Academic Session: 2014-15 J J E E E E P P R R E E P P A A R R A A T T O O R R Y Y T T E E S S T T - - 2 2 ( ( J J P P T T - - 2 2 ) ) (JEE ADVANCED PATTERN) Target : JEE (Main+Advanced) 2015 Please read the next page & last page of this booklet for the instructions. (Ñi;k funsZ'kksa ds fy;s bl iqfLrdk ds vxys ,oa vfUre i`"B dks i<+sA) Resonance Eduventures Pvt. Ltd. CORPORATE OFFICE : CG Tower, A-46 & 52, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.) - 324005 Ph.No. : +91-744-3012222, 6635555 | Toll Free : 1800 200 2244 | 1800 102 6262 | 1800 258 5555 Reg. Office : J-2, Jawahar Nagar, Main Road, Kota (Raj.)-324005 | Ph. No.: +91-744-3192222 | FAX No. : +91-022-39167222 Website : www.resonance.ac.in | E-mail : [email protected] | CIN: U80302RJ2007PTC024029 Date: 17 May, 2015 | Duration : 3 Hours | Max. Marks: 180 CODE - 0 PAPER-1 DO NOT BREAK THE SEALS WITHOUT BEING INSTRUCTED TO DO SO BY THE INVIGILATOR tc rd ifjos"kd funsZ'k ugha nsa rc rd iz'u i=k dh lhy dks ugha [kksaysA COURSE : VIJETA (JP), VISHWAAS (JF), VIJAY (JR) & VIVEK (JCC)
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This section contains 17 multiple choice questions. Each question has four choices (A), (B), (C)and (D) out of which ONLY ONE is correct.bl [k.M esa 17 cgqfodYi ç'u gSaA çR;sd ç'u esa pkj fodYi (A), (B), (C) vkSj (D) gSa] ftuesa ls dsoy ,d lgh gSA
1. The tangent and normal to the parabola y2 = 8x drawn at (2,4) intersect the line x + y = 3 at thepoints A and B respectively. If AB subtends a right angle at the vertex of the parabola then sum ofall possible values of isijoy; y2 = 8x ds fcUnq (2,4) ij Li'kZ js[kk rFkk vfHkyEc] ljy js[kk x + y = 3 dks Øe'k% A rFkk B ijdkVrs gSaA ;fn AB ijoy; ds 'kh"kZ ij ledks.k vUrfjr djrk gS] rks ds lHkh laHko ekuksa dk ;ksx gS&(A) 2 (B) 1 (C) 0 (D) –1
2. Number of integral values of x such that the inequality 10
3. The sum of all integral values of a for which one root of equation (a – 5) x2 – 2ax + a – 4 = 0 issmaller than 1 and the other root is greater than 2, must be equal toa ds mu iw.kk±d ekuksa dk ;ksxQy ftlds fy, lehdj.k (a – 5) x2 – 2ax + a – 4 = 0 dk ,d ewy 1 ls derFkk nwljk ewy 2 ls cMk gS] cjkcj gS&(A) 18 (B) 259 (C) 262 (D) 261
Space for Rough Work / (dPps dk;Z ds fy, LFkku )
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(A) 1 + x + y + z = 0 (B) 1 + xyz = 0(C) 1 + xy + yz + zx = 0 (D) xy + yz + zx = xyz
9. Tangent is drawn to the ellipse x2 + 2y2 = 6 at point (2, 1). If A and B are the feet of perpendicularsfrom the two focii on the tangent, then length AB is equal tonh?kZo`Ùk x2 + 2y2 = 6 ds fcUnq (2, 1) ij Li'kZ js[kk [khaph tkrh gS ;fn A rFkk B Li'kZ js[kk ij ukfHk;ksa dsyEcikn gS rc AB dh yEckbZ gS(A) 3 (B) 2 (C) 6 (D) 12
10. The length of latus rectum of the parabola whose parametric equations are x = t2 + t + 1, y = t2 – t + 1,
where t R, is equal to
