Your Target is to secure Good Rank in JEE(Main) 2015 Path to Success ALLEN CAREER INSTITUTE KOTA (RAJASTHAN) T M FORM NUMBER (ACADEMIC SESSION 2014-2015) PAPER CODE SCORE – I DATE : 07 - 03 - 2015 01CT314063 PHASE – ELS, ELC, ELD & ELP Corporate Office ALLEN CAREER INSTITUTE “SANKALP”, CP-6, Indra Vihar, Kota (Rajasthan)-324005 +91-744-2436001 [email protected]CLASSROOM CONTACT PROGRAMME www.allen.ac.in JEE (Main) : LEADER COURSE 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, pager, 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 isfUly dk iz;ks x fcYdqy oftZr gS aA 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 Sj 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 iz dkj dh ikB~ ; lkexz h eq fær ;k gLrfyf[kr dkxt dh ifpZ ;ks a ] is tj] 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@gkW y 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 MAJOR TEST Test Pattern : JEE (Main) IMPORTANT INSTRUCTIONS egRoiw.kZ funsZ'k
Transcript
Your Target is to secure Good Rank in JEE (Main) 2015
Path to Success
ALLENCAREER INSTITUTEKOTA (RAJASTHAN)
T M
FORM NUMBER
(ACADEMIC SESSION 2014-2015)
PAPER CODE
SCORE – I DATE : 07 - 03 - 2015
0 1 C T 3 1 4 0 6 3
PHASE – ELS, ELC, ELD & ELP
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, pager, 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 thatof water. Suppose you have identical massesof alcohol 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 allowedto come into thermal equilibrium, with no lossof heat to the surroundings. The finaltemperature of 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. A pan balance has a container of water with anoverflow spout on the right-hand pan as shown.It is full of water right up to the overflow spout.A container on the left-hand pan is positionedto catch any water that overflows. The entireapparatus is adjusted so that it’s balanced.A brass weight on the end of a string is thenlowered into the water, but not allowed to reston the bottom of the container. What happensnext ?
1. ,Ydksgy dh fof'k"V Å"ek] ty dh rqyuk esa vk/khgksrh gSA vkids ikl ,Ydksgy rFkk ty ds cjkcj æO;ekugSA ,Ydksgy izkjEHk esa TA rkieku ij gS] tcfd tyizkjEHk esa TW rkieku ij gSA vc bu nksuksa æoksa dks ,dgh ik= esa feykdj rkih; lkE;koLFkk esa vkus fn;k tkrkgSA ;gk¡ ifjos'k esa dksbZ Å"ek âkl ugh gksrkA bl feJ.kdk vafre rkieku gksxk%&(1) TW dh rqyuk esa TA ds vf/kd lehi(2) TA dh rqyuk esa TW ds vf/kd lehi(3) TA rFkk TW ds Bhd e/; esa(4) ;g iz;qDr ,Ydksgy ds vk;ru ij fuHkZj djsxkA
2. ,d HkkSfrd rqyk ds nk¡;s iyM+s esa ty ls Hkjk ,d ik=
j[kk gSA ;g ty ls fp=kuqlkj VksaVh rd Hkjk gqvk gSA
midj.k larqyu dh voLFkk esa j[kk gqvk gSAjLlh ls tqM+s
gq, ihry ds ,d Hkkj dks ty esa mrkjk tkrk gS ijUrq bls ik=
ds iSans ij ugha j[kk tkrk] rc %&
Kota/01CT3140632/35
Target : JEE(Main) 2015/07-03-2015
SPACE FOR ROUGH WORK
(1) Water overflows and the right side of thebalance tips down.
(2) Water overflows and the left side of thebalance tips down.
(3) Water overflows but the balance remainsbalanced.
(4) Water overflows but which side of thebalance tips down depends on whether thebrass weight is partly or completelysubmerged.
