jee mains mock test 1-29-03 14

8/12/2019 JEE Mains Mock Test 1-29-03 14

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FIITJEELtd. North West Delhi Centre, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000

FIITJEEJEE MAINS MOCK TEST-1

Target IIT - JEE 2014QP CODE: 120634.0

Time : 3 hours Maximum Marks : 360

Please read the instructions carefully. You are allotted 5 minutes specifically for this purpos e.

You are not allowed to leave the examination hall before end of the test.

Instructions

1. Immediately fill in the particulars on this page of the Test Booklet with Blue / Black Ball Point Pen. Use ofpencil is strictly prohibited.

2. The Answer Sheet is kept inside this Test Booklet. When you are directed to open the Test Booklet, takeout the Answer Sheet and fill in the particulars carefully.

3. The test is of 3 hoursduration.

4. The Test Booklet consists of 90 questions. The maximum marks are 360.

5. There are threeparts in the question paper A, B, C consisting of Physics, Chemistry and Mathematicshaving 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for correctresponse.

6. Candidates will be awarded marks as stated above in instruction No.5 for correct response of eachquestion. (one fourth) marks will be deducted for indicating incorrect response of each question. Nodeduction from the total score will be made if no response is indicated for an item in the answer sheet.

7. There is only one correct response for each question. Filling up more than one response in any questionwill be treated as wrong response and marks for wrong response will be deducted accordingly as perinstruction 6 above.

8. Use Blue / Black Ball Point Pen only for writing particulars / marking responses on Side-1and Side-2ofthe Answer Sheet. Use of pencil is strictly prohibited.

9. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobilephone, any electronic device, etc. except the Admit Card inside the examination hall / room.

10. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in theRoom / Hall. However, the candidates are allowed to take away this Test Booklet wi th them.

11. Do not fold or make any stray marks on the Answer Sheet.

Name of the Candidate (in Capital Letters) :_____________________________________

Enrolment Number :_________________________________________________________

Batch :________________________ Date of Examination : ________________________


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IIT2014,JEE MAINS MOCK TEST-1(PCM)_2

SECTION - 1PHYSICS

1. A rectangular loop has a sliding connector PQ of length and resistance Rand it is moving

with a speed v as shown. The set-up is placed in a uniform magnetic field going into theplane of the paper. The three currents I1, I2and I are

(A) 1 2B v 2B v

l I , IR R= = =

(B) 1 2B v 2B v

l I , I3R 3R

= = =

(C) 1 2B v

l I IR

= = =

(D) 1 2B v B v

l I , I6R 3R

= = =

2. Let C be the capacitance of a capacitor discharging through a resistor R. Suppose t1is thetime taken for the energy stored in the capacitor to reduce to half its initial value and t2is thetime taken for the charge to reduce to one-fourth its initial value. Then the ratio t1/t2will be

(A) 1 (B) 12

(C)1

4 (D) 2

3. A ball is made of a material of density where oil< < waterwith oiland waterrepresentingthe densities of oil and water, respectively. The oil and water are immiscible. If the above ballis in equilibrium in a mixture of this oil and water, which of the following pictures representsits equilibrium position?(A) (B)

(C) (D)

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4. A particle is moving with velocity v K(yi xj),= +

where K is a constant. The general equal for

its path is(A) y = x2+ constant (B) y2= x + constant(C) xy = constant (D) y2= x2+ constant

5. Two long parallel wires are at a distance 2d apart. They carry steady equal current flowing

out of the plane of the paper as shown. The variation of the magnetic field along the line XX is given by(A) (B)

(C) (D)

6. A thin semi-circular ring of radius r has a positive charge q

distributed uniformly over it. The net field E

at the centre O is

(A)2 2

o

qj

4 r (B)

2 2o

qj

4 r

(C)2 2

o

qj

2 r

(D)

2 2o

qj

2 r

7. The combination of gates shown below yields(A) OR gate (B) NOT gate(C) XOR gate (D) NAND gate

A

B

X

8. A diatomic ideal gas is used in a car engine as the working substance. If during the adiabatic

expansion part of the cycle, volume of the gas increases from V to 32V the efficiency ofthe engine is(A) 0.5 (B) 0.75(C) 0.99 (D) 0.25

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9. Let there be a spherically symmetric charge distribution with charge density varying as

o

5 r(r)

4 R

=

upto r = R and (r) = 0 for r > R, where r is the distance from the origin.

The electric field at a distance r(r < R) from the origin is given by

(A) o

o

4 r 5 r

3 3 R

(B) o

o

r 5 r

4 3 R

(C) o

o

4 r 5 r3 4 R

(D) o

o

r 5 r3 4 R

10. The potential energy function for the force between two atoms in a diatomic molecule

is approximately given by12 6

a bU(x) ,

x x= where a and b are constants and x is the

distance between the atoms. If the dissociation energy of the molecule is

at equilibriumD [U(x ) U ],= = D is

(A)2b

2a (B)

2b

12a

(C)

2b

4a (D)

2b

6a

11. Two identical charged spheres are suspended by strings of equal lengths. The strings makean angle of 30 with each other. When suspended in a liquid of density 0.8 g cm3, the angleremains the same. If density of the material of the sphere is 16 g cm3, the dielectric constantof the liquid is(A) 4 (B) 3(C) 2 (D) 1

12. Two conductors have the same resistance at 0C but their temperature coefficients of

resistance are 1and 2. The respective temperature coefficients of their series and parallelcombinations are nearly