ijoy; ftlds izkpfyd lehdj.k x = t2 + t + 1, y = t2 – t + 1, tgk¡ t R, ds ukfHkyEc dh yEckbZ cjkcj gS&(A) 2 (B) 4 (C) 8 (D) 6
11. If A, B and C are three events such that P(B) =3
4, P(A B C) =
1
3 and P(A B C) =
1
3 then
P(B C) =
;fn A, B ,oa C rhu ?kVuk,¡ bl izdkj gS fd P(B) =3
4, P(A B C) =
1
3,oa P(A B C) =
1
3rc
P(B C) =
(A)1
12(B)
5
12(C)
3
4(D)
1
3
Space for Rough Work / (dPps dk;Z ds fy, LFkku )
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This section contains 3 multiple choice questions. Each question has matching lists. The codes forthe lists have choice (A), (B), (C) and (D) out of which ONLY ONE is correct.bl [k.M esa 3 cgqfodYi iz'u gSA izR;sd iz'u esa lqesyu lwph gSA lwfp;ksa ds fy, dksM ds fodYi (A), (B), (C)
rFkk (D) gS , ftuesa ls flQZ ,d lgh gSA
18. Match List I with List II and select the correct answer using the code given below the lists :lwph I dks lwph II ls lqesfyr dhft, rFkk lwfp;ksa ds uhps fn, x, dksM dk ç;ksx djds lgh mÙkj pqfu;s %List - I /lwph - I List - II/ lwph- II
P. The maximum number of point of 1. 128intersection of 6 straight lines and 4 circles is6 ljy js[kkvksa ,oa 4 o`Ùkksa ds izfrPNsn fcUnqvksa dh vf/kdre la[;k gS&
Q. The number of even factors of 38808 is 2. 7538808 ds le xq.ku[k.Mksa dh la[;k gS&
R. Number of ways of distributing 7 different books to 2 children is 3. 547 fofHkUu iqLrdksa dks 2 cPpksa esa ckaVus djus ds rjhdksa dh la[;k gS&
S. 3 fair dice are thrown. The probability that the sum of the 4. 108numbers appearing is 15 is equal to 5/p, then p =rhu fu"i{kikrh ikls QSads tkrs gSA mu ij vkus okys vadksa dk ;ksxQy15 vkus dh izkf;drk 5/p gks] rks p =
Codes :P Q R S
(A) 2 3 1 4(B) 2 1 3 4(C) 1 3 4 1(D) 1 1 3 4
Space for Rough Work / (dPps dk;Z ds fy, LFkku )
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19. Match List I with List II and select the correct answer using the code given below the lists :lwph I dks lwph II ls lqesfyr dhft, rFkk lwfp;ksa ds uhps fn, x, dksM dk ç;ksx djds lgh mÙkj pqfu;s %List - I /lwph - I List - II/ lwph- II
P. The greatest distance between x2 + y2 – 2x – 2y + 1 = 0, 1. 3x2 + y2 – 10x + 4y + 20 = 0 is 3, then is equal too`Ùkksa x2 + y2 – 2x – 2y + 1 = 0 rFkk x2 + y2 – 10x + 4y + 20 = 0
ds e/; vf/kdre nwjh 3gS] rks =Q. Numerical value of radius of the circle circumscribed about 2. 7
a square of area 200 sq. units is200 oxZ bdkbZ {ks=kQy ds ,d oxZ ds ifjo`Ùk dh f=kT;k dk la[;kRed eku gSa&
R. x2 + y2 + 2xy + 2x + 2y + = 0 does not represent a pair of real 3. 0straight line if is equal tox2 + y2 + 2xy + 2x + 2y + = 0 ,d okLrfod ljy js[kk ;qXe dks iznf'kZrugha djrk gS] ;fn =
S. If a chord of the circle x2 + y2 – 4x – 2y + k = 0 4. 10
23. In the diagram shown, a conducting rod is being translated on two perpendicular rails with a
constant velocity V1 i + V2 j . If a uniform magnetic field B is directed perpendicular into the plane
of the paper then find out the motional emf induced in the triangular loop at the instant shown.
