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This booklet contains 44 printed pages. ~~ii~1flo 44 i, RBS No.: 170 9255 77 PAPER -1 : PHYSICS, CIIEMI T RY & MATllEMATJCS \A¥-1'3.f~cn1 - 1 : ~ ~. ~~om 11fora
Do not open this Test Booklet u nti l you .u-e asked to do so.
W~~qiltf!fncfi-f~~ncfi~-f~I Read carefully the Instructions on the Bock Cover of thls Test Booklet.
w~ ~ ~ fQ-oo' amrorr'Q't~1lt(~ qil ~ ~ "Ql1 1111porla11t l11structic111S: qSfq'J_Uf f.rt1r :
Te t Booklet Code
\A~I 1 . Immediately £ill in U,e particulars on Olis page o f the Test I . ,rtt~ ~if;~~ 1'\ ~~~~~if~
Booklet wiUl only Black Ball Point Pe11 provided in Ule ~ 1m ~ tlifrhTTR ~ q:, ~ ~ ,:ff 1 examination hall -,,
2. The Answer Sheet is kept inside Utls Test BooklcL When you 2. ~ ta! 1tl ~ ~ ~ ~ WI t I~ ~ mn ~ are directed to open Ule Test Booklet, take out Ulc Answer "Grli:'R ~ ~ ~ m on{ 'q';t ~ qi'{ '1:IW~ ~ \ff I Sheet and fill in Ule particu tars carefully. 3. ffi .ti ~ 3 tl'z t I
3. The test is of 3 hours duration. 4. 1tl ~~if 90 mi 1 ~ ff 360 f 1
4. !!:~~eS:,~et consists of 90 questions. The maximum S. ~~~if tt:, 'ltf1l A, B, C t, f-;mt ,n:qq; 'ltf1l il S. There a_re time parts in the question paper A, B, C ~ ~ . ~ ~ ~ TTfvra ~ 30 m f 3fr{ ~
consisting of Physics, Chemistry and Mathemalics having m ~ a:tct; ~ f I ~ '5ITT ~ tm om % full, 4 ( ;m) 30 questions in each part of equal weightage. Each question ~ f.{trlful ~ ~ f 1 is allotted 4 (four) marks for correct response. -~ ~ ~ .....i:i ~ -. ~ pJ_.., •
6. Gmdulates w1U be awarded marlcs as stated nboae iri rrislnichon 6· ~o,q,qqi "'' """"' ..,c,, Tm"' ICT"< <J'f<t<fff '""«,.., W7§W S No.Sforcomd ~ISeOf eiJdl qrtabori. 1h (ane-fo11 rlh) marlcsof A<llljffi< 3iffi' ~ ffl / ~ JIR ~ Tfffi1 ot1( ~ fc:fli tJie total mmfcsallotted lo tliequestio,1 (i.t . l 1nmk)Wtll bedtducwl JlT-1 l1i ffiT{ f.rflfm, ~ Wlil. if 'R ~ (f(<fi-m'IT() for indicating incornct resporise of e1Jd1 qr1est,or1. No dtducbon ( ~ 1 3iffi) 'iliTZ fff11T 'JIT'q1TT / ~ m- V;i if f<l;fit J1R from the tollll sa,,t will be ,mW if no rtspoll~ IS mdu·.altd for 011 3af ':rlf WIT 1fllT ~ m ;;;;;, ~ 'ff 'lit{~ -:rtf q,'f ~ item in the answu sir.at. J'"
7. There is only one correct response for each question. Filling 7. ~ Vi"I <fil -m 11;cfi '8\ "mt om t I ~ 1t ~om~ "<R up more than one response in any question will be treated as ~~om "1Wfl ~ 3frt ~ ~ 6 ~ ~ ~ ~ wrong response and marks for wrong r~ponsc will be mq ~ 1 deducted accordingly as per instruction 6 above. 8. om lf:il % '{"o- l ~ rpo-2 "<R cfffi:rn ~ ~ -am affit;a
8. For writing particulars/ marking responses on Side-1 .ind ~.,,.-. • _...;. ~ Side-2 of the Answer Sheet use only Black Ball Point 1'1'11 ..,i., Qll 'HrtJT ~ ,:j ~ ..,..,'4 Till ~ q,ic-r iifff fZfric provided in the examination hall. q:, <fil 't\ WWI ~ I
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11. On completion of Ule test Ule candidate must hand over the ( ~ 4043) ~ ~ 1
Answer Sheet to Ule invigilator on duty in Ole Room/ Hall. 11. 'qffl]'l lPlT!<f ffi "<R, oMtff ~ / 1'@ ~~~om lf:il ~ However, Uucandldatesartallowtd to takuway this Test Mt.fcfi<S'I ~ tfftf t I ~ 3/'<R'RTfl'ff{~ Booklet will, than. ti# ff ;;rr wri' f J
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same as that on this booklet. ln case of discrepancy, the ~ cfi'{ ~ % tme:11 ~ 3fr{ onl lf:il cfi'I ifi1f ~ candidate should ir:nmediateJy report Ule matter to Ule fqffift t 1 3TTR ~ f\r,{ l't 11) ~tit ~ ~ ~ afR Invigilator 'or teplacement of both Ule Test Booklet and the om lnl ~ ~ ~ f-m~ cfi1 ~ 3{cfT@ ~ 1 Answer Sheet. m'<, ~· "
13. Do not fold 01 make an stn muk on the Answer Sheet. 13. offl" lff 'lfrr "=f ~~"=ff ~ lff ~ f.mT=f Wfflt I
PART A - PHYSICS
ALL THE GRAPHS/ DIAGRAMS GTVEN ARE
SCHEMATIC AND NOT DRAWN TO SCALE.
1.
2.
A man grows into a giant such that his 1.
linear dimensions increase by a factor
of 9. Assuming that his density remains
same, the sh·ess in the leg will change by a
factor of :
(1)
(2)
(3)
(4)
9
1 9
81
1
81
A body is thrown vertically upwards. 2.
Which one of the following graphs
correctly represent the velocity vs time ?
(1)
(2)
(3)
t V
t V
t V
t-+
~A -~~ raJJ: ~ ~ mr:Fi/ ~ &/<fi frtZJi 3UhsiJ4 g= 3th-~~ 3qm7 ~&1Mrl ~t, ~ ~ , 1J:<fi f6l~11a&i1~ 1'.jFfq -q ~ ~ qfo:1fda mo1 % fcn ~ ~ ~ 9 :ff1 ~ ~ ~ I i:rr::iT fcn ~~if c!iT{ qflc:1J1 -:,@
~tm~ifll-q~fcmR:fflm~ ?
(1)
(2)
(3)
(4)
9
1
9
81
1
81
~ rors cfi1 ~m ~ cnl' cWfi ~ ~ % 1 f.,t:, -q "it ~ m mtn ~ ~ m21 ~ cfi1 ~~%?
(1)
(2)
(3)
( "\)
t V
t V
t V
t V
t -+
SP ACE FOR ROUGH WORK / "{qi ~ $ ~ ~
3.
4.
A body of mass m =10- 2 kg is moving in 3.
a medium and experiences a frictional
force F = - kv2. Its initial speed is
v0 = 10 ms - 1. lf, after 10 s, its energy is
1 8 mva2, the vaJue of k will be :
(1) 10- 3 kg m - 1
(2) 10- 3 kg s- 1
(3) 10- 4 kgm-1
A time d ependent force F = 6t acts on a 4.
particle of mass 1 kg. If the particle starts
from rest, the work d one by the force
during the first 1 sec. will be :
(1) 4.5 J
(2) 22 J
9J
m =10-2 kg t:'="~411 ~ ~ ~ ~ ::t":7.;"g
it ~WI% 3ffi ~ ffl Gffi F= -kv2 cfil
3'11,"1q ~en t 1 ~ cfi1 vn:~~ ~TJ
v0 =10n:1s- 1 t 1 ~10s~~~~
i mv a2 ! ell k cfil "GR WIT :
(1) 10- 3 kg m - 1
(2) 10- 3 kg s - 1
1 kg t:,oll4H cfil ~ cfi'Ol, ~ ~ ~ f.f,n: (time dependent) ~ F = 6t cfil ~cqq cfiUf1
t I <:JR cfiUT fcl{l41cff4T~ ~ tm ~ 1 s 'if ~ GT<T M Tf<TI cnr:t WIT :
(1) 4.5 J
~ 22J
(3) 9 J
(4) 18 J
SPACE-FOR ROUGH WORK / ~ cfiT<f ~ ~ ~
s.
6.
Th e moment of ine rtia o f a uniform 5.
cylinder of length land radius R about itc;
perpendicula r bisector is I. What is the
ratio l/ R such that the moment of inertia
is minimum?
(1) l (2)
J3 2
(3) 1
3 (4) J2
A slender uniform rod of mass M and 6.
length l is pivoted at one end so that it can
rotate in a vertical plane (see figure). There
is negligible friction at the pivot. The free
end is held vertically above the pivot and
then released . The angular acceleration
of the rod when it makes an angle 0 with
the vertical is :
z
X
(1) 3g . e - sm 21
2g . e (2) - SID
3[
(3) 3g cos e 21
(4) 2 g cos a 3[
~~ R 02.TI~ I ~~wrr=,iim ~ ~ efi',~ f&'l-t~ ~ "BTG?.i ~ ~ I% I ~ ~ ~ fiY ct4 'G'R ~ ~ 3lJtWf 11 R cp.n mm ?
