Your Target is to secure Good Rank in JEE(Main) 2015 Corporate Office ALLEN CAREER INSTITUTE “SANKALP”, CP-6, Indra Vihar, Kota (Rajasthan)-324005 +91-744-2436001 [email protected]www.allen.ac.in Do not open this Test Booklet until you are asked to do so. 1. Immediately fill in the form number on this page of the Test Booklet with Blue/Black Ball Point Pen. Use of pencil is strictly prohibited. 2. The candidates should not write their Form Number anywhere else (except in the specified space) on the Test Booklet/Answer Sheet. 3. The test is of 3 hours duration. 4. The Test Booklet consists of 90 questions. The maximum marks are 360. 5. There are three parts in the question paper A,B,C consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct response. 6. One Fourth mark will be deducted for indicated incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the Answer Sheet. 7. Use Blue/Black Ball Point Pen only for writting particulars/marking responses on Side–1 and Side–2 of the Answer Sheet. Use of pencil is strictly prohibited. 8. No candidate is allowed to carry any textual material, printed or written, bits of papers, mobile phone any electronic device etc, except the Identity Card inside the examination hall/room. 9. Rough work is to be done on the space provided for this purpose in the Test Booklet only. 10. On completion of the test, the candidate must hand over the Answer Sheet to the invigilator on duty in the Room/Hall. However, the candidate are allowed to take away this Test Booklet with them. 11. Do not fold or make any stray marks on the Answer Sheet. bl ijh{kk iqfLrdk dks rc rd u [kksysa tc rd dgk u tk,A 1. ijh{kk iq fLrdk ds bl i` "B ij vko';d fooj.k uhys @dkys ckWy ikbaV is u ls rRdky HkjsaA is fUly dk iz;ks x fcYdqy oftZr gSaA 2. ijh{kkFkhZ viuk QkeZ ua- (fu/kkZfjr txg ds vfrfjä) ijh{kk iqfLrdk @ mÙkj i= ij dgha vkSj u fy[ks aA 3. ijh{kk dh vof/k 3 ?kaVs gS A 4. bl ijh{kk iqfLrdk esa 90 iz'u ga SA vf/kdre vad 360 gSaA 5. bl ijh{kk iqfLrdk esa rhu Hkkx A, B, C gSa ] ftlds izR;sd Hkkx esa HkkSfrd foKku] jlk;u foKku ,oa xf.kr ds 30 iz'u gS a vk S j lHkh iz 'uk s a ds va d leku gS a A iz R;s d iz 'u ds lgh mÙkj ds fy, 4 (pkj)va d fuèkk Z fjr fd;s x;s gS a A 6. izR;s d xyr mÙkj ds fy, ml iz'u ds dqy vad dk ,d pkSFkkbZ vad dkVk tk;sxkA mÙkj iqfLrdk esa dksbZ Hkh mÙkj ugha Hkjus ij dqy izkIrkad esa ls ½.kkRed vadu ugha gksxkA 7. mÙkj i= ds i`"B&1 ,oa i`"B&2 ij okafNr fooj.k ,oa mÙkj va fdr djus gs rq dsoy uhys@dkys ckWy ikbaV isu dk gh iz;ks x djs aA isfUly dk iz;ksx loZFkk oftZr gSA 8. ijh{kkFkhZ }kjk ijh{kk d{k @ gkWy esa ifjp; i= ds vykok fdlh Hkh izdkj dh ikB~ ; lkexzh eqfær ;k gLrfyf[kr dkxt dh ifpZ;ksa ] eksckby Qks u ;k fdlh Hkh izdkj ds bysDVªkfud midj.kks a ;k fdlh vU; izdkj dh lkexzh dks ys tkus ;k mi;ks x djus dh vuqefr ugha gSaA 9. jQ dk;Z ijh{kk iqfLrdk es a ds oy fu/kkZfjr txg ij gh dhft;s A 10. ijh{kk lekIr gks us ij] ijh{kkFkh Z d{k@gkWy Nks M+us ls iwoZ mÙkj i = d{k fujh{kd dk s vo'; lkSa i ns a A ijh{kkFkhZ vius lkFk bl ijh{kk iqfLrdk dks ys tk ldrs gS aA 11. mÙkj i= dks u eksM+ s a ,oa u gh ml ij vU; fu'kku yxk,s aA IMPORTANT INSTRUCTIONS egRoiw.kZ funsZ'k Path to Success ALLEN CAREER INSTITUTE KOTA (RAJASTHAN) T M ALL INDIA OPEN TEST # 01 DATE : 25 - 01 - 2015 TARGET : JEE (Main) 2015 ENTHUSIAST & LEADER COURSE Test Type : Major Test Pattern : JEE (Main) FORM NUMBER PAPER CODE 00CE314001 Hindi (ACADEMIC SESSION 2014-2015) CLASSROOM CONTACT PROGRAMME
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Your Target is to secure Good Rank in JEE (Main) 2015
Corporate OfficeALLEN CAREER INSTITUTE
“SANKALP”, CP-6, Indra Vihar, Kota (Rajasthan)-324005
Do not open this Test Booklet until you are asked to do so.
