atbematics (Written)
l!l<l 10% IBM <1>fu.>liirn <1J<1lll <1>c1,; 1 IBM,; l!l,; 01w1Ti<1 <1>P1iil* r<h .,.-«· ¢,!,?
Solve: P (L) = 95%; P (I)= 10% P (L n I) = P (L) x P(I)
f.!tcfu = P(L)-P(L) x P(I) P(L)
= 1-·P{I) = 1- .10=0.90=90% tacos-1 x)= sin(tan-1 2) l!lil ,fll)ilfil 1
Solve: tan(cos-1 x)=sin(tan-1 2)
( -1 ') • ( • -I 2 ) [f fi ]=> tan tan -
x - = sm sm Js rom 1g.
I..nl
I
2 1-x 2 4 2 2 2 , 5 .fs =>- x -=Ts => =
5 =>5-5x =4x =>9x =5 => x- =
9 => x = ±
Js Js x;t-- "lfl'lffl-lt :.x=-(Ans) 3 3
03. lil i'!"m l!l<!i 2ffC" 10 kg '(JlSw!il l!l<!ilu <I& "WI, .'.l!P' I m lil '@o,'i'!
. -oil1"1_fll411C<l I '@9111 ITTl:9111 ffl'l 30 kg wt W'! C1vlJ '() '()ts?'! f.lcfu I Solve: <:lll<lRI, 'Wfi'! 'l_il! .
Im
w R=-30 kg-wt
I
20 2x30 R=P+w =>30=10+w :::>w =20kg-wt =>-=-- =>f.=3m(Ans) I f.
6 ffi '() 4 9f,fit $11 C 6 mil l!llfi1t $, <fliW1i WI I lil $; <f.i'!1 "1ml cir,, ,i,m ? Solve:
Mat6) 6
(ii)l!lHfiTI'l'l'ffi =6 C
5 x4 C
2 =90
:. t'l!1U 'l'!'IJT °
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05. l<lC<l, f(x)=x 11'<!!1l'll'Rm'llN x=e 1
Solve: f(x) = x • ; f'(x) = dx
!. d ( x • !J
!. ! dx d =x' [.J..-+lnx- - -(u )=u (--+lnu.-x dx dx x dx u dx dr
(')1[d ,. ,vdu dv
lnx
x·.;-
x-2xlnx x4
!._2 1,-2 =>x 1 (1-lnx]=O:.x· =0
1 - ln x = 0 '®. 1 - 1 x = 0 => lnx =1= lne => x =e
!.) -d(f"(c)= x'·1· ) [I In-c],- +e• 2 -----l 1 ] =O+e'!. -d( x=eWI x' =0 dx e· e1 e e e
!.[ 3
(-
1)= e' x ll1 :. x = c Wi f(x) 1 (Showed) (i51'<!<11 "iR>l\!J fn RC!l <ll!ll W<: :
06. <!l<!iffl '51f @ iITTJ 16, @ Ji -!171 ..!Fl sll' I-ill!:: I Glf y '1R'rnI
Solve: 1S"fW5 = 2ae l!J, 2ae = 16 => 2a{F2)= 16 => a =4J2° .... (i)
' b2 b2 bl a a a
. e· =1+ 2 =>(F2f =1+
2 =>2=1+2
=>--L = 1 => x2 -y2 =32 (Ans.) 32 32
o- i\BC <!!<!$qi 1 Fl AB <!!<It AC l!J C'1'1l 4 q I A, B <!l<l C ri"l., m
W'1l '5W<iS <l 8, 8 <!l<! 16 kg-m qcf WI '8 'ifR>"i f.icfu 'if.<! I olve: !3C = J A82 + AC2 = J42 + 42 = 4-hm ·.:Cf A <l 8'1TC<!l'l1ll,fl!f.l A<l Bm<!l'l1lloj"ij,flll'!m
4./i !,s '.ff AB-;, z.TP- I AG..LGH<l BH..LGH I C ::: :: - . -AG= BH = x ('®)
,;=_: F(x+4)=16[:.CG..LGH] =>Fx+4F=l6 =>8+4F=l6 = : =: wt (Ans.) i..g-
:'\=) =>2x=8 =>x=4m <"" -- .<s- . .\8£i!<l AB 4m A 8<!!1l 1 x
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08. X ,!!<! ?fV:I' C<rl'1 <!>@ X = y2 ,!!<!t y = X - 2 'lffi f.;,fu <ll'<! I
Solve: (0, 1)
y2 = x . . . . (i)
. _1±.Ji+8.. y- 2
= 1±3 =2 -l 2 '
y2 = x ..... (i) y = x-2 ..... (ii) (i)'8 (ii)t y= y2 -2 :::>y2 -y-2=0 :. y=-1,2
(4,2)
y=x-2
(9, 0)
---y2=x
y=2 WI (i)l.!I, x=4 y=-IW!, (i).!! x=I iffe0l'm R'rnW!I
{t1: 2x2 4 . =-[1-0]=-sq.urut
3 3 4
=J(Fx-x+2ftx
(x +a).!!<! 21 7it°<ffi <J 729, 7290, <!l<lt 30375 WJ a <!l<! °lW1 f.:cf,J <ll'<! I
Solve: (x +a)"= x" +x"-1a + n(n -l) x"-2a1 + ....... +a" [N91 <s"i"il I )! 2!
"=729 (")· n-i =7290 (") (iii)·:::> n(n -l)x".=30375X .... I , X a .. , . II • 21 2 I . x
n(n 2
; n (729{': J = 30375
:::> n(729). = 7290 [·: x" = 729]
n 2 -n 5 :::>--=- n 2 6
=>6n 1 -6n =5n2
= 6
Ph sics Written)
10. cm300 m -:l<l'>1U?;f'IJ 500 m -:l<l'>1Uc;; 1 Mm <'1fT.71! -sm i'l' 'ffl' f.$ '5111f.1 • .,:.; ,m'<I C<m'f f.w=l."1 m?
Solve:. t"fil :. ucosat=500 . . . . . (i) -:l<! h=!gt 2
2
:. 300 - h = u sin at - ! gt 2 ::::, 300 = u sin at ... (ii)
2 .. . u sin at 300 3 _1 3 (11)-:-(1): --=-. -::::, 1ana =
-: ::::,a= tan - (Ans.)
ucosat :,00 :, 5
vom!s
h 300m
1 1. .,i<l'ffl 11'l 200 m _''l <'lfl'.<'l r,,.,(j 500 kg '>',f.; 1 20% '51"rnl -.: V ?
, mgb , ( 500x9.8x 2QO'\ Solve: P =-; 20% ':;;'l!i5lq"iUi 11=!00%-20%=80% = "'
t 60 J p• 16.33 16 33 :.:ii p 11=-=16.33kw ::::,0.8=--kw ::::, P =-'-kw =20.416kw P P 0.8
. 11P= mgb :::c,P= mgb =( 500x9.8x200)w =20 416w =20. 416kw(Ans.)
t 111 0.8x60 12. ff l l.4gcm-3 <.!i<1t'll'illi!l 0.8x!010Nm·2
2x l<f Nm-2 m?1Wm1
Solve: B = ddp => dV = dp V; V'= V -dV = V -dp V m constant. v 8 B
v
v(,-!) =
.975 gmcm = ll. grncm-
13. -:l<l'>1U -s <.!i<l'ffl ctfi'lRi•rn "frlfil m.m 1i'lfliif,tll 80 dB -:l<it 78 dB. ,!)zyrn 'lff.l!t?
Solve: Pvc=80dB; Prv=78dB Now, 80=l 0log 10 (1
1 :c) ::::,Ivc=l08Io
( 1rv J ::::, Irv = 107
· 3 Io +108 1 o = (101
· 8 + IO'V1
lo lo
P=l0log 10 dB = !Olog
10 Jo 1° dB =82.124dB
!.; <-:,J•.M <lJ<!m -:l<l'>1U 60 W GSL ef-ms -:l<l'>1U 13 W CFL ffi ffmJ vJ 1i Tk. 30 -:l<! Tk. 250 zj% Tk. 4 WI <.!ii!l 'llt d 4 ';2 .t :::f.- 'ut CFL mm m?