(1) t (2)
J3 2
(3) 1
3 (4) l2
't:(cfi ~ol.l 411 M ~ ~ l en, "Qoffi ~ 1'(cf;
~~~ ~fm"r ~ tf-m:m fcf;~
't:(cfi~m~if~~tcm~) 1
~~tfrfut~t1 ~~~rnt<fil~ ~~~lR~~~sifralt°I ~ ~~-?t em~tm~~ (Cf{UT mTTT :
z
X
(1) 3g . e - Sill 2[
2g . (2) -sme
31
(3) 3g cos e 21
(4) 2g cos e 31
A/ Page 4 SPACE FOR ROUGH WORK / rq; ~ ~ ~ ~
7.
8.
The variation of acceleration due to gravity 7.
g w ith d is tance d from centre of the
earth is best represented by (R =Earth's
radius) :
(1) ~ 0
(2) ~ 0 R
(3) ~ d 0 R
(4) ~ O R
A copper ball of mass 100 gm is at a 8.
temperature T. It is dropped in a copper
calorimeter of mass 100 gm, filled with
170 gm of water at room temperature.
Subsequently, the temperature of the
system is found to be 75°C. T is given by :
(Given : room temperature=3D°C, specific
heat of copper= 0.1 cal/ gm0 C)
(1) 800°C
(2) 885°C
(3) 1250°C
(4) 825°C
'l~ ~ ~ ~ ~ d ~ "BT~ '.,!{l(i:{lll ~ g qi'[
~ f.it:f ii it ~ mili ii -m m1 GWn 7Tln %? (R= 'l~ qft ~ )
(1) ~ 0
(2) ~ 0 R
~ (3y
0 R
(4) ~ 0 R
100 gm ~61.l q11 qfffi oTit ~ ~ ~ cfiT ~
T ! I ~ ~ 170 gm 1:fRT ~ \ft~ 100 gm ~ ~ ~ c\;~1D4'lc:<, "fi cfl1R ~ cfT'Cl'llR -q'{
t -q ~ 'R7:fi ~ ! I dc<F{qlq_ ~ cfiT
~ 75°C ~~l1 TcfiTllRmTTT:
(R7:flt": cfl1RcfiT~=3D°C, ~~m2 ~ =0.1 cal/ gm°C )
(1) 800°C
(2) 885°C
(3) 1250°C
(4) 825°C
SPACE FOR ROUGH WORK / ~~~~~ ..
An external pressure Pis a pp Lied on a cube 9.
a t 0°C so tha t il is equally comrre.,sed from
0°C ~ ~ sQ. ~ tR 1:R ~ ~ p ww:rr ~ % ~ ~ "B'ifi cWn "il cflJcTI: ~ G'l fsa mmt, tR~~~cn1~~~ K~~ ~ ~cxt l ~tA'cfil lllf m~~ii~tm~~-q;) fcficRT ~ ~?
all sid es. K is the bulk modul us of th<.'
material of the cu be and a is its coefficient
of linear expansion. Suppose we want to
bring the cu be to its origina l size by
heating. The tem pera ture should be raised
by :
p
(l ) 3a K
p
(2) aK
3a (3) PK
(4) 3PKa
10. CP and C.0
a re specific h eats a t constant
pressure and constant volume respectively.
It is observed that
CP - c=i, = a for hydrogen gas
CP - ~ = b for nitrogen gas
The correct relation between a and b is :
(1) 1
a = - b 14
(2) a = b
(3) a=14 b
(4) a = 28 b
p (l) 3aK
p
(2) aK
3a (3) PK
(4) 3PKa
10. ~ ~ cl~ ~ 3lT«<l, "tR ~ ~
~ : cP o~ c0 f 1 ~~ifq,
~1~~'111 ~ ~I cp - ct'= a
1l~{I\J11 ~ ~ I cp - ~ = b
a 3mb ~ ~cnl~~m1TT:
(1) 1
a=- b 14
(2) a= b
(3) a = 14 b
(4) a = 28 b
A/ Page 6 SPACE FOR ROUGH WORK / ~ cfITlf ~ ~ ~
11 . The temp era ture of an o pen room of
volume 30 m3 increases from 17°C to 27°C
due to the sunshine. The atmospheric
pressure in the room remains 1 x 10s Pa.
If n, and n1 are the number of molecules in
the room before and after heating, then
1y- n, wiU be:
(1) - 1.61 X 1023
(2) 1.38 X 1023
(3) 2.5 X 1025
(4) -2.5 X 1Q25
12. A particle is executing simple harmonic
motion with a time period T. At time t = 0,
it is at its pos ition of equilibrium. The
kinetic energy - time graph of the particle
will look Like :
(1) KEb~
01 t T T t -+
(2)
(3)
(4)
11. ~ cb1 ~ it iTcfi ~ ~ 30 m 1 3lf1.@"1
cfR9 cfitR cfi1 or:JttA 17°C ~ ~ 27°C m \JJ@1 t I q;,:f{ * ~ ~·~ ~ 1 x105 Pa ft~%1 7.IR~~~~3TI cbl~.rtfm'B~~~itsPm: n, q
11! % cf! nf- n, cfi1 i:fR mm :
(1) - 1.61 X ] Q:?.."l
(2) 1.38 X 1023
(3) 2.5 X 1025
(4) - 2.5 X 1025
12. ~ cfi'O'l, 3ilctd<tik1 T "it t1"ffi ~ Trfu ~ ~ t°I ~ t=O~~ {i1'41ct~cbl~it t1 f.i'Cl-q "it ~mmln~ ~m21~ ~ ~~~t?
9)
(2)
(3)
(4)
KE~
0~
KE~ O~ t-
4 2
A/ Page 7 SPACE FO R ROUGH WORK / ~ cfiTlf * ~ ~
I
13. An observer is moving with half the speed
of light towards a sta tionary microwave
source e mitting waves at frequency
10 GHz. What is the frequency of the
microwave measured by the observer ?
(speed of light = 3 x 108 ms - 1)
(1) 10.1 GHz
(2) 12.1 GHz
(3) 17.3 GHz
(4) 15.3 GHz
13. ~ ~a-fcfi W-fim TJfu cifr :mm 11fu it 1 o c., ~ ~ ~ ((<ti ~( tl_e;:i:r m (microwa ,
m cfiT ~ ~ Wt %° I ~PJq; GJU l'.ITtft '11ft 11~ cf{TPfiT ~ cfiPlR WTI : (~ cfft "'q@=3 x1Q8 ms- 1)
(1) 10.1 GHz
(2) 12.1 GHz
(3) 17.3 GHz
(4) 15.3 GHz
14. An elec tric dipole h as a fixed d ip ole 14. ~~it~ cfiT ~ fu~ ~ p % -.i --+
mom ent p , whlch makes angle 0 with --+ /\
1%" x- 3le.-T ~ e q;)ur Gfl@T t I ~ ~ E, = E i
respect to x-axis. When subjected to an -q: m 1f{ ~ c@ ~ ~= ,.k qiT 3f:i'qc,
-+ /\ electric fie ld E1 = E i , it experiences a
-+ /\ to rque T1 =,. k. Whe n subjec ted to
--+ I\
a n othe r e lectric fi eld E2 = J3 E1 j it
-+ --+ experiences a torque T2 = - T1 . The angle
e is:
(1) 30° (1) 30°
(2) 45° (2) 45°
(3) 60° (3) 60°
(4) 90° (4) 90°
A/ Page 8 SPACE FOR ROUGH WORK / "{qi ~ ~ ~ ~
GHz
·ave)
~8:G
I\
= E i
15. A capacitance of 2 µ.F is required in an
electrical circuit across a potential
difference of 1.0 kV. A large number of
1 µ,F capacilors arc available which can
withstand a potentia l difference of not
more than 300 V.
The minimum numbe r of capacitors
required to achieve this is:
(1) 2
(2) 16
(3) 24
(4) 32
16. In the given circuit diagram when the
curren t reaches steady state in the circuit,
the charge on the capacitor of capacitance
C will be:
r1
C
r2
(1) CE
(2) CE r1 (r2 + r )
(3) CE __!L_ (r+r2 )
(4) CE - r1_ (r1 + r)
15. ~ ~ ~~ -q ~ 2 µ.F mfurr ~ ~tlTITT qi) 1.0 kV fq~ ~ ~3TI ~ ~ WTRT
t I 1 µ,F mfurr ifi" ~ ~ °tjllTfti \lfT f% 300 V fct'4'cfRTI: ~ ~ cfi"{ "B"cfia { ~
~
i,
"3tfUc@ ~~ qi) "5fIB ~ ~ ~ ~ ~ ~~ cpl 3llci~llcfidl mrft?