3. In the given figure, two elastic rods A & B arerigidly joined to end supports. A small mass‘m’ is moving with velocity v between the rods.All collisions are assumed to be elastic & thesurface is given to be frictionless. The timeperiod of small mass ‘m’ will be :[A=area ofcross section, Y = Young’s modulus, L=lengthof each rod ; here, an elastic rod may be treated
as a spring of spring constant YAL ]
Y Y
(1) 2L mL2v AY
+ p (2) 2L 2mL2v AY
+ p
(3) 2L mLv AY
+ p (4) vL2
(1) ty ckgj fudy vk;sxk rFkk rqyk nka;h vksj >qdtk;sxh
5. An electromagnetic wave of wavelengthl0 (in vacuum) passes from P towardsQ crossing three different media of refractiveindex m, 2m and 3m respectively as shown infigure. fP and fQ be the phase of the wave atpoints P and Q. Find the phase difference fQ –fP. [Take : m=1]
6. A disc is rotating with constant angular velocityabout an axis passing through centre C andperpendicular to the plane of disc. An insect ismoving over the disc along radial direction withconstant velocity with respect to the disc.Acceleration of the insect at the instant whenits distance from centre is r, will be :-
C I w
(1) rw2 towards the centre(2) rw2 away from the centre(3) Less than rw2 in magnitude(4) Greater than rw2 in magnitude
7. Two small bodies of mass of 2 kg each attachedto each other using a thread of length 10 cm,hang on a spring whose force constant is200 N/m, as shown in the figure. We burn thethread. What is the distance between the twobodies when the top body first arrives at itshighest position? (Take p2 = 10)(1) 60 cm(2) 70 cm (3) 80 cm(4) None of these
6. ,d pdrh fu;r dks.kh; osx ls blds ry ds yEcor~
rFkk dsUæ C ls xqtjus okyh v{k ds lkis{k ?kw.kZu dj jgh
gSA ,d dhM+k pdrh ds Åij pdrh ds lkis{k fu;r osx
ls f=T;h; fn'kk esa xfr dj jgk gSA tc ;g dsUæ ls r nwjh
8. A steel wire is used to stretch a spring.An oscillating magnetic field drives the steelwire up and down. A standing wave with threeantinodes is created when the spring is stretchedby 4.0 cm. What stretch of the spring producesa standing wave with two antinodes with samefrequency?
steel wire Pull
Spring
(1) 4 cm (2) 12 cm (3) 9 cm (4) 6 cm9. The limbs of a U-tube glass are lowered into
vessels A and B, A containing water. Some airis pumped out through the top of the tube C.The liquids in the left hand limb A and the righthand limb B rise to heights of 10 cm and12 cm respectively. The density of liquid B is
Hkqtk A o nka;h Hkqtk B esa nzoksa dk Lrj Øe'k% 10cm o12 cm gSA nzo B dk ?kuRo gksxk
12
BA
(water) (liquid)
C
(1) 0.75 g/cm3 (2) 0.83 g/cm3
(3) 1.2 g/cm3 (4) 0.25 g/cm3
Kota/01CT3140636/35
Target : JEE(Main) 2015/07-03-2015
SPACE FOR ROUGH WORK
10. Two masses m1 and m2 are connected by astring of length l. They are held in a horizontalplane at a height H above two heavy plates Aand B made of different material placed on thefloor. Initially distance between two masses isa < l. When the masses are released undergravity they make collision with A and B withcoefficient of restitut ion 0.8 and 0.4respectively. The time after the collision whenthe string becomes tight is :-(Assume H>>l)
(1) 2 25 a
2 2gH-l
e = 0.8
A B
e = 0.4
m1 m2
a < l
H
(2) 2gH
(3) 2 23 a
2 2gH-l
(4) None of these
11. Two thin parallel slits are made in an opaquescreen. When a monochromatic beam of lightpasses through them at normal incidence, thefirst bright fringe in the transmitted light occursat ±45° with the original direction of the lightbeam on a distant screen when the apparatus isin air. When the apparatus is immersed in aliquid, the same bright fringe now occurs at± 30°. The index of refraction of the liquid is :-
(1) 2 (2) 3 (3) 43 (4)
32
10. nks æO;eku m1 o m2 ,d l yEckbZ dh jLlh }kjk tqM+sgq, gSA bUgsa Q'kZ ij j[kh vyx&vyx inkFkks± ls cuh nksHkkjh IysVksa A o B ds Åij H Å¡pkbZ ij {kSfrt ry esajksd dj j[kk x;k gSA izkjEHk esa nksuksa æO;ekuksa ds e/;nwjh a < l gSA tc bu æO;ekuksa dks xq:Ro ds v/khufojkekoLFkk ls NksM+ fn;k tkrk gS rks ;s A o B ds lkFkVdjkrs gSa ftuds fy;s izR;koLFkku xq.kkad Øe'k% 0.8 o0.4 gSA VDdj gksus ds fdrus le; i'pkr~ ;g jLlh rutkrh gS (ekuk H>>l gS)
(1) 2 25 a
2 2gH-l
e = 0.8
A B
e = 0.4
m1 m2
a < l
H
(2) 2gH
(3) 2 23 a
2 2gH-l
(4) buesa ls dksbZ ugha
11. ,d vikjn'khZ insZ esa nks iryh lekUrj fLyVsa cuk;htkrh gSA tc ,d ,do.khZ; izdk'k iqat bu fLyVksa lsyEcor~ vkiru dh fLFkfr ls xqtjrk gS rks ikjxfer izdk'kesa nwj fLFkr insZ ij izFke pedhyh fÝUt] izdk'k iqat dhewy fn'kk ls ±45° ij izkIr gksrh gS tc fd ;g midj.kok;q esa j[kk gSA tc bl midj.k dks ,d æo esa Mqck fn;ktkrk gS rks ;gh pedhyh fÝUt ± 30° ij izkIr gksrh gSAæo dk viorZukad gS %&
statement is incorrect (Dimension of x = L1) ?(1) m = –1(2) Dimension of C = L1
(3) Dimensions of a = L–1
(4) None of these13. In the P-V diagram shown, the gas does 5 J of
work in isothermal process ab and 4 J in adiabaticprocess bc. What will be the change in internalenergy of the gas in straight path c to a?