1, c: \foney required to rep lace the pre vious one = (250 -30)tk = 220 tk .:: ' .::.::o = {0.047)kw x t hour x 365 x 4 [Basically how much e nergy you will save, 60-13=4 .i
220 _; = = 3.206 hours . .! ,O(l.!-x365
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15. mt"il:"l' 'It 'l 42°<!!<1t mt m 'ltW '1 48" WI fl mt 'It 'l f.lcfu
1 1 Solve: µ = -- = 1 .494; ,µ ... = -- = 1.3456 '
1 sin 42° " sin 48°
fl mt 'It 0 WI, . 0 1 1 ,µw 0 . -1(1.3456) 64 20 CA )sm =-=--=- :::::;, =sm -- = . · ns.
· µ, • µ& • µ, 1.494 ,µw
16. ,!I 5 McV , b m ,!I "l W 'Jl?,i Cl!'WI C'il'l,1!8 «iit'l.ef.:<> .. c m 1 ii .a lTR 1.s T WI , t9fil 'Jl?ot <1oi f.l,rn 1 , <.!l<!t "ll
l.7xl0- 27Kgt I.6xI0-19C I
I [ 2 x 8 x I 0-1 3 l . Solve: EK =5xl06 xl.6xl0· 19J =>-mv 2 =8x!O-n:::::;, v = 27
ms I
2 l.7xW-
= 30.678x 106m/s: F = qvBsin 90° = (!.6x 10·19 x30.678x 106 x i.5)N = 7.3628x 10·12 N (Ans.) 17. <!! 3x!O.., m2 1!l<lt'5!"fllliJ!! 727'C 1f.!sffl"!'T<!'l?'5!
'lWl'?( 5.?x!O-s Wm"2 K""] Solve: E = oA T' ... ... (i) -K5.7x IO"'}x (3x 10_, }x(727 + 273)4 s-1 = 1.71 x 1·0-1 J IS (Ans.) lffil, T
2 fw,i.i1 :.E
2 =3E; E
2 =crAr; .. .. . (ii)
(ii)+( i)· = T24 :::::;, 3E = T24 =>T =l316.07K(Ans.) I E T4 E (IOOOK)4 l
S. ems f.l 2.3 eV •1 680 nm C"i"'lll f.lf-r s ill:(S'!l
mr"t'f"R? Solve: cj> = 2.3cV
E= he =(6.636x!0-34x3xl08 )
19
)ev =l.8297eV A. 680 x 10·9 1.6 x 10·19
cj>>E :..miif:i.J11(Ans.)
Chemist ritten
l.O g l!l ?if<l'l 25.0 mL 1.0 M HCI !i<!t'l <lllll 1 '1'l'lr<l5 ""'i.ffl<>f 2l"M 50.0 mL !i<l'l <'lltll 1 15?1 '<l 'It f.lcfu I Solve: 11rn, l:f1W<l <ll1ff M C03
MC0 3 +2HCl---tMq +Hp+C0
2
HCI + NaOI-1----t NaCl+ Hp I --C.-.. 25 _3
50 I _3 ""co =-[M="'1«1<>.,,'Sil); n11c1 =-3 x1=25x!O mole; nN,m1 =-3 x-=5x!O mole.. , ' M 10 ' 10 10 - - ....,:;, 2 -l -3 00 ( --i.,,2nMC0,+nN,ou = n
11c1 =>M+5xlO =25xl0 =>M=l Ans.)
-:-.fl::. n CaC0 3 (Ans.)
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20. 4.60p!Nll .n<I$ <!l<l'!ll 5<1'1 cw::il m 1 .illW(j <!) O.OIM .!) 10.0mL!i<l'l vrni 1 .!l 0.0 IM '51Jlf>ic'otE4 (mL) 5'!'1 C'il'l WI? (pl<, = 4.75]
S 6 K., 10 0 0 -4 ? olve: pH=4. : p =4.75: nacid =-1 x . I =lx!O mole: n,,11 =. IO
<ffii, <!!<l'l<l = V L: JTWR '<! eqn "l. K (Salt] - n v -O!S n pH= p '+ log-- => 4.6 = 4.7) + log-.!!L_ => 10 = :. n,,i, = 7.079x 10-smole
(acid] n V Ix 10·
Again, ns,i, = V5,i, xMs.:, => 7.079xl0- = v ... , x0.01 => V,.i, =7.079x!0-3 L = 7.079mL (ans.) 21. (a) CW.'1 ·•i'tJltt0,, e <::o ;;"ffffe .!l 'fil 'IT,li IWTil'l\'i: c<l5R
5<1'1 ? '1 :11mfu 5<1'1 ? '1 }lf!j'2 iir,m,r.«, '1 ,
Solve: (a) 5<1'1 FcCl 3 .!!Hr 5<1'1
B<l'1 = clll .!l<I$ '1!'!'1 Na -.m ™ a4i\:, <m -.m HC)'ITT!TI f.!fJRTT: NaCNS+ FcCl3 Fc(CNS)]Cl2 + NaCl
N "11<15<1'1 (b) 'I"!! ,!I'll'! <!l a- <!lP.t'-"ll "111 {J }l I -II '!lTil qji-;)Jl I
NH2 == I
..A.-. Solve: (b) ; ;,,,,_,,,.,: H - C - COOH '!Ii ,,,..,. 'I"!! <liBf'l <.'l"C\!i C<liT'! "'ffi.lWI ¢ 1
H 22. (a) t'1iS }ll!ln! c<IIITT <ill <ill€ <ill r . .,dJ,.,(E ? (<liWl f.liv f.i {J'ffi1l fu
Solve: (a)' (Pb) t"1<1>d;1e,1"®, H2SO 4 fo;511, 11"1'm: Pb02 (s)+Pb(s)+2H2S04 (aq) 2PbS04 (s)+2H20(1)
(b) 27°C"ilITT!rn<.'lffi 0.02molcbn-1 HO .!!llB<!'i<lllll 1f.lcrn
Solve:(b)i5!11l'1: _!_H2 -e·2W E\,11 =0V, n=l, T=300K 2
Ecca = E0 "11 - RT ln[W] = 0- &.3 !4 x 300
ln[0.02] = 0.JOI IV (Ans.)nF I x96500 _: r,;,j=
a) CaCO 3 i:<li HCI -£if-ws ffl ['51 B<!<l fir<!Wi'- 1' e: CaC01 +2HCl----tCaCl2 +Hp+C02 CaCl2, H20-t2i"f'll
C02l:f':rt - C . <q <!<" "l Kl '1 ffl Na 2S203:5<!'1 f.ml
t; :C::3), -4K.12K2S04 +Cu2I2 + I2
. - :,:!.:5=0, Na,S,0 6 + 2 al
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Na 2 C0
Solve: Na 2 C0
2
24. (a) 9f1f.@ o1?'!'!J m GTf.R "fNHll lTl'!l I Ill "l'<lC t.s ':.., "ll<l'!:T ? llPlf!lf.Rs fii',j1 Solve: (a) .ii 91'1-om <!i1lR -..t -.. 1 .l!l<>i-im1'Wl .. 11Pl-:"IITT 2NaBr+Cl
2 -->2NaCI + Br
(b) dsp2 , sp3d <!!<ft sp3d2 tim R-IWi R6?
Solve:(b) dsp2 <1; sp3d ·rrliHl ; sp3d2 25. (a) 'l!llfJ'C'I! Zn(Hg)i!l11 "llt .<flra(fum) llllfJ'C'I! c!?1di•-1i\C<t> 1<11rn r.<-,;'0., &
ll1'!11-ifl1'6">11 Solve:
I Solve:
HgCJi HC .. CH+HCI CH
2 =CIICl('lt)
150-200){: 26. (a) <li"ffil m !l<ft'l l'f"El \cf C1!1'1 'IW?