(1) 2
(2) 16
(3) 24
(4) 32
16. ~~~~ll~mu~ll~~ t "ffi mfun C ~ ~mft;r ~ ~ "cfiT "G'R mTTI :
r1
C
r2
(1) CE
(2) CE r1 (r2 + r)
(3) CE __!L_ (r+r2 )
(4) CE - r1_ (r1 + r)
A/ Page 9 SPACE FOR ROUGH WORK / W ~ ~ ~ ~
1 7. 2\' 2\' 2\1 17. 2\' 2\' 2V
CEI~,n CE,~ t'° 1~J 2 \ ' 2 V 2 V 2 V 2 \ ' 2 V
In the above circuit the current in each
resistance is :
(1) 1 A
(2) 0.25 A
(3) 0.5 A
(4) 0 A
18. A magnetic needle of magnetic moment
6.7x10-2 Am2 and moment of inertia
7.5 x 10-6 kg m2 is performing simple
harmonic oscillations in a magnetic field
of 0.01 T. Time taken for 10 complete
oscillations is :
(1) 6.65 s
(2) 8.89 s
(3) 6.98 s
(4) 8.76 s
"3i'Cf{ ~ llil ~~ ii ~ >l'firot1 it mu llRWll:
9') 1 A
(2) 0.25 A
(3) 0.5 A
(4) 0 A
18. ~ ,j.1.slchl4 ~ 6.7x10 -2 Am2~~
~ 7.5 X 10 - 6 kg m2 cf@l 1lklcfii4
~ 0.01 T tITT@T ~ 1l1.slchl4 ~it~ 3-
~ ~-uft % 1 10~~qit~Wf
(1) 6.65 s
(2) 8.89 s
(3) 6.98 s
(4) 8.76 s
A/ Page 10 SPACE FOR ROUGH WORK / "ttn ~ ~ ~ ~
if mu cl
(1{ci~,
~ m ~ men, rir mm :
When a current of 5 mA is passed through
a galvanometer having a coil of resistance
15 n, it shows full scale deflection. The
value of the resistance to be put in series
with the galvanometer to convert it into a
voltmeter of range 0 - 10 V is :
(1) 1.985 X 103 fl
(2) 2.045x103 !1
(3) 2.535 x103 fl
(4) 4.005 x103 !1
19. 15 fl ~ jiO~;(-fi "SITTfU~ ~ ~~114tl{ °B ~ 5 mA cfi1 mu ~ cfi1 ~ t m ~ 1l1'f ~ fcta)tf ~ t1 ~ 0-10 V ~ t° fct~ if ~ ~ fu-q ~ "tlR t- ffl'=l ~ ~~ 1')14k< ~ m~ ~ sfiB if WTRT mm?
(1) 1.985 x1Q3 !1
(2) 2.045x 103 !1
(3) 2.535 X l a3 fl
(4) 4.005 X 1Q3 fl
20. In a coil of resistance 100 n, a current is 20.
induced by changing the magnetic flux
through it as shown in the figure. The
magnitude of change in flux through the
~'4cf,14 ~ t-~ ~ 100 n Mt.l cn1 jiO:Sd1 if mo tTTU ~@if~ Tf"lfl t I jiO:Sffi ~ ~ c{@ ~if~ cfl1 ~
mm= coil is:
10
Current (amp.)
i
10
mu (~)
i - Time 0.5 sec
(1) 200 Wb (1) 200 Wb
(2) 225 Wb (2) 225 Wb
(3) 250 Wb (3) 250 Wb
(4) 275 Wb (4) 275 Wb
A/ Page 11 SP ACE FOR ROUGH WORK / ~ q;T<f ~ ~ ~
21. An elec tron bea m is accelerated by a
potential difference V to hit a me ta llic
target to produce X-rays. It produces
continuous as w ell as characteristic X-rays.
If Amin is the smallest possible wavelength
of X-ray in the spectrum, the variation of
log Amin with log V is correctly represented
in:
(1) log Amin
(2) log Amin
(3) log Amin
21. x-fcfitui~crn~~~~~icf?l1 fi:fi{011-ii .., q;J' fcf~ \ ' it ~ ~ ~ q;r ~ ~ 2
-
3lNftro fcf;'lfl -if1m t I nm fffl cRl (characteristic) 1(q' 3lrcrCTf (continuous)
x-fcRuf~~ f 1 ~x-fcRul~~ ~ ~'lfcf ~t4 Amin % m log Amin q'.il
logV~lTI?.l~~ m~~~ -rr:n % ?
(1) log Amin
(2) log Amin
(3) log Amin
A/ Page 12 SPACE FOR ROUGH WORK / ~ cfiT<f ~ ~ ~
23
• Fc "' Rcf>{o13~ :fl1 ~ 'tlt 22.
A diverging lens with magnitude of focal
length 25 cm is placed at a distance of
15 cm from a converging lens of magnitude
of focal length 20 cm. A beam of parallel
light falls on the diverging lens. The final
image fo rmed is:
~~ ,tinuous)
T~ll
I
'
(1) real and at a distance of 40 cm from
convergent lens.
(2) virtual and a t a distance of 40 cm
from convergent lens.
(3) real and at a distance of 40 cm from
the divergent lens.
(4) real and at a distance of 6 cm from
the convergent lens.
23. In a Young's double slit experiment, slits
are separated by 0.5 mm, and the screen
is placed 150 cm away. A beam of light
consisting of two wavelength s, 650 nm
and 520 nm, is used to obtain interference
fringes on the screen. The least distance
from the common central maximum to the
point where the bright fringes due to both
the wavelengths coincide is :
(1) 1.56 mm
(2) 7.8mm
(3) 9.75 mm
(4) 15.6 mm
22. ~ 25 cm fflJUT ci>1 ~ ~ ~ 3ltimfl ~ cfll ~ 20 cm 'tffillTUJ ci,1 ~ ~ ~ 3lf'lmU ~ ~ 15 cm ci,l ~ ~ tm ~ t° I ~ 'BtlTcR ~ ~ ~ ~ ~ 3lftITT@
mol i I qft.0114' S1faf~14 mi,T :
(1) co~fqcf; am 31NmU ml ~ 40 cm ~
~
(2) 3lNlm am 3lf'lmU ~ ~ 40 cm ~ ~
(3) ql~fqcf; am 3ltrmU ~ ~ 40 cm ~
~
(4) q l~fqcf; am 3"IT'fffTU ~ ~ 6 cm c;;_u ~
23. <trt~~~WWT-ii, ~~~q,1~ 0.5 mm ~ ~ ci,1 ~ ~ <;;.U 150 cm t" I ~ ~ ~I ~ 650 nm am 520 nm q,l ~ ~uf ~ I cfll ~ ~ 64C1lcf;{OI ~ tAA -q ~~i,~~~~~
~~zy:n~q,1~ ~ ~
mmt q,l~~m=
(1) 1.56 mm
(2) 7.8 mm
(3) 9.75 mm .. ..._
(4) 15.6 mm
A/ Page 13 SPACE FOR ROUGH WORK / ~ qiT<f ~ ~ ~
24. A parttcle A of mass m and mitial velcx1ty 24. ~64411 m ~ ~ WI ti ~ ~ q:.r
t • collide~ with a particle B of mass m 2
,.,·h.ich is at rest. The collision is head on,
and ~lastic. The ra tio of the de-Broglie
wavelengths X. A to X.8 after the collision is :
('J)
(2)
(3)
(4)
25. Som e e ne rgy levels of a molecule a re
shown in the figure. The ra tio of the
wavelengths r = X. 1/X.2, is given by:
- 2 E-+---''---
- 3E -
4 (1) r =-
3
2 (2) r=-
3
3 (3) r =-
4
1 (4) r =-
3
( j)
(2) '/
(3)
(4)
25. ~ ~ ~ ~ ~«roqi)mit~~ l I ~tzn ~ 3TfITo r = X.1/>.2 cfiT "4'R TI11l
- 2 E --+------''---
-3E-
4 (1) r =-
3
2 (2) r=-
3
3 (3) r =-
4
1 (4) r = -
3
A/ Page 14 SPACE FOR ROUGH WORK / ~~~ ~ ~
A radioactive nucleus A with a half life T,
decays into a nucleus B. Al t =O, there is
no nucleus B. At sometime t, the ratio of
the number of B to that of A is 0.3. Then,
t is given by :
(1) T
t = -log 2
2 log 1.3
(2) t = T log 1.3 log 2
(3) t = T log (1.3)
(4) T
t = log (1.3)
27. In a common emitter amplifie r circuit
u s ing an n-p-n trans is tor, the phase
diffe rence be tween the input and the
output voltages will be :
(1) 45°
(2) 90°
(3) 135°
(4) 180°
28. In amplitude modulation, s inusoidal
carrier frequency used is denoted by we
and the signal frequency is denoted by wm.
The bandwidth {Awm) of the signal is such
tha t Awm <<we. Which of the following frequencies is not contained in the
modulated wave ?