(A) 1 2 1 2,2

+ + (B) 1 21 2, 2

+ +

(C) 1 21 21 2

,

+ +

(D) 1 2 1 2,2 2

+ +

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13. A point P moves in counter-clockwise direction on a circularpath as shown in the figure. The movement of P is suchthat it sweeps out a lengths s = t3+ 5, where s is in metresan t is in seconds. The radius of the path is 20 m. Theacceleration of P when t = 2s is nearly(A) 13 m/s2 (B) 12 m/s2(C) 7.2 m/s2 (D) 14 m/s2

14. For a particle in uniform circular motion the acceleration a

at a point P(R, ) on the circle ofradius R is (here is measured from the x-axis)

(A)2 2v v cos i sin j

R R + (B)

2 2v v sin i cos jR R

+

(C)2 2v v cos i sin j

R R (D)

2 2v v i jR R

+

15. The above is a plot of binding energy per nucleon Eb,against the nuclear mass M; A, B,, C, D,, E, F correspondto different nuclei. Consider four reactions:

(i) A + B C + (ii) C A + B + (iii) D + E + and (iv) F D + E + where is the energy released? In which reactions is positive?(A) (i) and (iv) (B) (i) and (iii)(C) (ii) and (iv) (D) (ii) and (iii)

16. A p-n junction (D) shown in the figure can act as arectifier. An alternating current source (V) isconnected in the circuit.

(A) (B)

(C) (D)

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17. If x, v and a denote the displacement, the velocity and the acceleration of a particleexecuting simple harmonic motion of time period T, then, which of the following does notchange with time?

(A) a2T2+ 42v2 (B)aT

x

(C) aT + 2v (D)aT

v

18. In an optics experiment, with the position of the object fixed, a student varies the position ofa convex lens and for each position, the screen is adjusted to get a clear image of the object.A graph between the object distance u and the image distance v, from the lens, is plottedusing the same scale for the two axes. A straight line passing through the origin andmaking an angle of 45 with the x-axis meets the experimental curve at P. The coordinatesof P will be

(A) (2f, 2f) (B)f f

,2 2

(C) (f, f) (D) (4f, 4f)

19. A thin uniform rod of length and mass m is swinging freely about a horizontal axis passing

through its end. Its maximum angular speed is . Its centre of mass rises to a maximumheight of

(A)2 21

3 g

(B)

1

6 g

(C)2 21

2 g

(D)

2 21

6 g

20. Let P(r) =4

Qr

Rbe the charge density distribution for a solid sphere of radius R and total

charge Q for a point p inside the sphere at distance r1 from the centre of the sphere, themagnitude of electric field is

(A) 0 (B)2

o 1

Q

4 r

(C)2

1

4o

Qr

4 R (D)

21

4o

Qr

3 R

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21. One kg of a diatomic gas is at a pressure of 8 104N/m2. The density of the gas is 4 kg/m3.What is the energy of the gas due to its thermal motion?(A) 3 104J (B) 5 104J(C) 6 104J (D) 7 104J

22. A motor cycle starts from rest and accelerates along a straight path at 2 m/s2. At the startingpoint of the motor cycle there is a stationary electric sire. How far has the motor cycle gone

when the driver hears the frequency of the siren at 94% of its value when the motor cyclewas at rest? (speed of sound = 330 ms1).(A) 49 m (B) 98 m(C) 147 m (D) 196 m

23. Consider a rubber ball freely falling from a height h = 4.9 m onto a horizontal elastic plate.Assume that the duration of collision is negligible and the collision with the plate is totallyelastic. Then the velocity as a function of time the height as function of time will be

(A) (B)

(C) (D)

24. A charge Q is placed at each of the opposite corners of a square. A charge q is placed ateach of the other two corners. If the net electrical force on Q is zero, then the Q/q equals

(A) 2 2 (B) 1

(C) 1 (D)1

2

25. A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation

of temperature

along the length x of the bar from its hot end is best described by which of the followingfigure.

(A) (B)

(C) (D)

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26. A transparent solid cylindrical rod has a refractive index of

2.

3It is surrounded by air. A light ray is incident at the mid

point of one end of the rod as shown in the figure. The

incident angle for which the light ray grazes along the wallof the rod is

(A) 1 1sin2

(B) 1 3sin2

(C) 12

sin3

(D) 11

sin3

27. Three sound waves of equal amplitudes have frequencies (v 1), v, (v + 1). They superposeto give beats. The number of beats produced per second will be(A) 4 (B) 3(C) 2 (D) 1

28. Two wires are made of the same material and have the same volume. However wire 1 hascrossectional area A and wire-2 has cross-sectional area 3A. If the length of wire

1 increases by x on applying force F, how much force is needed to stretch wire 2 by thesame amount?(A) F (B) 4F(C) 6F (D) 9F

29. In an experiment the angles are required to be measured using an instrument. 29 divisionsof the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallestdivision of the main scale is half-a-degree(=0.5o), then the least count of the instrument is(A) one minute (B) half minute(C) one degree (D) half degree

30. An inductor of inductance L = 400 mH and resistors of

resistances R1= 2and R2= 2are connected to abattery of emf 12V as shown in the figure. The internalresistance of the battery is negligible. The switch S isclosed at t = 0. The potential drop across L as afunction of time is

(A) 6e5t V (B) 3t12

e Vt

(C) 6(1 e1/02) V (D) 12e5tV

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SECTION - 2CHEMISTRY

1. Knowing that the Chemistry of lanthanoids (Ln) is dominated by its +3 oxidation state, whichof the following statement is incorrect ?(A) Because of the large size of the Ln (III) ions the bonding in its compounds is

predominantly ionic in character.(B) The ionic sizes of Ln (III) decrease in general with increasing atomic number.(C) Ln (III) compounds are generally colourless.(D) Ln (III) hydroxides are mainly basic in character.