1. Immediately fill in the form number on this page of the Test Bookletwith Blue/Black Ball Point Pen. Use of pencil is strictly prohibited.
2. The candidates should not write their Form Number anywhere else(except in the specified space) on the Test Booklet/Answer Sheet.
3. The test is of 3 hours duration.
4. The Test Booklet consists of 90 questions. The maximum marks are360.
5. There are three parts in the question paper A,B,C consisting ofPhysics, Chemistry and Mathematics having 30 questions in eachpart of equal weightage. Each question is allotted 4 (four) marks forcorrect response.
6. One Fourth mark will be deducted for indicated incorrect responseof each question. No deduction from the total score will be madeif no response is indicated for an item in the Answer Sheet.
7. Use Blue/Black Ball Point Pen only for writting particulars/markingresponses on Side–1 and Side–2 of the Answer Sheet.Use of pencil is strictly prohibited.
8. No candidate is allowed to carry any textual material, printed or written,
bits of papers, mobile phone any electronic device etc, except the
Identity Card inside the examination hall/room.
9. Rough work is to be done on the space provided for this purpose inthe Test Booklet only.
10. On completion of the test, the candidate must hand over the AnswerSheet to the invigilator on duty in the Room/Hall. However, thecandidate are allowed to take away this Test Booklet with them.
11. Do not fold or make any stray marks on the Answer Sheet.
bl ijh{kk iqfLrdk dks rc rd u [kk sysa tc rd dgk u tk,A
HAVE CONTROL ¾® HAVE PATIENCE ¾® HAVE CONFIDENCE Þ 100% SUCCESS
1. The specific heat of alcohol is about half that ofwater. Suppose you have identical masses ofalcohol and water. The alcohol is initially attemperature TA. The water is initially at adifferent temperature TW. Now the two fluidsare mixed in the same container and allowed tocome into thermal equilibrium, with no loss ofheat to the surroundings. The final temperatureof the mixture will be :-
(1) closer to TA than TW
(2) closer to TW than TA
(3) exactly halfway between TA and TW
(4) dependent on the volume of alcohol used.
2. Consider a uniformly charged hemisphericalshell of radius R and charge Q. If field at point
3. A particle move on an circular overbridge withconstant speed. The friction coefficient variesso that the speed remains constant. Which ofthe following graph shows the magnitude offriction.
q
(1) q
f
(2) q
f
(3) q
f
(4) q
f
4. A beaker of height H is made up of a materialwhose coefficient of linear thermal expansionis 3a. It is filled up to the brim by a liquid whosecoefficient of thermal expansion is a. If nowthe beaker along with its contents is uniformlyheated through a small temperature T the levelof liquid will reduce by (given a << 1) :-(1) 5aTH (2) 3aTH
5. Consider telecommunication through opticalfibres. Which of the following statements isNOT true ?
(1) Optical fibres can be of graded refractive index
(2) Optical fibres are subjected to electromagneticinterference from outside
(3) Optical fibres have extremely lowtransmission loss
(4) Optical fibres may have homogeneous corewith a suitable cladding
6. A circular conducting loop of radius R carries acurrent I. Another straight infinite conductorcarrying current I passes through the diameterof this loop as shown in the figure. Themagnitude of force exerted by the straightconductor on the loop is :-
RO
I
(1) pµ0I2 (2) µ0I
2
(3) 2
0I2
mp
(4) 2
0Imp
5. izdk'kh; rarqvkas }kjk gksus okys nwjlapkj ij fopkj dhft,A
gksdj xqtjrk gSA ywi ij lh/ks pkyd }kjk vkjksfir cy
dk ifjek.k gksxk%&
RO
I
(1) pµ0I2 (2) µ0I
2
(3) 2
0I2
mp
(4) 2
0Imp
H-4/38
SPACE FOR ROUGH WORK
ALL INDIA OPEN TEST/JEE (Main)/25-01-2015
00CE314001
7. The figure shows the cross section of a long
cylindrical conductor through which an axial
hole of radius r is drilled with its centre at point
A. O is the centre of the conductor. If an
identical hole were to be drilled centred at point
B while maintaining the same current density
the magnitude of magnetic field at O :-
A
120°
30°
B
O
r
(1) will increase
(2) will decrease
(3) will remains the same
(4) May increase or decrease depending on the
value of r.
