f tl,- 2~\~ JI SIPCS-O:lx/14
Set Code: A Seal of Superintendent of Examination Centre & Signature of Invigilator
To bIl filled in by candidate by Ball-Point pen only Roll Number
~----------------------~I I Signature of Invigilator :
Name of Candidate :
Name of Invigilator:
Time: . No. of Questions : 100
SIPCS-01X/14
Set Code: A
TO CANDIDATES
1. (a) Candidates are allowed 10 minutes to fillup the basic .' information about themselves in the OMR answer sheet such as Name, Roll No., etc. (b) After this, question booklet will ~e given to the candidates • they are required to do the following: (i) Examine the booklet and to see that all paper seals at the edge of the booklet are intact Do not accept the question booklet if sticker seals are not intact. . . (ii) Tally the number of pages alongwith no. of questions printed on cover of the booklet In case of any discrepancy please get the booklet changed. This should be done within S minutes of receiving the question booklet, after which neither the question booklet will be replaced nor will extra time be given. (iii) Check that question booklet contains the questions of all relevant subjectsltopics as required and stated in the lSDK and no repetition or omition of questions is evident. (iv) After examining the question booklet please enter the Serial No. of the question booklet at the appropriate place in the answer sheet and the corresponding circles be darkened with Black ball-point pen. (c) Candidates are not permitted to mark answers in the Answer Sheet in these IS minutes. TWO Hours more will be given for marking all the answers. (For instructions
I I I I
Declaration: I have read and understood the directions given below. 'f'da D Signatureo <;andi te: ate: .
'"
INSTRUCTIONS
512328
Serial No. of Answer Sheet
I I I I I
Number of Pages in Booklet: 48
~.
Sr.No.
regarding markinl
Sr.No.
512328
2. (a) On page 1 of Answer Sheet in upper half portion, write Name of Exam, Name of Exam Centre and Date of Exam. Put your signatures also. On the lower half portion of this page fill in the boxes 0 of the first topmost line in capital letters, your surname and name (in English). Write one letter in each box Below each letter darken with Black ball-point pen the circle 0 bearing same letter. (b) On page 2 of Answer Sheet fill in your Roll No., Set Code, Sr. No. of Question Booklet etc. ~ writing in the 0 and below it by darkening corresponding O. (c) On page 2 of Answer Sheet only the answers to questions are to be marked. The instructions for this are available on the back cover page of this question booklet. (d) All entries to be made by Black ball-point pen. 3. Optical Mark Reader (OMR) machine prepares the result by reading the entries made in the circles 0 with the Black ball-point pen on page 1 and 2 of the Answer Sheet, hence the candidate must be extremely careful in marking these entries and must not commit errors. 4. Please do not write anything extra except what is asked for. S. Use of any Calculator, Mobile Phones or any other Electronic Gadgets and Log Tables etc., is Strictly Prohibited. 6. Rough work should be done on the blank pages provided after each Section or Subject. Extra paper will not be supplied. 7. Use of Whitener in the O.M.R. answer sheet is not allowed. In case if it is used, UFM case will be registered and candidature will be cancelled.
o
the answers please see the back cover page of this Question Booklet)
-
...'" .~... ,
\
--
~ I
SIPCS-01X114
SET-A Maximum Marks: 100 atfQC6dQ ~: 100
Time for marking all 100 Questions: 2.00 Hours ~ 1001Woit1&l ~~15f~: 2.oo'm
Note 1.
This paper has Three sections, Section-A Chemistry: (Q.No.01 to 33), Section-B Physics : (Q.No. 34 to 66) and Section-C Mathematics : (Q.No. 67 to 100).
2.
This question booklet contains 100 questions numbered from 1 to 100 and each question carry 1 mark. All questions are compulsory. There is no negative marking.
3.
Tally the number of pages alongwith no. of questions printed on cover page of the booklet. Also check that question booklet contains the questions of all relevant subjects/topics, as required and stated above and no repetition or omition of questions is evident.
4.
If any discrepancy is found in the Question booklet the same can be replaced with another correct question booklet within first 15 minutes.
5.
Before answering the questions please read carefully the instructions printed on the back cover page of the question booklet and strictly follow them. Indicate your answers by blacking
bubbles carefully only on theO.M.R. Answer Sheet provided. 6.
Use of any type of calculator, mobile phone or any other electronic equipment and log table etc. is strictly prohibited.
1.
~
2.
~
(>T.Sti.34 ~ 66)
~
~~"q3(.q~
100 ~~
~I ~ 3.
t ~"'31
('fR ~
~.q
~
~-~
~
: (>T.Sti. 01
~
CfiT~
~
~
~CfiI.q~~~/'fWT~fcf;~Wrr11mt, '"1'tft(ff~~~'"1'tft
4.
~-!!R
.q ~
~
~
:
~CfiTtllNt~
~
I
ctT~
w.rr ~
~ 33) ~-GJ
: (>T.Sti.67 ~ 100) I 1 ~ 100oq;~~~~~
~ijll('qCf) 'l~iCf)"1 '"1'tft
!!R
~
tR
~~
~ctT~~~~~ ~CtT .~ ~ ~
I~
~~-
~o)
I tR ~
w.T1l 15 ~.q
cq~clCf)(~
~-!!R
~I
5.
~~~~~~~~Cf)I~~~tR~~"CfiTt4H'lciCf)~~~~ ~ "tfR'R qf{ I
~ 6.
m~~ eft l1f
an.~.am:. a:a«ftl
"tR {'I1c(~I;ft'(cfCf)~
~
~
~
cbl~1( I
M
,:ft>rCfiRCfiT~cl~~l(,
~
Cfil ~"Cf)("1l
~
'ijcqi~cl-q;);r(ffM,:ft~~
~
~~Cf~iRCf)3QCf)(Oi~~~
tl
SIPCS-01X114
-2-
Set-A
#
•
Section- A Chemistry (Q.No. 01 to 33)
1.
WU'C - at (\414 •• WAT (lie 'We
Which is most acidic among these?
1.
~~~.t?
(A) As20S
(A) As20S
(B)
Sb20S
(B)
Sb20S
(C)
N20S
(C)
N20S
(D) P20S
01 '1l 33)
(D) P20S
~
2. ••
Which of these is most basic?
2.
(A)
seo,
(A) Se02
(B)
Al203
(B)
(C)
Sb203
(C)
(D) Bi203 3.
The maximum osmium is
oxidation
state of
3.
~O3
Sb203
(D) Bi203
.
3tT('Iillqq
(osmium)
aiicfttlcMol ~.
(A) + 6 (B)
+7
(B)
+7
(C)
+8
(C)
+8
The electronic gadolinium is
eft ~ qq'J t ?
(A) +6
(D) +3
4.
(~).t?
~~~I(oftq
(D) +3
configuration
(A)
[Xe] 4f85do 6s2
(B)
[Xe] 4f15d1 682
(C)
[Xe] 4f35ds 6s2
(D)
[Xe] 4f65d2 652
of
4.
~ s1 M\ i'Zlq q iIIT $M CI{I Ph., ~
"41 ('I tP.IT
t?