2. A liquid was mixed with ethanol and a drop of concentrated H2SO4was added. A compoundwith a fruity smell was formed. The liquid was :(A) CH3OH (B) HCHO(C) CH3COCH3 (D) CH3COOH

3. In which of the following arrangements, the sequence is not strictly according to the propertywritten against it?(A) CO2< SiO2< SnO2< PbO2: increasing oxidising power

(B) HF < HCl < HBr < HI: increasing acid strength(C) NH3< PH3< AsH3< SbH3: increasing basic strength(D) B < C < O < N: increasing first ionization enthalpy.

4. Which of the following statements is incorrect regarding physiosorption ?(A) It occurs because of van der Waals forces.(B) More easily liquefiable gases are adsorbed readily.(C) Under high pressure it results into multi molecular layer on adsorbent surface.(D) Enthalpy of adsorption (Hadsorption) is low and positive.

5. Given: 3 2o o

Fe /Fe Fe /FeE 0.036 V ,E 0.439 V+ += = . The value of standard electrode potential for

the change, ( ) ( )3 2Fe aq e Fe aq+ ++ will be :

(A) -0.072 V (B) 0.385 V(C) 0.770 V (D) -0.270 V

6. Solid Ba(NO3)2 is gradually dissolved in a 1.0 104 M Na2CO3 solution. At what

concentration of Ba2+will a precipitate begin to form? (Kspfor BaCO3= 5.1 109).

(A) 4.1 105M (B) 5.1 105M(C) 8.1 108M (D) 8.1 107M

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7. Which one of the following reactions of Xenon compounds is not feasible ?

(A)3 6 2

XeO 6HF XeF 3H O+ +

(B)4 2 3 2

3 XeF 6H O 2 Xe XeO 12HF 1.5O+ + + +

(C)2 2 2

2 XeF 2H O 2 Xe 4HF O+ + +

(D) [ ]6 7XeF RbF Rb XeF+

8. The set representing the correct order of ionic radius is :(A) Li+> Be2+>Na+> Mg2+ (B) Na+> Li+>Mg2+> Be2+(C) Li+> Na+> Mg2+> Be2+ (D) Mg2+> Be2+> Li+> Na+

9. The bond dissociation energy of B F in BF3is 646 kJ mol1 whereas that of C-F in CF4is

515 kJ mol1. The correct reason for higher B-F bond dissociation energy as compared tothat of C- F is :(A) smaller size of B-atom as compared to that of C- atom(B) stronger bond between B and F in BF3as compared to that between C and F in CF4(C) significant p- p interaction between B and F in BF3whereas there is no possibility of

such interaction between C and F in CF4.

(D) lower degree of p- pinteraction between B and F in BF3than that between C and F in

CF4.

10. Which of the following pairs represents linkage isomers ?(A) [Cu(NH3)4][PtCl4] and [Pt(NH3)4] [CuCl4](B) [Pd(PPh3)2(NCS)2] and [Pd(PPh3)2(SCN)2](C) [Co(NH3)5NO3]SO4and [Co(NH3)5SO4]NO3(D) [PtCl2(NH3)4]Br2and [PtBr2(NH3)4]Cl2

11. If 104dm3of water is introduced into a 1.0 dm3 flask at 300 K, how many moles of waterare in the vapour phase when equilibrium is established ?(Given : Vapour pressure of H2O at 300 K is 3170 Pa; R = 8.314 J K

1mol1)

(A) 5.56 103mol (B) 1.53 102mol(C) 4.46 102mol (D) 1.27 103mol

12. From amongst the following alcohols the one that would react fastest with conc. HCl andanhydrous ZnCl2, is(A) 2Butanol (B) 2Methylpropan2ol(C) 2Methylpropanol (D) 1Butanol

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13. In the chemical reactions,NH2

2 4NaNO HBF

HCl, 278 KA B

the compounds A and B respectively are

(A) nitrobenzene and fluorobenzene(B) phenol and benzene(C) benzene diazonium chloride and fluorobenzene(D) nitrobenzene and chlorobenzene

14. Consider the following bromides:

Me Br Me

Br

MeMe

Br

(A) (B) (C)The correct order of SN1 reactivity is(A) B > C > A (B) B > A > C(C) C > B > A (D) A > B > C

15. The main product of the following reaction is

( ) ( ) 2 46 5 2 3 2Conc.H SO

C H CH CH OH CH CH ?

(A) C

H

CH(CH3)2

C

H

H5C6

(B) C

CH3

CH3

C

H

C6H5CH2

(C) C

CH(CH3)2

H

C

H

C6H5

(D) CH2C

H3C

C6H5CH2CH2

16. The presence or absence of hydroxyl group on which carbon atom of sugar differentiatesRNA and DNA?(A) 2nd (B) 3rd(C) 4th (D) 1st

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17. Trichloroacetaldehyde was subjected to Cannizzaros reaction by using NaOH. The mixtureof the products contains sodium trichloroacetate and another compound. The othercompound is :(A) trichloromethanol (B) 2, 2, 2-trichloropropanol(C) chloroform (D) 2, 2, 2-trichloroethanol

18. a and b are van der Waals constants for gases. Chlorine is more easily liquefied than

ethane because(A) a and b for Cl2< a and b for C2H6(B) a for Cl2< a for C2H6 but b for Cl2> b for C2H6(C) a for Cl2 > a for C2H6 but b for Cl2< b for C2H6(D) a and b for Cl2> a and b for C2H6

19. In context of the lanthanoids, which of the following statement is not correct ?(A) All the members exhibit +3 oxidation state(B) Because of similar properties the separation of lanthanoids is not easy.(C) Availability of 4f electrons results in the formation of compounds in +4 state for all the

members of the series.(D) There is a gradual decrease in the radii of the members with increasing atomic number

in the series.