Solve: Zn CuSO 4 Cu "Am I Zn(s) + CuSO 4 (aq) ZnS0
4 (aq) + Cu(s) (b)·H2004 1!lil:<>rrnC<ll"i!?' Solve: 2PbS0
4(s)+2HP c1wg;ng >Pb0 2
-Pb+2H 2 S0
4
(s) (I) (s) (s) (aq) .ii C11 "f1R \ll<ft .ii 'iR H
2 S04
'll'm H 2 SO 4 .ii11 9flll I
(C) <f1tiI 1lNf 9fTf.rn <11""1 '1f?5 .l!l crnl i l!lll l!l ;r]lffil'12flrl'l 1il'G I Solve: 9fTf.rn 8 <lfP'l '['8 <IT'P9f "A .l!l'RF!!rn 'lt'l' lTR! 1 <lm <ITt""fll "tml"l "llt'll 'ITlll vt'"'f "l'R-ll 11 "lfu .2ira,;1rrn cm ii I
:1. (a) full.lllf<r'l -o 1w1w·· 'lli!"!j"i,cf 0t'1 , l!lv>RI 91'1<H!l 'l!Tll ,!Fl \ll!<fl RI m Solve: llll.lli\S ll1C!llt.1l'IS g g 8 02 *-8Ci11<1il
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2 C=CTI
2 -CH 2 -)0
"Im toml 'l!llfl"Cll ("Im iR!llrn I 80kg ( W"lmRI Solve:. 64grn CaC
2 28 grn
= gm =35xl0 3 grn =35kg (Ans.) 64
d!bMmittti\ Read the following passage and answer the question numbers 28-29 that on the basis of the information provided in the passage.: Galileo was born 1564 at Pisa Italy. He was the eldest of seven children. His father was a musician and a scholar. Galileo himself played the organ and the flute, but it was his contributions to science that made him famous. Al first young Galileo had a tutor at home in Pisa. Then he went to school in a monastery at Florence. His father later sent him to the University of Pisa to study medicine, but Galileo was more interested in mathematics and physics. He left Pisa without finishing medicine course. But in 1589 at the age of 25 he became a Professor of mathematics. In 1609 Galileo made a small telescope. When he tuned his telescope on the sky, he gradually discovered four moons circling the planet Jupiter, crater on the moon, spots on the sun and rings round Saturn. He also observed that the planet Venus has phases like the moon. This could only mean that Venus travels round the sun. Galileo became convinced that the Earth and all other planets orbit the sun. At that time the Christian church thought that any idea that the earth was not the centre of our universe went against the Bible. A book published by the astronomer Copernicus in 1543 setting out such a theory was officially banned by the church. Galileo's views on the subject and the books he wrote got him into serious troubles with the church. As the church was very powerful in those days, Galileo was forced to say publicly that he did not agree with the ideas of Copernicus in order to avoid torture and even death. Although he made this declaration, he neve,: changed his real belief. Galileo died in 1642 at the age of seventy seven.
28 . (a) Answer whether the following statements arc true or false. If false, provide the correct information. (i) Although Galileo was the son of a musician, science was of grater attraction for him than music. (ii) Copernicus was the first man to know that all the planets in our solar system move round the
sun (iii) According to ecclesiastical belief of Gal ileo's time the sun was the centre of our
universe. (iv) Galileo's father was an ordinary man having little education. (b) Fill in the gaps with correct form of verbs provided in the brackets. (a) Galileo __ (know) as the inventor of telescope. {b) Though his father wanted him to be a doctor, he __ (finish) his medical course. (c) He __ (choose) teaching as his profession. d) He knew that the Earth with other planets __ (move) round the sun. ! !1e __ (threaten) with torture and even death by the church.
: he: (a): (i) True (ii) True ?i.se Correct Ans.: The earth was the centre. : ' Co:-rect Ans.: His father was a scholar.
(ii) did not finish (iv) move (v) ws fhrIMPn
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29. Answer each of the following questions in one complete sentence. (a) How did Galileo contribute to science? (b) What did Galileo do with his telescope'! (c) Why did Galileo have trouble with the church? (d) What notion do you get about the church of Galileo's time? (c) What do you know about the schooling of Galileo? Solve: (a) Galileo invented telescope and observed planetary motions and underwent scientific experiments. (b) Galileo observed the planetary motions and discovered that actually sun was the centre of our solar system. (c} Galileo had trouble with church because his discoveries were against the words of Bible. (d) I think that the church of his time was of ill culture, they did not understand the meaning of there religion rather they gave wrong explanation. (e) Galileo had a tutor at home in Pisa, then went to a school in a monastery at Florence, later went to university of Pisa to study medicines.
30. (a) Fill in the blanks with correct form ofvcrbs: (i) I never thought I __ (sec) you again. (ii) He __ (do) everything he could to help me. (iii) Most of the earth's surface __ (cover) by water. (iv) I tried to pacify him but he went on __ (grumble). (v) The e-mail __ (send) a week ago. (b) Fill in the bl.anks with appropriate prepositions. (i) He has a reputation __ honesty. (ii) She said nothing __ reply. (iii) You must conform ___ the regulations. (iv) I shall look the matter. (v) We went to the airport to see ___ our uncle.
:\lath (MCQ)
f(x) = x2 -xi <!lt g(x) = x2 + I (fog )(2) .!Iii 'llR m- (a) 0 (b) 15 (c) 25 (d) 5
Solve:(b) (fog) (2} = f(g(2)); f (x) = x2 - xi
g(x)=x2 +I =52-21 =f(22 +l)=f(S) =25-10=15
x = .!. {-1+.J-J) <!lt y= .!.(-1-f-J) (1-x-y+xy) <!Iii 'llR m- 2 2
(a) 0 (b) I (c) 2 (d) 3 Solve:(d} x = .!.(-1 + f-3) = ro; y = .!.(-1- f-3)= ci
2 2
1-x-y+ xy = l-ro-ro2 +ro.ro2 = l-ro-ro2 +cil = 1-(ro+ci>2)+1[ro3 = 1] = l-{-l)+t[.· 1+w+ro2 =0] =l+l+l =3
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[Ans: would sec] [Ans: did] f Ans: is covered] [Ans: grumbling] (Ans: was sent]
[Ans: for] [Ans: in] [Ans: to] (Ans: into] [Ans: oil]
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03. k <!I 'llf.l W'! (k + !)x2 +2(k +3)x +2k + 3 l!l "l.<f-1,f WI?(a) 3,2 (b) 3,-2 (c) -3.2 (d) -3,-2Solve: ilffe!l'u 1.f<l<fwi (k+l)x2 +2(k+3)x+2k+3=0 "B mD = [2(k +3)]2-4(k + IX2k +3) 0 =4(k +3)2 -4(2kl + 2k+3k +3)=>0=4[(k2 +6k+9)-(2k2 +5k+3)] =>0= -k2 +k+6 =>k2 - k-6 =0 .=>(k-3Xk+2)=0 :. k =-2,3 04. k <!I t<1SR A= [k -3 - 2 ] $_.,..,,1f&'<<1 m 'll?-2 k-2
(a) 3 {b) 2 (c) s±J0 2 ad"(A) Solve: A -1 =--; A m'llwi !A!=O!Ai (d) 2
IAl=jk_-i3 k--221 0=(k-3Xk- 2) -(-2X-2) => 0= k2 -3k-2k+6 -4 =>0=k2 -5k+2 =>k= 5± = S± = 5±.Ju2 2 2 05. A Jx3<!Fl IA!=-7 j(2AJ-'[.!iiPll'lWl-
(a) - (b) - (c) _! 14 56 7Solve: A is a 3 x 3 matrix
So Let A = [ r] ; 2A = rn }! Ir l IA[ = , f I= -7 We know, IA-1 1 = !I
[Prove yourself] 1
[ 2a 2b 2c
] Now, 1(2A) 1 1 = - I( \I l(2A) = 2d 2e 2f 2A11 ' 2g 2h 2i
2(d) --7
=2x2x21 rl[c: =1 J[c>2 ][c>i] = 23(-7) =-56 :.1(2Af'l= l(Z(-516 Shortcut: n A wlJ l(mA = m"JA[ : 8() I'& W:l <!l<llfG offi'Wl <!l m- CW3 "!ml? 2) -! (b) 8! (c) 7.!. (d) !
