"t'ft-W � ��'I�? ®2 @3 ©4 @5 � D fletvel MnO, + :-c -) Mn2 ' , 40 2

51. � � ""m.� 'l!t'5t "!""IFMJl>I � �� lffi!?® � @ l"lmi!T © �"' @�

· !P1f C flify� Poaccac C'ffi.iml �ll T"'!f<'lTI'17�1[Rcf:�I

52. <T!��"lit �� ,rr» �?® Nymphaea nouchali ® Nymplu,.ta s1elfC1ta© Nym lwea ruhra @ Nymplwea pubes�em

, A : · e >$fl '"IT?ft'it (1\'.vmphaea pubescens).<'!f61 "fl� (/1,)wphaea rubr�I.� "fl� (Nymphaea no11chah) � �� <'fill-� �o>rei '5f.:m �'I I [R�f: �1>w.l

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sJ. cm � �r-i C1l � t<fTlfr-! mi I 60. � M'� � � 'l'!M � mm � t<r�C'fiR��mm�? I �m<>1��? �� @�C<il� @CO2 @NII; � �«-� @cef.: �l<11� I © c114 @ Oi m":

�jn.1>flilve! c�211� 'lllf!� -a-rn �. 61.��m.lJitr�'Pl��tH<li?-� (/_A,:_f.<11"1 ._��t ;)�� 'Ill w.< ..a� J ® Salmo11e/Ja @ Vibno � � c� <Ii@ I ,l)fi; /:!!� � • © A:otobacwr @ Bacillus

5-! .f'C,q,5 C1lST"-l �m �im, � 'ft? � C �hi] A:otobacter. l'seudo111011as. � � @� Ciostridium ��f-6 4Ji<Sd,firnl 'lri <l'rI � � ��<Ii!>� @C'Wl<'I �e1 � .;i� Clli<t � � � �"Ir! m, m?Jj C ljllye! "1fftct'6 � � � 0R <w-1 � �<1"51 � � I [Ref:'< c;.·n,w;�'il •IRcf:�I 62.��RI��?

5S , � ffil: � � � �"llffP! @ � �J:,.ltlllt>llil��?

I ©

�f� � �� ® �t� © ��ID,; @�� 63. � "'!""Jtffi''11, nra•"snt.m ,.,,,ctf>dm ..._,_,,....�9I B fl,tvel 'ifu �,rr,; Cmtl1Tt� �If! f4S � �? � � :ljfg �'!lTT.<! PRJ!� <f(.qf I � ��l<a @ �'1-l �� l':lf. <�8JJ(!i';r, � I iRcf: '1>11�l

me:

Sf>.�,� om�� R> q"fT �? .irns �'®� ti� � ��<> 'G� 9fi'�� ., @l<l>lt•l-i<>,� __,�.....,�,.....,.

,<f1 f�'& � ��"[,: © �� @�<R<:>l� 9f1!';, C"fi1i'1 �ii �i5 � //1'1f<l 91".;l�Cm ��- � � �iii�� "111-.f � , '1:'11-l· �. �- ,ui( '<�r.'-'! <!l �;��I� 1 "IJlml C""s>""ICil"'."'""'<-:,';!�:..-.,,,.,,C<>"J,11,a ::;r.-� � I �CiR>� � � � ii �"1 � t:l;Ji(.i:'<�"l�.JJ � I ;sj"� �C>t�m��·

�cnfv.;� liRd: !il>fl't) �� ?

�� I IKd :�l'if" ('t� �)) s · � �""ii � C<l �.r.ram ... =,.,.-:n,,:;«11m.:H' © )�:¢:) @ )¢:¢

� 'llilt C'5'i �ul � � m� l"l<::ol<1il �t•lll{I�-., � ��"RI � � @ � © �.911'5 3 : I I IRtf: ?.:T>•ra)

ffiii"fflivel �""Ill) �'"ii 65. CJl,ICl!ICl\lC>I C-<lSf'l C� 9fl'<l� 'l!t!I?

�lc,itil!Nl �) "i , " , . � � 111$':<1 @ � (� @mle4STf�"

� "'"�"'=" , ,

•• � ISWI I <!l�9 ©�t� @�� C� <W,Y •. 1 .. 0_, �� 1fRcf:�M-I ml� 1<.��l<i�B1>1 �� (.� C�"f.¢

S'- f,rms �� · � �� ? -.'l.f.u ;r"lfut l2l1!'� <l ..o� f� � 911{$!.'T <!rn ;;:.1 � ��, .. �,i Q \ ® <IJTCl/�,f'i �i R�'T!C� I .!)"i!J "11Rr-6 ?:!�� l!Jqt C<1J,1r.l11C'l!l� � �tlt<11C'31/,..,!'i-.

