-
INSTRUCTIONSA. General :
1. This Question Paper contains 87 questions.2. The question
paper CODE is printed on the right hand top corner on this sheet of
this booklet.3. No additional sheets will be provided for rough
work.4. Blank paper, clipboard, log tables, slide rules,
calculators, cellular phones, pagers and electronic gadgets
in any form are not allowed.5. The answer sheet, a
machine-gradable Objective Response Sheet (ORS), is provided
separately.6. Do not Tamper / mutilate the ORS or this booklet.7.
Do not break the seals of the question-paper booklet before
instructed to do so by the invigilators.8. Write your Name, Roll
No. and Sign in the space provide on the back page of this
booklet.
B. Filling the Top-half of the ORS :Use only Black ball point
pen only for filling the ORS. Do not use Gel / Ink / Felt pen as it
might smudge the
ORS.9. Write your Roll no. in the boxes given at the top left
corner of your ORS with black ball point pen. Also, darken
the corresponding bubbles with Black ball point pen only. Also
fill your roll no on the back side of your ORSin the space provided
(if the ORS is both side printed).
10. Fill your Paper Code as mentioned on the Test Paper and
darken the corresponding bubble with Black ballpoint pen.
11. If student does not fill his/her roll no. and paper code
correctly and properly, then his/her marks will not bedisplayed and
5 marks will be deducted (paper wise) from the total.
12. Since it is not possible to erase and correct pen filled
bubble, you are advised to be extremely careful whiledarken the
bubble corresponding to your answer.
13. Neither try to erase / rub / scratch the option nor make the
Cross (X) mark on the option once filled. Do notscribble, smudge,
cut, tear, or wrinkle the ORS. Do not put any stray marks or
whitener anywhere on theORS.
14. If there is any discrepancy between the written data and the
bubbled data in your ORS, the bubbled data willbe taken as
final.
C. Question paper format and Marking scheme :15. The question
paper consists of 3 parts (Physics, Chemistry & Mathematics).
Each part consists of Four
Sections.16. For each question in SectionI, you will be awarded
3 marks if you darken the bubble corresponding to the
correct choice for the answer and zero mark if no bubbled is
darkened. In case of bubbling of incorrectanswer, minus one (1)
mark will be awarded.
17. For each question in SectionII, you will be awarded 4 marks
if you darken the bubble(s) correspondingto the correct choice for
the answer and zero mark if no bubbled is darkened. There is no
negativemarking for incorrect answer(s) in this section.
18. For each question in SectionIII, you will be awarded 4 marks
if you darken the bubble(s) correspondingto the correct choice for
the answer and zero mark if no bubbled is darkened. There is no
negativemarking for incorrect answer(s) in this section.
19. For each question in SectionIV, you will be awarded 3 marks
if you darken the bubble(s) correspondingto the correct choice for
the answer and zero mark if no bubbled is darkened. There is no
negativemarking for incorrect answer(s) in this section.
DO
N
OT
BRE
AK TH
E SE
ALS
W
ITH
OUT
B
EIN
GIN
STR
UCTE
D TO
DO
SO
BY
TH
E IN
VIG
ILAT
OR
Please read the instructions carefully. You are allotted 5
minutes specifically for this purpose.
Date : 26-12-2012 Duration : 3 Hours Max. Marks : 300
CODE 0MAJOR TEST-1 (MT-1) (JEE MAIN)
TARGET : JEE (IITs) 2013 COURSE : VIJETA (JP) & VISHWAAS
(JF)
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RESONANCE JPJEEMAINSXII261212C0-1
(SPACE FOR ROUGH WORK)
PART-A
SECTION - I
Straight Objective TypeThis section contains 12 mult iple
choicequestions. Each question has choices (1), (2),(3) and (4) out
of which ONLY ONE is correct.
1. Area of each conducting plates 1, 2, 3, 4, 5 and 6 isA. The
system is kept in air. Then the capacitancebetween A and B is : (1
& 4, 2 & 5 and 3 & 6 are pairof parallel plates).
(1) dA3 0
(2) 32
dA0
(3) 23
dA0
(4) d3A0
2. The current through 15 V battery is :
(1) 1A(2) 2A(3) 3A(4) 4A
3. Two circular plates of radius R are kept at distanceh to make
a parallel plate capacitor as shown infigure. Then the capacitance
of this capacitor is.