2 2
- ; "'--- C...t.. 7! Sehe: -:;o.R!10ul'1«JM =(8-1)!=7!; <ll'Sft'4J'f<l'is4w10f :.1•1r.01m-.,R"/Jl =-2 - • . - : '. - ! : l - .......... 100 'i5l'I ?f'l W C<ll WI fb) IO(lo100_1)_ IOO (c) .!.Q(10100_1)_ 100 (d) .!.Q(i0100_1)-ioI 9 9 9 9
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0 = 9 + 99 + 999 + ..... up ton
=> 9S 0 = (10-1 )+ (102 -1)+(103 -1)+ ... up ton
::>9S 0 ={10+ 102 + 103 + ... + 10• )-(I +1+ 1+ ... up ton)
10° -1 ·,.· -1 1-r" ::>9S 0 = l0---nftr!m S =a--;r>l=a--;r<I]
10-1 " r-1 l-r
=> 9S = IO (10• -1)- n => S = 10(10• -1)-n 9 n 81 9 . , l O ( 100 ) 100 .. 100"fli"flf"C1JI n=lOO :.S
100 =-10 -1 --
81 9 08 . x <!Ill "l!1m '5RJ (!,-xi (1, x) <!l<I (x2 ,-1) <!I Cll"<lrn ?
(a) -1, 0, I (b) 2, 3, 4 (c) -3, 2, 3 (d) -4, 3, 4 Solve: <!I 'lil<'!Cil*-1 .
l l -/ L o
Or I - x = 0 => x = I
=>l-x2 x+l 0=0[r;=r1 -r2 ,r1 2=r2 -r3] x=-1,0,1
0 -2x 0 1
x 2
-1 I
09. x2 +y2 +2x+c=0 <!l<I x2 +y2 +2y+c=orern""'!"f c<!lil1f!,I-
(a) 0 {c) I
Solve: x2+y2+2x+c=O; c 1 (-l,O ); r,=
x2+ y2+2y+c=O; c2 ( 0,-I); r2 =
c,c2 = J(-1-of+(o+1f =ful=-n
(d) 2
2 =r.+r
2 =>.J2= Jl-c+ =>.f2=2Jl-c
=>.J2=2·JI-c =>2=4(1-c) =:>..!..=1-C=>c=l- = 2 2 2
Note: <!I if 'fllR <f!"'IVlT 'lll""rooM ,rn [ Iii W"1 <fiilJ ' iffef y= x1"' WI ;(!)m-
(a) 2lnx (b) l(21nx}x x Solve: y = x'"' dy = x'"'[lnx .l+tnx..!.Jdx x x
[-: ! (uv )=uv
=xm•r ln
x l
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(a)_! (b) c (c) ! c c
(d) -e
(lnx) 2
=rln x x)ll; f"(x)= x
(lnx)4 x
For ma x imum or minimum f'(x)=O :. lnx -,I =0 =>ln x -1 =0 =>lnx =l=lnc =>x=c (In x)"
12(!-0)-0-1{2. !) f"(x)l!l x=c W'I f"(c)= e ( c -!>o :. x=c w,m
1 c 12. 12 m !'l'i1 l!l7l5iu ¥1J 1'ftG'i! llllll 9 kg 1 , 5.25 m 1ffei 1!17l5iu ifu'i!
WC<l"i'!ITTlm- (a) 65kg (b) 6lkg (c) 63kg (d) 47.25 kg Solve: ______ iz_m ___ _
.75m 5.25m
:.-=- =>W=63kg 0.75 5.25
1 3 . l!l7l5iu 8 km b- 1 Ci!C'l I '1Tfi C 16 km h "1 Ci!C'l I!! <!"' Cffi m "! C<U'R 'lllt '!1ITT51t<f ? (a) 120' (b) 150' Solve: ,d Scenario- 1 <fv'"I
(c) 135"
u 16
(d) 90"
14. 1!13cmllmlC<l'11¥11W'I ? (a) O.Scm (b) l.Ocm (c) !.5cm Solve: <fiRli .. t"l"f111J '1 Short 1
- f=<IJq"f
(d) 2 .0cm
•. • (i); BC twt FS=.!_m() 2
• • • (ii) 2 2"\2 2"\2
=1-(i)
U 2_U
AC u
_ - 1 s(n-1)2 . . T::, -<:it'"IC<l'1'$WI x x=--[forobJCCt1veJ n (2n -!) ·
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lP)'I iorn fllnr l!l<fi!u l!l<ll 9 kg i5ffi .!) 6 kg om s "l"Cil I "fllffil'f 'f -(a) l.662ms-2
( c) 1.862ms-2 Solve: ,fllffil'l 'I F=9-6x9.819+6 = l.962m/s2
,r
6kg 9kg
(b) l.762ms-2
(d) 1.962ms-2
16. ax+y+l=O, x+ y+a=O x+ay+l=O R a l!liPlR-(a) 1,-2 (b) -1,2 (c) 1, 2 (d) -1,-2 Solve: -.slilrn "WI 1 } !I= 0 :=> la O 1 1 a1 a 1 I- a a-I
211 0 II c c =>(a-I) 0 -1 a =0 re;=-( I )' c =-( 2 )] -I I 1 a-1 a-I ==> {a-lY[l(-1-a)-o+ 1(0-1)]= 0 [r1 f.rnl] :=> (a -1)2 [-1-a-0-1] =0 (a-1)2 {-a- 2 )= 0 :. a-1=0:=>a=I; -a-2 =0:=>a=-2 :.a=l,-2 17. 1!1<15 1 2 'Sr'l<l'f -irctiJ 8 ,AA 7 wim'1 9f!Wl-irc"IJ 5?(a) 360 (b) 390 (c) 336 (d) 480Solve: =8 :."fliffi!il<!1j=l 2-8=4 :."f!ifC<lil =8c x4c =336
, l
I (c) - .Ji
(d) ../32 Solve: sin[ cos-1(-i)+ tan-1( )] = sin[120° + 30°] =sinl50° = i Shortcut : Use Calculator
3. [x y][ :J[:Jl!l9'1TF! (a) [x2a+xyh xyh+y2b] (b) [x2a+2xyh+y2b] (c) [x2a+xyh] (d) [ 2x2a+xyh+2 y2b]xyh+y2b Solve: [x y][ : ][:] = [ax+hy hx +by][; J = [ax2 + hxy + hxy + by2 ] = [x2a + 2xyh + y2b J Shortcut: a, b, h, x, y 1!19 'lTF! m m calculator -!! calculate 1
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20. <!! f.R;u 'to <( <( ff<!1 ffl I '1 "flif""'fm 1 A l!lq B ffl, A '<1<11 B '-'111 :!!Gl ? (a) 0.50 (b) 0.72 (c) 0.91 (d) 0.93 Solve: Herc the events arc iudcpcndcnt :. P(A) = 0.7; P(B) = 0.7 P(AuB) = P(A) + P(B)-P(AnB) = P(A) + P(B)-P(A)P(B) = 0.7 +0.7-0.7x0.7 = 0.91
21. a '-'111 'IITC'!il (1 +axf l!lil R•·,·.-1. x i £ x' .!il '! 'i1!1<l ? s (a) -4
Solve: T,. 1 =8c 18.'(ax)' r
(c) s
(d) 16
8! 8! =>-=-a [a"#Omfilfuf.i;iij 3!5! 4!4!
I a x'<!!i11fl<.'1 =Sc a3 --= l 3!(5}4! 4(3!}4!