8. There are 10 turns in coil M and 15 turns in coilN. If a current of 2A is passed through coil Mthen the flux linked with coil N is1.8 × 10–3 Wb. If a current of 3A is passedthrough coil N then flux linked with coil Mis:-(1) 1.2 × 10–3 Wb (2) 2.7 × 10–3 Wb(3) 1.8 × 10–3 Wb (4) 4.05 × 10–3 Wb
7. fp= esa ,d yEcs csyukdkj pkyd ds vuqizLFk dkV
dks fn[kk;k x;k gS ftlesa fcUnq A ij dsfUær f=T;k r
8. dq.Myh M esa 10 ?ksjs gSa rFkk dq.Myh N esa 15 ?ksjs gSaA
;fn dq.Myh M esa 2A /kkjk izokfgr djrs gSa rks dq.Myh
N ls lEc¼ ¶yDl 1.8 × 10–3 Wb gSA ;fn dq.Myh
N esa 3A dh /kkjk izokfgr djsa rks dq.Myh M ls lEc¼
¶yDl gksxk %&
(1) 1.2 × 10–3 Wb (2) 2.7 × 10–3 Wb
(3) 1.8 × 10–3 Wb (4) 4.05 × 10–3 Wb
H-5/38
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ALL INDIA OPEN TEST/JEE (Main)/25-01-2015
00CE314001
9. A radio station has two channels. One is AM at
1020 kHz and the other is FM at 89.5 MHz.
For good results you will use
(1) longer antenna for the AM channel and
shorter for the FM
(2) shorter antenna for the AM channel and
longer for the FM
(3) Same length antenna with work for both
(4) Information given is not enough to say which
one to use for which 10. An electron is projected
wall
xa b
v0
B
normally from the surfaceof a sphere with speed v0
in a uniform magneticfield perpendicular to theplane of the paper such thatits strikes symmetrically opposite on the spherewith respect to the x-axis. Radius of the sphereis 'a' and the distance of its centre from the wallis 'b'. What should be magnetic field such thatthe charge particle just escapes the wall:-
11. In the situation as shown in figure time periodof vertical oscillation of block for smalldisplacements will be :-
kk m
qq
(1) m
2 cos2k
p q (2) m
2 sec2k
p q
(3) m
2 sin2k
p q (4) m
2 cosec2k
p q
12. A charged particle with charge q and mass mstarts with an initial kinetic energy K at thecentre of a uniformly charged spherical regionof total charge Q and radius R. Charges q andQ have opposite signs. The spherically chargedregion is not free to move and kinetic energy Kis just sufficient for the charge particle to reachboundary of the spherical charge. How muchtime does it take the particle to reach theboundary of the region?
(1) 3
o4 mRqQ
pep (2)
3o4 mR
2 qQpep
(3) 3
o4 mR4 qQ
pep(4) None of these
11. fp= esa iznf'kZr fLFkfr esa vYi foLFkkiuksa ds fy, CykWdds Å/okZ/kj nksyu dk vkorZdky D;k gksxk%&
13. A silicon specimen is made into a p-typesemiconductor by doping, on an average, oneindium atom per 5 × 107 silicon atoms. If thenumber density of atoms in the silicon specimenis 5 × 1028 atom m–3, then the number of acceptoratoms in silicon per cubic centimeter will be(1) 2.5 × 1030 atom cm–3
(2) 2.5 × 1035 atom cm–1
(3) 1 × 1013 atom cm–3
(4) 1 × 1015 atom cm–3
14. Two different coils have inductances L1 = 4mHand L2 = 2mH. At a certain instant the currentin the two coils is increasing at the same constantrate and power supplied to the first coil is fourtime that of in second coil. If e, I and U indicatethe potential difference, current and energystored of the inductance respectively than whichof the following is correct.
14. nks fHkUu dq.Mfy;ksa ds izsjdRo L1 = 4mH rFkkL2 = 2mH gSA fdlh {k.k nksuksa dq.Mfy;ksa esa /kkjkleku fu;r nj ls c<+ jgh gS rFkk igyh dq.Myh dks nhxbZ 'kfä nwljh dq.Myh dh rqyuk esa pkj xquk vf/kdgSA ;fn e, I o U Øe'k% foHkokUrj] /kkjk rFkk izsjddq.Myh dh laxzfgr ÅtkZ dks O;ä djrs gSa rks fuEu esals dkSulk lEcU/k lR; gSa %&
(1) 3
1 1 1
2 2 2
U I e4
U I e
æ ö æ ö= =ç ÷ ç ÷
è ø è ø
(2) 3
1 1 1
2 2 2
U I e4
U I e
æ ö æ ö= =ç ÷ ç ÷
è ø è ø
(3) 3
1 1 1
2 2 2
U I e2
U I e
æ ö æ ö= =ç ÷ ç ÷
è ø è ø
(4) 1/3
1 1 1
2 2 2
U I eU I e
æ ö= =ç ÷
è ø
H-8/38
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ALL INDIA OPEN TEST/JEE (Main)/25-01-2015
00CE314001
15. In figure a point charge +Q1 is at the centre ofan imaginary spherical surface and another pointcharge +Q2 is outside it. Point P is on the surfaceof the sphere. Let FS be the net electric flux
through the sphere and PE
r be the electric field
at point P on the sphere. Which of the followingstatements is TRUE?
Å Q1 Å Q2
P
(1) Both charges +Q1 and +Q2 make nonzerocontributions to FS but only the charge +Q1
makes a nonzero contribution to PE
r.