(1) Wm
(2) WC
(3) (&)m + W C
(4) wc-wm
26. ~lf.s4lc(f<Rq -=nf'qcf;-A ~ 3lZ-~ T
t", ~ e.-TZI ~ -=nf'qcf;- B Tf ma1 t° I ~ t = 0
lf{ ~ \ft 1'f'qcf;- B 1'-@ % I ~ ~ t lf{
-=mW B o?.n A cfi1 tf&n ~ ~ 0.3 t m t ~"t[RmrTI:
(J)
(2)
(3)
(4)
l = ! log 2 2 log 1.3
t = T log 1.3 log2
t = T log (1.3)
t = T log (1.3)
27. n-p-n {IT."1R.U)ffl~~~ 3ffi-ifcfi
W:Jttcf> 1:JITT"?.l -q f::i~F.?1a om f.rrra fcf'lcfl ~ ~~~"t[RmrTI:
~ 45°
(2) 90°
(3) 135°
(4) 180°
28. 3Tf7.ITtl' ~ if ~(qst,l ll ~ 3lFJfu qil W C
~ cf?.n fur.@~ qil Wm~~ f I fur.@
cfi1 ~ ~ (Awm) cf;1 ~ oW ~ f fqi
Awm <<we. Rt;{ it ~ ~ 3lFJfu 'll§f('id
mit~ wtt ?
(1) Wm
(2) we
(3) wm + wc
"-4) wc- wm
A/ Page 15 SPACE FOR ROUGH WORK / "{Q; cfild ~ ~ ~
I.
29. Which of the following s tatements is 29. f1Yfc1f@a ii 'i:I ~ '11 cf)~ TfFio % ?
false?
(1) Wh eats ton e bridge is the most
sen sitive when a ll the four
resistances are of the same order of
magnitude.
(2) In a balanced w heatstone bridge if
the cell and the galvanometer are
exch an ged, the null point is
disturbed.
(3) A rheostat can be used as a potential
divider.
(4) Kirchhoff' s second law represents
energy conservation.
30. The following observations were taken for
determining surface tension T of water by
capillary method :
diameter of capillary, D = 1.2Sx10- 2 m
rise of water, h = 1.45 x 10-2 m.
Using g = 9.80 m/ s2 and the simplified
re la tion T = r h g x 103 N/m , the 2
possible error in surface tension is closest to :
(1) 0.15%
(2) 1.5%
(3) 2.4 %
(4) 10%
(1) ~l2R.H ~ cffr ~ ~ 3lf'tlcn Zf
mm t ~ T.fTti mm clil -qft.:rruy u mcnt 1
(2) ~ B0
9,fi.1a c(;l?..fil1 ~ 'tl, ~ V
i'l(,cj ii 412{ ~ 3TI'i:rn ri ~ 1:f{ ~
fc!eyq ~ 'Sl'Wcm ffl % I
(3) 'Cfcfi' mu f14 ,i en 'ch1 fc!'qq fc!~ er c,W~~~i1
(4) fcn{tjj(fi cfiT ~ A7.ltl ~ ifl miw 'ch1 zymn ti
30. ~ "5ta;MT ~ ~ fcif'tl fr tfRt cfiT ~ cRT
T ffl ifl @<) fct;1:rr ~ % I
~ cfil '&ITTI, D=1.25x10 - 2 m
'iRT "ch'!~. h =l.45 x 1Q - 2 m
g = 9.80 m/ s2 (fm ·~n:c-ft~(f "B.:q-;.
T= r h g x103 N/m , cit~ ffl s 2
~ o-lfcf if ~,nfc@ 1fl cfil f1chld q 'tTR ~
P,) 0.15%
(2) 1.5 %
(3) 2.4%
(4) 10%
A/Page 16 SPACE FOR ROUGH WORK / '{Q; ciini ~ ~ ~
~? .. PART B - CHEMISTRY mTT B - -rnn:R ~
31. Given 31. KlIT Tf<fl t
ttnuT C(graphitc) + 02(g) -) C02(g) ; C(graprute) + Oi(g) -) COi(g) ;
.1.H0 = -393.5 kJ mol - 1 ArH 0 = - 393.5 kJ mo! - 1
Hi{g) + ! Oi(g) -) H20(1) ; Hi(g) + !Oi(g)-) H20(1);
mr~ ~rH0 = - 285.8 kj rnol - 1 ~tJ0 = -285.8 kJ mot - 1
r 1R ~ C02(g) + 2H 20(1) -) CH.i(g) + 202(g) ; C02(g) + 2H20(1) -) CHig) + 202(g) ;
AtJ0 = + 890.3 kJ mol - 1 Atf0 = + 890.3 kJ mol - 1
Based o n the above thermochemical "3m: ~ ~ 3i&.l{mlllf1ch B41ch{Ofl ~ 3lltffi
~ cfi1 equations, the va lue of ArH0 at 298 K for 1R 298 K 1R an~ the reaction C(graphite) + 2H2(g) -) CH4(g)
C(graphite) + 2Hi(g) -) CHig) will be : ~ Atf O cfil "tfR WIT :
~ma.fU! (1) -74.8 kJ mo1- 1 (1) -74.8 kJ mol - 1
(2) - 144.0 kJ mol - 1 ~ - 144.0 kJ mo1- 1
(3) +74.8 kJ mo1- 1 (3) +74.8 kJ mol - 1
1ft:a o-flq (4) + 144.0 kJ mol - 1 (4) + 144.0 kJ mol - 1
1 g ra m of a carbona te (M2C03) ~ chl~~l CM2C03) ~ 1 1l'lll cti1 HCl ~ 32. on 32.
trea tment with excess H Cl produces am~ l)' 3lf~ ~ ~ i am ~ 0.01186 mole of CO2. The molar mass of 0.01186 t:t@ CO2 ~ mcft % I M2C03 cfil
M2C03 in g mo1- 1 is: ll@< s;_oqq11 g mo1- 1 ii~ :
~~ (1) 118 .6 (1) 118.6
(2) 11.86 (2) 11.86
~~ (3) 1186 (3) 1186
1R'Wll: (4) 84.3 (4) 84.3
33. AU is equal to : 33. AU~~t~t:
(1) Adiabatic work (1) '/
~cfil..f
(2) Isothermal work (2) W-1 d I cfl c1iT..f
(3) Isochoric work (3) ~ - au ii a f;1 ch c1iT..f
(4) Isobaric work (4) B qt:J csfl c1iT..f
A/ Page 17 SPACE FOR ROUGH WORK / ~~~~ ~
34. The Tyndall effect is obs1.?rved on ly when
following conditions are satisfied :
(a) The diamete r of the dis pe rsed
particles is much smaller than the
wavelength of the light used.
(b) The diame te r of th e dis p c:> rscd
particle is not much smaller than the
wavelength of the light used.
(c) The refractive indices of the
dispersed phase and dispersion
medium are almost simila r in
magnitude.
(d) The refractive indices of the
dispersed phase and dispersion
medium differ greatly in magnitude.
(1) (a) and (c)
(2) (b) and (c)
(3) (a) and (d)
(4) (b) and (d)
35. A metal crystallises in a face centred cubic
structure. If the edge length of its unit cell
is 'a', the closest approach between two
atoms in metallic crystal will be:
(1) J2 a
a (2) J2
(3) 2a
(4) 2J2 a
34. f2::sA "!l<q]q otjj fc:: J.314'1 ~ ~ f.fr;; ~
~ "ITT"fil % :
(a) -qfta)ft«i cfiOfi qi1 oqrn' ~ Vcfiffi i dl11~Ul <h1 ¥Rf ii cfso Z§RT m I
(b) -qfta)ft«i cfiOfi qi1 o!lm' ~ ~ i d {q~uf cfIT ~ ii ~ fflGl 1ITT m I
(c) 'tlfta)'ftIB ~ o?.TI 'tlft~ .:n~ ~ dl4c:Hf1ich 1:fWnUT c,Tf\:fll ~ ~ m I
(d) 'tlfta)'ftIB ~ o?.TI 'tlft~ .:n~ c)-
614clct1ich 1:fWnUT ~ f"Ft m I
(1) '·
(a) cf?.TI (c)
(2) (b) o?.TI (c)
(~ (a) o~ (d)
(4) (b) o?.TI (d)
35. ~mg~~ "ER m"iRT i:i f~af<:1? mmt-1 'l!R~~mr<tr~~ 'a' t. m ~~i:i~~an~$ Bf?ich2.d4 ~ mrft :
(1) J2 a
a (2) J2
(3) 2a
(4) 2J2 a
A/ Page 18 SP ACE FOR ROUGH WORK / "{tfi ~ ~ ~ ~
E~l:/O = 1.36 V, E~r3+ / Cr =-0.74 V
~~ ~ I E~r,oi-;crH = l.33 V, E~ln04/ Mn'.?+ = l .S l V ·
Amo ng lhe fo llowing, the s tronges l
reducing agent is :
(1) Cr3+
(2) o -(3) Cr
(4) Mn2+
37. The freezing point of benzene decreases
by 0.45°C when 0.2 g of acetic acid is
added to 20 g of benzene. U acetic acid
associates to form a dimer in benzene,
percentage association of acetic acid in
benzene will be :
(K, for benzene=S.12 K kg mol- 1)
(1) 74.6 %
(2) 94.6 %
(3) 64.6 %
(4) 80.4 %
· fstiR.f<?ld 38. The radius of the second Bohr orbit for
~ 'a' hydrogen atom is:
ITT~ m (Planck's Const. h=6.6262x10 -34 Js;
mass of electron=9.1091 x10-31 kg;
charge of electron e = 1.60210 x 10- 19 C;
permittivity of vacuum e0
= 8.854185x10- 12 kg-1m-3A2)
(1) o.529 A (2) 2.12 A (3) 1.65 A (4) 4.76 A
36. ~TT<nt
E~r20~-/Cr3+ = 1.33 V, E~ln04/ t-ln2+ = 1.51 V.