(1) hR20
(2) hR20
(3) h
R22 20
(4) None of these
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RESONANCE JPJEEMAINSXII261212C0-2
(SPACE FOR ROUGH WORK)
4. The direction of force on electron at point O due todipole P
is.
(1)
(2)
(3)
(4)
5. The equalent resistance between A and B is.
(1) R (2) 2R
(3) 2R (4) None of these
6. A plane mirror is moving in a circle in front of astationary
point object O as shown in fig. Then pathof image of object is.
(1) circle (2) straight line(3) ellipse (4) parabolic
7. A beam of electrons striking a copper targetproduces
X-rays.Its spectrum is as shown. Keepingthe voltage same if the
copper target is replacedwith a different metal, the cut-off
wavelength andcharacteristic lines of the new spectrum will
changein comparision with old as :
(1) Cut-off wavelength will remain unchanged whilecharacteristic
lines will be different.
(2) Both cut-off wavelength and characteristic lineswill remain
unchanged.
(3) Both cut-off wavelength and characteristic lineswill be
different.
(4) Cut-off wavelength will be different whilecharacteristic
lines will remain unchanged.
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RESONANCE JPJEEMAINSXII261212C0-3
(SPACE FOR ROUGH WORK)
8. Consider the circuit containing resistors and anideal
battery. Potential difference V
a Vb is equal
to (where points 'a' and 'b' are as shown)
10
11
205 15
32V
a b
(1) 5V (2) 10 V(3) 12.5 V (4) 5 V
9. Two large oppositely charged insulated plates havea uniform
electric field between them as shown.The distance between the
plates is increased by asmall amount. Which of the following
statementsis/are correct.
Statement(i) The electric field strength decreases.
Statement(ii) The electrostatic force of attractionbetween the
plates increases.
Statement(iii) The potential difference between theplates
increases.
(1) (i) only (2) (ii) only(3) (iii) only (4) (i) and (iii)
only
10. In a series LR circuit, the voltage drop acrossinductor is 8
volt and across resistor is 6 volt. Thenvoltage applied and power
factor of circuitrespectively are:
(1) 14 V, 0.8 (2) 10 V, 0.8(3) 10 V, 0.6 (4) 14 V, 0.6
11. A current i in a circular loop of radius b producesa
magnetic field. At a fixed point far from the loop(on its axis) the
magnetic field is proportional towhich of the following
combinations of i and b ?
(1) ib(2) ib2(3) i2b(4) i/b2
12. A negative charge is given to a loop and the loop isrotated
in the plane of paper about its centre asshown. The magnetic field
produced by the ringaffects a small magnet placed above the ring
inthe same plane of paper.
(1) the magnet does not rotate(2) the magnet rotates clockwise
as seen byobserver from below
(3) the magnet rotates anti-clockwise as seen frombelow
(4) none of the above
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RESONANCE JPJEEMAINSXII261212C0-4
(SPACE FOR ROUGH WORK)
SECTION - IIStraight Objective Type
This section contains 5 multiple choice questions.Each question
has choices (1), (2), (3), (4) and(5) out of which ONLY ONE is
correct.
13. Figure shows a hemisphere of charge Q and radiusR and a
sphere of charge 2Q and radius R. Thetotal potential energy of
hemisphere is UH and thatthe sphere is US. Then.
(1) 2UH = US (2) 2UH < US(3) 2UH > US (4) UH = US(5) Data
insefficient
14. Refractive indices of 2 different media withseparating
boundary at the diagonal of rectangularglass slab are shown. Total
angle of deviation ofthe ray as shown in the figure, when it
emerges inair is :
(1) 120 (2) 90(3) 60 (4) 45(5) 30
15. A negative test charge is moving near a longstraight current
carrying wire . A force will act onthe test charge in a direction
parallel to thedirection of the current, if the motion of the
chargeis in a direction:
(1) towards wire(2) the same as that of current(3) opposite to
that of current(4) perpendicular to both the direction of
currentand the direction towards wire.
(5) None of these
16. In the circuit shown, cells are of equal emf E but
ofdifferent internal resistances r1 = 6 and r2 = 4 .Reading of the
ideal voltmeter connected acrosscell 1 is zero. Value of the
external resistance R inohm is equal to-
Cell1
E E
Cell2
r1
R
r2
V
(1) 2 (2) 2.4(3) 10 (4) 24(5) zero
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RESONANCE JPJEEMAINSXII261212C0-5
(SPACE FOR ROUGH WORK)
17. The negatively and uniformly chargednonconducting disc as
shown, is rotatedclockwise. The direction of the magnetic field
atpoint A in the plane of the disc is :
(1) into the page (2) out of the page(3) up (4) down(5) zero
SECTION - III
Multiple Correct Answers TypeThis sect ion contains 8 multiple
correctanswer(s) type questions. Each question has 4choices (1),
(2), (3) and (4), out of which ONEOR MORE is/are correct.