(2) Both charges +Q1 and +Q2 make nonzerocontributions to FS but only the charge +Q2
makes a nonzero contribution to PE
r.
(3) Only the charge +Q1 makes a nonzerocontribution to FS but both charges +Q1 and
+Q2 make nonzero contributions to PE
r.
(4) Only the charge +Q2 makes a nonzerocontribution to FS but both charges +Q1 and
+Q2 make nonzero contributions to PE
r.
15. fp= esa ,d fcUnq vkos'k +Q1 dkYifud xksyh; lrg
(2) nksuksa vkos'k +Q1 rFkk +Q2] FS esa v'kwU; lg;ksx
nsrs gSa ijUrq dsoy vkos'k +Q2, PEr
esa v'kwU; lg;ksx
nsrk gSA
(3) dsoy vkos'k +Q1] FS esa v'kwU; lg;ksx nsrk gS
ijUrq nksuksa vkos'k +Q1 rFkk +Q2, PEr
esa v'kwU;
lg;ksx nsrs gSA
(4) dsoy vkos'k +Q2] FS esa v'kwU; lg;ksx nsrk gS
ijUrq nksuksa vkos'k +Q1 rFkk +Q2, PEr
esa v'kwU;
lg;ksx nsrs gSA
H-9/38
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00CE314001
16. A composite heavy rope of two materials issuspended vertically from a high ceiling. Theratios of different quantities for upper to lowerrope are :
length uL 1L 2
=l
, cross sectional area uA 2A 1
=l
,
density ud 2d 3
=l
. What is the ratio of maximum
stress in the two ropes.
Lu
Ll
(1) 23
(2) 34
(3) 56
(4) 45
17. Two polaroids are placed in the path ofunpolarized beam of intensity I0 such that nolight is emitted from the second polaroid. If athird polaroid whose polarization axis makes anangle q with the polarization axis of firstpolaroid, is placed between these polaroids, thenthe intensity of light emerging from the lastpolaroid will be :-
17. nks /kzqodksa dks I0 rhozrk okys v/kzqfor iqat ds iFk esa blizdkj ls j[kk tkrk gS fd f}rh; /kzqod ls dksbZ çdk'kckgj uk fudysA ;fn bu nksuksa /kzqodksa ds e /; ,drhljs èkqzod] ftldh /kzqo.k v{k izFke /kzqod dh /kzqo.kv{k ls q dks.k cukrh gS] dks j[kk tkrk gS rks vafreèkzqod ls fudyus okys izdk'k dh rhozrk gksxh%&
(1) 20I
sin 28
æ ö qç ÷è ø
(2) 20I
sin 24
æ ö qç ÷è ø
(3) 20I
cos2
æ ö qç ÷è ø
(4) I0 cos4 q
H-10/38
SPACE FOR ROUGH WORK
ALL INDIA OPEN TEST/JEE (Main)/25-01-2015
00CE314001
18. A point particle of mass 0.5 kg is moving along
the x-axis under a force described by the
potential energy V shown below. It is projected
towards the right from the origin with a speed
v. What is the minimum value of v for which
the particle will escape infinitely far away from
the origin ?
–4 –3 –2 –1 1 2 3 4 5
1
2
3
4
V(in J)
x(in m)
(1) 2 2 ms–1
(2) 2 ms–1
(3) 4 ms–1
(4) The particle will never escape
18. æO;eku 0.5 kg dk ,d fcUnqd.k fp= esa iznf'kZr fLFkfrt
ÅtkZ V }kjk O;ä fd;s x;s cy ds v/khu x-v{k ds
vuqfn'k xfr dj jgk gSA bls ewyfcUnq ls nk¡;h vksj v
pky ls iz{ksfir fd;k tkrk gSA v dk U;wure eku fdruk
gksuk pkfg, rkfd d.k ewyfcUnq ls vuUr nwjh rd iyk;u
dj lds%&
–4 –3 –2 –1 1 2 3 4 5
1
2
3
4
V(in J)
x(in m)
(1) 2 2 ms–1
(2) 2 ms–1
(3) 4 ms–1
(4) d.k dHkh Hkh iyk;u ugha djsxkA
H-11/38
SPACE FOR ROUGH WORK
ALL INDIA OPEN TEST/JEE (Main)/25-01-2015
00CE314001
19. A wheel of radius R with an axle of radius R/2is shown in the figure and is free to rotate abouta frictionless axis through its centre andperpendicular to the page. Three forces(F, F, 2F) are exerted tangentially to therespective rims as shown in the figure. Themagnitude of the net torque acting on the systemis nearly :-