20. Which of the following statements regarding sulphur is incorrect ?(A) The vapour at 200oC consists mostly of S8rings(B) At 600oC the gas mainly consists of S2molecules(C) The oxidation state of sulphur is never less than +4 in its compounds(D) S2molecule is paramagnetic.

21. Phenol is heated with a solution of mixture of KBr and KBrO3. The major product obtained inthe above reaction is(A) 3-Bromophenol (B) 4-Bromophenol(C) 2, 4, 6- Tribromophenol (D) 2-Bromophenol

22. The molecule having smallest bond angle is :

(A) NCl3 (B) AsCl3(C) SbCl3 (D) PCl3

23. The incorrect expression among the following is:

(A)system

total

GT

S

=

(B) In isothermal process Wreversible =

2

1

VnRTln

V

(C)0 0H T S

lnKRT

= (D)

0G /RTK e=

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24. The density of a solution prepared by dissolving 120 g of urea (mol. Mass = 60 u ) in 1000gof water is 1.15 g/mL. The molarity of this solution is:(A) 0.50 M (B) 1.78 M(C) 1.02 M (D) 2.05 M

25. How many chiral compounds are possible on monochlorination of 2methyl butane ?(A) 8 (B) 2

(C) 4 (D) 6

26. For a first order reaction, (A) products, the concentration of A changes from 0.1 M to0.025 M in 40 minutes. The rate of reaction when the concentration of A is 0.01 M is :

(A) 1.73 105M/ min (B) 3.47 104M/min(C) 3.47 105M/min (D) 1.73 104M/min

27. Iron exhibits + 2 and +3 oxidation states. Which of the following statements about iron isincorrect ?(A) Ferrous oxide is more basic in nature than the ferric oxide.(B) Ferrous compounds are relatively more ionic than the corresponding ferric compounds(C) Ferrous compounds are less volatile than the corresponding ferric compounds.(D) Ferrous compounds are more easily hydrolysed than the corresponding ferric

compounds.

28. Kffor water is 1.86 K kg mol1. If your automobile radiator holds 1.0 kg of water, how many

grams of ethylene glycol (C2H6O2) must you add to get the freezing point of the solutionlowered to 2.8C ?(A) 72g (B) 93g(C) 39g (D) 27g

29. Iodoform can be prepared from all except :(A) Ethyl methyl ketone (B) Isopropyl alcohol(C) 3Methyl 2 butanone (D) Isobutyl alcohol

30. In the given transformation, which of the following is the most appropriate reagent?CH = CHCOCH3

OH

CH = CHCH2CH3

OHReagent

(A)2 2

NH NH ,OH (B) Zn-Hg/HCl

(C) Na.Liq.NH3 (D) NaBH4

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SECTION - 3MATHEMATICS

1. The real number k for which the equation, 32x 3x k 0+ + = has two distinct real roots in [0, 1](A) lies between 1 and 0 (B) does not exist(C) lies between 1 and 2 (D) lies between 2 and 3

2. If 2 4A sin x cos x= + , then for all real x

(A)13

A 116

(B) 1 A 2

(C)3 13

A4 16

(D)3

A 14

3. If

1 3

P 1 3 3

2 4 4

=

is the adjoint of a 3 3 matrix A and A 4,= then is equal to:

(A) 5 (B) 0(C) 4 (D) 11

4.( ){ }

x 2

1 cos 2 x 2lim

x 2

(A) equals 2 (B) equals 2

(C) equals1

2 (D) does not exist

5. At present a firm is manufacturing 2000 items. It is estimated that the rate of change of

production P w.r.t. additional number of workers x is given bydP

100 12 xdx

= . If the firm

employs 25 more workers, then the new level of production of items is:(A) 3500 (B) 4500(C) 2500 (D) 3000

6. ABCD is a trapezium such that AB and CD are parallel and BC CD . If ADB , = BC = pand CD = q, then AB is equal to

(A)2 2

2 2

p q

p cos q sin

+ +

(B)( )

( )

2 2

2

p q sin

pcos qsin

+

+

(C)( )2 2p q sin

pcos qsin

+

+ (D)

2 2p q cos

pcos qsin

+ +

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7. The value of( )1

2

0

8log 1 xdx

1 x

+

+ is

(A) log28

(B) log2

2

(C) log2 (D) log2

8. A ray of light along x 3y 3+ = gets reflected upon reaching x-axis, the equation of thereflected ray is:

(A) y 3x 3= (B) 3y x 1=

(C) y x 3= + (D) 3y x 3=

9. The domain of the function ( )1

f xx x

=

is

(A) ( )0, (B) ( ), 0

(C) ( ) { }, 0 (D) ( ),

10. If z is a complex number of unit modulus and argument , then 1 zarg1 z

+ +

equals:

(A) (B)