a b
cV
P
(1) 9J (2) 1 J (3) 4 J (4) 5 J14. There are three sources of sound of equal
intensities with frequencies 101, 103 and 106Hz. What is the beat frequency heard if all aresounded simultaneously?(1) 2 Hz (2) 4 Hz (3) 6 Hz (4) 8 Hz
15. It is found that an increase in pressure of100 kPa causes a certain volume of water todecrease by 5 × 10–3 percent of its originalvolume. Then the speed of sound in the wateris about (density of water 103 kg/m3)(1) 330 m/s (2) 1414 m/s(3) 1732 m/s (4) 2500 m/s
12. fn;k x;k gS ax m exe dx a e C= +ò , rks dkSulk dFku xyr
gS (x dh foek = L1) %&(1) m = – 1(2) C dh foek = L1
(3) a dh foek = L–1
(4) buesa ls dksbZ ugha
13. iznf'kZr P-V vkjs[k esa xSl lerkih; izØe ab esa 5 J rFkk
:¼ks"e izØe bc esa 4J dk;Z djrh gSA lh/ks iFk c ls ard xSl dh vkarfjd ÅtkZ esa gq, ifjorZu dk eku gksxk
dk 5 × 10–3 izfr'kr de gks tkrk gSA ty esa /ofu dh
pky yxHkx gksxh (ty dk ?kuRo = 103 kg/m3)(1) 330 m/s (2) 1414 m/s(3) 1732 m/s (4) 2500 m/s
Kota/01CT3140638/35
Target : JEE(Main) 2015/07-03-2015
SPACE FOR ROUGH WORK
16. At shallow depth h, the pressure in the oceanis simply given by P = P0 + rgh, in which r isthe density of water and P0 is the air pressure.As we go deeper, the high pressure causes thewater to compress and become denser. Whichof the following sketches illustrates the correctdependence of the pressure on the depth h ?
(1)
P
P0
h
(2)
P
P0
h
(3)
P
P0
h
(4)
P
P0
h
17. Find maximum amplitude for safe SHM (blockdoes not topple during SHM) of a cubical blockof side 'a' on a smooth horizontal floor as shownin figure (spring is massless)
18. A rod of length 1000 mm and coefficient oflinear expansion a = 10–4 per degree is placedsymmetrically between fixed walls separatedby 1001 mm. The Young’s modulus of the rodis 1011 N/m2. If the temperature is increased by20°C, then the stress developed in the rod is :-
1000mm
1001mm
(1) 100 MPa (2) 50 MPa(3) 200 MPa (4) 400 MPa
19. Kinetic energy of a particle executing simpleharmonic motion in straight line is pv2 andpotential energy is qx2, where v is speed atdistance x from the mean position. It timeperiod is given by the expression
(1) 2 qp
p (2) 2 pq
p
(3) 2 qp q
p+ (4) 2 p
p qp
+
18. yEckbZ 1000 mm rFkk a = 10–4 izfr fMxzh js[kh; izlkj
21. For the situation shown in the figure, waterflows on the surface of a fixed plate. Thevelocity of water as a function of distance 'y' is
given as : 2y yu 2
h hé ùæ ö= a -ê úç ÷
è øê úë û. Determine the
magnitude of the shear stress that the waterapplies at the base of the plate. Coefficient ofviscosity is h.
hy x u
Water
Free surface
(1) 3
hah
(2) 2
hah
(3) 4
hah
(4) hah
22. A ball is of mass m, strikes a smooth ground atangle a as shown in figure and is deflected atangle b. The coefficient of restitution will be
a b
(1) tana/tanb (2) cosa/cosb
(3) sina/sinb (4) tanb/tana
21. çnf'kZr fp= esa ,d fLFkj IysV dh lrg ij ty izokfgr
gks jgk gSA nwjh 'y' ds Qyu ds :i esa ty dk osx
2y yu 2h h
é ùæ ö= a -ê úç ÷è øê úë û
}kjk fn;k tkrk gSA ty }kjk IysV
ds isans ij yxk;s tkus okys vi:i.k izfrcy dk ifjek.k
D;k gksxk ;fn ';kurk xq.kkad h gks\
hy x u
Water
Free surface
(1) 3
hah
(2) 2
hah
(3) 4
hah
(4) hah
22. m nzO;eku dh xsan fp=kuqlkj a dks.k ij ,d fpduhlrg ls Vdjkrh gS rFkk la?kkr ds i'pkr~ b dks.k ij tkrhgS] rks izR;koLFkku xq.kkad gksxk&
a b
(1) tana/tanb (2) cosa/cosb
(3) sina/sinb (4) tanb/tana
Kota/01CT31406312/35
Target : JEE(Main) 2015/07-03-2015
SPACE FOR ROUGH WORK
23. In the given figure light is incident at an angleq with the normal to a plane containing twoslits of separation d. Select the expression thatcorrectly describes the positions of theinterference maxima in terms of the incomingangle q and outgoing angle f.