SIPCS-OIX114
(A)
[Xe] 4f8 5do 682
(B)
[Xe] 4f' 5d1 652
(C)
[Xe] 4f3 5ds 6s2
(D)
[Xe] 4f6 5d2 6s2
- 3-
Set-A
5.
The equivalent weight of K2Cr207 in acid medium is equal to
it
K2Cr2 07 enT. $fIf)H"'G
(B)
1/2Molecular
Weight
(A) atlolRtCfi
(C)
1/6Molecular
Weight
1/5 Molecular Weight
In LiAIH4, the ligand is
6.
(B)
112
at IOIRtCfi
(C)
116
~loIRtCfi
(D)
1/5
~lolRtCfi sm
LiAIH4 it HI$fl •.g (ligand) Cfm t
(B)
H-
(B)
H-
(C)
H
(C)
H
[MA2B41
(B) (C)
"
(D) ~~~~
Which of these coordination complexes does not show geometric isomerism? A and B are monodentate ligands. (A)
7.
~
~ q;T;r~q;,
~~?
A
am
[MA3B31
(B)
[M~B31
[MA4B21
(C)
[MA4B21
(D) MAsB
8.
° t?
(CH3)3C MgBr c€"r D2 '(I~14f.fCfi ~
(A) (C~)3CD
(CD3)3CD
«:
(D) MAsB
(CH3)3CMgBr with D20 gives
(C)
isomerism) B ~j•• j~'1lGHI$~ •.g
(monodentate ligand) ~ I [MA2B41
(CH3)3COD
~Tflmr
(01¥iI€4i1cH'lI(geometrical
(A)
(B)
?
(A) H+
(D) None
8.
~
mmt?
(A) H+
7.
~
(A) Molecular Weight
(D)
6.
5.
CflIT ~
c); m?T
(A) (CH3)3CD (B) (CH3)3COD (C)
(D) (CD3)30D
(CD3)3CD
(D) (CD3)30D
SIPCS-OIXl14
- 4 ..
Set·A
9.
The correct nucleophilicity order is
9.
(A) CH;
~
,?
"i\FcWtt"'tRhf{;t~i\ ~qicti ~
tiT
(A) CH;
CH;
(C) CH;
•
(C) CH;
F-
(D)
10. The haloform reaction is not shown by
10. ~
F-
~
-q;'-;r ~m"qiT1f (Haloform)
~~~?
(A) Acetone
(A) t{~G)Oi
(B) 2 - chloropropane
(B) 2 - ctH'Iil4(1qOi
(C) Ethanol
(C) ~
(D) Methanol
(D)
11. Which is the strongest acid?
11.
(A) CH=CH (B)
CH;
~
fq~
~ cnT.r SlcstH(1Q
(A) CH=CH
C2H6
(B)
C2H6
(C) CH2=CH2
(C) CH2=CH2
(D) C6H6
(D) C6H6
12. Which gi yes acetylation?
?
~,
aspirin
upon
12. ~
~ ~
t{t'1 fQ f{Oi~,
tiT
41fTtcti t{~Q#I:tIOi
?
(A) 0 - Hydroxy benzoic acid
(A) 0 - gl$~CRft a""lt1$cti~
(B) m - Hydroxy benzoic acid
(B)
ill -
(C)
P - ~1$41CRfla""lt1$cti~
(C) P - Hydroxy benzoic acid (D) P - dihydroxy benzoic acid
SIPCS-01X114
-am
gl$iI~
a;;;J1l$cti~
(D) P - sl$gl$41CRfl a~l$cti ~
Set·A
-5i
13.
What is the product C in the series? CH3CN
B
NalC2HsOH
Cu/573K
,
A
13.
HN02,
7
CH3CN
7
>C
B
(A) C~COOH
(B)
C~C~NHOH
(C)
C~CHO
(C)
C~CHO
(D)
C~CO~
(D) C~CO~
~ ~
(B)
(A) a;:;itl$H
Aniline
P - Nitroaniline
2)
3t1fR "
(B)
~f.l Rwt01
(C)
~RU.ctf"'HI$s
~f.lRwt",
(D) P - ~
Which is incorrect in deoxymyoglobin?
4\fll4)qft;rm
~
!ftfll4)t?
(A) Fe is in high - spin state
16.
~4. ~
(A) Benzylamine
(D)
HNO
C
CU1573K)
C~C~NHOH
Acetanilide
A
NaIC2H50H)
(B)
(C)
t?
C CflIT
(A) C~COOH
14. Of these, the most basic compound is
15.
f4l:;r ~.q.
15. trauCR:fh::1I41~1H\ fit 01c#iT Gmffl'~T1wrff
t?
~
(B) Fe is in +2 oxidation state
(A)
Fe~-~~.q.t
(C)
Fe is not present in the plane of the porphyrin ring
(B)
Fe
c#iTauf$4)(ul amm + 2 t
Fe
41(Chl$R01
Fe is Present in the plane of the porphyrin ring
(C)
(D)
(D)
Fe 41(Chl$.R01 'WTc#iT~.q.irmt
The temperature of the surface of the sun is about 6000 K. If we produce a temperature of 7000 K by focussing the sun ;.rays with a big lens, this will violate which law of thermodynamics
16. ~
t
'WTc#iT~.q.
~ ~ ct)f dlQiU01 ~ 6000 K I ~ l't ~ tit PcFi(unqIT 'tC6 ~ ~
tit ~~I<4dl
CfR7000 K dlQiilO1
~ ~
oT~
~CfRd,
3iiSiWlfil4i\
(B) First Law (C)
Second Law
·(A) ~
(~)
(B)
f.tm:r f.tm:r f.tm:r
~
(C) ~
(D) Third Law
(D) ~
SIPCS-OIXl14
- 6-
~qft;r
?
~~ct)f~Wrr
(A) Zeroeth Law
~ t
f.p;p:r
Set-A
"
17. The uncertainty in the position of __
$tSl~T~ ~ ~ (q)ftiI~i01) c€t , 31f.lllilH1di I~GfR (¥1t~"1GQ) c6t 31f.1llillddi ~~ ?
17. ~
~t
electron is zero. The uncertainty in its momentum would be. (A)
00
00
(B)
> hl2ic
(B)
> hI 27r
(C)
< hI 27r
(C)
< hI 27r
(D)
~
(D) zero
18. The protein responsible s
(A)
for blood
18. ~-mJiT
~
~ ~
clotting is
{l,",GH~t
(A) Albumins
(A)
({(WI1~~ "(Oi
(B)
Globulins
(B)
JiHI~;
(C)
Fibroin
(C)
fCbcq(l$01
•
(D) Fibrinogen
~
m
mtr.r
?
(D) fCbcqR'1)~"1
19. The number of tripeptides formed by
19. (ft;r ~
31Qi$'1) ~
three different amino acids are
aqGi$gGA~t?
(A) 3
(A)
(B) 4
(B) 4
(C) 5
(C) 5
(D)
(D) 6
~ ~~-
3 "
'.
6
20. ' Infrared spectroscopy
for organic compounds involves electromagnetic waves with wave number
20.
31CffiIi~ctpi .q Cfilfif.liji at1flictii~ ~ •
~"'~
fihd01i
'dim q)f ~
(A) 4000-800~. lft-l
(B) 4000-667cm-1
(B) , 4000-667 ~. lfi"-l
(C) 5000-800cm-l
(C) 5000-800 ~. lfi"-l
(D) 5000-667 crrr"
(D) 5000-667~. 1ft-l
,
";fMR
~t?