(C) (D)2

11. If ( ) ( )f x dx x ,= then ( )5 3x f x dx is equal to:

(A) ( ) ( )3 3 2 31

x x x x dx C3

+ (B) ( ) ( )3 3 3 31

x x x x dx C3

+

(C) ( ) ( )3 3 2 31

x x x x dx C3

+ (D) ( ) ( )3 3 3 31 x x 3 x x dx C

3 +

12. Equation of the ellipse whose axes are the axes of coordinates and which passes through

the point (3, 1) and has eccentricity2

5is

(A) 2 25x 3y 48 0+ = (B) 2 23x 5y 15 0+ =

(C) 2 25x 3y 32 0+ = (D) 2 23x 5y 32 0+ =

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13. If the linesx 2 y 3 z 4

1 1 k

= =

and

x 1 y 4 z 5

k 2 1

= = are coplanar, then k can have:

(A) exactly two values (B) exactly three values(C) any value (D) exactly one value

14. The number of values of k for which the linear equations 4x ky 2z 0; kx 4y z 0;+ + = + + = 2x 2y z 0+ + = posses a non zero solution is

(A) 2 (B) 1(C) zero (D) 3

15. Consider:

Statement I : ( ) ( )p q p q is a fallacy.

Statement II : ( ) ( )p q q p is a tautology.(A) Statement I is true; Statement II is false.(B) Statement I is false; Statement II is true.(C) Statement I is true; Statement II is true; Statement II is a correct explanation for

Statement I(D) Statement I is true; Statement II is true; Statement II is not a correct explanation for

Statement I.

16. If the equations 2x 2x 3 0+ + = and 2ax bx c 0, a,b,c R,+ + = have a common root, then a :b : c is:(A) 1 : 3 : 2 (B) 3 : 1 : 2(C) 1 : 2 : 3 (D) 3 : 2 : 1

17. If the mean deviation about the median of the numbers ,2 ,.......50 is 50, then equals

(A) 3 (B) 4(C) 5 (D) 2

18. The term independent of x in expansion of

10

2/3 1/ 3 1/2

x 1 x 1

x x 1 x x

+ +

is

(A) 210 (B) 310(C) 4 (D) 120

19. Let A and B be two symmetric matrices of order 3.Statement 1 A (BA) and (AB) A are symmetric matrices.Statement 2 AB is symmetric matrix if matrix multiplication of A and B is commutative.(A) Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation

for Statement 1(B) Statement 1 is true, Statement 2 is false(C) Statement 1 is false, Statement 2 is true(D) Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for

Statement 1

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20. If x, y, z are in A.P. and 1 1tan x, tan y and 1tan z are also in A.P., then:

(A) 6x 3y 2z= = (B) 6x 4y 3z= = (C) x y z= = (D) 2x 3y 6z= =

21. The intercepts on x-axis made by tangents to the curve,x

0

y tdt, x R= , which are parallel

to the line y 2x,= are equal to(A) 3 (B) 4 (C) 1 (D) 2

22. Let [.] denote the greatest integer function then the value of1.5

2

0

x x dx is:

(A) 0 (B)3

2

(C)3

4 (D)

5

4

23. The circle passing through (1, 2) and touching the axis of x at (3, 0) also passes throughthe point:

(A) ( )5, 2 (B) ( )2, 5

(C) ( )5, 2 (D) ( )2, 5

24. If ( )A 2, 3 and ( )B 2, 1 are two vertices of a triangle and third vertex moves on the line2x 3y 9,+ = then the locus of the centroid of the triangle is:(A) x y 1 = (B) 2x 3y 1+ = (C) 2x 3y 3+ = (D) 2x 3y 1 =

25. If ( )1

y sec tan x ,

= thendy

dx at x 1= is equal to:(A) 1 (B) 2

(C)1

2 (D)

1

2

pace for rough work


18/33



26. The expressiontan A cot A

1 cot A 1 tan A+

(A) tan A cot A+ (B) secA coescA+ (C) sin A cos A 1+ (D) sec A cos ecA 1+

27. If the trivial solution is the only solution of the system of equations

x ky z 0

kx 3y kz 0

3x y z 0

+ =

+ =

+ =

then the set of all values of k is:

(A) { }R 2, 3 (B) { }R 2

(C) { }R 3 (D) { }2, 3

28. A multiple choice examination has 5 questions. Each question has three alternative answersof which exactly one is correct. The probability that a student will get 4 or more correctanswers just by guessing is:

(A)5

11

3 (B)

5

10

3

(C) 517

3 (D) 513

3

29. Consider the differential equation2 1y dx x dy 0

x

+ =

. If ( )y 1 1,= then x is given by:

(A)

1

y2 e4

y e (B)

1

y1 e3

y e +

(C)

1

y1 e1

y e+ (D)

1

y1 e1

y e +

30. ( ) ( )x 0

1 cos2x 3 cos xlimxtan4x

+ is equal to:

(A) 1 (B) 2

(C)1

4 (D)

1

2

pace for rough work


19/33



FIITJEEJEE MAINS MOCK TEST-1Target IIT - JEE 2014

QP CODE: 120634.0ANSWERS

SECTION I (Physics)

1. B 2. C 3. B 4. D

5. A 6. C 7. A 8. B

9. B 10. C 11. C 12. D

13. D 14. C 15. A 16. C

17. B 18. A 19. D 20. C

21. B 22. B 23. C 24. A25. B 26. D 27. C 28. D

29. A 30. D

SECTION II (Chemistry)