4 .. 8 4 4 x <!111·, = Ca =>a=- 4 5
22. tanx + tan2x +tan3x = tanx tan2x tan3x'1 x <!111 l!R m-
(a) mt 12 (b) mt
4 (c) nn 3 (d) mt
5
Solve: tanx +tan2x +tan3x = tanx tan2x tan3x => tanx +tan2x =-tan3x(l-tanx tan2x) tanx+tan2x ru: => -tan3x => tan3x =-tan3,c => 2 tan3x =0 => tan3x = 0 => 3x = rm: => x = -
1-tanx tan2x 3 Shortcut: Use Calculator
23. C<lSR "l"il <!I raF!IT' C<l<I 11 7ms-1 ,Sms- 1 <!1q 13ms·1 't.::i::. C<l"1'm!il C<li!'l m- ( a) 30° (b) 60° (c) 45° (d) 900 Solve:<!1$ 7m/se 8m/s<!l!lWf 13m/s<!!!l,fl!Ref.l :.(13)2=(7t+{8}7 +2.7.8coso. [1fl]l 7m/
;r(., 13m/s.
lf-72-82 I . => cos a = a,; a 2x7x8 2 13m/s
=> a = 600 8m/s 24.* 36kg'5r.ffil <!lt'>filFli"ITTflll'l<lofll <!1<!5 '-'l11C<l<I 'il 15km "ffe<I?
(a) 4 N (b) 6 N (c) 2.S N (d) 1.6 N 15x10J
Solve: 6V=15km/hr =--mis =4.1667m/s :.6t=60sec 3600
F=rm =ml\v·= 36x4.1667 =Z.5N
' -
26_ Jex (l+sinx)dx<!!il"l!R-1 + cosx
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(a) ex cos(i)+c (b) e' sin (%}-c (c) e• tan(f )+c (d) e' coi(i)+c
;
1 + cos x 2cos2 2 2 .-Po x . , ( ) 2 x 1 q1, f(x)=tan- .. f x =sec-.-2 2 2 :. I= J e'[f'(x)+ f(x)]dx = c'f(x) +c [·: J e'[f(x) + f'(x)]dx = e'f(x)+ c] = ex ( tani)+ c
27. tan-I . <!Jil$J-(cos x -sin x) COSX +sm x (a) I (b) -I
1 (c) -2 (d) 2 _1(cosx-sinx) -i[ ::: <!:] _1(1-tanx) Solve: y = tan . = tan . = tan --cos x + sm x cosx + smx l+tanx
cosx cos x
[ tan-tanx J ( ) =tan -1 4 rt =tan- 1 tan -x =-x :. dy =-Il+tan-tanx dx
:S elC"l'l'iJ166WJl"IFll,fSlllt? (a) 33 (b) 11 (c) 24 (d) 12 Solve: ,fSlll n wl ,i"'iJI "C
2 '.:'l'llcili,"C 2 =66 => n(n-l)=66 =>n2-n =l32 =>n2 -n-132=0
2 :.n=l±.Ji+s28 =1±23 =12,-11 :.n=l2·: n :;c-ll 2 2 y2 = 9x t P C<!>tfu 12 WI <!I t Wl-2) 9.50 (b) 18.25 (c) IO.SO (d) 20.25
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Solve: m, SP = PM = x + a
Ill, y2 =9x => y 2 ={{)x :.a =(y2 =4ax l!lil <mi I]
144 Ill, p y=l2 .'.}2 2=9x =>X=-=16 9
:.SP=x+a =16 +2 =18.2 5 4
30. y=px 2 +qx.""2 . 2x 2y'-xy'-
(a) 2y (b) 0 (c) Y (d) 2y2
( 3 2) ( 1 ...!.) 3 _.!. 1 _.!. 2x2y"-xy' =2x2 2p+
4 qx 2 -x 2px-
2 qx 2 =4px2 +
2 qx 2 -2px2 +
=2px2+2 qx-i ={px2 +qx-i)=2y
3 1. A= 8i-1-3klll<lt B= 3i+4]-sk. '5TWI s isorn X "Im
(a) 3M (b) (c) (d) 35'/2 IO IM lM IO
Solve: B lllit <rn A lllit "f =AcosO = A.B = (8)(3)+(4)(-1)+(-3)(-5) 3 5 35.fi.
181 3 2+4 2 +(-5)2 =
5.fi. =
10
(b) ±I
Solve: 3 scc4 0+8 = 10 scc2 0 => 3x2 +8 -lOx =0 [ x =sec2 Oimi]
=>X= IO±.Jioo:96 =10±2=2i
6 6 '3
(d)±1,±1
scc2 0=2 -==>l+tan2 0=2 -::>tan0=±1; scc2 0= -::>l +tan2 0=i-::>tan0=± 3 3 v3
33. 'illMIPl""'l"ffi<f 2x-4y-9=0 lll<lt 6x-12y+7=011?
(a) fi (b) 17 () 17
(d) ...!2._ 5 3.Js
Solve: "'1"M>•mll = 2R
: 2x-4y-9=0 ... (i); 6x-12y+7=0 -::>2x-4y+2=o ... (ii) 3
I 7 34
,_=-(-4)2 2.Js 6.J5
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34. <!l<!ifu "Jl (-1,3) <!l<l (4,-2)f?ml C'>W-i 1f1iil 'll m r·w ?'I:" D-(a) 2J5 (b) 3,12 . . (c) 2 4 2 _ (d) :, 1 _:_: Solve: .:+ 2'. = 1; (-1,3)-)-=I + i =l ... (1), ( 4,-2)-)----- l ... (u)2 -b ab a b ab 2 Solving (i) and (ii ) b a=2, b=2 ·. =·h2 + 22 =2.Ji \!11<! mm 911'-' WI (a)'2Ji:3 (b)3J2:2 (c)2:JF3 (d)2h:4Solve: From the fig. ( p ) = _Q_ = Q/3 :. _Q = ...JL. ::::;, sin a=!sin a-90° sin90° sina I 3sina 3
. ')2 - l 2.Ji Agam, cosa=-I-l3J [a<r =-3 <!l">R, P "Rf .. r P + Q cos a = 0 ::::;,cosa=-!_ ::::;,- 2.Ji =- ::::;,P:Q=2h:3
Q 3 Q _;6. 200 m <!l<i 300 111 @1 <!l<llfu rz•,.; cm <!l C!fo'!"R <1 40 km 11· 1 l!l<i 30kmh-10C"l <lPl!'<ffil I <Ti'1J "lm <!l'ill "1 ?(a) 2 minutes (b) 3 minutes (c) 4 minutes Solve: '!! (<tf<ITT m 40km I h <!lil 1 t z.rni [ t hour -!!<ml] 40t = 30t + 0.2 + 0.3 ::::;, t = 0.05 hour ::::;, t = 3 min utcs(Ans.)