FR/2
R2F
45°F
(1) 3.5 FR (2) 3.2 FR(3) 2.5 FR (4) 1.5 FR
20. In the figure shown a mass 1 kg is connected toa string of mass per unit length 1.2 gm/m. Lengthof string is 1 m and its other end is connected tothe top of a ceiling which is accelerating up withan acceleration 2 m/s2. A transverse pulse isproduced at the lowest point of string. Timetaken by pulse to reach the top of string is :
1kg1m
a=2m/s2
(1) 0.1 s (2) 0.01 s (3) 0.05 s (4) 0.5 s
19. f=T;k R okys ,d ifg;s dks fp= esa n'kkZ;k x;k gS rFkkbldh /kqjh R/2 f=T;k okyh gSA ;g blds dsUæ lsgksdj xqtj jgh rFkk dkxt ds ry ds yEcor~ ?k"kZ.kjfgrv{k ds ifjr% eqä :i ls ?kw.kZu djrk gSA rhu cyksa(F, F, 2F) dks fp=kuqlkj bldh ifjf/k;ksa ij Li'kZjs[kh;:i ls vkjksfir fd;k tkrk gSA fudk; ij dk;Zjrifj.kkeh cyk?kw.kZ dk ifjek.k yxHkx gksxk %&
FR/2
R2F
45°F
(1) 3.5 FR (2) 3.2 FR(3) 2.5 FR (4) 1.5 FR
20. fp= esa 1 kg æO;eku dks izfr ,dkad yEckbZ æO;eku1.2 gm/m okyh jLlh ls tksM+k x;k gSA jLlh dh yEckbZ1 m gS rFkk bldk nwljk fljk Nr ds 'kh"kZ ls tqM+k gS tks2 m/s2 Roj.k ls Åij dh vksj Rofjr gks jgh gSA jLlhds fuEure fcUnq ij ,d vuqizLFk Lian mRiUu fd;ktkrk gSA LiUn }kjk jLlh ds 'kh"kZ rd igq¡pus esa fy;kx;k le; gksxk %&
ij foLFkkfir gks tkrk gSA oksYVehVj dk ikB~;kad vkjsf[kr
fd;k x;k gSA R rFkk C ds inksa esa rjax dk vkorZdky T
D;k gksxk\
VC
21
CV
R
T
2V/3
V/3
t2 t1
Voltage
time
(1) RC ln3 (2) 2RC ln 2
(3) RC2 ln3 (4)
RC3 ln3
H-16/38
SPACE FOR ROUGH WORK
ALL INDIA OPEN TEST/JEE (Main)/25-01-2015
00CE314001
29. Statement-1 : A photodiodes operates in reversebias.Statement-2 : The fractional change due to thephoto-effects on the minority carrier dominatedreverse bias current is more easily measurable thanthe fractional change in the forward bias current.(1) Statement-1 is true, Statement-2 is true,
Statement-2 is the correct explanation ofStatement-1.
(2) Statement-1 is true, Statement-2 is true,Statement-2 is not the correct explanationof Statement-1.
(3) Statement-1 is true, Statement-2 is false.(4) Statement-1 is false, Statement-2 is true.
30. Starting from rest on her swing at initial heighth
0 above the ground, Saina swings forward. At
the lowest point of her motion, she grabs herbag that lies on the ground. Saina continuesswinging forward to reach maximum height h
1.
She then swings backward and when reachingthe lowest point of motion again, she simple letsgo off the bag, which falls freely. Saina'sbackward swing then reaches maximum heighth
30. lk;uk ,d djrc ds nkSjku ,d jLlh dks idM+s gq,èkjkry ls h
0 ÅapkbZ ij fojkekoLFkk esa gSA vc og vkxs
dh vksj > wyrh gqbZ viuh xfr ds fuEure fcUnq ijèkjkry ij j[ks ,d cSx dks mBkrh gSA og mlh fn'kk esa>wyrs gq, vf/kdre ÅapkbZ h
1 rd igqap tkrh gSA vc
og iqu% ihNs dh fn'kk esa ykSVrh gS rFkk xfr ds fuEurefcUnq ij igqapus ij og cSx dks NksM+ nsrh gS tks fd eqDr:i ls fxjrk gSA vc og ihNs dh fn'kk esa vf/kdreh
(4) Angular wave function of Pz orbital isproportional to cos q (Given : q is anglefrom z-axis)
32. A heat engine is operating between 500K to300K. If the engine absorbs 100J heat, thenwhich of the following is impossible amountof heat rejected by the engine.