18. Path of charged particle, if only magnetic force actson it
can be.
(1) circle(2) helix with constant pitch(3) helix with variable
pitch(4) cycloid
19. Which of the following converges themonochromatic parallel
beam of light incidenting onit. (all are kept in air)
(1) (2)
(3) (4) None of these
20. Figure shows a LCR 'circuit connected with a dcbattery of
emf and internal resistance R. After along time (initially the
capacitor was uncharged):
(1) Current through the inductor is R8
(2) Charge stored in the capacitor is 4C
(3) Charge stored in the capacitor is 2C
(4) Potential difference across the terminals of
battery is 4
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RESONANCE JPJEEMAINSXII261212C0-6
(SPACE FOR ROUGH WORK)
21. Which of the following statements is/are correct foran x-ray
tube ?
(1) On increasing potential difference betweenfilament and
target, photon flux of x-rays increases
(2) On increasing potential difference betweenfilament and
target, frequency of x-rays increases
(3) On increasing filament current, cutoffwavelength
increases
(4) On increasing filament current intensity of x-rays
increases
22. In standard Young double slit experiment, visiblelight ( (
390 nm, 700 nm)) is used in both theslits. Distance between the
slits is 2 mm, anddistance of screen from the slits is 1 m. A thin
glassslab ( = 1.5) of thickness 6 m is placed in front ofslit S2.
Light of which wavelength (s) is missing at
point P, which is directly in front of slit S2.
(Neglectdispersion of light)
(1) 400 nm (2) 500 nm
(3) 32000
nm (4) 31600
nm
23. In the circuit shown the capacitor and inductor do
not have energy initially. Then
(1) the current flowing through the battery at t = 0is /2R
(2) The current flowing through the battery at t = 0is 2/3R
(3) The current flowing through the battery at t = is 2/5R
(4) The current flowing through the battery at t = is /2R
24. Pick up the correct statements :
(1) The changing (with time) magnetic field neednot be in
existence at the location of induced electricfield.
(2) A uniform magnetic field increasing at constantrate, induces
an electric field which is constant andnon conservative.
(3) Non zero force exerted by uniform and constantmagnetic field
on a moving charged particle doesno work but always changes
momentum of theparticle.
(4) All the above statements are wrong.
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RESONANCE JPJEEMAINSXII261212C0-7
(SPACE FOR ROUGH WORK)
25. In a co-ordinate system shown, non-uniform
magnetic induction B = k|x|B0 exist, where B0 is
a positive constant, x- is x-coordinate of point in
shown space and k is unit vector in positive z-
direction. A square coil placed in this system isrotated with
uniform angular speed about y axis.The coil may be placed in four
ways as shown. IfeI, eII eIII and eIV are the rms emfs induced in
thesefour cases, which of the following will be correct.
(1) eI = eII (2) eIII < eI(3) eIII > eIV (4) eII >
eI
SECTION - IV
Reasoning TypeThis sect ion contains 4 reasoning typequestions.
Each question has 4 choices (1), (2),(3) and (4), out of which ONLY
ONE is correct.
26. STATEMENT-1 : For the situation shown in thefigure two
monochromatic identical coherent lightsources produce interference
pattern on the screen.The intensity of minima nearest to S1 is not
exactlyzero.
STATEMENT-2 : Minimum intensity is zero wheninterfering waves
have same intensity at the locationof super position.
(1) Statement-1 is True, Statement-2 is True;Statement-2 is a
correct explanation forStatement-1.
(2) Statement-1 is True, Statement-2 is True;Statement-2 is NOT
a correct explanation forStatement-1
(3) Statement-1 is True, Statement-2 is False(4) Statement-1 is
False, Statement-2 is True
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RESONANCE JPJEEMAINSXII261212C0-8
(SPACE FOR ROUGH WORK)
27. STATEMENT-1 : In alpha decay of differentradioactive
nuclides, energies of alpha particles hasbeen compared. It is found
that as energy of alphaparticle increases the half life of the
decaydecreases.
STATEMENT-2 : More is the energy in any decayprocess, more is
the probability of decaying thenuclide which leads to faster rate
of decay.