(A) 4000-800cm-1
SIPCS-01X114
(~)
Set-A
-7 -
•
21.
Oct -4-ene shows C=C frequency in its infrared spectrum at (A)
1680-1600cm-1 (very weak)
1680-1600~.
(8) 1680-1600cm-1 (strong)
(B)
1680-1600
(C)
(C)
1680-1600
1680-1600cm-1 (medium)
Carbonyl transition
compounds
the
22.
1t*, n - 1t *
(C)
a - a*,n - a*,1t -1t
Benzylamine reacts with nitrous acid to form
23.
a- a*,1t -1t
(B)
a - a*,1t -1t*,n"":'1t*
(C)
a - a* ,n - a* ,1t -
(D)
~~~~
~~
~
~ ?
*
~ cp:fT~
(A) Azobenzene
(A) ~~la;#}'1
(B)
Benzene
(B)
(C)
Benzylalcohol
(C) .4'#iI$M 3iMC6I~M
;;
1t *
m~ ~';~
-3P=M' ~
(lftI4~Cf) ~
(D) Phenol
~
(A)
*
(D) None of these
tni";r ~ ~
Cf)1~l;t1$M41fT1Ch
a-a*,1t-1t* a - a* , 1t -
lft-l (~Cf)"I~I() ~. lft-l ("I'#iC{tt) ~. lft-l (~)
.(D) ~mm~)-ij~Wft
exhibit
(B)
f.t ift C = C
-4-
?
(A)
(A)
23.
~"I -ij ~
~cp:fTt
(D) No peak in this range 22.
31cRm ~
21.
~
~ ~
i
?
~ •.i\"i
(D) thl"iTt'1 •
. 24.
Benzaldehydeand formaldehyde when mixed together and heated in aq. NaOHgive (A) Benzyl alcohol formate
24.
and sodium
\
Sodium benzoate alcohol
(C)
Sodium benzoate and sodium formate alcohol
mort? (A) ~~
~~
3iTI mft
lhl(qa
(B)
(D) Benzyl
~\lt~t'1fg~l$g:iR chl4t{t'1fg~l$g~fi:t~ CfiT ~ NaOH -ij TJ1f ~ ~ cp:fT>mf
and methyl
and methyl
(B) mft
m~lft~ll"M'
(Oilfg4 "I 4\i11~a :iR (Oilfg4 "I cti,\(qa
(D) ~~
~~
3iTIlft~
"' 3it'1C6j~M
alcohol
SIPCS-01X114
-8-
Set ..A
25. Wolff- Kishner reduction can be used
25. ~-Rt;~I'H
for which conversion reaction? (A) Benzaldehydeintobenzylalcohol (B)
Benzophenoneintodiphenylmethane
(B)
(C)
Cyclohexanoneintocyelohexane
(C)
(D)
Cyclohexanoneintocyclohexanol
Al(OC2Hsh)
A.
C~HsONa)
C~CHO
B
C~Cliz0H;
(C)
C~CHzOC~CH3;C~COC2H5
(D)
C~COOC2H5; C~ClizCOOC2~
A
&R
i?
B~
)A
C2HsONa)
B
(A) CH3 COOH ; C~Cliz0H (8) C~ C~OH; en, C~OC~C~ (C) C~ CHpc~C~;C~COC2H5 (D) ~COOC~5;~~COOC2~
C~ClizOClizC~
The addition ofBH3 to a C = C bond is
~-ij
.
Al(OC2Hsh
(B)
-q
26. ~"'iRrlf&(1 ~
(A) C~COOH;C~C~OH
28.
4~lchl"iI'i"C6l. gl$fq;'il$~
"1$CRWII'tM"iI'i"C6l"1$Cfffl'f#tl'i-ij (D) "1$Ck"i'tl&flwfl'i q,l "1$ctMt~wflH-ij
,
27.
-« qi);r
rn (1"lq~Cfi4RCCd4 fcfiqy \ifT ~ t ? (A) i#1l{~~81$s q,l i#11$H 3i~chl8H -ij
26. WhatareAandBintheseriesC~CHO
•
ai4;oJA
27.
C=C-ijBH3~~cfit~~
·t?
(A) Anti""Matkownikoff syn-addition
(A) ~
(B)
Anti-Markownikoff .anti-addition
(B), ~-iil
(C)
Markowuikoff
syn-addition
(C)
iil{Cf)lotIChI9i ~-l{rg~I'i
(D) Markownikoff
anti-addition
(D)
iil{Ch,;ftCh'9i~-l{fi~I'i
The addition of bromine to trans-2butene produces
28.
~
-iiI
~ lfT?l 'i11ft;r ~ ~
.-2- ~
~~irnTt?
(A) a pair of enantiomers (B)
a meso compounds
SlRt~kt ~ ~ 'l{Cf) (B) 'l{Cf) lfu:fl ~filili
(C)
a compound with a single chiral centre
(C) ~
(A)
(D) a pair of diastereomers
29. Which lowers the density
(D)
of the
(C)
A+B Both
ftn~ (.rt~) cl;~ ~ ~~fi)Cfi t}:(OtHt~lii{ ~ 'l{Cf) ~
(A) ~nGciil ~
(A) Schottky defect Frenkel defect
~
29. ~~.~~~q,l~'CfiUfTt?
material? (B)
-«
(B) ~$f
(C)
A + B Gf;iT
(D)
¢
-«
"ctill ~
(D) None of these
SIPCS-Ol.Xl1.4
- 9-
Set-A
o.
1.
Colloidal particles size range is
30.
(A) 10 run to 1000 run
(A) 10run~
(B) Inm to 200 run
(B) 1 run~200run
mu
(C)
IOmJl to 1000
(D)
10-5 to 10-7 cm
Which forms micelles in aqueous solution above certain concentration?
31.
(D)
10-5~ 10-7 em
~
~ • ~f.l~d \iWf Pc4MI04'1.q~
(B) Urea
(B)
~
(C)
(C)
Sl~fll$M
75% of a first order reaction was completed in 32 min. 50% of the reaction was completed in :
(B)
24min
(C)
32min
~
~~
3i41f.lI04Q
32. ~ lr$f 32 ~
am (Order) ~fIilO4l .q 1{fi~.
50% ~
I~
75%, 3tfilfftiql qrr.
lR "\U 'San:
(A) 16~' (B)
24ffR
(C)
32~
(D) 4~
Unit of rate constant for zero order reaction is :
33.
~ ~ ~ f.l104diCh(Zero order rate constant) ~ ~ (unit) ~ t ? (A) mole L -1
S-1
(B) mole" L-1 (C)
fll.,.dl ~ 3m (ql$~M) GRmt ?
(D) ql$ft~f.l104q CRWI1(I$S
(D) 4min
(A) mole L-1
mu
*"0$&
(A) 16min
3.
10 mu ~ 1000
"' (A) 41t\~1'lii.
Dodecyl trimethyl ammonium chloride
1000 run
(C)
(A) Glucose
(D) Pyridinium chloride
2.
cti\Mlqit\q q;uft~·ancm~~t?