(1) 80 J (2) 75 J
(3) 70 J (4) 20 J
33. In which of the following case percentageincrease in rate constant will be maximum.
Ea(Kcal/mol) Temp. Change (K)
(I) 40 200 – 210
(II) 80 200 – 210
(III) 40 300 – 310
(IV) 80 300 – 310
(1) I (2) II
(3) III (4) IV
31. fuEu esa ls dkSulk dFku xyr gS -
(1) 4d d{kd ds fy, xksyh; uksMks dh dqy la[;k 3
gksrh gS
(2) py d{kd ds fy, xz ry dks.kh; uksM gksrk gS
(3) 's' d{kd ds fy,, ukfHkd ij Y 2 vf/kdre gksrk gS
(4) Pz d{kd dk dks.kh; rjax Qyu cos q ds lekuqikrhgksrk gS (fn;k gS: q, z-v{k ls dks.k gS)
(3) vkFkksZjksfEcd fØLVy esa izR;sd vUrjki`"Bh; dks.k
90º dk gksrk gS
(4) prq"dks.kh; fØLVyh; ra= esa pkj bdkbZ lsy gksrs gS
H-19/38
SPACE FOR ROUGH WORK
00CE314001
ALL INDIA OPEN TEST/JEE (Main)/25-01-2015
38. Select the incorrect statement using phasediagram of a substance
C
O
BAP2
P1
P
TT6 T1T4 T2 T5 T3
(1) At pressure P2, T4 is melting point(2) Substance will be in liquid state if
temperature T is 'T4 < T < T5' at P2 pressure(3) At T3 temperature vapour pressur of liquid
is P1
(4) Sublimation temperature is always less thantriple point
39. According to the kinetic theory of gases, in anideal gas, between two successive collisions agas molecule travels -(1) In a straight line path(2) with an accelerated velocity(3) In a circular path(4) In a wavy path
40. To obtain maximum mass of NO2 from a givenmass of a mixture of NH3 and O2, the ratio ofmass of NH3 to O2 should be
42. In Which of the following process nitrogenundergoes in oxidation process :
(1) N2 ® HN3 (2) N2O4 ® 2NO2
(3) NO¯3 ® N2O5 (4) N2O ® NO
43. Case hardening is a process of heating steel inatmosphere of :
(1) Carbon dioxide
(2) Ammonia
(3) Charcoal
(4) Oxygen
44. For an octahedral complex, which of thefollowing d-electronic configuration will givemaximum magnitude of crystal fieldstabilisation energy, in terms of DO :(1) Low spin d5 (2) Low spin d4
(3) High spin d7 (4) High spin d6
41. Na H O2 (A) (B) (C) (D)
(E) + F(g)
CO2 SO2
D
SO2 ds vkf/kD;esas ok"iuvkf/kD;
D
(G) + H
;kSfxd D gS :
(1) Na2SO3
(2) Na2S2O5.xH2O
(3) Na2S
(4) Na2SO4
42. fuEu esa ls dkSuls izØe esa ukbVªkstu dk vkWDlhdj.k gksjgk gS :
(1) N2 ® HN3 (2) N2O4 ® 2NO2
(3) NO3 ® N2O5 (4) N2O ® NO
43. fuEu esa ls fdlds ok;qeaMy esa LVhy dks xeZ djus dsizØe dks dsl dBksjhdj.k dgk tkrk gS :
(1) dkcZu MkbvkWDlkbM
(2) veksfu;k
(3) pkjdksy
(4) vkWDlhtu
44. fuEu esa ls dkSulk d-bysDVªkWfu; foU;kl ,d v"VQydh;ladqy ds fy,] DO ds inksa esa fØLVy {ks= fLFkjhdj.kÅtkZ dk lokZf/kd ifjek.k nsxk :(1) fuEu pØ.k d5 (2) fuEu pØ.k d4
(3) mPp pØ.k d7 (4) mPp pØ.k d6
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45. Dichloronitronium ion [ONCl2]+ and thionyl
chloride (OSCl2), which has higher
Cl – µX – Cl bond angle.(where X = central atom N and S)
(1) µCl N Cl- - > $Cl S Cl- -
(2) µCl N Cl- - < $Cl S Cl- -
(3) µCl N Cl- - = $Cl S Cl- -(4) None of these
46. Which of the following molecule has zerodipole moment :
(1)
OH
OH(2)
Cl
Cl
(3)
OH
NO2
(4) All of these
47. Which of the following species show(s)synergic bonding :
58. Give the major product of the followingreaction
O
H
N CH COCl3AlCl3
Major product
(1)O
H
N
COCH3
(2)
O
H
NCOCH3
(3)O
H
N
H COC3
(4)O
H
N
COCl
58. fuEu vfHkfØ;k dk eq[; mRIkkn nhft,s&
O
H
N CH COCl3AlCl3
eq[; mRikn
(1)O
H
N
COCH3
(2)O
H
NCOCH3
(3)O
H
N
H COC3
(4)O
H
N
COCl
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59.1. BH / THF3
2. H O / OH2 2–
Product of reaction is -