(1) Statement-1 is True, Statement-2 is True;Statement-2 is a
correct explanation forStatement-1.
(2) Statement-1 is True, Statement-2 is True;Statement-2 is NOT
a correct explanation forStatement-1
(3) Statement-1 is True, Statement-2 is False(4) Statement-1 is
False, Statement-2 is True
28. STATEMENT-1 : Although the surface of goggleslenses are
curved, it does not have any opticalpower.
STATEMENT-2 : In case of goggles both the curvedsurfaces have
equal radii of curvature and havecentre of curvature same side.
(1) Statement-1 is True, Statement-2 is True;Statement-2 is a
correct explanation forStatement-1.
(2) Statement-1 is True, Statement-2 is True;Statement-2 is NOT
a correct explanation forStatement-1
(3) Statement-1 is True, Statement-2 is False(4) Statement-1 is
False, Statement-2 is True
29. STATEMENT-1 : Heavy nuclides tend to havemore number of
neutrons than protons.
STATEMENT-2 : In heavy nuclei, as there iscoloumbic repulsion
between protons, so excessof neutrons are preferable.
(1) Statement-1 is True, Statement-2 is True;Statement-2 is a
correct explanation forStatement-1
(2) Statement-1 is True, Statement-2 is True;Statement-2 is NOT
a correct explanation forStatement-1
(3) Statement-1 is True, Statement-2 is False(4) Statement-1 is
False, Statement-2 is True.
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RESONANCE JPJEEMAINSXII261212C0-9
(SPACE FOR ROUGH WORK)
30. A hydrogen electrode is immersed in a solutionwith pH = 0
(HCl). By how much will the potential(reduction) change if an
equivalent amount of NaOHis added to the solution.
(Take 2Hp = 1 atm) T = 298 K.
(1) increase by 0.41 V
(2) increase by 59 mV
(3) decrease by 0.41 V
(4) decrease by 59 mV
31. Equal volume of two solution having pH = 2 andpH = 10 are
mixed together at 90C. Then pH ofresulting solution is : (Take Kw
at 90C = 1012)
(1) 2 + log 2
(2) 10 log 2
(3) 7
(4) 6
32. The incorrect statement is :
(1) Vapour pressure of a liquid always increasesby increasing
temperature.
(2) Vapour pressure only depends on temperatureand not on the
nature of substance.
(3) Vapour pressure does not depend on thequantity of the liquid
taken and the surfacearea of the liquid.
(4) Vapour pressure is not a colligative property& is
independent of the concentration of theliquid.
33. When borax is dissolved in water :
(1) B(OH)3 is formed only
(2) [B(OH)4] is formed only
(3) both B(OH)3 and [B(OH)4] are formed
(4) [B3O3(OH)4] is formed only
PART- BAtomic masses : [H = 1, D = 2, Li = 7, C = 12, N = 14, O
= 16, F = 19, Na = 23, Mg = 24,Al = 27, Si = 28, P = 31, S = 32, Cl
= 35.5, K = 39, Ca = 40, Cr = 52, Mn = 55, Fe = 56, Cu = 63.5,Zn =
65, As = 75, Br = 80, Ag = 108, I = 127, Ba = 137, Hg = 200, Pb =
207]
SECTION - IStraight Objective Type
This section contains 12 questions. Each question has 4 choices
(1), (2), (3) and (4) for its answer, out of whichONLY ONE is
correct.
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RESONANCE JPJEEMAINSXII261212C0-10
(SPACE FOR ROUGH WORK)
34. Which one of the following statements is correct:
(1) Brownian movement is more pronounced forsmaller particles
than for bigger ones
(2) Sols of metal sulphides are lyophilic
(3) Schulze-Hardy law states, the bigger the sizeof the ion, the
greater is its coagulating power
(4) None of these
35. Sodium nitroprusside when added to an alkalinesolution of
sulphide ions produces purplecolouration due to the formation of
:
(1) Na[Fe(H2O)5NOS]
(2) Na4[Fe(CN)5NOS]
(3) Na3[Fe(CN)5NOS]
(4) Na4[Fe(H2O5)NOS)]
36. Which of the following are bidentate monoanionligands ?
(1) Acetylacetonato
(2) Oxalato ion
(3) Dimethylglyoximato
Select the correct answer using the codes givenbelow :
(1) 1 only
(2) 1 and 3 only
(3) 3 only
(4) 2 and 3 only
37. Ammonia gas is not prepared by :
(1) reduction of sodium nitrite or sodium nitrateby the reaction
of zinc dust and sodiumhydroxide.