1. C 2. D 3. C 4. D

5. C 6. B 7. A 8. B

9. C 10. B 11. D 12. B

13. C 14. A 15. A 16. A

17. D 18. C 19. C 20. C

21. C 22. C 23. C 24. D

25. B 26. B 27. D 28. B

29. D 30. A

SECTION III (Mathematics)

1. B 2. D 3. D 4. D

5. A 6. C 7. D 8. D

9. B 10. A 11. A 12. D

13. A 14. A 15. D 16. C

17. B 18. A 19. A 20. C

21. C 22. C 23. A 24. B

25. C 26. D 27. A 28. A

29. C 30. B


20/33



Hints & SolutionsPhysics

1. BSol. A moving conductor is equivalent to a battery of emf

= vB(motion emf)

Equivalent circuitI = I1+ I2

Applying Kirchoffs law

I1R + IR vB= 0 (1)

I2R + IR vB= 0 (2)

R

I1

R

I2

Adding (1) and (2)

2IR + IR = 2vB

2vBI

3R=

; 1 2

vBI I

3R= =

2. C

Sol.22 t/T 2 2t /T0

oq1 q 1U (q e ) e

2 C 2C 2C

= = = (where = CR)

12t /1U U e

=

12t /1 1

1U U e

2

= ; 12t / 11 T

e t ln22 2

= =

Now, t/ Toq q e=

t/2To o

1q q e

4

=

t2= Tln4 = 2Tln2

1

2

t 1

t 4=

3. B

Sol. oil< < waterOil is the least dense of them so it should settle at the top with water at the base. Now theball is denser than oil but less denser than water. So, it will sink through oil but will not sink inwater. So it will stay at the oil-water interface.


21/33



4. D

Sol. v Kyi xj= +

dx dyKy, Kx

dt dt= =

dy dy dt Kx

dx dt dx Ky= =

ydy = xdxy2= x2+ C

5. ASol. The magnetic field in between because of each will be in opposite direction.

Bin between=o oi i j ( j)

2 x 2 (2d x)

= oi 1 1 ( j)

2 x 2d x

at x = d, Bin between= 0

for x < d, Bin between= ( j )

for x > d, Bin between=

( j) towards x net magnetic field will add up and direction will be ( j)

towards xnet magnetic field will add up and direction will be ( j )

6. C

Sol. Linear charge densityq

r

=

2

K.dq E dEsin ( j) sin ( j)r

= =

2

K qr E d sin ( j)rr

=

=2

0

K q sin ( j)r

= 2 20

q ( j)2 r

7. ASol. Truth table for given combination is

A B Y

0 0 1

1 0 1

0 1 1

1 1 1

This comes out to be truth table of OR gate.

8. BSol. The efficiency of cycle is

2

1

T1

T =

for adiabatic process

TV1= constant

For diatomic gas7

5 =


22/33



1 11 1 2 2T V T V =

1

21 2

1

VT T

V

=

;

71

21 2T T (32)

=

= T2(25)2/5= T2 4

T1= 4T2

1 31 0.754 4

= = =

9. BSol. Apply shell theorem the total charge upto distance r can e calculated as followed

dq = 4r2.dr. = 2 o5 r

4 r .dr.4 R

=3

20

5 r4 r dr dr

4 R

r 32

0

0

5 rdq q 4 r dr dr

4 R

= =

=

2 4

0

5 r 1 r 4

4 3 R 4

2kqEr

=

=2 4

020

1 1 5 r 1 r 4

4 4 3 R 4r

E = o

o

r 5 r

4 3 R

10. C

Sol.12 6

a bU(x)

x x=

U(x ) 0= =

as,13 7

dU 12a 6bF

dx x x

= = +

at equilibrium, F = 0

62a

xb

=

2

at equilibrium 2

a b bU

2a 4a2abb

= =

2

at equilibrium

bD [U(x ) U ]

4a= = =

11. CSol. From F.B.D. of sphere, using Lamis theorem

Ftan

mg= (i)

when suspended in liquid, as remains same,

F

tan

mg 1d

=

(ii)

T

F

mg

Using (i) and (ii)


23/33



F F

mgmg K 1

d

=

where,F

FK

=

F F

mgmg K 1

d

=

or 1K 2

1d

= =

12. DSol. Let R0be the initial resistance of both conductors

At temperature their resistance will beR1= R0(1 + 1) and R2= R0(1 + 2)

for, series combination, Rs= R1+ R2

s0 1R (1 )+ and 2 1 0 2R (1 ) R (1 )= + + +

where s0 0 0 0R R R 2R= + =

0 s 0 0 1 22R (1 ) 2R R ( )+ = + + or 1 2s

2

+ =

for parallel combination, 1 2p1 2

R RR

R R=

+

0 1 0 2p0 p

0 1 0 2

R (1 )R (1 )R (1 )

R (1 ) R (1 )

+ + + =

+ + +

where, 0 0 0p00 0

R R RR

R R 2= =

+

2

0 0 2 1 2p

0 1 2

R R (1 )(1 )

2 R (2 )

+ + + + =

+ +

as 1and 2are small quantities 12is negligible

or 1 2 1 2p 1 21

[1 ( ) ]2 ( ) 2

+ + = = +

+ +

as 21 2( ) + is negligible

1 2p2

+ =

13. DSol. S = t3+ 5

Speed,ds

v dt= = 3t2

and rate of change of speed =dv

dt= 6t

tangential acceleration at t = 2s, at= 6 2 = 12 m/s2

At t = 2s, v = 3(2)2= 12 m/s

centripetal acceleration,2

c

v 144a

R 20= = m/s2

net acceleration = 2 2t ia a+

14 m/s2


24/33



14. CSol. For a particle in uniform circular motion,

2va

R=

towards centre of circle

2v a ( cos i sin j)

R=

or2 2

v v a cos i sin jR R

=

y

ac

ac

P (R, )

15. ASol. 1streaction is fusion and 4threaction is fission.

16. CSol. Given figure is half wave rectifier.

17. B

Sol.2 2 2

2

aT xT 4 4T

x x TT

= = = = constant.