S-1
(B) mole:'L:' S-1
S-1
(C) . S-1
S-1
(D) mole? L2 S-1
(D) mole+L' S-1
SIPCS-01X114
-10 ...
Set-A
Space for Rough Work
I··"{g) ~
SIPCS ..01X114
~
-11-
~
G1.I~
Set- A
Space for Rough Work I ~
SIPCS-01X114
1fn?f
$~
-12-
\3141&
Set-A
Space for Rough.Work l~, ,ctmi ~ ~
"'·18
iO
SIPCS-01X114-13
-
Set-A
Space for Rough Work / ~
SIPCS-01X114
CfiTd ~
-14 ~
~
\i1~16
Set-A
Section-B Physics (Q.No. 34 to 66) 34.
Two vibrations at right angles to one another are described by the equations: x = 10 cos 51tt and y = 10 cos (51tt + rr12)
~
.,ftftrcl; wm. 34 -« 66) ~ ~m cli t"iGrCrn ~rr.r = lOcos 5 1tt 'tCi y. = lOcos (Jr. 15.
34.
~ x
(51tt + rr12) tuftCh(On ~ 5Hd:?fd ~ , ~ "fiq Rotd '5I"1'1Cf ~ ~ RotHI~
Lissajous. figure associated with combined motion is described by following equation:
~
.(B)
r+y= r-y=
:
r + y = 100
100 (C) y=-x
(C) y=-x (0)
'ChTHiftCh(Olt
(A) y=x
(A) y=x (B)
-11'
(D)
100
35. The correct statement for a driven
35. ~
r- y=
100
510nRa ~
~ ~
oscillator at resonance is' :
it lilt ~ t :
(A) Amplitude has maximum value .
(A) ammf 'ChT1fR ~
(B)
Velocity-has its maximum value
(B)
~'ChT1fR
~
~
~
~
(C) Power input is minimum (D)
'. 36.
Phase difference between displacement and driving force is 1tI4
A rectangular film of a certain liquid is 5 em long and 3 em broad. The work needed for increasing its surface 'area to 30 em? is 3 x Ifr4 joules. The surface tension of liquid is' :
(C) ~"'dq ~
0!Rf
(0) ~~
510nRd
36.
~l:CJcfft 3 'cm ~
atlllldlChj( 'Q'Uf5
(B)
(B)
0.1 N/m
~
t
,
0.1 ~
/
(0) .5 x 1()4~
5 x l()4N/m
SIPCS-01X114
'Q'Uf 'ChT'5m
I Tit Tit Tit
(C) 3 x 1()4~/
l()4N/m
lR
em ~~
~30cm2~~~3 x lQ-4~ 'ChTat Iq:tli cti 'Cfi'Ili t , l:CJ'ChTD 'd"'ITCf t :
(A) 0.4 ~
(D)
CfWlid(
1t/4
(A) O.4N/m
(C) 3 x
~it
-15-
/
Tit· Set-A
37. A vector A
field
A is defined
= V fjJ. is a scalar
as
function. The
~~
a circule of radius R is :
qRCfl~(1
I
¢J~~
m~~Tf(ff~1
value of line integral ~ A . d I around
am
&l~ A, A=VfjJ
~m
37. ~
I R~~-v=r~T.ffU3iR
m :aq.,Cfl~"f
~A.
dl
cnl
l:t'R ~ :
(A) 1tR2IAI (B)
21t RIAl
(e)
Zero
(D)
21t R
38. A molecule of Hel (dipole) is kept in an
(A)
1tR2IAI
(B)
21tR IAI
(e)
~
(D)
21t R
38. ~
cnT3fC!t 1()4~
Hel(~)
"fiRm ~ ~
~
electric field of intensity 1()4 volts/m. Initially dipole axis is making an angle of 300 with the electric field. Distance between H+and ct- is 1.6 Ao. The Torque acting on the dipole is :
~1~~wR~~~~:
(A) 2.56 x 10-25Joule.
(A) 2.56 x 10-25~
.q ~
/1ft.
~ 13tThl.q
~3{at~ ~
~~ 30o~.~ ~ I H+~ el-~ mJ;f 1.6A 0 (jft ¢
(B)
1.28 x 10-25Joule.
(B)
1.28 x 10-25~
(e)
2.217 x 10-25Joule.
(e)
2.217 x 10-25~
(D)
2.3 x 10-25~
(D) 2.3 x 10-25Joule.
, •
I 39.
An inductance of 50 Henri and a resistor of Ion are connected to a 2 volt battery. Time constant and final current in the circuit are :
39.
~
50 ~ cnT '(OqS\(Cflf€l~ 10 n cnT >rfffi)u 2 ~ (jft ~ ~ ~ ~ I '4ttf?T
cnT~
f.l4(1iCfl~
~~
urn
! f r
~ l:t'R ~ :
(A) 0.5 see, 0.2 amp. (B)
(e)
5 see, 2 amp. 5 see, 0.2 amp.
(D) 0.5 see, 2 amp.
(A)
0.5
~ChO$,
0.2 ~
(B) 5
~ChOs,
2 ~a:tft4(
(e)
5
~ChO$,
0.2 ~
(D)
0.5
~ChO$,
\
I I
2 ~a:tft4(
f
I SIPCS-01X114-16
-
Set-A
\
40.
A proton of energy 5 MeV is moving downwards in a vertical plane with magnetic field of 1.5 Tesla. Magnetic field is in the horizontal plane and is pointing from South to North. The force on proton is :
...
5 MeV~CfiT~~(Wf-ij 1.5 .~ ~ ~ktchl~ abr -ij 3l~ alR\QI"1 t I ~ktchl~ abr ~ fun ~
~
3ffi.mm~ qftQIUI mm:
1Wr-ij~~~~ lR~~~CfiT
(A) 7.37 x 10-12N
(A) 7.37 x 10-12 ~
(B) 5.37 x 10-12N
(B)
(C) 4.37 x 10-12N
(C) 4.37
(D) 6 x 10-12N
(D) 6x 10-12 ~
41. Ina hydrogen atom an electron makes 6.8 x 1015 revolutions/sec. round the proton in a circular orbit of radius 5.1 x 10- II m. The equivalent magnetic moment is :
42.
40.
5.37 x 10-12 ~ X
10-12 ~
41. ~1$il\it"1 q(ql'a -ij $H~"1 miR ~ "i3fTU 5.1 x 10-111ft. ~ ~ ~'dl&il( 'Q'W -ij6.8 x 101~m~ciit~~
.am
~t
~kt"~
I~
~WlfRl:
(A) 9.8 x 10-24Amp. m2
(A) 9.8 x 10-24 3t1Xft.1ft2
(B) 8.9x 10-24Amp. m2
(B)
(C) 4.9 x 10-24Amp. m2
(C) 4.9 'x 10-24 3t1Xft.
(D) 4.45 x 10-24Amp. m2
(D) 4~45x 10-24 3t1Xft.1ft2
Current in a 10·mR coil increases uniformly from zero to one ampere in 0.01 sec. The induced emf in the coil
42.