(2) hydrolysis of calcium cyanamide.
(3) heating ammonium chloride with slaked lime.
(4) heating of (NH4)2Cr2O7
38. Write the basicity order of the following :
CH3 CH2 NH2 (CH3)2NH 23 NHCCH||O
(I) (II) (III) (IV)
(1) (II) > (I) > (III) > (IV)
(2) (I) > (III) > (II) > (IV)
(3) (III) > (I) > (II) > (IV)
(4) (I) > (II) > (III) > (IV)
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RESONANCE JPJEEMAINSXII261212C0-11
(SPACE FOR ROUGH WORK)
39.
,NaOH
%50
/H
product
Product is :
(1)
(2)
(3)
(4)
40. /NaOH ; the major product is
(1)
(2)
(3)
(4)
41. A neutral type amino acid migrates at anode at
(1) pH > pI
(2) pH < pI
(3) pH = pI
(4) it depends on structure of amino acid
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RESONANCE JPJEEMAINSXII261212C0-12
(SPACE FOR ROUGH WORK)
SECTION - II
Straight Objective TypeThis section contains 5 questions. Each
questionhas 5 choices (1), (2), (3), (4) and (5) for its answer,out
of which ONLY ONE is correct.
42. Among the following, the species that is bothparamagnetic
and coloured is :
(1) [MnO4]2
(2) [TiCl6]2
(3) [VO4]3
(4) CrO2Cl2(5) [MnO4]
43. Which one of the following statements isincorrect?
(1) In the aluminothermite process, aluminiumacts as reducing
agent.
(2) Lead is extracted form its chief ore by bothcarbon reduction
and self reduction.
(3) Zinc is extracted from its chief ore by carbonreduction.
(4) Extraction of gold involves the leaching of orewith cyanide
solution followed by reductionwith zinc.
(5) In Hall-Heroult process, the electrolyte usedis a molten
mixture of alumina, sodiumhydroxide and cryolite.
44. Ionisation constant of each HA (weak acid) andBOH (weak
base) are 3.0 x 107 each at 298K.The percentage degree of
hydrolysis of BA at thedilution of 10L is :
(1) 25
(2) 50
(3) 75
(4) 40
(5) Data is insufficient
45. Identify final product in the following :
.)eq2(H/HOBr
(1) C CHBr2
||O
(2) C CH Br2
||O
(3) (4) CH CHO
Br
(5)
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RESONANCE JPJEEMAINSXII261212C0-13
(SPACE FOR ROUGH WORK)
46. The following compound on hydrolysis will give :
(1) A pair of anomers
(2) A pair of enantiomeris
(3) A pair of epimers
(4) A pair of chain isomers
(5) A pair of molecules having common tautomer
SECTION - III
Multiple Correct Answer Type
This section contains 8 questions. Each questionhas 4 choices
(1), (2), (3) and (4) for its answer,out of which ONE OR MORE
is/are correct.
47. In the fluorite structure if the radius ratio is
1
23
,
how many ions does each cation touch ?
(1) 4 anions
(2) 12 cations
(3) 8 anions
(4) No cations
48. A solution containing Br ions is treated with eachof the
following. Which of these will not liberatebromine gas (in acidic
medium) ?
(1) Cl2(2) HI
(3) I2(4) SO3
49. The ozone layer in the earth's upper atmosphereis important
in shielding the earth from veryharmful ultraviolet radiation. The
ozone, O3,decomposes according to the equation 2O3(g) 3O2(g). The
mechanism of the reaction is thoughtto proceed through an initial
fast, reversible stepand then a slow second step.
Step 1: Fast, reversible O3(g) O2(g) +O(g)
Step 2: Slow O3(g) + O(g) 2O2(g)
The which of the following is correct ?
(1) Step 2 is rate determining step
(2) The rate expression for step 2 is ddt O[ ]3= k[O3][O]
(3) For Step 1 , molecularity is 1
(4) For Step 2 , molecularity is 2
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RESONANCE JPJEEMAINSXII261212C0-14
(SPACE FOR ROUGH WORK)
50. Which of the following complexes is(are)paramagnetic ?
(1) [Mn(CN6)]3
(2) [Cr(NH3)6]3+
(3) [Fe(CN)6]4
(4) [Co(CN)6]3
51. Consider the reactions shown below ;
Which of the following statement (s) is/are correct?