� @��"F!Fl)

tBaAfloJ\'el CQ �..., �fa.•!m! �'l. � � 66.��?�,.. �<rn!oflqt��<S�Si��'5ITTS @�m� @71t�� <>iit�� <J:'1t� �, CQ'llil- �t � 1 ©��T.!iQ?.tlllrn @�f�� me � : !Ref· "1(1",r.,;J 167. BCG � �r,, �c� � OOll �?

59. �(c�,�� 1!!� � Ni� t'-� �? , ® c"lffeie ® c�"1WT� R @ATP&ADP @PEP&ATP ©'Wlifl @ll'� ©fAD&ATP @ATP&NADPH, �� , . lltMl fitii_

. ,j - � �� "I/� � (A�vco11actenu111Gi"'"�I D 1�b'"I �t�<til � vi«1��1<= ,.._,..,..,.... ......._

t11berc11/osis) <!l� �� Cillfl 1 !Ref: �l>il'll l'<I� ��.,,I'<'�""' C� '1t'IH>"1 "{!l I <!l l!lilfJml ..............J 1120 � 02 f.i*5 �1 \'lqt NADP ��· m 68· �<m�Pf<l•i'! fi'r1t �"ft<l'll � o::�.,.,�fJ � �?

\iAOPH t 11·�� 1 I ®�� @<!r:.R'-'f!I

. . � . © � f.;.ro @iSR � 2AOP 1 2P1 1- 2 •ADP + 41120 "l.i;!ltif'iiit 2A fl'

"I a��

�� "ll'-IDl1'l!rn Mill � 1!0i 2NJ\l)P + 11 + 21-12 0 + 02 Mi!T<!lrol"I CO, >y<> � <>I�<!� 1

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1 Admission Tech

69. � � � t;� �"�If� f.1,6�7 @�� ®�� ©l!ii� @�'iTI! RAF&iiil��: • � '<l � �·w11�ct1fsis1 � �'1

w=l'<l ...,-� ll<lt'l <l>U! I

• ��t?II! �� ;ffe � CinI <!>till I (Ref: "'15!'•"1! 70.��.Jl��?

75. � <111:>1� ORI C�<ll l<l>T-1 � �

��<1'7® �lRI ® f�R'!!Tt'I ©� @?fJRf� R c IBJfye! "<� ,:-rn:"I � Q/T� � �i:•f•jCil .Jl�'t<'!I � Qf� f.ls;ij � "'iltQf 'iltQf �� Cf� 1.Jl�CQfl<lS��,i:;f�� 1.Jl� �� '<3 � <fWl � � I (Rel: �r.,)

76. !Av&...q = 60, IAI = 34, IBI = 27, IAvHI = 7 �IC!=�?@O @2 ©6 @7 fi!F�

77. x' ·- sx3 + 7x2 - 7x,:. 20 = 0 � ·� "I{"! I + 2i Ill<!'. I -2i��1.�1l'\�Wl'[email protected] @3,--! ©- I 4 Rtctl@e!�� •ii•!

0

@W<� ® �('It� ©�� @�� 78.�"P, = 6x01'J�

RJ 8 tlitel �� <11% 'ffe � ICill'l'f a�w m : <.!!� \llt:l'iil 'l!ll�� .w, 1

71.C-<fltil �� pH f.fn<f �?®�r!Jl"f!l ®� ©� @� RJ B d§tve! � � f.1� � pH fllmci'llll(Jtll��<Sf"��<m!

72.1lll��'gJ�� @<.!l�irtu"<ll rnR @mtl'f � ©"IR��

RI" flo1vel \ll<l>iG � �� <ll1lR'l1rnl61 <11 � .Jlfor

�,.,pt,; <Ii I ell 1 9f'if . I F) �<llf("I '<!Ill)

C"il: ?i6E � � ilfG'™"&J �"1<fl� ii ��l!Rcf:"il•l'•'ll

73.�t.C 'i �,n'll�? .@(Of� ®f� © � � @� 'ivl �j!lvcl �t. c� f.lg� f�� . , � "ill,� �i3rn 'IR?>l � I ,�<Pl � l� f.U'r5 � <ITli '<l \SA � m'!1 � llt'b-llf61C\!i � \ll<lt � � m'!1 f-RJ� 'Sfll1 � I � � �� <.!I'll '1'tl(Jtll �'C'CiSilltl! � � I (Ref: '>111!-'IJ

74. � � � � f.{:'r5 \lf 7@� @-m-� © � @� pJj A -� � <11 � � R8'f'5 �� .Jl<f. � �<l<!R? (� �. �llfll <11� '<l 9l1f.i .Jl"ilt �'jp!Tlf<f. � (.,l�C>lliSi,�>l

\ll�) "'11'1 <ll'C1I <l>

"-l�i

l

� 'i'!ifll, �. � <l I m•rt<nllt� I (Ref:�,

�2 1 6+x"" 18:::>8-i·y 12=>x -10 :. y""4 82.3x2 -4y+ 6x-S "'O �t��

�Wt? 2 3 3

@3 ®4 ©2

IPll::iiJIMJ 3x2 - 4y + 6x - 5 - 04 S , 4 S => x2 -3 y T 2x . 3 = 0 � x- � 2x - 3 y � 3