iznf'kZr fp=k esa ,d pkyd NM+ nks yEcor~ iVfj;ksa ij fu;r osx V1 i + V2 j ls LFkkukUrfjr xfr djrh gSA;fn ,d leku pqEcdh; {kS=k B dkxt ds ry ds yEcor~ vUnj dh vksj gSA rc f=kHkqtkdkj ywi esa fn[kk;s x;s{k.k ij izsfjr xfrd fo|qr okgd cy Kkr djksA
X X X X X X X X X X X X X X XX X X X X X X X X X X X X X XX X X X X X X X X X X X X X XX X X X X X X X X X X X X X XX X X X X X X X X X X X X X XX X X X X X X X X X X X X X XX X X X X X X X X X X X X X XX X X X X X X X X X X X X X XX X X X X X X X X X X XX X X X X X X X X X X X X X XX X X X X X X X X X X X X X XX X X X X X X X X X X X X X X
(L1,0)
(0,L2)
(A) 1 1 2 2BL V BL V (B) 1 2 2 1BL V BL V (C) 1 2 2 1BL V BL V (D) 1 1 2 2BL V BL V
24. Starting from t = 0, activity of a radioactive sample is A1 at time t1 and A2 at time t2. If is average
life of sample then the number of nuclei decayed in time (t2 – t1) is
t = 0 ls izkjEHk djrs gq,, ,d jsfM;ks/kehZ izfrn'kZ dh lfØ;rk t1 le; ij A1 rFkk t2 le; ij A2 gSA ;fn blizfrn'kZ dh vkSlr vk;q gks rks (t2 – t1) le; esa fo?kfVr gksus okys ukfHkdksa ds la[;k gksxh &
(A) A1 t1 – A2 t2 (B) 1 2(A A )
2
(C) (A1 – A2) (t2 – t1) (D) (A1 – A2) .
Space for Rough Work / (dPps dk;Z ds fy, LFkku)
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27. A ray of light traveling along the positive z–axis is reflected twice by plane mirrors :
(i) for the first time, by a mirror whose normal is along – ˆ ˆ( i + k)
(ii) for the second time, by a mirror whose normal is along ˆ ˆ ˆ( i j k) ,
where the symbols have their usual meanings. The final ray is along/kukRed z–v{k ds vuqfn'k lapfjr ,d izdk'k dh fdj.k lery niZ.k }kjk nks ckj ijkofrZr djrh gSA(i) izFke ckj ml niZ.k }kjk ftldk vfHkyEc – ˆ ˆ( i + k) ds vuqfn'k gSA(ii) f}rh; ckj ml niZ.k }kjk ftldk vfHkyEc ˆ ˆ ˆ( i j k) ds vuqfn'k gSAtgk¡ ldsarksa ds vius lkekU; vFkZ gS] vfUre fdj.k fdlds vuqfn'k gksxhA(A) ˆ ˆj k (B) ˆ ˆk + i (C) ˆ ˆ ˆ2j + 2k - i (D) ˆ ˆ ˆ(j + k - 2i)
28. An infinitely long, straight wire carrying current I1 passes through the center of a circular loop ofwire carrying current I2 as shown in figure.The infinite wire is perpendicular to the plane of the loop. Which of the following describes themagnetic force on the loop due to the infinite wire.(A) Force on the loop due to infinite wire is upward, along the axis of the loop.(B) Force on the loop due to infinite wire is downward, along the axis of the loop.(C) Although net force on the loop due to infinite wire is zero, but due to magnetic interaction
between infinite wire and loop, a tensile stress is developed in the loop.(D) There is no magnetic force on the loop due to infinite wire.
This section contains 3 multiple choice questions. Each questions has matching lists. Thecodes for the lists have choices (A), (B), (C) and (D) out of which ONLY ONE is correct.bl [k.M esa 3 cgqfodYi ç'u gSaA çR;sd ç'u esa lqesyu lwph gSA lwfp;ksa ds fy, dksM ds fodYi (A), (B), (C)
vkSj (D) gSa] ftuesa ls dsoy ,d lgh gSA38. In List- an optical system is shown. List- tells about optical events. Match the proper entries from
List- to List- and select the correct answer using the code given below.
List- List-(P) (1) Parallel beam of light which incidents from
medium M-1 emerges out as converging in
medium M-2
(Q) (2) Parallel beam of light which incidents from
medium M-1 at angle i 0 emerges out as
parallel beam in medium M-2, will have lesser
diameter than the diameter of incident beam.
(Assume No TIR)
(R) (3) Parallel beam of light which incidents frommedium M-1 emerges out as diverging inmedium M-2.