(1) [X] is a yellow coloured precipitate.
(2) [X] is soluble in ammonia solution.
(3) [Y] gives green coloured solution with excessof sodium
hydroxide solution.
(4) The conversion of Cr2O72 to [Y] is an redoxreaction.
52. Identify a reagent from the following list which caneasily
distinguish between 1-butyne and 2-butyne.
(1) Na metal
(2) H2, Lindlar catalyst
(3) dilute H2SO4, HgSO4
(4) ammonical Cu2Cl2 solution
53. The correct order of leaving group ability is/are :
(1) >
(2) >
(3) >
(4) >
54. RX + Mg Ether RMgX OHCH3 n-Butane
What can be R in the above reaction sequence ?
(1) n-Butyl
(2) sec-Butyl
(3) n-Propyl
(4) Isopropyl
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RESONANCE JPJEEMAINSXII261212C0-15
(SPACE FOR ROUGH WORK)
SECTION - IV
Reasoning TypeThis section contains 4 reasoning type
questions.Each question has 4 choices (1), (2), (3) and(4), out of
which ONLY ONE is correct.
55. Statement-1 : In water, orthoboric acid behavesas a weak
monobasic Lewis acid.
Statement-2 : In water, orthoboric acid acts as aproton
donor.
(1) Statement-1 is True, Statement-2 is True;Statement-2 is a
correct explanation forStatement-1.
(2) Statement-1 is True, Statement-2 is True;Statement-2 is NOT
a correct explanation forStatement-1
(3) Statement-1 is True, Statement-2 is False
(4) Statement-1 is False, Statement-2 is True
56. Statement-1 : On increasing dilution, the
specificconductance keep on increasing.
Statement-2 : On increasing dilution, degree ofionization of
weak electrolyte increases andmobility of ions also increases.
(1) Statement-1 is True, Statement-2 is True;Statement-2 is a
correct explanation forStatement-1.
(2) Statement-1 is True, Statement-2 is True;Statement-2 is NOT
a correct explanation forStatement-1.
(3) Statement-1 is True, Statement-2 is False.
(4) Statement-1 is False, Statement-2 is True.
57. Statement : 1 Enantiomers arenonsuperimposable on each
other.
Statement : 2 All isomers are nonidenticalcompounds.
(1) Statement-1 is True, Statement-2 is True;Statement-2 is a
correct explanation forStatement-1.
(2) Statement-1 is True, Statement-2 is True;Statement-2 is NOT
a correct explanation forStatement-1
(3) Statement-1 is True, Statement-2 is False
(4) Statement-1 is False, Statement-2 is True
58. Statement 1 : The reactivity order is :
for Br2/KOH reagent
Statement 2 : Presence of OMe groupincreases rate of Hofmann
bromamide reactionby increasing electron density in migratingphenyl
group.
(1) Statement-1 is True, Statement-2 is True;Statement-2 is a
correct explanation forStatement-1.
(2) Statement-1 is True, Statement-2 is True;Statement-2 is NOT
a correct explanation forStatement-1.
(3) Statement-1 is True, Statement-2 is False.
(4) Statement-1 is False, Statement-2 is True.
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RESONANCE JPJEEMAINSXII261212C0-16
(SPACE FOR ROUGH WORK)
PART- C
SECTION - IStraight Objective Type
This section contains 12 questions. Each questionhas 4 choices
(1), (2), (3) and (4) for its answer, outof which ONLY ONE is
correct.
59. The maximum value of f(x) = cosx on the set of realnumbers
satisfying x4 + 36 13x2 is
(1) cos2 (2) cos3
(3) 1 (4) cos1
60.
4
222
2
)9x6x(n)xx1881(n)xx1881(n
dx =
(1) 2 (2) 1
(3) 2n21 (4) 3n2
1
61. If the determinant 11xcos1xsin
xcosx6cos2xsinxcos1x4cosx2cos3
34
22
3
expressed in terms of powers of cosx then the valueof constant
term is
(1) 4 (2) 3
(3) 9 (4) 8
62. If nf x 4 x ,n N and rf 0 represents the rth
derivative of f(x) at x = 0, then the value of r
r 0
(f 0 )r!
