JEE MAINS Solved Paper 2013

7/25/2019 JEE MAINS Solved Paper 2013

1/24

Instructions

1. This test consists of 90 questions.

2. 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 marks for correct

response.

3. Candidates will be awarded marks as stated above for correct response of each question. 1/4mark will

be deducted for indicating 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.4. There is only one correct response for each question. Filling up more than one response in any

question will be treated as wrong response and marks for wrong response will be deducted according

as per instructions.

Physics1. A uniform cylinder of length Land mass

M having cross-sectional area A issuspended, with its length vertical from afixed point by a massless spring such thatit is half submerged in a liquid of density

at equilibrium position. The extension x0of the spring when it is in equilibrium is

(a) Mg

k

(b) Mg

kLA

M1

(c) Mg

kLA

M1

2

(d) Mg

kLA

M1 +

2. A metallic rod oflengthl is tied to astring of length 2land made to rotatewith angular speed

on a horizontaltable with one end of the string fixed. Ifthere is a vertical magnetic field Bin theregion, the emf induced across the ends ofthe rod is

(a)2

2

3B l(b)

3

2

3B l

(c) 4

2

2B l(d)

5

2

2B l

SolvedPaper 2013

Joint Entrance ExaminationJoint Entrance ExaminationTime :3 hrs MM :360

2l l


2/24

3. This question has Statement I andStatement II. Of the four choicesgiven after the statements, choose theone that best describes the twostatements.

Statement I A point particle of massmmoving with speed vcollides withstationary point particle of mass M. Ifthe maximum energy loss possible is

given asf mv12

2

, thenf

m

M m=

+

.

Statement II Maximum energy lossoccurs when the particles get stucktogether as a result of the collision.

(a) Statement I is true, Statement II is true;

Statement II is the correct explanation of

Statement I

(b) Statement I is true, Statement II is true;

Statement II is not the correct explanation

of Statement I

(c) Statement I is true, Statement II is false

(d) Statement I is false, Statement II is true

4. Let [ ]0 denotes the dimensionalformula of the permittivity of vacuum.

IfM=mass, L=length,T=time andA=electric current, then(a)[ ] [ ]0

1 3 2= M L T A(b) [ ] [ ]0

1 3 4 2= M L T A(c) [ ] [ ]0

2 2 1 2= M L T A(d) [ ] [ ]0

1 2 1 2= M L T A

5. A projectile is given an initial velocityof ($ $)i j+2 m/s, where $i is along theground and $jis along the vertical. Ifg= 10 m/s2 , the equation of itstrajectory is

(a) y x x= 5 2

(b) y x x= 2 5 2

(c) 4 2 5 2y x x= (d) 4 2 25 2y x x=

6. The amplitude of a damped oscillatordecreases to 0.9 times its originalmagnitude is 5 s. In another 10 s, itwill decrease to times its originalmagnitude, where equals(a) 0.7 (b) 0.81 (c) 0.729 (d) 0.6

7. Two capacitorsC1 andC2are charged to 120 Vand 200 V respectively. It is found that byconnecting them together the potential oneach one can be made zero. Then,

(a) 5 31 2C C= (b) 3 51 2C C=(c)3 5 01 2C C+ = (d) 9 41 2C C=

8. A sonometer wire of length 1.5 m is made ofsteel. The tension in it produces an elasticstrain of 1%. What is the fundamentalfrequency of steel, if density and elasticity ofsteel are 77 103. kg/m3 and 2.2 1011 2N m/

respectively?(a) 188.5 Hz (b) 178.2 Hz

(c) 200.5 Hz (d) 770 Hz

9. A circular loop of radius 0.3 cm lies parallel toa much bigger circular loop of radius 20 cm.The centre of the smaller loop is on the axis ofthe bigger loop. The distance between theircentres is 15 cm. If a current of 2.0 A flowsthrough the smaller loop, then the flux linkedwith bigger loop is

(a) 9.1 10 11 Wb (b) 6 10 11 Wb(c) 3.3 10 11 Wb (d) 6.6 10 9 Wb

10. Diameter of a plano-convex lens is 6 cm andthickness at the centre is 3 mm. If speed oflight in material of lens is 2 108 m/s, thefocal length of the lens is

(a) 15 cm (b) 20 cm (c) 30 cm (d) 10 cm

11. What is the minimum energy required tolaunch a satellite of mass mfrom the surfaceof a planet of mass M and radius R in acircular orbit at an altitude of 2 R?