(1)
OH
HH
CH3
(2) CH3
CH3
(3) CH3OH (4)
H
HOH
CH3
60. Product of reaction is :O
O
N–H (i) NaOBr
(ii) H+
(1)COOH
NH2
(2)
CH –COOH2
NH2
(3)
COOH
CH –NH2 2
(4)
O
NH
59.1. BH / THF3
2. H O / OH2 2–
vfHkfØ;k dk mRikn gS&
(1)
OH
HH
CH3
(2) CH3
CH3
(3) CH3OH (4)
H
HOH
CH3
60. vfHkfØ;k dk mRikn gS&
O
O
N–H (i) NaOBr
(ii) H+
(1)COOH
NH2
(2)
CH –COOH2
NH2
(3)
COOH
CH –NH2 2
(4)
O
NH
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61. A variable straight line AB divides thecircumference of the circle x2 + y2 = 25 in theratio 1 : 2. If a tangent CD is drawn to thesmaller arc parallel to AB, such that ABCD isa rectangle, then locus of C & D is (as shownin the figure) :-
D C
A BO
(1) 2 2 175
x y4
+ = (2) x2 + y2 = 36
(3) x2 + y2 = 40 (4) x2 + y2 = 2062. The number of shortest
A
M
N
Dpaths from point A to D(as shown in figure)(1) 276(2) 186(3) 150(4) 126
63. If n is a factor of 72, such that xy = n,then number of ordered pairs (x, y) are :-(where x, y Î N)(1) 40 (2) 50(3) 60 (4) 70
61. ,d pj ljy js[kk AB, o`Ùk x2 + y2 = 25 dh ifjfèk dks1 : 2 vuqikr esa foHkkftr djrh gSA ;fn y?kq pkiij AB ds lekUrj ,d Li'kZjs[kk CD bl izdkj [khaphtkrh gS fd ABCD ,d vk;r gS] rks C rFkk D dkfcUnqiFk gksxk (fp=kuqlkj)
D C
A BO
(1) 2 2 175
x y4
+ = (2) x2 + y2 = 36
(3) x2 + y2 = 40 (4) x2 + y2 = 2062. fp=kuqlkj fcUnq A ls D rd
prqFkk±'k esa fLFkr gS rFkk fcUnq P ij [khaph xbZ Li'kZ js[kko vfHkyEc nh?kZ v{k dks Øe'k% T rFkk N ij feyrs gSa]
rks 2 1 2 1
2 1 2 1
(| F N | | F N |)(| F T | | FT |)(| F N | | F N |)(| F T | | FT |)
+ -- +
dk eku gksxk
(tgk¡ F1 rFkk F2 Øe'k% ukfHk;k¡ (ae,0) rFkk (–ae,0) gS)
(1) 1 (2) 2a (3) 2b (4) ae
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70. Let a1, a2, ........ a101 is a group of real numberssuch that ai > ai+1 for all values of i and meansquare deviation of the group is minimum aboutthe number 'a51', then mode of the group willbe -(1) 2a51 (2) a51
(3) a50 (4) a52
71. Which of the following statement is atautology?
(1) ( )( ){ } ( ) ( ){ }p q t p q r p té ùÙ Ú Ù ® Ú Ù Úë û
( )~ q r ~ p« Ú ®é ùë û
(2) ( )( ){ } [ ]p q t p (q r) pÙ Ú Ù « Ú ®
(3) ( )( ){ } [ ]p q t p q r pÙ Ú Ù « Ù Ù
(4) ( )( ){ }p q t p tÙ Ú Ù « (where t denotes tautology)
(1) ( )( ){ } ( ) ( ){ }p q t p q r p té ùÙ Ú Ù ® Ú Ù Úë û
( )~ q r ~ p« Ú ®é ùë û
(2) ( )( ){ } [ ]p q t p (q r) pÙ Ú Ù « Ú ®
(3) ( )( ){ } [ ]p q t p q r pÙ Ú Ù « Ù Ù
(4) ( )( ){ }p q t p tÙ Ú Ù «
(tgk¡ t, iqu#fDr dks n'kkZrk gS)
72.{ }( ){ }
{ }
{ }
1x
x
x 1
e1 x
elim1 cos x+®
+ -
-
(tgk¡ {.} fHkUukRed Hkkx Qyu dks n'kkZrk gS)
(1) 0 (2) 2e3
(3) 3e2
(4) fo|eku ugha gSA
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73. Number of points of discontinuity of thefunction ƒ(x) = sin({ 2x + [2x] + [3–x]}) forx Î [0,4] is(where [.] and {.} denotes greatest integer andfractional part function respectively) -(1) 5 (2) 4 (3) 15 (4) 16
74.( )
( ) ( )
2
2
d sin
1 sin cos 3
q
- q qò is equal to-
(1)
p
q
pæ öq +ç ÷+ç ÷pç ÷q -ç ÷
è ø
l
tan6
seccos cos2 6n e C
3 cos cos6
(2)
p
q
pæ öq +ç ÷+ç ÷pç ÷q -ç ÷
è ø
l
tan6
coscos cos2 6n e C
3 cos cos6
(3)
p
p-q
pæ öq +ç ÷+ç ÷pç ÷q -ç ÷
è ø
l
tan6
sec( )cos cos2 6n e C
3 cos cos6
(4)
p
p-q
pæ öq +ç ÷+ç ÷pç ÷q -ç ÷
è ø
l
tan6
cos( )cos cos2 6n e C
3 cos cos6
(where C is constant of integration)
73. mu fcUnqvksa dh la[;k] tgk¡ Qyu
ƒ(x) = sin({2x + [2x] + [3–x]}), x Î [0,4] esa vlarr~
(where C is constant of integration)76. Area bounded on the left by y-axis, below by