is equal to
(1) 2n
(2) en
(3) 5n
(4) 4n
63. A person while dialing a telephone number, forgetsthe last
three digits of the number but remembersthat exactly two of them
are same. He dials thenumber randomly. The probability that he
dialed thecorrect number, is equal to
(1) 1135
(2) 127
(3) 154
(4) 1270
64. If A,B,C are set then A (B C) is equal to(1) A (B C)(2) A B
C(3) A (B C)
(4) none of these
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RESONANCE JPJEEMAINSXII261212C0-17
(SPACE FOR ROUGH WORK)
65. If I = 1
0
2dxxcos then
(1) I
21
,
31
(2) I < 23
(3) I < cos1
(4) I
81
cos,1sin 2
66. If the mean of x in distribution
Variate X 1 2 3 4 5
Frequency of X 4 5 k 1 2
is 2.6, then the value of k is
(1) 8(2) 10(3) 12(4) 18
67. Let a relation R in the set N of natural numbers bedefined
as (x, y) x2 4xy + 3y2 = 0 for allx, y N. The relation R is
(1) reflexive(2) symmetric(3) transitive(4) an equivalence
relation.
68. Let p,q be statements. Negation of statementp ~ q, is
(1) ~ q p
(2) ~ p q
(3) p q
(4) p q
69. x im x
2
2
3xx3x5x
is equal to
(1) e4
(2) e2
(3) e3
(4) e
70. A curve passes through the point (2a, a) and issuch that sum
of subtangent and abscissa isequal to a. Its equation is
(1) (x a) y2 = a3
(2) (x a)2 y = a3
(3) (x a) y = a2
(4) (x + a) y = a2
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RESONANCE JPJEEMAINSXII261212C0-18
(SPACE FOR ROUGH WORK)
SECTION - IIStraight Objective Type
This section contains 5 questions. Each questionhas 5 choices
(1), (2), (3), (4) and (5) for its answer,out of which ONLY ONE is
correct.
71. If x1, x2, x3, x4 are the roots of the equation x4 x3sin
2
+ x2 cos2 x cos
sin
= 0, where
(0, ). Then
4
1iixtan
1 is equal to
(1) 2
(2) 2
+
(3)
(4)
(5) +
72. If a i 2 j k , b j k , then the point of
intersection of lines abar
and babr
is
(1) i j k
(2) i 3 j
(3) i j 2k
(4) 3i j k
(5) i j 2k
73. Let f(x) = 2
cosec1 21x
. Then
(1) 1x
lim f(x) = 0
(2) 1x
lim
f(x) = 2
(3) 3x
lim f(x) = 1
(4) 3x
lim
f(x) = 1
(5) 3x
lim
f(x) = 2
74. The contents of urn and are as follows,Urn : 4 white and 5
black ballsUrn : 3 white and 6 black balls
One urn is chosen at random and a ball is drawnand its colour is
noted and replaced back to theurn. Again a ball is drawn from the
same urn,colour is noted and replaced. The process isrepeated 4
times and as a result one ball of whitecolour and 3 of black colour
are noted. Theprobability that the chosen urn was is
(1) 287125
(2) 12764
(3) 28725
(4) 19279
(5) 49250
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RESONANCE JPJEEMAINSXII261212C0-19
(SPACE FOR ROUGH WORK)
75. Area of the region bounded by the curve y = x2 andy = sec1
[sin2x] (where [ . ] denotes the greatestinteger function) is
(1) 3
(2) 32
(3) 34
(4) 36
(5) 32
SECTION - IIIMultiple Correct Answer Type
This section contains 8 questions. Each questionhas 4 choices
(1), (2), (3) and (4) for its answer, outof which ONE OR MORE
is/are correct.
76. If f(x) is real valued continuous and differentiable
function satisfying (f(x))2 = x
022 ))t('f()t(f
dt + 2013
then which of following are possible.
(1) f(x) = 2013 ex
(2) f(x) = 2013 ex(3) f(x). f(x)= (f(x))2
(4) f(x) = 2013 + 2x
77. A normal is drawn at a point P(x, y) of a curve. Itmeets the
x-axis and y-axis at points A and B
respectively such that OA2
+ OB3
= 1, O being
origin. Equation of such curve passing through point(1, 1) can
be
(1) x2 + y2 4x 6y + 8 = 0
(2) x2 + y2 2x 3y + 3 = 0
(3) 2x2 + 2y2 x y 2 = 0
(4) x2 + y2 4x + 6y 4 = 0
78. If f(x) = x2, 1 x 4, g(x) = sec1x, x 1 then
(1) Domain of gof(x) is [1, 4] {1}
(2) Domain of gof(x) is [1, 4]
(3) Range of gof(x) is [0, sec1 16]
(4) Range of fog(x) is
4
,02
79. If f(x) = 0 for x < 0 and f(x) is differentiable at x =
0,then for x > 0, f(x) may be
(1) x2
(2) x
(3) sin x
(4) x3/2
-
RESONANCE JPJEEMAINSXII261212C0-20
(SPACE FOR ROUGH WORK)
80. If G is the centroid and O is the circumcentre of
thetriangle with vertices (1, 2, 0), (0, 0, 2) and(2, 1, 1), then
equation/s of line OG is/are
(1) x = y = z
(2) y = 1, z = 1
(3) 12x
= 12y
= 12z
(4) 11x
= 11y
= 11z
81. If p, q, r are any three statements and t is a tautologythen
which of the following is/are CORRECT ?