f.p:;:{ -q 'B Sli4(1d4 3,jq'ql~Ch i :
(1) Cr3+
(2) c 1-
(3) Cr
(4) Mn2+
37. ~ C(f~R.c:h ~ cf;l 0.2 g ~ ~ 20 g 'rt ~ ~ t° en~ cf;l ~ 0.45°C 'B q;-q
m~t-1 ~ttfofc.c:h~~'rf~ ~ ~ (~) ~ten ef{iR.c:h ~ cf;l sifa~1aa1 ~ mTTT :
(~ ~~ Kf = 5.12 K kg mol- 1)
(1) 74.6%
(2) 94.6%
(3) 64.6%
(4) 80.4%
38. ~1H't"11 ~~~cm cfi?JT qi'f a1-'o1.11~
mm= (~ ~ h =6.6262x 10- 34 Js;
~t9cf?l1 cf;l ~oll4H = 9.1091 X 10 - 31 kg;
~t-lcf?T1 ~ ~ e =l.60210 x10- 19 C;
f.rcrnJ cf;l cm~ ~a i ch
e0
= 8.854185 x 10-u kg - 1m-3A2)
(1) o.529 A (2) 2.12 A (3) 1.6s A (4) 4.76 A
A/ Page 19 SPACE FOR ROUGH WORK/ ~ cfint $ ~ ~
'
!1
39. Two reactions R1 and R2 have identical
pre-exponential factors. Activation energy
of R1 exceeds that of R2 by 10 kJ mo1 - 1. lf
kl and k2 are rate constants for reactions
R 1 and R2 respectively at 300 K, then
ln(k2/ k1) is equal to:
40.
(R= S.314 J mol - 1K- 1)
(1) 6
(2) 4
(3) 8
(4) 12
pKa of a weak acid (HA) and pKb of a weak
base (BOH) are 3.2 and 3.4, respectively.
The pH of their sal t (AB) solution is :
(1) 7.0
(2) 1.0
(3) 7.2
(4) 6.9
41. Bo th lithium and magnesium display
several similar properties due to the
diagonal relationship; however, the one
which is incorrect, is :
(1) both form nitrides
(2) nitrates of both Li and Mg yield N02
and 0 2 on heating
(3) both form basic carbonates
(4) both form soluble bicarbonates
39. ~ -m"~~- R1 c'f9.fl R2 ~ '{<:{ ~dlct~
~~~~I R1 ctl tifsflllOI ~ R2 ~ tif~llOI ~ if 10 kJ mo1 - I ~ ~ 1 7.lP. 311'~ R1 o~ R2 ~ ~ 300 K 'tfT ~ f.i<rnicti sfi1=ro: k1 o~ k2 mm tn(k2/k 1) f.:rc: ,:j "B ~ qW;f{ m7TI ?
(R =8.31-! J mol 1K I)
( l ) 6
(2) 4
(3) 8
(4) 12
40. ~ ~ ~ (HA) ~ pKa 0211 ~ ~ 8.-fficn (BOH) ~ pKb ~: 3.2 o?.n 3A % I ~ "ffqUl (AB) ~ ~ cfiT pH ml :
(1) 7.0
(2) 1.0
(3) 7.2
(4) 6.9
41. fcrc1,of ~ ~ cfiRiJT, "ffif~ 0211 ~141fiilll4
~ ~ ~~TT~ qi"{a f m ,ft, w 1'.(q, ~ PT~ t, t :
(1) -zy:ri 11~?1~:S ~ ~
(2) "ffif~ 0211 ~,.flfo~4. ~ ~ m 11$ TWt ~ 1l\ N02 o?.n 0 2 ~ f
(1) ~ e.mTll cfilql~2 ¢f1ra f
(4) -zy:rt ~e11~ne1 ~1~cfi1isfl~2 ¢f1@' i
A/ Page 20 SPACE FOR ROUGH WORK / ~~~~~
· , 2 Which of the following species is n ot 42. f.r'1 ii~ mm flf1:tniil 3l·hi14cfilll ~ % ? ~ 4. ~~
:f,"~
3.4 i, l :
paramagnetic ?
(1) 02
(2) . B2
(3) NO
(4) co
(1) 02
~) B2
(3) NO
(4) co
43. Which of the follow ing reactions is an 43. R1=1' -q' ~ ~ m 3Tiimfi'lfT 3l4 'tl<41 qT,M
example of a redox reaction ? (~) 3lf~ "cfi'T 3<!.1~<01 % ?
(1) XeF6 + H 20-? XeOF4 + 2HF
(2) XeF 6 + 2H20 ~ Xe02F 2 + 4HF
(3) XeF4 + 0 2F2 ~ XeF6 + 0 2
(4) XeF2 + PF5 -? [XeF] + Pf 6 -
(1) XeF6 + ~O ~ XeOF4 + 2HF
(2) XeF6 + 2H20-? Xe02F2 + 4HF
(3) XeF4 + 0 2F2 ~ Xef 6 + 0 2
(4) XeF2 + PF5 ~ [Xef] + PF6 -
44. A water sample has ppm level 44. 1(cfi' ~ ~ "G i:ft.i:ft.1(J:{. (ppm) m 'ctt concentration of following anions f.r'1 ::fiOll<.l1i 'ctt ~%I
F- =10; soi- =100; N03 =SO
The anion/anions that make/makes the
water sample unsuitable for drinking is/
are:
(1) only p
(2) only sol-
(3) only N03
(4) both soi- and N03
45. The group having isoelectronic species is:
(1) 0 2- , p- , Na, Mg2+
(2) o-, p - , Na+, Mg2 +
(3) 0 2- , p - , Na+, Mg2 +
(4) o-, p - , Na, Mg+
F- =10; so~- =100; N03 =SO
~1~ ::fiOlll11 -m ~ ~ cf,l' m t-~ 3lj4g~ iif1IBT %;~ t t;~ :
(1) -qr,r p-
(2) -qr,r so~-
(3) "Il1'r N03
(4) soi- o~ No3 ~
45. ~WI~ BLl~~~T-i'l wMl-,, t t : (1) 02- , p-, Na, Mg2+
(2) o - ,F-,Na+,Mg2+
([) 02-, p-, Na+, Mg2+
(4) o - , p-, Na, Mg+
A/ Page 21 SPACE FOR ROUGH WORK / Ten cfiT<t "a:i ~ ~
I \ I
I
I.
46. The producls oblained when chlorine gas
reacts with cold and dilute aqueous NaOH
arc:
(1) c1 - and cio-
(2) ci - and C102
(3) CIO and CI03
(4) 002 and Cl03
47. In the following reac tions, ZnO is
respectively acting as a/an :
(a) Zn0+Na20 ~ Na2Zn02
(b) ZnO + CO2 ~ ZnC03
(1) acid and acid
(2) acid and base
(3) base and acid
(4) base and base
48. Sodium salt of an organic acid 'X' produces
effervescence with cone. Hi504. 'X' reacts
with the acidified aqueous CaC1i solution
to give a white precipitate which
decolourises acidic solution of KMn04 .
'X' is:
(1) CH3COONa
(2) Na2C20 4
(3) C6H 5C00Na
(4) H COONa
46. ~~fmcft~c!J~NaOHin-m~
31f\ffll ~ten~ m q@ ~ m11 =
(1) ci - o~ c10-
(2) c1 - o~ Cl02 r
9,) Cio- o~ OOi
(4) Cl02 o~ 003
47 . f.r8 3if'ml~ -q, ZnO~: cfiTll ffl:
(a) ZnO+Na20 ~ Na2Zn02
(b) ZnO + CO2 ~ ZnC03
(1) ~o~~
(2) ~o~~
(3) ~o~~
(4) ~o~~
48. ~ cfil4Rcfi 3lta "cfiT tilf.slll.f ~ 'X' 11R:
Hi5()4 ~ m~ ~<!.~<!.1~2 ~ t1 'X' ~ ~ CaC12 ~ "ffi?.l 31f\ffifi<n cfi«fT t 311"{
~ 3lq~ ~ t ~ KMn04 ~ ~ ~qi1~GRJ~!1 'X'!:
(1) CH3COONa
(2) Na2C20 4
(3) C6H5COONa
(4) HCOONa
A/ Page 22 SPACE FOR ROUGH WORK / 'tCfi ~ c}j ~ ~
llT :
49. The most abundant elements by mass in
the body of a healthy human adu lt a re :
Oxygen (6 J.4 °o ); Carbon (22. 9 °,o ),
HyJrogen (10.0°,o); and Nitrogen (2.6°~).