x-axis, right by x2p
= above left by y = cosx
and above right by y = sinx is -
(1) 1 (2) 2 (3) 2 2 (4) 2
77. If ( ) ( ) ( )+= Înx 1ƒ x e ; n N , then value of 'n' for
which ( ) ( )=nn 2ƒ" 1 67 2 e is-
(1) 1 (2) 2(3) 3 (4) 4
78. If ƒ is a differentiable function such thatƒ(2x + 1) = ƒ(1 – 2x) " xÎR then minimumnumber of roots of the equation ƒ'(x) = 0 inx Î (–5,10), given that ƒ(2) = ƒ(5) = ƒ(10), is-(1) 2 (2) 3 (3) 4 (4) 5
76. ck;sa ls y-v{k }kjk] uhps ls x-v{k }kjk] nk;sa ls x2p
=
}kjk] mGij ck;s a ls y = cosx rFkk mGij nk¡;s ls
y = sinx }kjk ifjc¼ {ks=Qy gksxk -
(1) 1 (2) 2 (3) 2 2 (4) 2
77. ;fn ( ) ( ) ( )+= Înx 1ƒ x e ; n N gks] rks n dk eku ftlds
fy, ( ) ( )=nn 2ƒ" 1 67 2 e gks] gksxk -
(1) 1 (2) 2(3) 3 (4) 4
78. ;fn ƒ ,d vodyuh; Qyu bl izdkj gS fdƒ(2x + 1) = ƒ(1 – 2x) " x Î R gS] rks x Î (–5,10)esa lehdj.k ƒ'(x) = 0 ds ewyksa dh U;wure la[;k gksxh]fn;k gS ƒ(2) = ƒ(5) = ƒ(10) gS -(1) 2 (2) 3 (3) 4 (4) 5
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79. Let a function
n(3x [3x]) ; 3x n;n Nƒ(x)
n(sgn(3x)) ; 3x n;n N- - ¹ Îì
= í = Îî
l
l,
(where [.] and sgn(x) denotes greatest integerfunction and signum function respectively)then number of point(s), where ƒ(x) isminimum in x Î (0, 5), is -(1) 0 (2) 4(3) 5 (4) 14
80. Area bounded by the tangents of the curvegiven by y = sinq cos2q ; x = sin2q cosq, whichare parallel to co-ordinate axes (other thanaxes), is-
(1) 4
27 (2) 274 (3)
1627 (4)
2716
81. If n
2n
n
I tan {x}dx-
= ò , then (where {.} denotes
fractional part function and n Î N) -(1) I1I2 = 8(sec21 – 2 – I1)
(2) I1I2 = 8(sec21 – 2 + I1)
(3) I1I2 = 8(sec21 + 2 – I1)
(4) I1I2 = 8(sec21 + 2 + I1)82. If focus divides a focal chord of the parabola
y2 = 16x into 2 parts having lengths a and c,such that a,b,c are in H.P., then value of b isequal to -(1) 2 (2) 4(3) 6 (4) 8
a rFkk c yEckbZ ds nks Hkkxksa esa bl izdkj gS foHkkftrdjrh gS] fd a,b,c gjkRed Js.kh esa gks] rks b dk ekugksxk -(1) 2 (2) 4(3) 6 (4) 8
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83. Let F1 & F2 be the foci of an ellipse 2 2x y
14 9
+ =
such that a ray from F1 strikes the ellipticalmirror at the point P and get reflected. Thenequation of angle bisector of the angle betweenincident ray and reflected ray can be -
(1) 5y x13
= + (2) 5y 2x13
= -
(3) x + y – 5 = 0 (4) 3x – 4y – 5 = 0
84. Number of integral points interior to the circlex2 + y2 = 10 from which exactly one real tangentcan be drawn to the curve
( ) ( )2 22 2x 5 2 y x 5 2 y 10+ + - - + =
are (where integral point (x, y) means x, y Î I)
(1) 12 (2) 14
(3) 16 (4) 18
85. If angles A,B,C of a DABC are 75º, 45º and60º respectively. Then ratio of the areas ofDOBC, DCOA and DAOB respectively is[where O is the circumcentre of the triangle]-
(1) 3 1: 2 : 6+ (2) 1: 2 : 3
(3) 2 3 :1: 3+ (4) 3 :1: 2
83. ekuk F1 rFkk F2 nh?kZoÙk 2 2x y
14 9
+ = dh ukfHk;k¡ bl
izdkj gS fd F1 ls ,d fdj.k] nh?kZoÙkkdkj niZ.k ls fcUnq
P ij ijkofrZr gksrh gSA rks vkifrr fdj.k rFkk ijkofrZr
(1) collinear(2) coplanar(3) non-coplanar(4) nothing can be said
89. 3 numbers are chosen from first 15 naturalnumbers, then probability that the numbers arein arithmetic progression-
(1) 25
(2) 6
85
(3) 15
215
3
CC
(4) 7
65
90. If P & Q are two non-singular matrices of thesame order such that Qr = I, for some integerr > 1, then P–1Qr–1P – P–1Q–1P is equal to -(1) O (2) 2I(3) I (4) –I(where I is identity matrix and O is null matrix)