(d) 3.5 minutes .2km c=J--- v=40km/h u=30kwJh.3km -!!<fill <ll'ffi! @"ill F = (si -6] + 3k)N ¥! -211m"l <!i'f!W<l d = (31 + dy] + 5k)m Jfll'1 1 dy <!l'll 'l!V; <I"-' W'! "1ffi1'1 "['U WI? (a)O (b)5 (c)6 (d) -6 Solve: W =F.d ::>0=5.3+(-6}dY +3.5 ::>0=15 -6dY +15 ::::;,6dY =30 ::::;,dY =5 -2i"<!i!P'fli> <!l m x(t)=16t-3t3CllIR ,JmJ t c,rc-<m 1 1Wli Tc<' <I t <!lil 'lfR-(a) 0.75s (b) l.30s (c) 5.30s (d) 7.30s Solve: x=l6t-3t3 ::::;,v=l6-9t2[v= ;]
,:;.,.,, 2 /16 Now, 1ll v=O :.16-9t =0 ::::;,t=f9 =l.3333seco::1.30sec CITT' -!l<!ifu "W!<!i '$ <!l ff 7l""'iC<li C<l'<'T1 I "I '1 WI- [Ans: b] (a) ?it <i Cffil wrr (b) h <!00 ,fl'!J,-l (c) h <!00 m'1! (d) 98ms·2 Solve: <ff["fU 'i<I "i1r m '1 ;p;rr,, 1
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40. I OOOkgmil <!l<!iW 'ii(ll,1<$11.ler C<lc<1 c>T%i1 "it'4 Gi&Sl-t 1 <l<l<! I 800N. l&Cl\,liSTlICG\il ;s9f"il -21Wl- (a) ON (b) l 1800N (c) 1800N (d) 9800N Solve: (a);!q<JP0<l<'l IF=O
41. 16 kg \5m1 <!l<!ifu f0 "iil 4 s <m"tt 8 N «1 1 C<lc<lil o;Ri,rs:i'-1 m-
(a) O.Sms·1 (b) 2.0rns·1 (c) 4.0ms" 1 (d) 8.0ms· 1
,W Fi'>t 8x4 Solve:(b); F=ma =>F=rn- =nV=-=>i'>V=-=2m/s nr m 16
42. ('ITT i'*-t''· 800 (;<>'. .c "I 200 N 1
'1-;mrn - (a) 0.25 (b) 0.125 (c) 0.50
F 200 Solve: (a); FK = 200N; R = 800N ; i = i = - = 0.25 R 800
(d) 4.00
43. "I 'lTCWl <!l<!IW <!l l 5.2xl0"11m<!Wllt <!l<!IW "':t 2.18xl06m s·1rn<1mcrm 1 9.lxl0-11kgm? [Ans: BJ (a) 3.8lx]0-6 N (b) 8.32xl0"8N (c) 2.17x10...:7N (d) l.2Sxl026N
m _ 9.lx10"31
31 Solve: m=--0-[·:v,c<!l"il1-t·w) = =9.10024x10- kg 1_ (2.18x106 }2 f-2"
(3x108}2
F = mV2
) 2
= 8_3169x 10_8NC [ 5.2xlo·II
[DlW!. '{3 mm m im 'lTrn 13•1-1 .,, WfGfJ m -11 C<l5'1 W"1 1] 44. f.!oo 111 wit? [Ans: CJ
(a) 'Sll 3M <!l<!Z l<l<1 V (b) \S"il 3M <!l<!Z C<IS'f 2V (c) 2M <!l<! m 3V (d) 'Sll M <!l<!Z C<!<14V I Solve: (a) <!Ji! wn EK = x 3M x V2 = 1.5MV2 2
(b) <!l"il EK = .!. x 3M x (2V)2 = 6M Y2
2
2
45. "(ffl M <!l<! <lW!l R <!lil "fll!i m­ G
[Ans: BJ
GM g M Solve: (b)· g=-· =>-=-' R2 G R 2
(d) M R
.!. .::<::"'; x = 2cos(50t) <1 , x <!lil •"i <!l<!Z t <!l"il '>frn"l1!"i v,.<==, !"ts".<''' ms-1<!lm- [Ans:C] -= :OOsin(50t) (b) 100 cos(50t) (c) 100
t: ;; : A = 2 = w = 50 ; v run = Aw = 2 x 50 = I OOms -i
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',{Y".JUVIJ V. \,)U!YI.;
47. <!"12ic!IK'iil cl'llfu 1% "lliM..£<1 WI cl"il 'lW! Ei'l "'[£ D? "" "iN 0.2. (a) 1% (b) 2% (c) 0.2% (d) 5o
e I dL dx!OO 0.2 . Solve: cr=0.2 · -= -· cl"<Fl cr=- => 0.2 =-- => d =-D =>d = D .:: 0.2° 0
' L 100' ' De D 100 48. cl<rii: m,i 250 mL "IWl 1.25 L "llR ei'llfu <>iWll wn 1 m,i ,s "Im "I T<>-;-z- - t•.,
80°Cei<1 20°CW! "!"ii "IW!<I "i51"1"ITTll WI? (a) 25°C (b) 30°C (c) 35°C Solve: (b); . )11" "i519f"ilf.lfl = 0
(d) 40°C
:. rn 1 s
1 (80-0) = rn
1 ps
1 (80-0)= v
2 (0-20)
=> 0.25(80-0) = 1.25(0-20); By s olving, 0 = 30°C -l9. cl<rii: - [Ans:AJ
(a) lf "'["IT R'"I <AT WI (c)
50. <!Y 0Flfi; 15ll i?f!<llstT?
(b) (d)OO!<!>ll
(a) ffl <f1IW! (b) ffl "llR Solve: (b ); fl -,1f.1·<1> 15191 C"<!P'l I
( c) <RTti'
2 Mach '1 .. ie_m i:JWWl cl'llfu -.iro <f.""llt<!> WI? (a)<!! (b)<f (c)<f (d)ol'l<f
. v + 2v 3v Solve: (c); Mach means the velocity of sound. f = -'--' f. = -' f. :. f = 3f. Vs Vs
200 rz <!l<filu f.l t IOHz? (a) 100 m (b) 50 m (c) 180 m (d) 200 m Solve: rn=200, f=IOHz, n=?
f=rrm =>10=200n =>n=0.05scc- 1 = 0·5 Hour-1 =>n=l80Hour-1
3600 5Trci' CW!<li M "" , N cli:l 1!7'9fr'f I l5T"il "I.Jl'C<l­ (a) ffl C'l'fl'rlS m'Sl offi (b) t<t1<1'fi M mcsf cl<lt c N (c) t M m bl ei<i c N mi' rffi"l'>;'f> (d) t M mi' rffi"f':1' ..!!<It C'1T'1<1> N mcsf &1R;{,:, Solve: (a); Both spheres are possitivcly charged. "fl 1!1f!! 30 Cm l.OxJ08 v "fl lit 2.ox10-2s;pmi f.rn• I,!/ 1!R'lj .. ffi ffl'l - la) l.5xl011J (b) 3.0xl09J (c) 6.0xl07J (d) 3.3xl06J Solve: (b ); E = qv = 30 x Ix I 08 = 3 x 109 J < <{'jcf 1il1RJol "!Ni I pF 1 "IITTKl '11 '1 "I "l! 'm9f Q!J1l Nell 91.cf <l>lli 1 lW'I 2 p FBT I C'l11V@ '5ll<1<flrri<!> - a) 0.25 (b) 0.50 (c) 2.0 (d) 4.0
-olvc:(d)· C =E, A . C =ke. A . C =!pf· C =2pF > I d'2 2d'l • 2
. C _ 2C k E. A _ 2 E, A k _ 4- =>-----=> -. z I 2d d f Admission Tech
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56.* 110 v ;rfC'<j ,j <!1<!$ mtWl. "J.""0 0.4 cm 2 \!)re 3000K 's!il"i"Ifl.@.j i5lfC'11 1
f<qi 2FlITT:i'f 1"!F! ? [cr = 5.7 x 10-s W m-2 K -.; ] (a) IA (b) I .SA (c) l.68A (d) 2A
Solve:(c)· E=AcrT4==Vxl _._ AcrT' =I =>l=0.4xl0-•x5.7x10-sx(3000)
4
=l.6789A' \' 110 57. 10 "fITTiil '-'l<l>fi, f ,,fq •. rnt"il .. <" 3.5 mH. ,,;;.,tm.l!oil l!c<!J 2 Af<i,J -21<ffi Wl "I
iw!J i]'f-;; Wl- (a) 0 Wb (b) 3.5xl0' \\b (c) 7.0xl0-4 Wb Solve: (c); \"9=LI =>10o=3.5xi0-'x2 =>=7xl0-\vb
58. BJt I!!?. '>i ..... .!: - '<""Z-s <!':<"' -
(a) m1 <,-.; ,.