d
fq
(1) 1sin sin m2 d
læ öf + q = +ç ÷è ø
(2) dsinq = ml
(3) ( )sin sin m 1dl
f - q = +
(4) sin sin mdl
f + q =
24. x-t graph for a uniformly accelerated particleis as shown in the figure. Then find the averagevelocity between points (i) and (ii)
x
t
q2=tan (3)-1(ii)
(i) 45°
(1) 3m/s (2) 2m/s (3) 4 m/s (4) 1.5 m/s
23. fp= esa izdk'k vfHkyEc ls q dks.k ij ,d ry ij
vkifrr gksrk gS ftlesa nks fLyVsa d nwjh ij j[kh gqbZ gSA
vkiru dks.k q rFkk fuxZeu dks.k f ds inksa esa O;frdj.k
mfPp"B dh fLFkfr dks n'kkZus okyk O;atd gksxk %&
d
fq
(1) 1sin sin m2 d
læ öf + q = +ç ÷è ø
(2) dsinq = ml
(3) ( )sin sin m 1dl
f - q = +
(4) sin sin mdl
f + q =
24. ,dleku Rofjr xfr dj jgs d.k dk foLFkkiu≤vkjs[k fp= esa iznf'kZr gSA fcUnq (i) rFkk (ii) ds e/;vkSlr osx Kkr dhft,A
25. The pattern of standing waves formed on astretched string at two instants of time (extreme,mean) are shown in figure. The velocity of twowaves superimposing to form stationary wavesis 360 ms–1 and their frequencies are 256 Hz.Which is not possible value of t (in sec) :-
(1) 9.8 × 10–4 (2) 10–3
(3) 2.9 × 10–3 (4) 4.9 × 10–3
26. A chain of length L and mass m is placed upona smooth surface. The length of BA is L–b.Calculate the velocity of the chain when its endreaches B.
q
A B
(1) 2 22gsin(L b )
Lq
- (2) 2 2gsin2 (L b )
Lq
-
(3) 2 2gsin(L b )
Lq
- (4) 2 2gsin(L b )
2Lq
-
25. le; ds nks {k.kksa (mPpre] ek/;) ij fdlh ruh gqbZ jLlh
esa cuh vizxkeh rjaxksa ds izfr:i dks fp= esa n'kkZ;k x;k gSA
26. L yEckbZ rFkk m nzO;eku dh ,d tathj fpduh lrg ds
Åij j[kh gSA BA dh yEckbZ L–b gSA tc bldk fljk
B ij igq¡prk gS] rks tathj ds osx dh x.kuk dhft,A
q
A B
(1) 2 22gsin(L b )
Lq
- (2) 2 2gsin2 (L b )
Lq
-
(3) 2 2gsin(L b )
Lq
- (4) 2 2gsin(L b )
2Lq
-
Kota/01CT31406314/35
Target : JEE(Main) 2015/07-03-2015
SPACE FOR ROUGH WORK
27. A ring of mass m is rolling without slippingwith linear velocity v as shown is figure. A rodof identical mass is fixed along one of itsdiameter. The total kinetic energy of thesystem is :-
(1) 75 mv2 (2)
25 mv2 (3)
53 mv2 (4)
54 mv2
28. A bob of mass m is attached to a string whoseother end is tied to a light vertical rod as shownin figure. The bob is swinging in horizontalplane with constant angular speed w. Thevertical rod is supported on a block of mass Mwhich is placed on a rough surface. What isminimum friction coefficient between groundand block for which block does not slip ?