(S) (4) Parallel beam of light which incidents frommedium M-1 at angle i 0 emerges out asparallel beam in medium M-2 will have largerdiameter than the diameter of incident beam.(Assume No TIR)
Codes :
P Q R S
(A) 3 4 2 1
(B) 3 2 4 1
(C) 2 4 1 3
(D) 4 3 1 2
Space for Rough Work / (dPps dk;Z ds fy, LFkku)
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39. In list- a system is shown, 2 numbers x and y are defined for each system. Value of either x or y isgiven in list-. Choose the proper value of either x or y from list- to list- and choose the correctanswer from the code given below :
List- List-(P)
4R
4
R
3R1
A solid sphere of radius R is made up by freezing two liquids one of density3 and another density , core of sphere of radius R1 is made up by liquid ofdensity 3 and rest by another liquid. Sphere is floating in a cylindricalcontainer having liquid of density 4, radius 4R and sufficient height. It is half
submerged. A ratio x is defined as : x =3
31
R
R
Now temperature is raised, neglect expansion due to increase intemperature everywhere, when whole liquid is melt its found that height of
liquid column in container raises by h. A ratio y is defined as : y =R
h
(1) 2
(Q)
2
3
2
h1
h0
h2
A uniform solid cylinder of density 2height h is floating inside 3-liquids asshown. All the three liquids are perfectly immiscible. There are movableseparators between each interface and so they stay at their place. Theseseparators doesn't apply any tangential force on cylinder, pressure variation
doesn't change due to separator. A quantity X is defined as : x = 2
1
2h
h
Now we define a number , such that if we displace the cylinder slightlydown wards and then it further goes down own its own value of is 1, if itscomes back then value of is 2. Similarly we define another number , suchthat if we displace the cylinder slightly upward and then if it further goesupward own its own value of is 3, if its comes back then value of is 4.Another number y is defined as : y =
(2) 5
Space for Rough Work / (dPps dk;Z ds fy, LFkku)
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Four identical charges are fixed on the periphery of a non conducting ring ofradius R as shown. Ring is rotated with constant angular velocity w.r.t. anaxis perpendicular to plane of the ring and passing through the centre of thering. Force acting on any of the charge particle only due to the magnetic
interaction between the charges is F =2 2
0q 1
Here & are pure number. x is defined as x =3
8
y is defined as y =
5
2
(3) 6
(S)
S
A B
C D
37°
53°
We have a spherical bubble of radius R, made up by liquid having surfacetension S. AB and CD are two parallel planes as shown in figure. Net force
of surface tension on part ABCD due to rest of the part isRS
. There is
no common factor in and . x is defined as x =3
14
y is defined as y =
5
(4) 3
Codes :P Q R S
(A) 1 4 3 2(B) 1 3 2 4(C) 3 1 4 2(D) 4 1 2 3
Space for Rough Work / (dPps dk;Z ds fy, LFkku)
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lwph–I esa ,d fudk; n'kkZ;k x;k gSA nks la[;k x rFkk y izR;sd fudk; ds fy, ifjHkkf"kr gSA x ;k y dk ekulwph-II esa fn;k x;k gSA lwph-II esa fn;s x;s x ;k y ds eku dks lwph-I esa nh xbZ la[;k ls lqesfyr dhft,A uhpsfn;s x;s dksMks dh lgk;rk ls lgh fodYi dk p;u dhft,A
40. Consider a given series LCR circuit as shown in figure. There are 10 switches. In list- switcheswhich are closed, is given and corresponding value is asked. In list- these values are given.Choose the proper value from list- to list- using the codes given below:
S1 S2 S3 S4
RXL = R XC
S5 S6 S7
S8 S9 S10
E2E1
E1 = E0 sint E2 = E0 sin(t + )List- List-
(P) It is observed that effective current in (1)2
5
the circuit in case if either S8, S6 and S7
or if S5 S6 S9 S10 or if S8, S9 and S10 are closed(Rest open) remains same. Value of is :
(Q) Switch S8, S9 & S10 are closed. Now its (2)2
observed if rest switches are opened orswitches S3, S4 are closed (remaining opened)effective value of current in the circuit is same
value of C4 X
5R
(R) Switch S8, S6, S7 are closed. Now effective (3)2
3
current if S1, S2 closed (Rest opened) is I1 and
if S3S4 closed (Rest Opened) is I2 value of
2
1
2
is
(S) Switch S5, S6, S9 and S10 are closed. Peak (4)8
5
value current if rest are opened is I3 and if
S2, S3 closed (Rest opened) is I4. Value of
2
3
4
is
Consider a given series LCR circuit as shown in figure. There are 10 switches. In list-I switcheswhich are closed, is given and corresponding value is asked. In list-II these values are given.Choose the proper value from list-II to list-I using the codes given below:Codes :
P Q R S(A) 2 4 1 3(B) 2 3 1 4(C) 3 1 2 4(D) 3 4 1 2
Space for Rough Work / (dPps dk;Z ds fy, LFkku)
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This section contains 17 multiple choice questions. Each question has four choices (A), (B), (C)and (D) out of which ONLY ONE is correct.bl [k.M esa 17 cgqfodYi ç'u gSaA çR;sd ç'u esa pkj fodYi (A), (B), (C) vkSj (D) gSa] ftuesa ls dsoy ,d lgh gSA
41. A hydrogen gas electrode is made by dipping platinum wire in a solution of HCl of pH = 10 and by
passing hydrogen gas around the platinum wire at one atm pressure. The oxidation potential of
electrode would be:
,d gkbMªkstu xSl bySDVªksM IySfVue rkj dks gkbMªksDyksfjd vEy ds pH = 10 foy;u esa Mqcksdj o blds pkjksarjQ 1 atm nkc ij gkbMªkstu xSl izokfgr djds cuk;k x;kA bysDVªkWM dk vkWDlhdj.k foHko fuEu esa ls D;kgksxk %(A) 0.59 V (B) 0.118 V (C) 1.18 V (D) 0.059 V
42. Dry air is first passed through a 0.1M KCl in water & then through 6M KCl solution. Which of the
following statements is not true ?