(d) 7.0x\0-i 'Nb
(c) "1,'<R 1.<r.< "ll'<R'i F-!i (d) .£-efG ITT E '-'l<i "l"l! B 'SR]
Solve: (c); To create a path difference 59. !Ohcnry ffl "1<!$ "ll<!J 12 /\rqi 1 '-'l 50ms-'-'l 600Vwr,:; -w=.
Wl -21<!lm 1!R ? (a)6 A (b)9 A (c)12 A (d)l5A
Solve: (b); i::=-L =:,600=-10 2 _ 3
::::>3=12-12 ::::>12 =9A ( I -I
) (I -12)
t 50x\O 60. 4 m0iw@ JJ'efi!l-'f!""h'I "lfGJ!l"ll 36 cm . 01'1l1f1ITTI C<!'T<WI<!>·
(a) 7.2 cm, 28 8 cm (b) 5 cm, 20 cm (c) 45 cm, 180 cm (d) 27 cm, 108 cm f 36 Solve: (a); -!.=4::::>f =4f ::::>fe =-=7.2cm f, • ' 5
f. +f, =36 ::::>4f,+f, ==36; ( =4f, =4x7.2 =28.8cm 61. ..!!<!$ 40 WV3 '-'l'efi!l 60 w q1 wi C<f5R c<r''lt @"'"''1 m1
(a) 40 W lamp (b) 60 W lamp (c)lf,mr;i (d)-rri"lil<f.i!"C<l Solve: (a); G <ll"ll <ft @l"l'-'"11.<l
- • 8 &'' • 62. miffil wr.i c !f!"l 3. x 10· mWl ,i oWf<lJl(jm ·l(j CIRRi PfKI a:ic.1·w•1 ,im:-
(a) l.3s (b) 2.5s (c) 8.0s (d) 8.0m in Solve: (b); d = 2x 3.8x 108ml"I ..!l<lR!lil 'm<!Rl 11
v = 3x 108 111 / s[Radar signal is an E-M wave]; t = = 2x 3·8x l08
2.Sscc v 3x 108
63. JJ'efi!l f.iWl V'rnl w; <!lftw?. G"c 1 C<l'R <\!'11 ZTI (a) (b) c (c) f.iWl i5ffilr! (d) RW1 Solve: (c); Posit ively charged neon ions proceed towards cathode.
i;..: 450 W <!lil IPS '-'lil "l!l'm1! 00 mR 1flJq fi "l1'iA 90 W '-'l<I ml; <!fRj 45 W a)-+ fans and 3 lights (b) 3 fans and 4 lights (c) 3 fans and 5 l ights (d) 4 fans and 4 ligh3 olH•: (a) -!!i:"""11 =4x90+3x45=495w [Ans:: _ !< 3x90+4x45=450w [SotheAnsis(B)] : .£?;""'" =3x90"'-5x45=495w (d)'-'1°9 =4x90+4x45=540w
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[:\ns: d]
Solve: We know that General Fonnula, E2 = p2c2 + m:c·1; m. = O :. E2 = p2c2 => p =
66. <!! 'l;l 'l;l"lm p - n -'Wl Fl'TI! <Vil!- (a) ?fm- c;.rc91 (b) \ @n: "R1 r,.rr.91 (c) Rl '519f ffi?f (d) - "ll'".;SW, Solve: Hall-effect experiment determines the maJority career of current now.
67. <!!R,-
[Ans: d]
(a) C:!lW<l (b) 1<1" 68. "ITTP'lfoil 'l•1'511CW111@f.mr•R -
(b) IDffl
(d)!!P'B
(a) C<I (b) (c) ( d) '11<1 70. 't!i 91'11'<1-
( a) f«!i firni <f'1'5fr<l' ll (c) fu-!i >:f1 ll
(b) F,«ll firnl 21
(d)fu-!i 71. <!!<;{-@ <!!!! :::;;'IJ ,;wis <ffi?
(a)<!! oTefi (c) .!lfu NCTJ f4,\:) .r1
(b) <!!fv r-,i;;ii m '11 (d) .!lfu .!l'<!>ffl .!lf<11,,{ r <rm
72. c<W1 0Pi2J <!l<1 C111J C<J wn <!I :i'l- "l'D "ff@? (a) (b)w,rnq (c) Solve: Polarisation is a unique property of transverse wave.
(d)
(Ans: a] [Ans: d]
[Ans: d) [Ans: d]
73. liWi'hl '3l<l",if"!! f.l!IN>:ji .!l C«li1 <r-<rC'1 C<l "ffi "IIB<ll!l•t fl<'I <!'11 - [Ans: d] (a)1 (b)•rirll<f (c)'°11.>JN?, (d)<f"IW Solve: According to the definition of electron affinity.
74_ ;w.oll c'lf?. l!1:l:fJ cw! <11 ? (a) Alp3 (b) Si0 2 (c)Li02
·s. 9f,fui-rriqri sif91B11Wil IIAm"i i FITTl 'w!$ (a) ls2 2s22p6 3s23p64s2
(c) ls22s22p63s2 3p6
(b) ls22s22p63s23p64s2 3d2
(Ans: d]
[Ans: a]
"6. Co(NHJ4 Cl3 <!!!! ff<!t"f 'lit "ITI!m'I Agi'-103 ff<l<f ClJ1°1 g0l'f'"f<i> AgCI .!l!! cm,, ,r<IJ1 (a) I (b) 2 (c) 3 (d) 0 [Ans: a] Solve: Co(NH3)4 Cl3 = [Co(NHJ,(C!}i ]' er [Co3
' .!lll ,if:iw1 "!"'in 6]
[Co(NHJi CI)2 ]cl+ Agi'-103 --> [co(NI-1,},i( Cl)i ]N03 + AgCI J. So I mole AgCI is precipitated [Ans: c] ·7, ,fffl%CcJrn \1J C<J>r,,ju '1-r<lCf f<ifu.m?
(a) Crp;- + 201-1--> 2Crp!- + HP (c)K+02 -->K02 (d) ·ca(HC03)2 --> CaC0 3 + C02 + Hp
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Solve: I
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f<fG!r,
78. .!)<1$ CW'rn f.rnt"f'=l' "l111Tl'fl w,,; b ,@ll? (a) 1f'l1Fl 11t C.2fW,l, "<3
(b) 1!'llt-1 '1t (l (2l"W-l ( c) ,jllf,I 'it (l c'1U-l (d) 'i'l1R 11t'l!J<!' "<3
Solve: They have the same number of electrons and protons. 79. "flfm 'ilil1ml 9!m "<3 ,s ;;.sd: ?
(a) IA, IIA, IIIA, IV A (b) llA, IlIA, IV A, VA (c) !IIA, !VA, VA, VIA (d) IIA, !VA, VA, Vl1A
80. 'I' 5<1'liu - (a) <!l <!] 1%'1 (b)l!lmil 1%5<1'1 (c) l!lPIITT> l!lPrm 5% n 'l (d) ,!!Pfm 5% 'l
81. '1ilmmffl-
(Ans: c]
(Ans: c]
[Ans: c]
<a> (b) (c)R (d) b '<l cm [Ans: b] 82. '5Wl im -a'!WPj '1 'a' 'llR! 'ITI:'lf -
(a) &-<fml<f (b)fffl<t (c)t?'ffil(d)b"<3cffl [Ans: a] [Ans: a]
(d)fu'W1'1 83. 2if1i?
(a) '5Jfil Ftil <J '1 (b) <!Wl (c) <!lvi 84. f.lmzjire'l (O-N-0)?
(a) N0 2 <NO;< NO; (b) NO;< N0
2 < NO;
[Ans: d]
Solve: N "rnll!'J:il mi m!l m ii '1 m ( VSEPR ) ll't'1" 'l I :. i!F'II: No; < N0
2 < No;
85. f.lm DNA '<l RNA <!l ,ii91.cf t"fl'iFl? [Ans: d] (a) Mangnesium(b) Sodium (c) Sulphur (d) Phosphorous Solve: Phosphorous (P)
86. f.lm lllm- >rn ll c,roi mRl ,m;'l! '<fITT'i? [ Ans: a J (a) -C
6 H
[Ans: b]
Lsr + Cl
88. f.rWl <!lm C<ISR ? 2 0 3 0 4 5
II II CH3 CH2 - C-CH
1 - C -OCH1 - CH
1 2 0 3 0 4 5 II II CH
3 Cll
1 -C-CI-1
1 -C-OCH
2 - CH
no. 3 is most acidic. 89. C<'TiS(II)mmq><fj?