kg respectively are brought into thermal contacttill they reach equilibrium. Before contact, theywere at T1, T2, T3(T1> T3). Assuming there isno heat loss to the surroundings, the equilibriumtemprature T is (s is specific heat of copper)
(1) 1 2 3
3T T T
T+ +
=
(2) 1 1 2 2 3 3
1 2 3
M T M T M TT
M M M
+ +=
+ +
(3) ( )1 1 2 2 3 3
1 2 33M T M T M T
TM M M
+ +=
+ +
(4) 1 1 2 2 3 3
1 2 3
M T s M T s M T sT
M M M
+ +=
+ +
30. In an industrial process 10 kg of water per houris to be heated from 20°C to 80°C . To do thissteam at 200°C is passed from a boiler into acopper coil immersed in water. The steamcondenses in the coil and is returned to theboiler as water at 90°C. How many kg of steamis required per hour.(Specific heat of steam = 0.5 cal/g°C, Latentheat of vaporisation = 540 cal/g)(1) 1g (2) 1 kg (3) 10 g (4) 10 kg
29. æO;eku M1, M2 o M3 kg okys rhu rkacs ds CykWdksa dks,d&nwljs ds lkFk rkih; laidZ esa ykdj lkE;koLFkk esayk;k tkrk gSA laidZ esa ykus ls iwoZ buds rkieku Øe'k%T1, T2, T3(T1> T3) FksA ekuk ifjos'k esa dksbZ Å"ek âklugha gksrk gSA ;fn rkacs dh fof'k"V Å"ek s gks rks lkE;koLFkkrkieku T gksxk %&
(1) 1 2 3
3T T T
T+ +
=
(2) 1 1 2 2 3 3
1 2 3
M T M T M TT
M M M
+ +=
+ +
(3) ( )1 1 2 2 3 3
1 2 33M T M T M T
TM M M
+ +=
+ +
(4) 1 1 2 2 3 3
1 2 3
M T s M T s M T sT
M M M
+ +=
+ +
30. ,d vkS|ksfxd izØe esa izfr ?k.Vs 10 kg ty dks 20°Cls 80°C rd xeZ fd;k tkrk gSA ,slk djus ds fy;s
200°C rki okyh Hkki dks ,d ckW;yj ls ikuh esa Mwch
gqbZ rkez dq.Mfy;kas esa izokfgr fd;k tkrk gSA Hkki
dq.Mfy;kas esa la?kfur gks tkrh gS ,oa ck;yj dks 90°Cij ty ds :i esa okil dj nh tkrh gSA izfr ?k.Vs fdrus
0.5 cal/g × °C ,oa ok"iu dh x q Ir Å"ek= 540 cal/gm)(1) 1g (2) 1 kg (3) 10 g (4) 10 kg
Kota/01CT31406316/35
Target : JEE(Main) 2015/07-03-2015
SPACE FOR ROUGH WORK
PART B - CHEMISTRY31. For the given series of reaction-
NH3(g) + O2(g) ® NO(g) + H2O(l)
NO(g) + O2(g) ® NO2(g)
To obtain maximum mass of NO2 from a given
mass of mixture NH3 and O2, the ratio of mass
of NH3 to O2 should be -
(1) 47 (2)
1716
(3) 1740 (4)
1756
32. A metal have work function 4 eV is exposedto photon of l = 1240Å. If a acceleratingpotential of 7.6 volt is applied, then the electronwith maximum kinetic energy will have speedequal to -
33. When 1.685 gram of an alkali metal chlorideis dissolved in 200gram water, the boiling pointof the solution is measured to be 100.051ºC.If the ionic solid has a crystal lattice with cationand anion radius 1.70Å and 1.80Å respectively.Find the edge length of solid assuming nodefect in the cyrstal -Given : Kb(H2O) = 0.51 Kkg mol–1
NA = 6 × 1023
[Li = 7, Na = 23, K = 39, Rb = 85.5,Cs = 133, Cl = 35.5]
(1) 7 Å (2)7 Å3
(3) 14 Å
3 (4) 3.5 Å
34. Following are the critical temperature of thesome gases :
Gases H2 He O2
TC(K) 33.2 5.3 154.3
From the above data what would be order ofliquefication of these gases.Start writing the order from the gas liquifyingfirst(1) H2, He, O2 (2) He, O2, H2
mijksDr vk¡dM+ks ls bu xSlksa ds nzohdj.k dk Øe D;k
gksxkA
Øe dks igys nzohr gksus okyh xSl ls izkjEHk dhft;sa
(1) H2, He, O2 (2) He, O2, H2
(3) O2, He, H2 (4) O2, H2, He
Kota/01CT31406318/35
Target : JEE(Main) 2015/07-03-2015
SPACE FOR ROUGH WORK
35. An alloy of metal 'A' 'B' and 'C' is found to have'A' constituting ccp lattice. If 'B' atom occupythe edge centres and 'C' is present at the bodycentre, the formula of the alloy is :-(1) A