8.9 x 10-24 3t1Xft.1ft2 1fi2
10 ~ 't.rft ~ ~UgH\ -ij0.01 ~Cfiog -ij QTU~~~~~~GB'&il~ 3i+xfl~(m~~ I ~ogt41-ijm~
IS :
~
~
(A)
1~
CfiTlTR
ittn :
(A) 1 volt (B)
-1 volt (B) -1 ~
(C) 0.5 volt (C)
0.5~
(D) -2 volt (D) -2~
SIPCS-01X114
Set-A
-17 -' 1
3. In a real gas obeying Vander Waals equation Boyle temperature (TB) and critical temperature (T c) are respectively : (A)
8a a TB= 27Rb' Tc= Rb
(B)
TB= R b ' Tc = 2TB
43. ~~-~cm;riR:I~~~ (T B) ~
(A)
dlqSflq
SJii\i\Ch d IqSflq (T c) SIitm: ~
:
T - 8a T-~ B- 27Rb' c- Rb
a
(C)
(C)
T, ., 2a T. = 8a B- Rb ' c 27R b
T - 2a T = B-
Rb' c
8a 27 R b
a
8
-T =-T, (D) T, B- Rb' c 27'
44. A carnot's engine absorbs 100 calories of heat from a source of heat at 400 K and gives up 80 calories to a sink. The temperature of sink is : (A) 500 K
45.
(B)
320 K
(C)
227 K
(D)
47 K
n
(B)
(1+! J
(C)
(3+ ~J
0))
(1+~J
1.tC6 'C6'(;{f ~
1.tC6 ~
~
~
~~ijf\ 400 ~~d1"1'Q"(3ict~n~d ~
80 ~~"If\ ~
d IqSflq llm
-ij ~
~
100
~
t
t I ffrcn
Cfif
:
(A) 500 ~&
In an ideal gas of molecules, with n degrees of freedom the ratio of specific heat at constant pressure (C) and specific heat at constant volume (C) will be: (A)
44.
B
45.
~~iR:I-ij~mciit~ld:st~~ n t I 'W iR:I~ &C!I3U ~ ~ f.:l~d GTGf 'Q"( Pctal J!~ (C ) ~ f.:l~d 3t1«
PctaU! ~
(C)v QiT.~
m:
,
(A) n
(C)
(1+ !J (3+ ~)
(D)
(1+~)
(B)
SIPCS-01X114
,
•
.
-18-
Set-A
I
I
SIPCS-01X114
------~~--------------------------
•
\~
-19-
Set- A
49. Ultrasonic waves are (choose correct statement)
49. 3i~~H")f.\Ch(lRT~)
(A) ~
of large wavelengths E.M. waves of high frequency
(C)
(D)
mll
~
Sound waves of large wave lengths
(C)
~
Sound waves of high frequency
(D) ~
so. ' Two waves with intensities in the ratio
so. GT mTt
atrc«ff t€t fu.
~o-
~. mTt mTt
tritT ~t
Pt"i
t, 64idCh{OI
9 : 1 produce interference. The ratio of maximum to minimum intensity is:
~t
(fu. ~.) ~
~
(A)
~ (~Cf)?r.{
q;y~~)
(A) Electromagnetic (E.M.) waves
(B)
~
'fffimm
~
~
9:1
q;y ~
'Ch«ft ~ I 64idCh{UI 'Q1:
6
~~.~dq~q;y~
t:
10: 8
(B) 9: 1 (C) 4: 1
(A)
10:8
(B)
9:1
(C) 4:1 (D) 2: 1
2:1
(D)
51. Two slits illuminated with red light of 650 nm wavelength are separated by a distance of 1 mm. The interference fringes are observed on a screen placed 1m from the slits. The distance between fifth bright fringe and third dark fringe is :
51~
m~
~T
650 nm ~
3lom;r 1 m.
-w.nm ~
m. ~
SlChIi:1ld ~ I
t 1~'Q1:~
~~~t€t~
1~.
~'fiiwf~~ sfit:
"CIqctlHl ~~1l~
(A) 0.65~.~. (A) 0.65mm (B)
(B) 1.63mm
1.63~.~.
(C) 3.25mm
(C) 3.25~.~.
4.88 mm
(D) 4.88~.~.
(D)
SIPCS-01X114
- 20-
Set-A
e
52. The resolving power of a grating in mthorder with N slits will be :
52. ~ N~VfhT"~ m-a: am.q ft;f\tptftl, tnGR (~~< ••~) 1)tft :
(A)
m+ N
(A)
(B)
m-N
(B) m-N
(C) mN (0)
'(C)
mN
(0)
N/m
N/m
53. A doubly refracting crystal has refractive indices of 1.65and 1.48for o and e ray respectively. The minimum thickness of crystal needed to introduce a phase difference of 'ITl2 in 0 and e ray for light of 600 nm is : (A)
1.76pm
(B)
2.76 Jl11l
53. ~fl3iqchfCfifffi+C!(WI.q "1"11(01 (o-ray) fffi'
";"dq
~
~ Cfi(WI iEt(
11'
(A) 1.76 Jl11l
2.76 nm
(B)
2.76 Jl11l
(C)
1.76nm
(0) 2.76nm
54. Let 'a' is the translational vector defining a cubic lattice. Then separation between two parallel (111) planes is :
(A)
34lq~Cfi
e fffi'
0~
~1Pft
(C) 1.76nm (0)
m s-N
54.
'qf;ff 1{C6lR 'II1(WICfiqft Qft\tlftd
lJfTMT1-t4l"';o(1'(01 "q 1"'9d( (111)
a
(A)
a
(B)
.J2
~tat
i
t
~ Wi( ~
m ~'1lOf, '{ft t :
a
.J2 a ~
(B) ~
(C)
(0)
a
a
(C)
-
(0)
-
2
2
a 3
SIPCS-01X114
a 3
- 21-
Set·A J
. X-rays of wavelength 0.7 A are diffracted from a cubic crystal (a = 2.8 A). The Bragg angle (glancing angle) for second order diffraction maxima from (100) plane is :
55.
0.7 A ~~ cfit &l -~ ~ ~ Rh~M (a = 2.8 A)~ ~qfJd ~ ~ I ~ (100) ~ ~ ~ ~ ~PcteHf"1 ~ ~ ~ Wr CfiTuT (glancing angle) ~:
(A)
sin" (0.25)
(A) sin:' (0.25)
(B)
sin:' (0.50)
(B)
sin:' (0.50)
(C)
sin" (0.70)
(C)
sin' (0.70)
(D)
sin:' (0.12)
(D)
sin:' (0.12)
• 6.
A ferromagnetic material is converted into paramagnetic material at a special temperature T. The temperature T is known as :
56. ~
Chilil.14 RCfi 'QGT~a(lil.14RCfi -ij ~
~~Ie
"dTtf (T)
'Q"{
q{l6ldfd
it \jfJ'ffi ~
I
dlqs;tiq TCf)~Mldl ~ :
(A) Critical temperature (B)
Boyle temperature
(C)
Curie temperature
(B)
(C) ~"dTtf (D)
(D) Debye temperature
7.
The Fermi energy of copper at zero kelvin represents
57.