18. ASol. It is possible when object kept at centre of curvature.

u = vu = 2f, v = 2f

19. DSol. T.Ei= T.Ef

21 l

2

= mgh

2 21 1m mgh2 3

=

2 21

h6 g

=

20. C

Sol.

1r

2

4 22 0 1

1 40 0

Qr4 r dr

R QrE4 r E

4 R

= =

21. BSol. Thermal energy corresponds to internal energy

Mass = 1 kgDensity = 8 kg/m3

3mass 1

Volume mdensity 8

= =

Pressure = 8 104N/m2

Internal Energy = 45

P V 5 10 J2

=


25/33



22. BSol. Motorcycle, u = 0, a = 2 m/s2

Observer is in motion and source is at rest.

0 0 0s

v v 330 v94 330 94n n n n 330 v

v v 100 330 100

= = =

+

094 33 33 6

v 330 m/s

10 10

= =

2 2v u 9 33 33 9 1089s

2a 100 100

= = = 98 m

23. C

Sol. 21

h gt ,2

= v = gt and after the collision, v = gt

(parabolic) (straight line)Collision is perfectly elastic then ball reaches to same height again and again with samevelocity.

24. ASol. Three forces F41, F42and f43acting on Q are shown

Resultant of F41+ F43= each2 F

=2

o

1 Qq2

4 d

Resultant on Q becomes zero only when q chargesare of negative nature.

4.2 2o

1 Q QF4 ( 2d)

=

2 2

dQ Q Q2

d 2d

=

Q Q

2 q2

= ;

Q Qq or 2 2

q2 2= =

25. B

Sol. We know thatdQ d

KAdt dx

=

In steady state flow of heat

dQ 1d dxdt kA

=

H Hk x k x = =

Equation H k x = represents a straight line.

26. D

Sol.3

Sin C2

= (1)

Sin r = sin (90 C) = cos C =1

2


26/33



2

1

sin

sinr

=

2 1sin

23 =

1 1sin3

=

27. C

Sol. Maximum number of beats = + 1 ( 1) = 2.

28. D

Sol. 1 1 1 1 11 1 2 2 22 2

A AA A

A 3A 3

= = = =

= 3

11 1

Fx

A = (i)

22 2

Fx

3A = (ii)

Here x1= x2

2 12 1

F F

3A A=

12 1 1

2

F 3F 3F 3= =

= 9F

29. A

Sol. Least count =o ovalue of main scale division 1 1 1 1

MSDNo. of divisions on vernier scale 30 30 2 60

= = = = 1 minute

30. D

Sol. 11

F 12I 6A

R 2= = =

22 2

dIE L R I

dt= +

ct/ t2 o o

2

E 12I I (1 e ) I 6A

R 2

= = = =

3

c

L 400 10t 0.2

R 2

= = =

t/0.22I 6(1 e )

=

Potential drop across L = E R2I2= 12 2 6(1 ebt) = 12 e5t

Chemistry1. C1. Ln3+compounds are mostly coloured.

2. DSol. Esterification reaction is involved

( ) ( ) ( ) ( )3 2 5 3 2 5 2H

CH COOH C H OH CH COOC H H O+

+ +


27/33



3. CSol. Correct basic strength is NH3> PH3> AsH3> BiH3

4. DSol Enthalpy of adsorption regarding physiosorption is not positive and it is negative.

5. C

Sol.3 o

Fe 3e Fe;E 0.036 V+

+ = ( )o o1

2 o

o o

2

G nFE 3F 0.036 0.108 F

Also Fe 2e Fe; E 0.439 V

G nFE

+

= = = +

+ =

=

= - 2F(-0.439) = 0.878F

To find Eofor ( ) ( )3 2Fe aq e Fe aq+ ++

Go= -nFEo= -1FEoo o o

1 2G G G= Go= 0.108F = 0.878F-FEo= +0.108F 0.878F

Eo

= 0.878 0.108 = 0.77 V

6. B

Sol. ( )3 3 3 32Ba NO CaCO BaCO 2NaNO+ +

Here 23

CO = [Na2CO3] = 104M

KSP= [Ba2+] 2

3CO 5.1 10

9= [Ba2+] (104) [Ba2+] = 5.1 105

At this value, just precipitation starts.

7. ASol. Remaining are feasible

8. BSol. Follow the periodic trends.

9. CSol. Option itself is the reason

10. BSol. NCSis ambidentate ligand and it can be linked through N (or) S

11. D

Sol.PV

nRT

=

53

1 1

3170 10 atm 1L

1.27 10 mol0.0821L atm K mol 300K

=

12. BSol. 3 alcohols react fastest with ZnCl2/conc.HCl due to formation of 3 carbocation and

2methyl propan2ol is the only 3 alcohol

13. C


28/33



Sol.