4B
2C (2) A
4B
4C
(3) A4B
3C (4) ABC
36. A(g) ® 2B(g)initially 2 moles of A are taken in 5 litre vessel.
After 20 min, [A]t = t[B]2 . Find half life time
of A in the first order reaction(1) 20 min (2) 10 min(3) 40 min (4) 5 min
37. Calculate Ecell
Pt(s)| 21atm
H (g) |HA-7
a(K =10 )1M || HB
–5a(K =10 )1M |
21atm
H (g) |Pt(s)
(1) 0.06 V (2) 0.03 V(3) 0.04 V (4) 0.05 V
38. At certain temperature (T) if conductivity ofpure water is 5.5 × 10–7Scm–1, then calculatepH of water at given temp.
39. 10 gram mixture of two gases A2(mol.wt. = 20)and B2 (mol. wt. = 30), which decompose byfirst order kinetics, was taken in a vessel. Thehalf life of decomposition of A2 and B2 are 2and 3 hours respectively. After 6 hours weightof mixture of A2 and B2 is found to be 2 gram.Find the weight of A2 in the initial mixture-(1) 4 gm (2) 6 gm (3) 8 gm (4) 2 gm
40. Which of the following have highest osmaticpressure at 300 K(1) 0.1 M CH3COOH (a = 0.7)(2) 0.1 M KCl (a = 1)(3) 0.1 M Na2SO4 (a = 1)(4) 0.1 M K2Zn[Fe(CN)6] (a = 1)
41. Consider the following statements :(a) When the lead-silver alloy rich in silver,
lead is removed by the cupellation process(b) Froth flotation can be applied for non
sulphide ore also using suitableactivator
(c) PbSO4 + H2SO4, electrolyte is used for therefining of Pb by electrolysis
(d) Any metal will not reduce the oxide of othermetals which lie above it in the Ellinghamdiagram.
Using 'T' for true and 'F' for false statementsin the given sequence, select the correct setof code(1) T T F T (2) T T F F(3) F T F T (4) T T T F
40. fuEu esa ls fdldk ijklj.k nkc 300K ij vf/kdregksxkA(1) 0.1 M CH3COOH (a = 0.7)(2) 0.1 M KCl (a = 1)(3) 0.1 M Na2SO4 (a = 1)(4) 0.1 M K2Zn[Fe(CN)6] (a = 1)
41. fuEu dFkuksa ij fopkj dhft, :(a) tc ySM&flYoj ,sykW; esa flYoj dh vf/kdrk gks
45. Which of the following is not halide ore ?(1) Cryolite (2) Fluorspar(3) Horn silver (4) Limonite
46. In which of the ƒ-block element number ofelectron in (n – 2)ƒ subshell is zero :(1) Ce (2) U(3) Th (4) None of these
47. Select the correct matching :(1) Pyro metallurgy : Extraction of Fe(2) Electro metallurgy : Extraction of Al(3) Hydro metallurgy : Extraction of Au(4) All above are correct
48. Compound A on borax bead test in reducingflame gives green colour bead. Compound Aon treatment with H2O2 followed by treatmentwith Pb(OAc)2 gives yellow ppt. The metal ionin the compound A is :
(1) Fe+3 (2) Mn2+ (3) Cr+3 (4) Ba2+
49. Thermal stability of BaCO3, CaCO3, SrCO3 andMgCO3 decreases in the order of :
(1) BaCO3 > SrCO3 > MgCO3 > CaCO3
(2) CaCO3 > SrCO3 > MgCO3 > BaCO3
(3) MgCO3 > CaCO3 > SrCO3 > BaCO3
(4) BaCO3 > SrCO3 > CaCO3 > MgCO3
45. fuEu esa ls dkSulk gSykbM v;Ld ugha gSa ?(1) Øk;ksykbV (2) ¶yksjLikj
(3) gkWuZ flYoj (4) fyeksukbV
46. fuEu esa ls dkSuls] ƒ-CykWd rRo ds (n – 2)ƒ midks'kesa bysDVªkWuksa dh la[;k 'kwU; gS :(1) Ce (2) U(3) Th (4) buesa ls dksbZ ugha
68. If equation in variable q, 3tan(q – a) = tan(q + a),(where a is constant) has no real solution, thena can be (wherever tan(q - a) & tan(q + a)both are defined)
(1) 15p
(2) 518
p(3)
512
p(4)
1718
p
69. In DABC, 8D = (b + c)(bc + 1), thencircumradius of DABC is (D denotes area oftriangle and b, c are length of sides AC and ABrespectively) -
(1) D (2) 12D
(3) 2D (4) 1D
70. If y
2y
dtx1 9t-