(A) Average energy of. the electron (B)
0:-
~"dTtf
Energy needed to remove the electron from the surface
~
~"dTtf
a=;(W"cf\4 "dTtf
cfit -q;lff ~
cmTIft~: cfit 3ffi:ro ~
(A)
$H~T4
(B)
~~>r8~$H~T4eit3Wl1T~
~ ~ (C)
'Q"{ ~
~16I~t4Cfi ~
Maximum energy of electron
(D) Minimum energy of an electron '
SIPCS-01X114
- 22-
.Set - A
58. The effect of depletion layer in p-n junction will increase: (A) Temperature increased
of junction
is
(B)
of junction
is
Temperature decreased.
58. p-n GiCQlot -ij ~qMleot lmfTt:
(C) Junction is in reverse bias (0)
59.
A particle of rest mass a speed of
(A) GiCf~lot~ nlQSfiq
-ijCfift mwt 1
I
(B)
GiCf~lot.~nlqSfiq
-ijcnfJfmwt1
I
(C)
.~Iot
-ij1
(0)
GiCf~lotam
":'0 moves
with
59. ~
(B)
'QTT.l ~
~
-ij1
..fi'
mo 'Pcro1fA6Qq.ot CfITC6UT
1
.J2moc.
11C6UT c:Jrr ~
4Ifd",f\twI
The total energy of
the particle is :
(A)
q;r JrqTCf
I I
Junction is in forward bias
c
•
~
1
-moc
(B)
.J2moc2
(C)
moc
Jimoc2
~-«
1:
2
(A) 2
~
c
.J2
.J2'
2
(C) ,
1
2
(0) --. 2.J2 'moc
60. The ratio of de-Broglie wavelengths
60. ~IOkeV~~-mR~
1 MeV
associated with a. proton of energy 10 ke V and a neutron of energy 1 Me Vapproximately is :
~~~~~s't-~m
(A) 1
(A) 1
~
CfIT ~
(B)
10
(B) 10
(C)
100
(C)
(0). 50
twl41w\
t:
100
(0) 50
SIPCS-01X114
------~---------------------L
~23-
Set-A
· The normalized wave function of a particle in the region 0 ~ x ~ a is
61.
~n
1f.'i Cf)lJT Cf)T SIft I"I I•.
o ~ x ~ a ~'ij 'I'(x) = ~cos
:x and
is
zero ~~
outside the region. "The expectation value of position of particle is :
~
"
{2" cos 7!x ~ V-;; a
'" (x) = O~ I cnureSrr
cnr Slf4I'?1i m;r ~ :
(A) 0
(A) 0
(B)
a/2
a/3
(C)
a/3
a
(D)
a
(B)
a/2
(C) (D)
2. The radius of a stable nucleus is 1/3 of radius of OSl89 nucleus. The mass number of the stable nucleus is : (A)
~~'ilm
",(x) =
mTJ 'tfi~
62.
~~~~~~OSI89~
eSrr ~ cfit~ ~ ~ eSrr S(C4"1I"1 ~
7
(A)
(B) 21
(C) 63
(C) 63
(D) None of the above
(D)
63.
(A) Perfectly coherent (B) Perfectly monochromatic (C) Less intense beam of light
~ :
7
(B) 21
63. Which is not a characteristic of a LASER light?
(1/3) ~ I ~
aQ4CM'ij ~ ~
~
f.n:;r 'ij ~ cttr.Jm ~am
LASER
~'ij~~? (A) 3mM ~ ~ cnMT ~ (B)
~~.~~~
(C)
cnJf ~
SlIChI'?1 -
$f
(D) Perfectly parallel beam of light (D) ~
SIPCS-01X114 1
- 24-
ft"lI"1lo:(1( ~
- ~
Sct-A 1
64. Maximum and minimum distances of 14x 109
a comet from sun are and 7 7 x 10 km, respectively. If maximum speed of comet is 6 x 1()2 km /sec then its minimum speed would be :
64. ~ ~c:JIT~~.~~ 'Snlm': 14
.~
f
I 3tlR
X
1093ffi 7
~rii~ t€t
"'9;4d'4 107 km
X
lTftr
~(flJ
6 x 1()2 km /sec'l, (fGf "'9;4d'4~
~
:
(A) 3 km/sec
(A) 3 km/sec (B)
4 km/sec
(B)
4 km/sec
(C)
6 km/sec
(C)
6 km/sec
(D) 8 km/sec
(D) 8 km/sec
• 65. Time period of oscillations of a mass
65. ~rnm~~~mSt;64'414q;r~
m suspended' from a spring is 2 sec. If an additional mass of 2kg. is . suspended along with it, time period increases by 1sec. The initial mass is :
2 ~Cfiog'll ~ 2 kg q;r 3ifiHhfi St;64 '41"1rnm ~ ('1GCfi I~'q'{ ~ 'CfiT('1' .q.
'Cfi'WI'
1 ~Cfiog c6T. ~
m~
'l I sllUircti
$(04'41"1 'l : ••
(A) 2kg (A) 2kg (B)
1 kg
(C)
1.6 kg
(D)
2.6 kg
66. The potential energy of an oscillator is U(x) = a + bx + cr + dx', Necessary condition for motion harmonic is : (A)
1 kg
(C)
1.6 kg
(D)
2.6 kg
Gl~ t€t fi:'~ U(x) = a + bx + cr + tJx3
66. ~q;
to simple
a=0
(B) b
(B)
~
11ftl ~ ~
(A)
a =0
'l
I~
311€4}jt4Cfi ~ 'l :
(B) b = 0
=0
c=0
(C) c = 0
(D) d= 0
(D) d = 0
(C)
~\iff
SIPCS-01X114
..25-
Set·A
Space for Rough Work I '{Wi Cfi'11.f'ii ~
GFI~
t
!
I,
SIPCS-01X114 J
-26-
Set-A
Space for Rough Work / '{!n'CfiN
SIPCS-01X114
•
~
- 27 -
~a"l
g
Set-A 1
"'f'l~
Space for Rough Workl~~~~
I
I
I!
I
1 tl
SIPCS-01X114
- 28-
Set-A
Space for Rough Work I ~ ~
SIPCS-01X114 1
*
-29-
~\iIa16
Set ..A ·1
~-~
Section - C Mathematics (Q.No. 67 to 100) 67.
For any vector
a,
lTfUro 67.
(B)
68.
2ei -2ei
2a -2ei
(A) (B)
(C) a
(C) a
(D) -a
(D) -a
Which of the following is not a cyclic group?
68.
r.t •.••R-tfutt1 .q ~
qfR 'fIT ~
~
~
~l?
(A) S3 (B)
a ~Wnt
=
is equal to (A)
SIi. 67 ~ 100)
tx (ax i) + J x (ei x J) + f x (ei x k)
Jx(axJ)+fx(axf)
ix(axi)+
(Jr. ~~Wr
(A) S3 2
{1,w,w }
(B)
{1, w, w2}
(C) {1,i,-i,-1} (C) {l, i, - i, -1} (D) {1,-1} (D) {1,-1} 69.
Radius of curvature p for the curve 69.
s = a log tan( : +
-
..
(A)
a seclf/
(B)
a sec2lf/
i}
is given by
s = a log tan ( : +
(S,lf/)~
qsnor ~
i) ~~
pcnr l:f'R
l
(A)
a seclf/
I
(B)
a sec2lf/
1 I
(C) a coslf/
(C) a cos If/
(D) a sinlf/
(D) a sinlf/
SIPCS-01X114
•
>tjI;
- 30 -
Set- A
70.