(a) 5

6

GmM

R (b)

2

3

GmM

R

(c)

GmM

R2 (d)

GmM

R3

12. A diode detector is used to detect anamplitude modulated wave of 60%modulation by using a condenser of capacity250 pico farad in parallel with a loadresistance 100 k. Find the maximummodulated frequency which could bedetected by it.

(a) 10.62 MHz (b) 10.62 kHz

(c) 5.31 MHz (d) 5.31 kHz

JEE Main Solved Paper 2013 27


3/24

13. A beam of unpolarised light of intensityI0is passed through a polaroid Aand thenthrough another polaroid B which isoriented so that its principal plane makesan angle of 45 relative to that of A. Theintensity of the emergent light is

(a) I0 (b) I0 2/

(c) I0 4/ (d) I0 8/

14. The supply voltage to room is 120 V. Theresistance of the lead wires is 6. A 60 Wbulb is already switched on. What is the

decrease of voltage across the bulb, whena 240 W heater is switched on in parallelto the bulb?

(a) Zero (b) 2.9 V

(c) 13.3 V (d) 10.04 V

15. The shown p-V diagram represents thethermodynamic cycle of an engine,operating with an ideal monoatomic gas.The amount of heat, extracted from thesource in a single cycle is

(a) p V0 0 (b) 13

2 0 0

p V

(c) 11

2 0 0

p V

(d) 4 0 0p V

16. A hoop of radius r and mass mrotatingwith an angular velocity 0is placed on arough horizontal surface. The initial

velocity of the centre of the hoop is zero.What will be the velocity of the centre ofthe hoop when it ceases to slip?

(a) r0

4 (b)

r03

(c) r0

2 (d) r0

17. An ideal gas enclosed in a verticalcylindrical container supports a freelymoving piston of massM. The piston and

the cylinder have equal cross-sectionalareaA. When the piston is in equilibrium,the volumeofthegas is V0and itspressureisp0. The piston is slightly displaced fromthe equilibrium position and released.Assuming that the system is completelyisolated from its surrounding, the pistonexecutes a simple harmonic motion withfrequency

(a) 1

20

0A p

V M (b)

12

0 02

V Mp

A

(c) 12

2

00

A pMV (d)

12 00

MV

A p

18. If a piece of metal is heated totemperature and then allowed to cool ina room which is at temperature 0. Thegraph between the temperature Tof themetal and time twill be closed to

19. This question has Statement I andStatement II. Of the four choices givenafter the statements, choose the one thatbest describes the two statements.

Statement I Higher the range, greater isthe resistance of ammeter.

Statement II To increase the range ofammeter, additional shunt needs to be

used across it.(a) Statement I is true, Statement II is true;

Statement II is the correct explanation of

Statement I

(b) Statement I is true, Statement II is true;

Statement II is not the correct explanation of

Statement I

(c) Statement I is true, Statement II is false

(d) Statement I is false, Statement II is true

28 JEE Main Solved Papers

2p0

p0

V0 2V0

B

A

C

D

O

T

t

(a)

O

T

t

(b)0

O

T

t

(d)0

O

T

t

(c)0


4/24

20. Inan L-C-R circuitas shown, bothswitches are openinitially. Now,switchS1 andS2,kept open. (q ischarge on thecapacitor and = RC is capacitance timeconstant). Which of the followingstatement is correct?

(a) Work done by the battery is half of the energy

dissipated in the resistor

(b) At t= , q CV= /2(c) At t=2, q CV e= ( )1 2

(d) At t= 2

, q CV e= ( )1 1

21. Two coherent pointsourcesS1 andS2areseparated by a smalldistancedas shown.The fringes obtainedon the screen will be

(a) points (b) straight lines

(c) semi-circle (d) concentric circles

22. The magnetic field in a travellingelectromagnetic wave has a peak value of20 nT. The peak value of electric fieldstrength is

(a) 3 V / m (b)6 V / m

(c) 9 V / m (d) 12 V / m

23. The anode voltage of a photocells keptfixed. The wavelength of the lightfalling on the cathode is graduallychanged. The plate current I of photocellvaries as follows

24. TheI-Vcharacteristic of an LED is

25. Assume that a drop of liquid evaporatesby decrease in its surface energy, so thatits temperature remains unchanged.What should be the minimum radius ofthe drop for this to be possible? Thesurface tension isT, denstiy of liquid isandLis its latent heat of vapourisation

