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

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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_.., •

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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