=+
ò and 2
2
d y kydx
= , then k equals
(1) 9 (2) 94 (3)
92 (4) 18
71. Consider ellipse E, hyperbola H and parabolaP such that each curve has focus (2, 3) andcorresponding directrix is x + y – 10 = 0. If(a, a1), (b, b1), (g, g1) are nearest vertices ofellipse, hyperbola & parabola to the givendirectrix, then
(1) a > b > g (2) b > g > a
(3) a > g > b (4) a < b < g
68. ;fn pj q esa lehdj.k, 3tan(q – a) = tan(q + a),(tgk¡ a vpj gS) dk dksbZ okLrfod gy uk gks] rks a gksldrk gS (tan(q - a) rFkk tan(q + a) nksuksa tgk¡ HkhifjHkkf"kr gS)
(1) 15p
(2) 518
p(3)
512
p(4)
1718
p
69. f=Hkqt ABC esa, 8D = (b + c)(bc + 1) gks] rks f=HkqtABC dh ifjf=T;k gksxh (D, f=Hkqt ds {ks=Qy dksn'kkZrk gS rFkk b, c Øe'k% Hkqtkvksa AC rFkk AB dhyEckbZ;k¡ gSa) -
(1) D (2) 12D
(3) 2D (4) 1D
70. ;fn y
2y
dtx1 9t-
=+
ò rFkk 2
2
d y kydx
= gks] rks k gksxk -
(1) 9 (2) 94 (3)
92 (4) 18
71. ekuk nh?kZoÙk E, vfrijoy; H rFkk ijoy; P blizdkj gS fd izR;sd oØ dh ukfHk (2, 3) rFkk blds laxr
fu;rk x + y – 10 = 0 gSA ;fn (a, a1), (b, b1), (g. g1)nh xbZ fu;rk ds fy, nh?kZoÙk] vfrijoy; rFkk ijoy;
ds lehiorhZ 'kh"kZ gks] rks
(1) a > b > g (2) b > g > a(3) a > g > b (4) a < b < g
77. Let P(n) : 3n < 1 × 2 × 3 × ..... × n, n Î N isalways true for n > l, then smallest value of lis
(1) 7 (2) 9
(3) 13 (4) can't determine
78. a, b, crr r are non coplanar vectors such that
P a b c,Q 4a 3b 4c= + + = + +r rrr r r r r
and R a b c= + a + brr r r are linearly dependent
vectors, then number of possible values of a is
(1) 0 (2) 1 (3) 2 (4) infinite
79. The converse of the statement
"If p < q, then p – x < q – x" is -
(1) If p < q, then p – x > q – x
(2) If p > q, then p – x > q – x
(3) If p – x > q – x, then p > q
(4) If p – x < q – x, then p < q
80. If line 2x 8 y sin z 1 , Rsin 1 cos
- - a -= = bÎ
b a,
sin 1b ¹ lies in the plane 2x – (sinb)y + (cosb)z= k " a Î R, then
(1) k = 8 – sina (2) k = 8 + sina
(3) k = 8 – cosb (4) None of these
77. ekuk n > l ds fy, P(n) : 3n < 1 × 2 × 3 × ..... × n,n Î N lnSo lR; gks] rks l dk U;wure eku gksxk
(1) 7 (2) 9
(3) 13 (4) Kkr ugha fd;k tk ldrk
78. a, b, crr r vleryh; lfn'k bl izdkj gS fd
P a b c,Q 4a 3b 4c= + + = + +r rrr r r r r
rFkk R a b c= + a + brr r r js[kh; vkfJr lfn'k gks] rks a
ds lEHko ekuksa dh la[;k gksxh
(1) 0 (2) 1 (3) 2 (4) vuUr
79. fuEu dFku dk O;qRØe (converse) gksxk
";fn p < q gks] rks p – x < q – x gS" -
(1) ;fn p < q gks] rks p – x > q – x
(2) ;fn p > q gks] rks p – x > q – x
(3) ;fn p – x > q – x gks] rks p > q
(4) ;fn p – x < q – x gks] rks p < q
80. ;fn js[k k 2x 8 y sin z 1 , Rsin 1 cos
- - a -= = bÎ
b a ,
sin 1b ¹ lery 2x – (sinb)y + (cosb)z = k" a Î R esa fLFkr gks] rks
(1) k = 8 – sina (2) k = 8 + sina
(3) k = 8 – cosb (4) buesa ls dksbZ ugha
Kota/01CT31406332/35
Target : JEE(Main) 2015/07-03-2015
SPACE FOR ROUGH WORK
81. The line x y 1a b
+ = moves in such a way that
2 2 2
1 1 1a b 2c
+ = , where a, b, c Î R0 and c is
constant, then locus of the foot of theperpendicular from the origin on the givenline is -(1) x2 + y2 = c2 (2) x2 + y2 = 2c2
(3) 2
2 2 cx y2
+ = (4) x2 + y2 = 4c2
82. In three dimensional space, ƒ(x, y, z) = xy + xz,then locus of all points which satisfies theequation ƒ(x, y, z) = 0 is -(1) pair of perpendicular lines(2) pair of a line and a plane which are parallel to each other(3) pair of perpendicular planes(4) pair of a line and a plane which are perpendicular to each other