(A) dilute solution will show loss in weight
(B) dilute solution will show gain in weight
(C) change in weight of dilute solution is proportional to its vapour pressure.
(D) concentrated solution will show gain in weight.
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Space for Rough Work ¼dPps dk;Z ds fy, LFkku½
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50. One mole of a substance is cooled at the rate of 0.4 kJ/min as shown in the graph at constantpressure.
AB represent cooling of liquid, BC represent conversion of liquid to solid, CD represent cooling ofsolid. The molar entropy of fusion is :fu;r nkc ij] ,d inkFkZ ds ,d eksy dks fuEu n'kkZ;s x;s vkjs[k ds vuqlkj 0.4 kJ/min dh nj ls B.Mk fd;ktkrk gSA
55. Which of the following polymer is biodegradable?fuEu esa ls dkSulk cgqyd tSovi?kVuh; gS \
(A) ( CH2–C=CH–CH2 )n
Cl
(B) ( CH2–CH=CH–CH2–CH2–CH )n
CN
(C) ( O–CH–CH2–C–O–CH–CH2–C )n
CH3 CH2CH3O O
(D) ( N–(CH2)6–N–C–(CH2)4–C )n
H O OH
56. Observe the following reactions & identify reactions that correctly match with their productsfuEu vfHkfØ;k dk voyksdu dfj;s o lgh mRikn ;qDr vfHkfØ;k dh igpku dhft,A
(P)
HO
2SOCl
Cl
(Q)
F
Alcoholic KOH
KOH
,YdksgkWfyd
(R)
Br
Alcoholic KOH
KOH
,YdksgkWfyd
(A) P,Q (B) Q, R (C) P,R (D) P,Q,R
57. The compound X (C7H9N) reacts with benzensulfonyl chloride to give Y (C13H13NO2S) which is
insoluble in alkali. The compound X is :;kSfxd X (C7H9N) csUthulYQksfuy DyksjkbM ds lkFk vfHkfØ;k djds ;kSfxd Y (C13H13NO2S) nsrk gS tks{kkj esa v?kqyu'khy gSA vr% ;kSfxd X gS&
(A)
NH 3CH
(B)
NH2
CH3
(C)CH3
NH2
(D)H C3
NH2
CH
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Space for Rough Work ¼dPps dk;Z ds fy, LFkku½
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This section contains 3 multiple choice questions. Each question has matching lists. The codes forthe lists have choice (A), (B), (C) and (D) out of which ONLY ONE is correct.bl [k.M esa 3 cgqfodYi iz'u gSA izR;sd iz'u esa lqesyu lwph gSA lwfp;ksa ds fy, dksM ds fodYi (A), (B), (C)
rFkk (D) gS , ftuesa ls flQZ ,d lgh gSA
58. List-I List-II
(P) Solution obtained by mixing (1) Anionic hydrolysis
1 mole CH3COONa & 0.5 mole HCl
(Q) Solution obtained by mixing (2) Buffer solution
1 mole HCOOK & 1 mole HNO3
(R) Solution obtained by mixing (3) Amphiprotic species
1 mole Na2CO3 & 1 mole HCl
(S) Solution obtained by mixing (4) Solution of weak acid
1 mole H2C2O4 & 2 mole of KOH
Code :
(P) (Q) (R) (S)
(A) 1 2 3 4
(B) 2 4 3 1
(C) 3 1 2 4
(D) 4 3 1 2
CH
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Space for Rough Work ¼dPps dk;Z ds fy, LFkku½
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