4 5 4 8 => x2 + 2x + I = 3 y -1 3 + I -=-> (x -'· I )2 -3 y"' 32 4 ,.. � .,,,,,,.,� 4=> (x + I) �-:; (y 1-2) :. '<iOfC,,.,zi"'' �'ill,-: �,•-:;-

) )

1 Admission Tech

1 Admission Tech

SJ. lfTt� )' =..[x'C9 I!)��? ii x >3 ® !xi:1:3 © lx,:s3 El B dlf eJ x2 •• 9 ?. 0 => lxl ?. J

lim c' - I S-l. -- = �'5?1..,. 0 X

�o

1?11 C fifiiij Ii rn e• -.l• _...-L...J_,._.._,,_,0 X

©I

@p:1<3

@2

_ lim e' ·, _, 0 x

[L' hospital applied]

� e0 -· I

'· � x = a(G - sin9), y = a(I - cosO) � � div= �7 (X 0 0 ®tan2 @co�

l'filnfl»vel clx 0 dS

· a acos

�� I · ·tsinO dO

.Ql �= asinO

©tane @cotO

I 2. Q 0 SIil? COS? ,�.Ql� - -

dx 2sin1 Q2

COSQ �-i -cotQ · dx a acosO

=>Q:o

_� I dx I -cos8 I

sin� 2

.<!l� ,� �-wi-11 � m>ttt��? @2m @'1nr © r'

e clfitv_;J V � -7t - y. -

�\'�'.fil--,j��

. I I '�:,,, ""�

,, ,, I @ ·2 tan x + c @ tan x © tan 2x @ Sin 2x i· c

m A dCJ.ve! f dx - J dx� · I 1- cos2x - 2cos2x

!19. I!)�� -ffl(&-ti·��.:�-�;;.i·�:;� .. � <!l�<ll'1°C�ll��? @ 1:2 @ 1:4 ©2:3 @3:1 m-c:

90. si11·1 x +sin·\=� )!);"r<T>11ctfii f.ls '1�7

@� @"\�f'f Sill X =- 2 >111 "),

:i IJ � C C<Jb1t<RI 1 rt;{ <!>'5 ? ®45°

@90°

a2 .,. b2 {. � ___ ah Ie 1\ABC-iicosC' �� 2a!J 2ah 2

.. C � cos 1 ½- 60°

... ... ... ... _. ... ... ... ... -) _,., •)

• 9.J.. 1\ .., i + 2 j - Jk '3 B = 3 i - j + 2k ?{1i'! ,H n '(l A - B 'I' �trnl.1! 'l!�i5l' C-<111<! q-;-57

® 30° ® 60° © 90° @ 120°.

E@flo1v11 i\ , 13 · 41 , J -k

A - U � -2, I· 3j 5k-8 · 3 + 5 0 :. co�o . r,7,

. r.;;. -:-:, rosO � ::-r.;;. r;.

�18\/38 vl8v38

::.? E) COS IO .'. 0 90°

93.1 �tm�1i��..,�7

@�:if @ G./ ",,

© a.b @ C-411� -rn

di A lllfii� ·; �m 'S"!il l; � ?'!." �RJC""�) -), ) .

= L2. = �. fi <1. ti! i:1 (it1

94. �� "1f�C<l>C�il � ��1@"lmt"lil @��"!ii ©� �"R @<:� ,rn Bc.llii•�-

�

1 Admission Tech

1 Admission Tech

95_ 1.c,,g:.a c4>c� 30° �ct ��"'1:;t-4>r.a=l 1.'<Msoit ,,s �cf �� I <.""""•-lP'"C61� �� -..:!S" 7 ® 1 :6 @ 1: 12 © 1: 18 @ l :24 . B¥i a IUNe1 � c-� 30° C<f;lct ��.._.,ti..,.,�

30° .. ��.,A, = 360n X 7'CT-

�� . A2 =-� .t:r2

ca:ic�. L.H.S. > R.H.S c:;:.:.c� �

1 12

97. �.., ?f'"':f.C� f.l1.:411'!'$<!> P '<3 2P ,..,,_�� ..,...,....,;c-n,r..,.. � � �� <1-,qc�:.a --n-��M,,.

® 30° ® 60°

&RMc�1

Shortcut.: �� C-<S'f<:i � 90° - 22.5° = 67.S G

@cos2x.

l l 00. y = a _ X �� Yn = <f>�? n 1 � n! n® (a - ·x)" 'SJ' (a - x)"( - 1) n! n! © -(-a----�x-)..-r @ ( a - - x)" ·

i!&fu A l&i&4a y1 � (- 1)-� � l -- -- (a- x) (a- x)- · l .2 1.2.3 3! Y2 = (a - x)" ' y, =-- (a -- �) (a - x)"' .. 1• n•

1 Admission Tech

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