If a1
= 1 and a = ~ n+
1
n
then lim an
70.
n-+oo
~
a1
= 1, a = ~ n+
1
n.
~
'ffi' lim an = n-+co
is equal to (A) 0 (A) 0
3
(B) (B)
3
(C) 4
(C) 4 (D)
71.
1
(D)
1
(A)
0
(B)
e
111
The series 1- 2 +3- 4 +-- upto
00
.
has the sum (A) 0 (B)
e
(C) log2 (C) log2 (D) (D)
•
00
00
72. The sum of the characteristic roots of
the matrix
[8
~6 2
-6
2]
7 ~ -4
~]~~~ ~~~[~ -6 7 -4
72. is equal to
CfiT~
(A) 5
(A) .5
(B)
(B)
3
(C) 18
3
(C) 18
(D) 20 (D) 20
SIPCS"'OIXl14 1
..31-
Set-A
2
73.
Value of
(D)
74.
fo (8 -
3
X )
-
1
1
f:(8-x3f3dx~
dx
is equal to
73.
XE
[0,1] and
74. ~f(x)
3
~
None of these
If f(x)
= x for
= x,
XE
[0,1]
am
P={O'~'~'l}
then Uif,p) is equal
to (A) 6
(A) 6
(B) 3
(B) 3
2 (C)
2 (C) 3
3
(D) 1
(D) 1
SIPCS-01X114
- 32-
Set-A
1 75.
(D-a)Q is equal to
(A)
75.
tan " s
1
(D-a)
(A)
Q ==
tan " s
(C) 0
(C) 0
(D) None of these
SIPCS-01X114
-33-
Set·A
•• i, 77. General
solution
of
PDE
az az _ . ----OIS 2
2
ax2
ay2
az az 2
2
ax2 - ay2 = 0 'Cfif~
77. PDE«4lCMol
~l
(A)
z =tA (y+ x)+
(A)
z =(A
(B)
z =tA
(y+ x)+
(B)
z = tA (y + x)+
(C)
z=tA(y+2x)+
(C)
z = tPl(y + 2x)+ tP2(y- 2x)
(D)
~~q;ff~
(D) None of these
r
78. If = xi + equal to
yJ + zk
then
div(r)
is
78.
(y + x)+ tP2(y-x) tP2(y -2x)
~ r = xi + yJ + zk ~ (A)
3
(B)
1
(C)
2
(D)
0
'ffi div (r) =
(A) 3 (B) 1
(C) 2
(D) 0
79. If V is the vector space of all polynomials of degree < 10, then dim V is equal to
79. ~V,~
10,ct?ft~~Cfil, ClI(O(t~Cfi~~ ~ ~ R, ~ ~l'ffi dim V =
(A)
11
(A)
11
(B)
10
(B)
10
(C)
9
(C)
9
(D)
1
(D)
1
SIPCS-01X114
- 34 -
'
mw
Set-A
~
80.
"Every finite group is isomorphic to some, permutation group". This result is known as
80.
Cayley theorem
(C) Lagrange theorem
(D) Fundamental
theorem
on
Homomorphism
81.
IfG is afinite cyclic group of order n then O(Aut (G» is equal to
81.
(A) (n) (B)
~~
~
~
m~
cfiT ~
m
~"
(A)
~m
(B)
~m
(C)
~m
(D)
'E1qlCfiIRdl
Sflq::atf~-Q;
~G~QRrqd~~~~n ~ ~ ~ O(Aut (G» = (A) (n)
n
(B)
(D) 1
82.
QRf'ld
\~CfiIRCfi
(A) Cauchy theorem (B)
"~
n
(D) 1
Which of the following is not a closed set?
82.
f.t""1f(;wffiid.q
~
~'m-
'E11i%1tf~
~
t?
(A) N (Set of natural numbers) (B)
Z (Set of integers)
(C)
R (Set of real numbers)
(D) Q (Set of rational numbers)
SIPCS-01X114
(D)
Q (~
- 35-
~:m
CfIT 'E1~tf)
Set-A
83.
Which of the following is a compact set?
83.
n.•.••RotRltf
-ij ~ ctfR
lIT ('4!Ji±'4 ~
l?
(A) R (A) R (B)
Q
(C)
N
(D)
~
~
ffiffir ~
Q
(C) N
(D) Cantor set
84;
(B)
Order of convergence of Regula-Falsi method is
84.
('4!fCd4
1.618
(A)
1.618
(B)
2
(B)
2
(C)
1
(C)
1
••••••.•
(D) ~~cirf~
(D) None of these
u = x + y -z,
3ffq('4~OI~
~l
(A)
85. If
cfiT
v = x - y + z,
85.
lf~
u = X + Y - z,
v = x - y + z, •
.SIPCS-01X114
-36-
Set- A
%
86. Value of
J sin.
5 xcos 4 x dx
is equal
86.
0
J
% sin" xcos" x dx-s
0
to
(A)
8
(e)
(D)
(B)
-
81t'
-
315
315 8
(e)
315
°
8
315
°
(D)
87. ~
87. If
~
ft», y) = {
xy x2 + y2
0
(x, y) #; (0,0)
(x, y) •• (0,0)
,
J(X'Y)={
~x~ y' (x, y)
(x,y)=(O,O)
= (0,0)
,,'riT
then (A)
8 45
45 81t'
(B)
(A)
Ix (0, 0) = 0, t,(0, 0) =
°
(A) f.x (0, 0) = 0, f.y (0, 0) =
°
(B) t, (0,0) = 1,
I, (0,0)
=-1
(B)
t, (0,0)
= 1,
f.y (0,0)
=1
(e)
t. (0,0) = 1, t, (0, 0) = 1
(D)
I.x (0, 0) = -1, f
(e). f.x (0,0) (D)
Ix (0,0) = -1, 1;. (0, 0) = 1
SIPCS-01X114
=1,
I, (0, 0) =-1
y
- 37 -
(0, 0) = 1
·.Set.;A
b
The improper integral
88.
J
1 (x _ a )n dx
1
b
88.
3r.Mf
QqlCfi(Ol
J(x_aYdx
3f~Qlfl
a
a
is convergent if (A)
n=l
(A)
n=l
(B)
n>l
(B)
n>l
(C)
n
(C)
n
(D) ~
(D) none of these
~ CFilt ~ "
(1 + i)" + (1 -
89.
-
011 is equal to
(n1C) 4
(A)
22n cos
(B)
22n sin (. 4 )
-
89.
(1 + 0"
+ (1 -
!!.
(A)
22 cos
(B)
22 sin
n1C
!!.
i)" =
(n1C 4)
(n1C) 4"" I'
n+2
(1C)
(C) 22 cos n
n+2
n+2
(1&)
(C) 2-2 cos :
4
(D)
I I
(1C)
22 sin n
(D)
4
n+2
I
I
(1C)
i
22 sin n
I
4
I
SIPCS-01X/.14
..38..
Set-A
90. If 1, a, /3,'Y.~ are roots of the equation x5 - 1 = 0 then(l ....a) (l-.{J)(l- y) (1 - 8) is equal to
I, a, P.