(1) p (q r) = (p
q) (p
r)
(2) p (~ p) = t
(3) ~ (p q) = (~p) (~ q)
(4) ~ (p q) = (p ~ q) (~ p q)
82. If c is an arbitrary constant then solution ofdifferential
equation x2dy y2dx xy2(x y) dy = 0can be
(1) c2y
yxxy
n2
(2) c2y
xyyx
n2
(3) cxye)yx( 2y2
(4) cxye)yx( 2y
2
83. Two equat ions 11 qn.r
and 22 qn.r
represent two perpendicular planes, where 1n
and 2n
are two unit vectors. One of these plane
is rotated through an angle 45 about line ofintersection of two
given planes then equationof plane in new position can be
(1) 21 nn.r
= q1 q2
(2) 21 nn.r
= q1 + q2
(3) 21 nn.r
= q1 + q2
(4) 21 nn.r
= q1 q2
SECTION - IVReasoning Type
This section contains 4 reasoning type questions.Each question
has 4 choices (1), (2), (3) and (4),out of which ONLY ONE is
correct.
84. STATEMENT-1 : If A =
a000a000a
, then |adj A| = a6
and |adj (adj A) | = a9.STATEMENT-2 : Let A be a square matrix
of order
n, then |adj A| = |A|n 1 and |adj (adj A)| = 2)1n(|A| (1)
Statement-1 is True, Statement-2 is True;
Statement-2 is a correct explanation forStatement-1.
(2) Statement-1 is True, Statement-2 is True;Statement-2 is NOT
a correct explanation forStatement-1
(3) Statement-1 is True, Statement-2 is False(4) Statement-1 is
False, Statement-2 is True
-
RESONANCE JPJEEMAINSXII261212C0-21
(SPACE FOR ROUGH WORK)
85. STATEMENT-1 : Number of solutions for the
equation 2x + 3x + 5x = 1001
is equal to one.
STATEMENT-2 : Let f(x) be a strictly increasingfunction and g(x)
be a constant function. Thennumber of solutions for f(x) = g(x) is
always equalto one.(1) Statement-1 is True, Statement-2 is
True;
Statement-2 is a correct explanation forStatement-1.
(2) Statement-1 is True, Statement-2 is True;Statement-2 is NOT
a correct explanation forStatement-1
(3) Statement-1 is True, Statement-2 is False(4) Statement-1 is
False, Statement-2 is True
86. Let c be arbitrary constantSTATEMENT-1 :
xcos1xsin1
ex dx = ex cot 2x
+ c
STATEMENT-2 :
))x(f)x(f(ex dx = ex f(x) + c
(1) Statement-1 is True, Statement-2 is True;Statement-2 is a
correct explanation forStatement-1.
(2) Statement-1 is True, Statement-2 is True;Statement-2 is NOT
a correct explanation forStatement-1
(3) Statement-1 is True, Statement-2 is False(4) Statement-1 is
False, Statement-2 is True
87. STATEMENT-1 : If c,b,a
are non coplanar unit
vectors equally inclined to one another at an angle , then there
will exist three scalar p, q, r such that
ba
+ cb
= ap
+ bq
+ cr
.
STATEMENT-2 : ba
is a vector perpendicular to
plane containing a
and b
and cb
is a vector
perpendicular to plane containing b
and c
so
ba
+ cb
will be non-zero only if c,b,a
are
coplanar.
(1) Statement-1 is True, Statement-2 is True;Statement-2 is a
correct explanation forStatement-1.
(2) Statement-1 is True, Statement-2 is True;Statement-2 is NOT
a correct explanation forStatement-1
(3) Statement-1 is True, Statement-2 is False(4) Statement-1 is
False, Statement-2 is True
-
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(Space for rough work)