(a)L T/ (b) T L/(c) T L/ (d)2 T L/

26. In a hydrogen like atom, electron makestransition from an energy level withquantum number n to another with

quantum number ( )n 1. If n >> 1, thefrequency of radiation emitted isproportional to

(a) 1n

(b) 1

2n

(c) 1

3 2n / (d)

13n

27. The graph between angle of deviation ( )and angle of incidence (i) for a triangularprism is represented by

JEE Main Solved Paper 2013 29

R

Y

G

B

O

I

V

R Y G B

O V

BGYR

O

I

V

OV

I

(a) (b)

(d)(c) Red

YellowGreenBlue

-

-

-

-

D

S1 S2

Screen

d

I

I

I

I

(a) (b)

(d)(c)

i iO O

(a) (b)

i iO O

(d)(c)

S1

S2

V

R

C

L


5/24

28. Two charges, each equal to q, are kept at

x a= andx a= on theX-axis. A particleof massm and charge q

q0 2

= is placed at

the origin. If charge q0 is given a smalldisplacement( )y a IV > I > III (b) I > II > III > IV

(c) III > I > II > IV (d) IV > III > I > II

Cl(I)

;

OH

OCH3(IV)

OH

CH3(II)

;

OH

NO2(III)

;

OH


6/24

38. For gaseous state, if most probable speed

is denoted by C*, average speed by Cand

mean square speed by C, then for a large

number of molecules, the ratios of these

speeds are

(a) C C C* : : =1.225 : 1.128 : 1(b) C C C* : : = 1.128 : 1.225 : 1(c) C C C* : : =1 : 1.128 : 1.225(d) C C C* : : =1 : 1.225 : 1.128

39. The rate of a reaction double when itstemperature changes from300 K to310 K.Activation energy of such a reaction willbe( 8.314 JK mol1 1R = and log )2 0 301= .(a) 53.6 kJ mol1 (b) 48.6 kJ mol1

(c) 58.5 kJ mol1 (d) 60.5 kJ mol1

40. A compound with molecular mass 180 isacylated with CH3COCl to get acompound with molecular mass 390. Thenumber of amino groups present permolecule of the former compound is(a) 2 (b) 5 (c) 4 (d) 6

41. Which of the following arrangementsdoes not represent the correct order of theproperty stated against it?(a) V Cr Mn Fe2+ 2+ 2+ 2+< < < : paramagnetic

behaviour

(b) Ni Co Fe Mn2+ 2+ 2+ 2+< < < : ionic size(c)Co Fe < Cr < Sc3+ 3+ 3+ 3+< : stability in

aqueous solution

(d) Sc < Ti < Cr < Mn : number of oxidation

states

42. The order of stability of the followingcarbocations

(a) III > II > I (b) II > III > I

(c) I > II > III (d) III > I > II

43. Consider the following reaction,

x y z xMnO C O H Mn4 2 42 + 2+ + +

+ +2yCO z2H O2 2

The values ofx y, andzin the reaction arerespectively

(a) 5, 2 and 16 (b) 2, 5 and 8

(c) 2, 5 and 16 (d) 5, 2 and 8

44. Which of the following is the wrongstatement?

(a) ONCl and ONO are not isoelectronic

(b) O3molecule is bent

(c) Ozone is violet-black in solid state

(d) Ozone is diamagnetic gas

45. A gaseous hydrocarbon gives uponcombustion 0.72 g of water and 3.08 g ofCO2 . The empirical formula of thehydrocarbon is

(a) C H2 4 (b) C H3 4(c) C H6 5 (d) C H7 8

46. In which of the following pairs ofmolecules/ions, both the species are notlikely to exist?

(a) H , He2+

22 (b) H , He2 2

2

(c) H , He22

2+ (d) H , He2 2

2+

47. Which of the following exists as covalent

crystals in the solid state?(a) Iodine (b) Silicon

(c) Sulphur (d) Phosphorus

48. Synthesis of each molecule of glucose inphotosynthesis involves

(a) 18 molecules of ATP

(b) 10 molecules of ATP

(c) 8 molecules of ATP

(d) 6 molecules of ATP

49. The coagulating power of electrolyteshaving ions Na+ , Al3+ and Ba2+ forarsenic sulphide sol increases in theorder

(a) Al Ba Na3+ 2 +

JEE MAINS Solved Paper 2013

Documents

Transcript of JEE MAINS Solved Paper 2013