(a) HN0 3
(c) HCI Solve: Only PbN03 is soluble.
(d) 4
(d) HotHp
90. xrirn <(rn'ffil <lJWTI.Wf!!i1 <!l<llfu 1!5/mqn: I 'ilJW!T-'ffil (<lW!) -
(a)-10-9 m (b) 1-IOOnm (c) 0.59xl0"8cm n mm C<!iR .?lfiFllfu '019f '@<1.9f?
(a) (b)<11""1 (c)"fw-1 .-iz. C<ISR cifts$ C'<ITT> c- <l'>il1 -11?
OH
(•) 6
Solve:@--CH,
NH,
(a) CH 3 Mg8r (b) HCHO (c)RCHO (d) ""'-c=O
-! <t>l-11$:®d,ll fii tl1'll m ,rrr; - RI.......-
(a) HCHO (b) HCHO+ RMgX (c) NaN02 + HX (d) HCN [Ans: d)
- <.!l<llfum"fTCillw,ci:ri519i'lf1il!l'!l<!l""i<.!1<1- [Ans:b] (a) "<t>'l!' "fllm (b) 'V'!J<!> '>fllTcm (c) &.n "f'l!r.ill (d) tir C<llFl 9f:1r3ll
'5 <!'l? [Ans:a] (a) rr 91lf.! (b) 9fRrn (c) '51Jl'1l<>l'1 (d)
• - 27°C i5f9flWilfl! <.!l<llfu 'i1'ifro <I <Im' J 3Q4cms -I , -
(a) 0 2
(b) C0 2
(c) NH 3
(d) S0 1
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3R: =3x8.316xl 07 x300 =44_015xlO'gm/molc
\ M M . c- (1304)2 There is no answer.
98. 40°C 'i5J''i'l1'f!ml N 20$ l!l?. l'lC!!l§il 'zz.n 45 min . ffl C'lS1 -
(a) 0.105min-1 (b) O.OlSmin (c) 0.02s-1 (d) o.01ss· 1 f/\ns: b]
Solve: K= 0·693 =0.015min-' 45
99. lTT'l ?fllf.m <3 .,.. , , '"i< - \.,!, CG"ri? [Ans: d] (a) I-!, (b)He (c) :\'itrogcn (d)-m
100. -;;'h- ""T .!­
(a) °J's" <c
[Ans: d] (d) m'l-'l 1<1fhm
[Ans: b] (a)-!.<-: 01:'!: (b) W. (57:!) ".'P'1 (c) ,;r.pj (d) ;;rI?. iS"i!: m r.,1 C<'iR m ffl
102. lWITTffl f<traRrrn Cl! "f'M "I @,i f/\ns: d] (a) "lfw•rfu; (b) (c) rirw rfu; (d) -::r·\i'ioi--1fus
103. f.Rsc!l<1,irn<t? [Ans:b] (a) NH0Cl(s) NH3 (g)+HCl(g) (b) Nll4Cl(aq) NH,'.(aq)+Cr(aq)
(c) C 12H2p11 (s) c1i1-12p11 (aq) (d) CaC0 1 (s).,.--=!Ca 2 '(g)+Coi-(g)
Solve: NH4Cl(aq) Ntl;(aq)+cr(aq) 104. 1Wl R!lfll (i5ll 238 <B<!t "iHllll'IP!<!i 'it'<lJI 92 ) l l!l<f.W a - <f.'fl f..*'1; I. 1S"llf"f\5 -
"l"J]l!l'ff.f<ls 11<!TI 'll'<IK."Vl [ Ans: al (a) 234 and 90 (b) 234 and 92 (c) 238 and 90 (d) 238 and 92
2)8 · 234
Solve: 92 · U - a ---t90 Th 105. 1\.llprn'i"!l? [Ans:c]
(a) Benzidine (b) Glycine (c) Adenine (d) Histidine Solve: Adenine is a base
106. 01-i cm•r C= 18.5%, H = 1.55%, Cl =55.04% \Jl<l 0=2181%©"1 1 C<Tl"ITITT111Z RIO "IWl? (a) CHCIO
Solve: C : H : Cl: O = : 1.55 : 5
5.04: 23.81 12 1 35.5 16
= 1.54: I.SS: 1.55: 1.48 "'I: I: I: 1 :.1o-J 'iZ CHCIO ,-- DNACl:3?
a, Adenine (b) Guanine (c) Uracil ::g C.2C0 3 ffl CaC0 3 r-fil?
o 550 g (b) 9.966 g (c) 9.881 g - he: 6.0nx102ir,'1.CaC0 3=100g
(d) Thymine
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(/\ns: a]
[Ans: c]
[Ans: b]
Admission Tech
For question numbers I 09-112, choose the correct oprion that ,1i1J complete the corresponding sentences.
I 09. She was very pleased by the appreciation she received like everyone els.:. ,he .:-:::oi.'d h.:mg _. (a)entcrtained (b)praiscd (c)playful (d),indicatcc '.\u, B,
110. Pioneer men and women endured terrible hardships, and ' . .\!:.;; :::>; (a) so do their children (b) neither did the children (c) also the child (d) so did their children
111. 111c changes in this city have occurred __ . :.\.ns: DJ (a) with swillness (b) rapidly (c) fastly (d) in rapid ways
112. IOOO species of linch have been identified. [Ans::\; (a) As many as (b) As many (c) As much as (d) Much as For question numbers 113-116, each sentence has four underlined words or phrases. The four underlined parts of the sentence arc marked (A), (B), (C) and (D). ldcnli fy the one undcrlmed world or phrase that must be changed in order to make the sentence correct.
113. Visitors were not pcrmilted ente ring the park after dark bccuasc ofthc lack Qf scctuity and Lighting. I AllS: BJ A B C D
114. Writers like William Shakespeare and Edgar Allan Poe arc not only prolific but too interesting. f Ans: DJ A B C D
115. I need both fine brown sugar as well ill? powdered stigar to bake a Hawaiian cake. [Ans: A] A B C D
116. Evm a professional psychologist may have difficultly talking calm and logically about his ow11 problems. A B C D
(Ans: BJ For questfon numbrs 117-120, read the following passge and choose the best answer from the four options marked (A), (B), (C) and (D) that following each question. Although speech is the most advanced form of communication, there arc many ways of communcating without using speech. Signals, sings, symbols, and gestures may be found in every kwon culture. The basic function of a signal is to impinge upon the environment in such a way that ii attracts allcnlion, as, for example, t.hc dots and dashes of a telegraph circuit. Symbols arc more d ifficult to discribe than either signals or signs because of their intricate relationship with the receiver's cultural perceptions, ln some culttires, applauding in a theatre provides performers with an auditory symbol of approval. Gestures such as waiving and hand shaking also communicate certain cultureal messages.
117. What docs the author say about the speech? [Ans: DJ (a) II is the only t1ire form of communication (b) It is dependent upon the advances made by inventors (c) II is necessary for communication lo occur (d) II is the most advanced form of communication
118. According to the passage, what is a signal? [Ans: CJ (a) The most difficult form of communication to describe (b) A form of communication which may be used across long distances (c) A fonn of communication that interrupts the environment ( d) The fonn of communication most related to cultural perceptions
119. The word "intricate" could best be replaced by which of the following? [Ans: BJ (a) inefficient (b) complicated (c) historical (d) uncertain
120. Applauding was cited as an example of [ Ans: q (a) a signal (b) a sign (c) a symbol (d) a gesture
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