The weight which a 75 kg person would
gain if all 1 H atoms are replaced by 2H
atoms is:
(1) 7.5 kg
(2) 10 kg
(3) 15 kg
(4) 37.5 kg
SO. On treatment of 100 mL of 0.1 M solution
o f CoC13.6H 20 with excess AgN03;
1.2 x 1022 ions are precipitated . The
complex is:
(1) [Co(H20)JC13
(2) [Co(H20)5Cl}C12.H20
(3) [Co(H20)4C!i]Cl.2H20
(4) [Co(H20 hC13].3H20
49. 1% ~ ~ ~ mn it i:rr,n cifT ~ "Xi C4§C114C1 "it P1ffi c{R9 Q(q ~: 3licffil.:il1 (61.4 °-o);
q;rcf1 (22.9%), ~l'.:i11 (10.0%); <f~l
1l~{1'1f1 (2.6°-o) I 75 kg cf-'iR c{R9 1% ollfcF,
~ fflT{ ~ -a'U 1 H ~3TI ~ 2H ~3TI ~ ~ ~ ~ m ~ 'ITT it -m ~ wft. ~ %:
(1) 7.5 kg
(2) 10 kg
(3) 15 kg
(4) 37.5 kg
SO. CoC13.6H20 ~ 0.1 M ~ ~ 100 mL ~ AgN03 ~ anf~cfll' -q· 3TI'4cf('f cITT~ ~
1.2x1022 3W-R 3TciW ma f I ~ % :
(1) [Co(H20)6]Cl3
(2) [Co(H20)5Cl]C12.H20
(3) [Co(H20)4C12]Cl .2H20
(4) [Co(H20hC13].3H20
A/ Page 23 SPACE FOR ROUGH WORK / ~ cfiTd ~ ~ ~
51. Which of the foll ll\\ ing compound c: wil l 51. tti:1111;;? ~11 ~'mfi7.11 ii f:p:::p:f 'iJ cfi'R m ~ 53.
form significant am()UJ1l of meta product 1?27~ cfl1 4~tiftuf lfBIT ~ "i:fitrrr? during mono-nitration reaction ?
NH2 N H~ I
6 (1) C) {1)
1':I ICOCH1 N I ICOCH3
0 I
(2) (2) 0 54.
Oil OH
(3) 6 f3) 6 (4)
c5H3 (4)
c5H3
52. Which of the fo l1owing, upon trea tment 52. f.rCi -q ~ cffR, tert-BuONa ~ m~ ~ with tert-BuON a followed by addition of cm ~ mlfR ~ ~ P@'R "tR, ~ ~ °tTl bromine water, fails to decolouri ze the cn1 ~ cm -q arnil~ mm t? colour of bromine ?
55.
(1) CYOY. (1) (Yo'( 0 0
(2) (2)
(3) CY'1. (3) CYl . Ol"'''• OlC,H, ,
(4) I (4) I r r
A/ Page 24 SPACE FOR ROUGH WO RK / ~~~~~
~ r,~'trl
I
The formation of which of lhe follow ing
polymers involves hyd rolysis reaction ?
(1) Nylon 6, 6
(2) Terylene
(3) N\'lon 6
(-!) Bakelite
54. Which of the fo llowing molecules is least
resonance stabilized ?
(1) C N
(2) 06-(3) 0 (4) 0
0
55. The increasing order of the reactivity of
the following halides for the ~1 reaction
is:
CH3CHCH2CH3 I
CH3CH2CH2Cl
Cl (I) (II)
p - H3CO - C6H4 - CH2Cl (ill)
(1) (I) < (Ill) < (II)
(2) (II) < (ID) < (I)
(3) (III) < (II) < (I)
(4) (11) < (I) < (III)
53. f.rc:r tjscicti'i -rf "B m "B tjs1;1q, -rf '3@ ~
3:if~ (4f.:.:ifua i?
(1) ~6,6
(2) ~
(,) ~6
(4) ~Ehcii~l
54. f.rc:r -rf "B cfi11 m ~ ~ j1 I fc;cfi ~ "B ~ ~t?
(1) 0 - N
(2) 06 (3) 0 (4) 0
0
55. SNl 3lf'ffifi<n t- ~ ~ ~ci l~ -sY 'cfi1 3TI\Jfs:fi41C'Gcfidi <ll1 ~ ~ t :
CH3CHCH2CH3 I
CH3C!iiCH2Cl
Cl (I) (II)
p - H3CO-C6H4 - CH2Cl (Ill)
(1) (I) < (III) < (II)
G> (II) < (Ill) < (I)
(3) (III) < (II) < (I)
{4) (II) < (I) < (lll)
A/ Page 25 SPACE FOR ROUGH WORK / ~ ~ c); ~ ~
56. The major product obtained in the 56. f.,x:::, 3:n'~ ii "Sn1<l m cffffi :I&l ~ t: following reaction is :
(1)
(2)
(3)
Br
lBuOK il
( + )C6H 5CH(OtBu)CH2C6H5
( - )C6H5CH(Ol"Bu)CH2C6H5
( ± )C6H 5CH(Ol"Bu)CH2C6H5
57. Which of the following compounds will
behave as a reducing sugar in an aqueous
KOH solution ?
(1) HOH2~ CH20H
HO OCH3
OH
(2) HOH2C
~CH20CH3 H
0 OH
(3) HOH2~CH20H
HO OCOCH3
OH
(4) HOH2~CH20H
HO
OH
Br
lBuOK C6Hs 6. X CH
6 5 ( +)
(1) ( + )C6H 5CH(OtBu)CH2C6H 5
(2) (- )C6H 5CH(Ol"Su)CH2C6B 5
(3) ( ± )C6H5CH(Ol"Su)CH2C6H5
(4) C6H5CH=CHC6H 5
5 7. ~ ~ KOH ~ if f.rCl if "ft cfi"I-:, BT
~ ~ 3iqi4lllc:h ~ ~ ~ if ~ cntrn?
(1) HOH2~CH,OH
HO OCH3
OH
(, ) HOH2C
~CH20CH3 H
0
OH
(3) HOH2~CH,OH
HO OCOCH3
OH
(4) HOH2C~CH20H
HO
OH
A/ Page 26 SPACE FOR ROUGH WORK / ~ cfiTd ~ ~ ~
::
59.
58. 3-Methyl-pcnt-2-ene on reaction with HBr 58. 4llcftll~:S cfi1 ~ ii, 3-~2R1-~-2-f.l',
in presence of peroxide forms an addition HBr ~ tll~ 3lf~ cfiB 1:f{ ~ ~ ~ product. The number of poss ible cRTffi t I~~~~ nifcrq ti41qllfcllll
stereoisomers for the product is : cfi1 lt&rr M :
(1) Two (1) ~
(2) Four (2) ~
(3) Six (3) £J:
(4) Zero
59. The correct sequence of reagents for the 59. f.r8 (C\4HHO! ~ ~ 3lf~ cfi1 ~ sf;l=I
following conversion will be : mTTT :
0
Q, 0
Q, ¢ ¢ CHO CH3 CHO CH3
(1) CH3MgBr, [Ag{NH3)ifOtr, (1) CH3MgBr, [Ag(NH3h J+oH- ,
H+/CH30 H / W /CH30H
(2) [Ag{NH3)ifOW, CH3MgBr, (2) [Ag{NH3)ifOH-, CH3MgBr,
W/CH30H W/CH30H
(3) [Ag(NH3)ifOH-, H+/CH30H, (3) [Ag(NH3)i fOH-, W/CH30H, CH3MgBr CH3MgBr
(4) CH3MgBr, H+/CH30H, (4) CH3MgBr, H+/CH30H,
[Ag(NH3)ifOH- [Ag(NH3)if OH-
A/ Page 27 SPACE FOR ROUGH WORK / ten cfiT<f ~ ~ ~
60. The majo r product obtained in the 60. f,,::, 3TI~ ii '5l'l1<f ::{'&i ~ % : following reaction is :
DIBAL - H
COOH
(l) ~ CHO COOH
(2) Q"OiO CHO
OH
(3) 6cCHO COOH
OH
(4) 6c0i0 CHO
OIBAL - H
COOH
(l) ~ CHO COOH
(2) Q"CHO CHO
OH
(3) 6cCHO COOH
OH
(4) 6cCHO CHO
A/ Page 28 SPACE FOR ROUGH WORK / ~ cfiT<f ~ ~ ~
PART C - MATHEMATICS
61. The function J: R ~ [ -~, ~ ] defined
62.
63.
!( X . as :\) =
2 , 1s :
l +x
(1) injective but not sutjective.
(2) surjective but not injective.
(3) neither injective nor surjective.
( 4) invertible.
If, for a positive integer n, the quadratic
equation,
x(x + 1) + (x + l)(x + 2) + ....
+ (x + n - 1) (x + n) = 10n
has n-vo consecutive integral solutions,
then n is equal to :
(1) 9
(2) 10
(3) 11
(4) 12
Let w be a complex number such that
2w+l= z where z = H . If
1 1 1
1 2 -w - 1 (1)2 =3k,
1 w2 7 w
then k is equal to :
(1) z
(2) - 1
(3) 1
(4) -z
61. ~ /: R -) [ -~, ~J, -m
62.