83. Planet M orbits around its sun, S, in an ellipticalorbit with the sun at one of the foci. When M isclosest to S, it is 2 unit away. When M is farthestfrom S, it is 18 unit away, then the equation ofmotion of planet M around its sun S, assumingS at the centre of the coordinate plane and theother focus lie on negative y-axis, is -
(1) 2 2x (y 8) 1
36 100-
+ = (2) 2 2x (y 8) 1
36 100+
+ =
(3) 2 2x (y 8) 1
64 100-
+ = (4) 2 2x (y 8) 1
64 100+
+ =
81. j s[kk x y 1a b
+ = bl i zdkj xfr djrh g S fd
2 2 2
1 1 1a b 2c
+ = gS] tgk¡ a, b, c Î R0 rFkk c vpj gks]
rks nh xbZ js[kk ij ewy fcUnq ls [khaps x, yEc ds ikn dk
84. Maximum number of points on parabolay2 = 16x which are equidistant from a variablepoint P (which lie inside the parabola), is -(1) 2 (2) 3(3) 4 (4) more than 4
85. Let in equilateral DABC,A(–1 + acosq, 2 + asinq),B(–1 + acosa, 2 – asina),C(–1 + asinb, 2 + acosb)
and length of median through vertex A is 2b,then equation of circumcircle of triangle ABCis (where a is consant) -
(4) 9x2 + 9y2 – 18x + 36y + 45 – 4b2 = 086. If x + by + c = 0 is normal to parabola y2 = 12x,
then complete set of all values of c is -(1) (–¥, –6) (2) (9, ¥)(3) ( , 6) (9, )-¥ - È ¥ (4) ( , ) {0}-¥ ¥ -
87. Let PQ and RS be the tangent at the extremitiesof the diameter PR of a circle of radius r. If PSand RQ intersect at a point X on thecircumference of the circle, then (PQ.RS) isequal to(1) (PX).(RX) (2) (QX).(SX)
(3) (PX)2 + (RX)2 (4) (QX)2 + (SX)2
84. ijoy; y2 = 16x ij fLFkr vf/kdre fcUnqvksa dh la[;k]tks pj fcUnq P (tks ijoy; ds vUnj dh vksj fLFkr gS) lsleku nwjh ij fLFkr gS] gksxh -(1) 2 (2) 3(3) 4 (4) 4 ls vf/kd
ifjf/k ij fLFkr fcUnq X ij izfrPNsn gksrh gS] rks (PQ.RS)cjkcj gksxk -
(1) (PX).(RX) (2) (QX).(SX)
(3) (PX)2 + (RX)2 (4) (QX)2 + (SX)2
Kota/01CT31406334/35
Target : JEE(Main) 2015/07-03-2015
SPACE FOR ROUGH WORK
88. The angle of elevation of the top of a mobiletower from three points P, Q and R (on a straightline through the foot of the tower) are a, b andg respectively. If all three points are lie on sameside of foot of tower and a : b : g = 1 : 2 : 3 andPQ = l, then height of tower is -(1) ltana (2) lsinb(3) lsing (4) ltan(a + b + g)
89. Let ƒ(x) = max{sin–1x, cos–1x}, then areabounded by x = –1, x = 1, y = ƒ(x) and y = 0is -
(1) 3 22p
- (2) 22 2
p+
(3) 22 2
p p+ (4) None of these
90. Let h(x) = x
0
g(t)dtò , where g(x) is a
differentiable and odd function " x Î R andg(x) is periodic with period 3.Statement 1 : h(x) + h(–x) = 0 " xÎR
Statement 2 : h(x) + h(–x) = x
0
2 g(t)dtò " xÎR
Statement 3 : h(3n) = 0 " nÎ Ithen which of the following statement(s) is/aretrue ?(1) Statement 1 & Statement 3(2) Statement 2 & Statement 3(3) Only Statement 1(4) Only Statement 2
88. rhu fcUnqvksa P, Q rFkk R (ehukj ds ikn ls xqtjus okyhljy js[kk ij) dk eksckbZy ehukj ds 'kh"kZ ls mUu;u
dks.k Øe'k% a, b rFkk g gSA ;fn lHkh rhu fcUnq ehukj
ds ikn dh leku fn'kk esa gks rFkk a : b : g = 1 : 2 : 3,oa PQ = l gks] rks ehukj dh m¡GpkbZ gksxh -
(1) ltana (2) lsinb
(3) lsing (4) ltan(a + b + g)89. ekuk ƒ(x) = vf/kdre{sin–1x, cos–1x} gks] rks x = –1,
x = 1, y = ƒ(x) rFkk y = 0 }kjk ifjc¼ {ks=Qy gksxk -
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