90. ~
1.a QiftW;(UI ~
-
1 = O~ ~
t 'ftl (1- a) (1- fj) (1- 1) (1- 8) = (A) 5
(A) 5
(B) 0
(B) 0
(C) 4
(C) 4
(0) 6
(D) 6
•
J
91. If = xl + yJ + zk and s is surface of sphere x2 + y2 + Z2 = 1 then
91.
1ffl{ x2
J = xl + yJ + zk ml
+ y2 + Z2 = 1 lfif
ffs J.nds
ffs J.nds
(A) 4K
(~) 4K
~
s,
ti\SII"'M
1Tl~
t 'ftl
=
• (B)
4K 3
(B)
4K 3
(C)
2K
(C)
2K
(D) 0
(D) 0
SIPCS-01X114
- 39-
sa- A
92. If Pn(x) is Legendre polynomial of degree n then Pz(x) is equal to
(B)
3
92.
2
-x -1 2
(B)
2
3
q;)
Pz(x) 1R11R ~
2
-x -1 2
(C) x2 -1
(C) x2 -1 (D) x --
l"fft
SW«md CfroIT
~ f{;w;ijs~.~
1
2
(D) x --
2
1 2 ~
94. "Every infinite bounded set of real numbers has a limit point" This result is known as
94. "~.:AftjfJI(1 q;lf~~~~l"
(A)
(A) Heine Borel theorem
~~~q
'i5f ~
~mw
"«
~-~m
(B) Bolzano-Weierstrass theorem (C)
(C) Rolle's theorem
(D)
(D) Cauchy theorem
SIPCS-01X114
m.r m ~m -40-
Set-A
95.
Number of ideals in a field is
95.
~
~ .q !!OI\itlctH1 c#IT~
~
t (A) 1 (A) 1 (B) 2 (B) 2
(C) 3 (C) 3 (D) 0
(D) 0
•
96" If A=[!
!]
then A (adj A) is equal'
96, ~
!]
A=[!
~mA(adjA)=
-to
(A)
[~
~]
(B)
[~
~]
(A)
[~
~]
(B)
[~
~]
(C)
[-1 0]
•. •
0
-1
(D) 2I
(D) 2I
SIPCS-01X114
-41-
Set-A
,
I 97.
If x,
=cos(;
Xl X2 X3 - -
upto
}iSm(; ) men 00
97.
is equal to
~
=COs(; }iSin(; }otm
x,
Xl X2X3
- -
upto
(A)
1
(A)
1
(B)
-1
(B)
-1
(C)
0
(C)
0
(D)
None of these
(D)
¢~cnTt~
4
98.
00
If Y = X
(A)
(B)
(C)
(D)
3
dy . log x then dx4 IS equal to
98. ~y=x
2
(A)
x
3
(B)
x
6
(C)
x
1
(D)
x
,
3
SIPCS-01X114
logx
=
•
mm
d4y --4
dx
=
2 x
• i
3 x
6 x
1 x
- 42-
Set-A
,
99.
If u ~ x $
x
au au ax + y ay
(~)+v(~)
then
99. ~
u
=
au ax
(A) u
X$(~ )
(B)
X$(~ )
(C)
0/( ~)
(C)
o/(n
(D)
0
(D)
0
•
100. If
x.Jl
+ y + y.Jl + x = 0; x '* y ,
. 100. ~
dy
x.Jl
+ y + y.Jl + x = 0, x'* y, m
dy -= dx
then dx is equal to •
1
1 (A)
I
(A)
(l+xt
(1+ X)2
1 (B)
oTwl
(A) u
(B)
•
(~}o/(~)
au ay
x-+y-=
is equal to
x $
1 (B)
(1+ X)2
(l+xt
(C)
1 1+x2
(C)
(D)
None of these
(D)
SIPCS-01X114
1 l+x2
~-«~~
- 43-
Set·A
Space for Rough Work/~~~~~
Gt"I~
ii
·I
I • i
SIPCS-01X114
,
~-
-44-
Set-A
I'
I
SpaceforR.tmg~
Workl~CfiTd'~·~
'iF'I~
•
•
SIPCS-01X114
~45-
Set-A
H
I
I
•
SIPCS-01X114
-46-
Set-A
Space for Rough Work/~~~~
SIPCS-OIXl14
Gt.,~
-47-
Set-A
SEAL INSTRUCTIONS REGARDING METHO OF ANSWERING QUESTIONS
• (~Black
ball-point ~CiiT~cnl)
(Please use Black ball-point Pen)
1. ~~cnrottcfrr 1. Method of Marking Answers:
'3rR~~m
To answer a question, please darken one bubble out of the given four, in the OMR Answer Sheet against that question.
:
3TI.~.3lR. '3rRWe ~~
m~~~~T.fR~~~~v.cn~ qj)~qm;rr~
I
/
2. 'l~i&i'1~: 2. Valuation Procedure: There are four alternative answers to a question, only one of them is correct. One mark will be awarded for each correct answer, if more than one bubble are darkened for a question, it will be presumed that the candidate does not know . the correct answer hence, no mark shall be awarded.
~m~T.fR~'3rR~,
~~v.cn'3rR
@~ ImCfiT@"3W ~~~~:W.fi
,
>rrnmrrrI~v.cn~~~~m~~
m~
rc.;1:Jtt~ qj) m CfiT @
ll1'1T ~
'3rR";{thn~~
3fu:~~
3. ~CfiT~~
3iq;~~~
•
I
GlS~'11:
'3rR~
3. Cancellation or Change in Answer: It will not be possible to change the marked bubble with black ball-point pen; therefore, correct answer should be carefully chosen before marking it on OMR Answer Sheet.
4. Handing over of Answer Sheet to
~~~~f.mRqj)~~~mrrrl 3Rf:"3rRctT ~
~ ~ @m"3rRCfiT
~
~~~I
4. ~~cfta1cf)CfiT~ (i)
cft~
:
qj) 3,Wtft2 ~
Invigilator :
~ ~ rc.; "3WWe ~
(i)
~
Please ensure that all entries in the answer sheet are filled up properly i.e. Name, Roll No., Signatures, Question Booklet No. etc.
(ii) CANDIDATES ARE PERMITTED TO CARRY AWAY THE QUESTION BOOKLET WITH THEM AFTER THE EXAMINATION.
5. Care in Handling the Answer Sheet: While using answer sheet adequate care should be taken not to tear or spoil due to folds or wrinkles andthe impression does ' not come behind the Answer sheet.
SIPes
~
-";{Tij,
~ ~
ql;IT ~
"ffivT ~,
>w.=f -~MCfi I q)T ~, ~~
lR
~R~d tR
@ft
~~, ~
f;rmfuf
cft"q) - cft"q) ,ft ~ ~ I ~
(ii) l:fttl$~l:ftt~qj)m~
'@1~~cfit ~~
~ I
.' "
,..,
... , "
I
3'd(~n2CfiTm~~~WQ~~
I
~I~~,~
~
5. 3'WtftG~~-ij~
:
(
I.
~~~~~~~~qm;rr~WQ mqm;ft~~rc.;~014iCfi"
3~R~ft2~W
~~~~I
-48 -
Set-A
~ ~
t