63.
/(.\) = X &JU -qft~ t: L + x2
(1) ~t~~-:m%1 (2) ~%~~~ti (3) -::rm~3m-::rm~t1 (4) olj&il.fUTilJ % I
~ ~ 'tHtOlfcfi n ~ ~ ~ B41cfi{OI
x(x + 1) + (x + 1)(x + 2) + ....
+ (x + n - 1) (x+ n) = lOn
~ ~ ~ t1111cnlll ~ t, en n ~ i :
(1) 9
(2) 10
(3) 11
(4) 12
llRT w ~ ~~ ~ V:W % fcfi 2w+l =z
~ z=R %1 ~
1 1 1
1 2 -w -1 w 2 =3k % 1 w 2 w 7
cf! kisRliR%:
(1)' z
(2) -1
(3) 1
(4) -z
A/ Page 29 SPACE FOR ROUGH WORK / ~~ <li ~ ~
If A= [ 2 -3) ~ A= [ 2 -~J %_ o1 adj {3A2 + 12A) 64.
1 , then adj (3A2+12A} is 64. --1 - 4
equal to : ~% :
(1) [s: 63) 72 n: 63)
72
(2) [51 8-1) 63 72 (2)
:3 72 [ -1 84)
(3) [ 72 - 84
-63) 51
(3) [ 72 - 84
-63) 51
(4) [ 72 -84) -63 51
(4) [ 72 -84) -63 51
65. If S is the set of distinct values of ' b' for 65. ~ S, 'b' cfiT ~ fclf'4?t TI cfiT ~ %~ which the following sys tem of linear ~ f.p:;r tfurcn fl4lch{OI ~
equations
x+y+z=1
x+ ay+z= 1
ax+ by+ z= O
has no solution, then S is :
(1) an infinite set
(2) a finite set containing two or more
elements
(3) a singleton
(4) an empty set
x +y+z= 1
x + ay+z= 1
ax + by + z= O
(1) ~ 31qftfqa ~ t-
(_;Y ~~ fl:{-.4~ t-~~7:ll ~ ~i
(3) ~'ITT~cf@T~i
(4) ~ ft:cffi fl~'i4q t°
A/ Page 30 SPACE FOR ROUGH WO RK / rq:; ~ <fi ~ ~
66. A man X has 7 friends, 4 of them are ladies
and 3 are men. His wife Y also has 7
friends, 3 of them are ladies and 4 are men.
Assume X and Y have no common friends.
Then the total number of ways in \.-Vhich >,. and Y toge ther can throw a party
inviting 3 ladies and 3 men, so that 3 friends
of each of X and Y are in this party, is :
(1) 468
(2) 469
(3) 484
(4) 485
67. The value of
(21c1 - rnc1) + (21c2 - LOci) +
( 21 C3 - 10C3) + ( 21 C4 - IOC4) + ..... +
(21c10 - ioc10) is:
(1) 221 _ 210
(2) 220 _ 29
(3) 220 _ 210
(4) 221 -211
66. "C(cf; olW@ X ~ 7 fi:t'3i t ~ 4 qfue1~ i oY.11
3 ~ t ~ i:rFn Y ~ qt 7 fi:t'3i t, mll 3 qf~e1~ om 4 ~ ~ 1 ?:ffi' "tlRT 11<n fcii x oY.11
Y<fil~~(common)Mmt1 m ~ ~ cf>1 ~ ~ X oY.11 Y ~ m~ 3 llfuffi3lf oY.11 3 ~ ~ ~ ~ ~ fcii x oY.11 Y ~ ~ ciR-"ffi1 m ~, t :
(1) 468
(2) 469
_9' 484
(4) 485
67. (21 c, - 1oc1) + (21c2 - ioc2) +
(21c3 - ioc3) + (21c4 - ,oc4) + ..... +
(21c10 - 1oc10) <fiT TfR t:
(1) 221 _ 210
(2) 220- 29
13) 220-210
(4) 221 _ 211
68. For any three posi t ive real numbers 68. ~ cfR ~ qlfdfc:lcfi ~3TI a, b om c
a, band c, ~~
9(25a2 + b2) + 25( c2 -3ac) = 15b(3a + c). 9(25a2 + b2) + 25(c2 - 3ac) = 15b(3a + c)
Then: t m: (1) b, c and a a re in A.P. (1) b, c om a 'Wfiffi: .mft ii i (2) a, b and c are in A.P. (2) a, b om c 'Wfiffi: .mft ii i (3) a, b and c are in G.P. (3) a, b om c :ronm .mft ii { (4) b, c and a are in G.P. (4) b, com a :ronm .mft ii {
A/ Page 31 SPACE FOR ROUGH WORK / ~ ~ ~ ~ ~
69. Let a, b, c R. If/(.,) = a., 2 + b.\ +c is such
that a +b+c=3 and
70 .
f (x + y) = /(:r) + /0;) + xy, V x, y e R,
10
then L /(n) is equal to: n - 1
(1) 165
(2) 190
(3) 255
(4) 330
lim cot x - cos x 1 x--+ ,r 3 equa s :
(1)
(2)
(3)
(4)
2 {1i - 2x)
1
16
1
8
1 -.J
1
24
71. If for x e ( 0, ±), the der iva t ive of
tan- 1 (
6xJx ) is Jx · g(x), then g(x) 1-9x3
equals:
3x../x (l) 1 - 9x3
(2)
(3)
(4)
3.r
1 -9x3
3
1 + 9x3
9
1 + 9x3
69. "'GRT n, b, c E R I ~/(x) - a,:?..:. h.t -..c~ t fen <l + b + c = 3 % cf~ 'B'll X, y f. R ~ ~ J (x + y) = /(1) + f(JJ) + xy
70.
10
t m I J<n> cfW.R % : n - l
(1) 165
(2) 190
(3) 255
(4) 330
lim cot x - co~ x ~ t : x--+; {1i - 2x)
(1)
(2)
(3)
(4)
l
16
1
8
I ... l
24
71. 1:iR x e (o, .:!.) ~~ tan-1( 6x.fx3
) cfil 4 1 - 9x
3ic!chC'11 Jx · g(x) t, 'ffi g(x) ~ % :
(1)
(2)
(3)
(4)
3x.Ji
1 -9x3
3x
1 -9x3
3
1 + 9x3
9
1 + 9x3
A/ Page 32 SPACE FOR ROUGH WORK / ~~ "ai ~ ~
72. The normal to the curve
y(x-2)(x -3) = x+6 at the point where
the curve intersects the y-axis passes
through the point :
(1) (%, %)
(2) (! _.!.) 2 I 3
(3)
(4)
73. Twenty meters of wire is available for
fencing off a flower-bed in the form of a
circular sector. Then the maximum area
(in sq. m) of the flower-bed, is :
(1) 10
(2) 25
(3) 30
(4) 12.5
72. c{sf, y(r-2)(r-3) =x +6 ~ 6B ~"If{,~
qsf, y- a:fa;t qi1 ~ t ~ TflJT a:{f',m f.ri:;,
-q~~~~m~ t-?
(1)
(2)
(3)
(4)
73. ~~<film, -m ~~ ~~m~ ~-qt <fil~ qj"8 t-~ ~~cl'R
~i, ol~<filfflcfil~~ (cf7f-rft. it ),% : (1) 10
(2) 25
(3) 30
(4) 12.5
74. Let 10 = J tann x dx, (n > 1). If 74. lfRll0 = Jtan°xdx,(n>1)t1 m 14 +I6 =a tans x+bxs+ c, where C is a
constant of integTation, then the ordered
pair (a, b) is equal to :
(1) (i, 0) (2) (i I - 1)
(3) (-i, 0) (4) (-i, 1)
14 + I6 =a tan5 x+ bxs+c 't ~ C ~ W:ll&it11 ~ t o1 snfi:ra ~ ( a, b) iiRl"if{ i :
(1) (i, o) (2) (i, -1) (3) (-i, 0)
(4) (-i, 1)
A/ Page 33 SPACE FOR ROUGH WORK / tq; ~ <ti ~ ~
,_ 4
f dx 75. The integral is equal to : l + cos l
(1) 2
(2) 4
(3) - 1
(4) - 2
76. The area (in sq. un its) of the region
{(x, y) : x ~ 0, x + ys3, x2 s4y and
ys1 + Jx } is:
3 (1) 2
(2)
(3)
(4)
7
3
-2
59 12
77. If (2 + sinx) dy + (y + 1)cos x = 0 and d.x
y(O) = 1, then y(;) is equal to :
(1) 2 3
(2) 1 --3
(3) 4 -3
(4) 1 -3
,_ 4
75 f dJ. =~ .. • tt'ilc:t"l<:1 ...,,,...,, 1:1
1 + COS X ll 4
(1) 2
(2) 4
(3) -1
(4) -2
76. ~hT {(x, y) : x ~ O, x + ys3, x2s 4y om
ysl + Jx} cfiT ~ (wf ~) "ij ! :
(1)
(2)
(3)
(4)
3 -2
7 3
5 -2
59 12
77. "liR (2 + sinx) dy + (y + l)cosx = 0 o~ cu
y(O)=l t oT y(;) ~t:
(1) 2 --3
(2) 1 --3
(3) 4 -3
(4) 1 -3
A/ Page 34 SPACE FOR ROUGH WORK / ~ ~ ~ ~ ~
78. Let k ~ an integer such that the triangle 78. -qT,T k 1lcfi ~ ~ % ~ ~~, ~ m-q with vertices (k, -3k), (5, k) and ( - k, 2) (k, -3k), (5, k) o?.n ( - k, 2) t ct,1 ~~
has area 28 sq. units. Then the orthocentre 2sq11~t, m~~~-~~~ of this triangle is at the point : 1R%.~t:
(1) (1, !1 ( I ) (1, ~) -l ,
(2) ( 1, -%) (2) ( 1, -i)
(3) ( 2, %) (3) ( 2, %)
(4) ( 2, -%) (4) ( 2, -%)
79. The radius of a circle, having minimum 79. ~ ~~~cfl, ~qsf;y = 4 - x2
area, which touches the curve y=4 - x2 o?.ll U913TI y = lxl qi) m ~ t cf,1 ~ t : and the lines, y = lxl is :
(1) 2(J2. - 1) (1) 2(-fi. - 1)
(2) 4(J2. - 1) (2} 4{J2 - 1)
(3) 4(J2 + 1) (3) 4(J2 + 1)
(4) 2(J2 + 1) (4) 2(J2. + 1)
80. The eccentricity of an ellipse whose centre 80. 1lcfi ~, ~ ~ '@ ~ lR t cf,1
is at the origin is .! . If one of its directrices 2
a~~dl .!t-1 ~~1lcfiRl-rnlx=-4t° 2 I
is x = - 4, then the equation of the normal m ~ ~ ( 1, %) lR ~ an\@q ct,T
to it at ( 1, %) is : (4qlq,{Oj t :
(1) 4x-2y = 1 (1) 4x-2y=1
(2) 4x + 2y =7 (2) 4x+2y =7
(3) x+2y = 4 (3) x+2y=4
(4) 2y - x = 2 J1)....-2y-x = 2
A/ Page 35 SPACE FOR ROUGH WORK / ~ ~ c}; ~ ~
81. A hyperbola passes through the p oint 81.
P(/2, ./3) and has foci at (±2, 0). Then
the tangent to this h yperbola at P also
passes through the point :
(1) (2.Ji., 3J3)
(2) (./3, /2)
(3) (- J2, - ,fi,)
(4) (3/2, 2-/3)
(1) (2/2, 3'13)
(2) ( J?, I .fi.)
(3) (-12, -J3)
(-l) (3.fi, 2./3)
82. The distance of the point (1, 3, -7) from 82. ~ ~ _;rr ~ (1, - 1, - 1) ~ ~ ~ t" the p lane passing through the point q~ ~l 3-Tf~~ ";111. tm31r (1, - 1, - 1), having normal perpendicular x - 1 y + 2 z - 4
--=--= ---am . x- 1 y+2 z- 4
to both the lines -- = -- = --1 - 2 3
x-2 y + 1 z+7 . an d -
2- = --=-i'"" = --=-i'"", 1s :
(1) 10
JB3 5
(2) /83
(3) 10
m 20
(4) m
1 -2 3
x-2_y+1_z+7 . ~...Af::r.:r -- - -- - -- ~ ~ Q q")I ,..,~
2 -1 - 1 '
(1, 3, - 7) ~ ~ % :
(1) 10
Js3 5
(2) Js3
(3) 10
.ff4
(4) 20
ff4
83. Uthe image of the point P(l, - 2, 3) in the 83. ~ fcf°s. P(l, - 2, 3) q;-1 ~
p lan e, 2x +3y- 4z+ 22 =0 measured 2x+3y-4z +22 =Q -q ~ Slfafc(q sill~
parallel to the line, ~ = I = !.. is Q then 1 4 5
PQ is equal to :
(1) 2Jifi.
(2) Jiff (3) 6Js
(4) 3Js
X y z, ·~ ~~ - = - = - cfi ~ 1:1 Q Q 01 PQ ~ 1 4 5 ' '
%: (1) 2Jifi.
(2) Jiff (3) 6.JS
. (4) 3Js
A/ Page 36 SP ACE FOR ROUGH WORK / TCfi ~ °* ~ ~
-+ /\ /\ /\ -+ /\ /\ i /\ /\ /\ -+ /\ /\ ,, 84. Let a = 2i + j - 2k and b = , + j. 84. 'tfRT a = 2i + J - 2k o?.TI b = ; + j i1
Let -; be a vector such that 17 - -:I = 3,
I(-; x b) x ;I = 3 and the angle bet ween
-+ -+ -+ t )
c and a x b be 30°. Then a · c is
equal to:
(1) 2
(2) 5
(3) 1 -8
(4) 25 8
85. A box contains 15 green and 10 yellow
balls. If 10 balls a re ra ndomly drawn,
one-by-one, with replacement, then the
variance of the number of green balls
drawn is:
(1) 6
(2) 4
(3) 6 25
(4) 12 -5
1(--i )) .... , --i -+ -+ a X h X C = , o?.TI C 3ITT a X b ~
~ . ~ --+) ~ (';{l"q cf;l cfiTUT 30"' t>, o1 a · C ~ ~ :
(1) 2
(2) 5
(3) l -8
(4) 25 8
ss. 1(<ii ~ ii 15 ~ o?.TI 10 i:fre1 TR f 1 ~ ~ -'{(cf; ~ llliiajlff, ~ mto, 10 iR f~ct11ffi ~ m ~ ~ ~ ~ cf;l
1fmUT t:
(1) 6
(2) 4
(3) 6
25
(4) 12 5
A/ Page 37 SPACE FOR ROUG II WORK / ~ 'cnfd $ ~ ~
6. For three C\ cnls A, B ~nd C,
P(Exactly o ne of A or B occurs)
= P(Exactly one of B or C occurs)
I = P(Exactly one of C or A occurs) = 4 and
P(AII th <.' three C\'ents occur
1 c;imultaneouslv) = -
6.
• J
Then the probability that at least one of
the events occurs, is:
(1) 7
16
(2) 7
6-l
(3) 3
16
7 (4) 32
87. U two different numbers are taken from
the set {O, 1, 2, 3, ...... , 10}; then the
probability that their sum as well as
absolute difference are both multiple of 4,
is :
12 (1) -
55
(2) 14 -45
(3) 7 -55
(4) 6 55
86. or:t ~3TI .\, B oerr C ~ ~
P( A 31~ B ii "fl ~ ~ m2o mm %)
= P( B 31?.fc:n Cit 'if ~ ~ ~ ~ t)
- P(C3l~Aii'it~~~m<ft%) = ! o?.ll 4
P( t1~ oB ~ ~ "I:ll~ ~ mm 5 1 ,, tt) = 1( (.,
m si,P-1q;a1 fcn q;tJ ~ q;tJ ~ ~ ~ m, % :
(1) 7
16
(2) 7 64
(3) 3
16
7 ( -1) 32
87. "lJR ~~ii:4~ {O, l, 2, 3, ...... , 10} it~~~ ~ f.iq;,R) ~, <'fl m 41 114,(1 o?.ll ~ 3TIR ~ M~11:JA, zyij iti °TfR iti ~ v-, <.fil SIIP-1<6di % :
(1)
(2)
(3)
(4)
12 55
14 45
7
55
6 55
A/ Page 38 SPACE FOR ROUGH WORK / ~~ -a;~~
88. If S(tan'.! x-cos2 x) = 2cos 2T + 9, then the 88. ?:!fc; S( tan 2 x - cos2 x) = 2cos 2.t + 9, o1 value of cos 4x is : cos 4x q;i i:rR % :
(1) 1
(1) 1 - -
3 r- · 3
(2) 2
(2) 2
- -9 9
(3) 7
(3) 7 --
9 9
(4) 3
(4) 3
5 5
89. Let a vertical tower AB have its end A on 89. l'.JRT ~ ~'tR llRR AB ~ % fefi ~ the level ground. Let C be the mid-point ftro A ~ 1R % I l'.JRT AB q;i l:I~ ~ C % of AB and P be a point on the ground such om~ 1R IBra ~ P ~ % fcfi AP = 2AB
that AP= 2AB. If LBPC= 13, then tan 13 is ~ LBPC = 13 t err tan 13 ~ % : equal to:
(1) 1
(1) 1
- -4 4
(2) 2
(2) 2 - -
9 9
(3) 4
(3) 4 - -
9 9
(4) 6
(4) 6 - -
7 7
90. The following statement 90. f.rc:r ~ (p-+q)-+[(-p-+q)-+q] is : (p-+q)-+[(-p-+q)~q] :
(1) equivalent to -p-+q (1) -p-+q ~ BGfl~ %
(2) equivalent to p~-q (2) p-+-q ~ BG~ %
(3) a fallacy (3) ~ ~,qm (fallacy)%
(4) a tautology (4) ~ 9.1{,fc:kl (tautology) % - 0 0 0- -oOo-
SPACE FOR ROUG H WORK / ~ cfiTd ~ ~ ~
A/Page 39