NH2

2NaNO

HCl, 278 K 2 3N BF HCl+ + +4HBF

N2Cl F

(A) (B)

Benzene diazoniumChloride Fluorobenzene

14. ASol. SN1 proceeds via carbocation intermediate, the most stable one forming the product faster.

Hence reactivity order for A, B, C depends on stability of carbocation

15. ASol. CH2- CH - CH - CH3

CH2- CH - CH - CH3

CH = CH HC

CH3

CH3

CH3OH

CH3

conc. H2SO4

loss of proton

(conjugated system)

Trans isomer is more stable & main product here

C

CH(CH3)2

H

C

H

(trans isomer)

16. A

Sol. In RNA, the sugar is - D Ribose, whereas in DNA the sugar is - D-2-deoxy Ribose.

17. D

Sol. OH3 3 3 22CCl CHO CCl COONa CCl CH OH

+

Cannizaro reaction is a disproportionation reaction. One aldehyde molecule is oxidized to

salt of the carboxylic acid, other one is reduced to alcohol. So, the compound is CCl3CH2OH.IUPAC name is 2, 2, 2, -trichloro ethanol.

18. C

Sol. Ease of liqueficationa

b

For ethane a = 5.49, b = 0.0638For Cl2a = 6.49, b = 0.0562

19. C


29/33



Sol. The general o.s of lanthanides is +3, only few elements exhibit +4 o.s.

20. CSol. S can exhibit a minimum oxidation state of -2.

21. CSol. In acidic medium, KBr + KBrO3in turn produces Br2. Phenol reacts with Br2(aq) to give 2, 4,

6-trinitrophenol.

22. CSol. As the size of central atom increases lone pair bond pair repulsions increases so, bond

angle decreases.

23. C

Sol. G0= RTln K and G0= H0- TS0

24. DSol. Total weight of solution = 1000 + 120 = 1120 g

120 1000Molarity 2.05M

60 1120 / 1.15= =

25. BSol. H3C -CH2- CH(CH3) - CH3on monochlorination gives

H2C(Cl) CH2 CH(CH3) CH3(I)

Achiral

H3C CH(Cl) CH(CH3) CH3(II)

Chiral

H3C - CH2- C - CH3

CH3

Cl (III)

Achiral

H3C - CH2- CH - CH3

CH2- Cl

(IV)Chiral

26. B

Sol.2.303 0.1

k log40 0.025

=

0.693k

20=

For a 1storder reaction, rate = k(A), rate =20.693 10

20

= 3.47 104

27. D

Sol. FeO More basic, more ionic, less volatile

28. B

Sol. Tf= Kfmw 1000

2.8 1.8662 1000

=

w = 93g


30/33



29. DSol. Iodoform is given by: 1) methyl ketones R CO - CH3

2) alcohols of the type R - CH(OH)CH3Where R can be hydrogen also

H3C - C - C2H5

H3C - CH - OH

H3C - C - CH - CH3

O

CH3

O CH3

ethyl methyl ketone

Isopropyl alcohol

3-methyl 2-butanone

can give iodoform test

30. ASol. ZnHg/HCl cant be used due to the presence of acid sensitive group i.e. OH

CH = CH - C -

OH

CH = CH - CH2- CH3

Cl

Zn Hg/HCl

O

CH3

and Na/Liq. NH3and NaBH4convert CO into CH(OH)

Mathematics

1. Let ( ) 3f x 2x 3x k= + +

( ) 2f ' x 6x 3= +

( )f x is an increasing function there exist no real values of k

3. As we known 1

adj A A

= where n is order of matrix A

( ) ( ) ( ) ( )2

1 3

1 3 3 4 12 12 4 6 3 4 6 16

2 4 4

= = + =

2 6 16 11 = =

5. ( )dp 100 12 x dp 100 12 x dx cdx

= = + 3 /2P 100x 8x C= +

At x 0, p 2000 C 2000= = = 3 /2P 100x 8x 2000= +

When x 25= P 100 25 1000 2000= +


31/33



P 3500=

6. In ADB , by sine rule

2 2

sinsin 2

AB p q

+ =+

2 2p q sinAB

cos cos sin sin+ =

+

In2 2 2 2

q pBCD, sin ,cos

p q p q = =

+ +

( )2 2p q sinAB

pcos qsin

+ =

+

C

B

P

q D

A

/2-

2 2p q+

8. Given line isx y

113

+ =

Passing through ( )3, 0 and ( )0, 1 , we know that image of (,) with respect to x axes is (,)

Reflected ray pass through ( )3, 0 and ( )0, 1 3y x 3 =

10. Given z 1= then

zz 1,= so,1

zz

=

Arg( )

( ) ( )

z 1 zArg z

1 z

+=

+

11. By Newton & libnitz rule

( ) ( )f x ' x=

Put 3x t= 2dt

3xdx

=

( )1

t f t dt3

= ( )1

t . ' t dt3

= ( ) ( )1

t t t dt3

=

( ) ( )3 3 2 31

x x x x dx3

=

13. If vector a = (1, 1, k), b = (k, 2, 1) c = (1, 1, 1) are coplanar

then [ ]abc 0= 1 1 k

k 2 1 0

1 1 1

=

2k 3k 0+ = 15. p q q p q p p q ( ) ( )p nq p q

T T F F F F FT F T T F F FF T F F T T F


32/33



F F T F T F F

p q q p ( ) ( ) ( )p q q p

T T TF F TT T TT T T

16. 2x 2x 3 0+ + = 2D 2 3x4 ve= = , then both roots are common and coefficient ratio are equal

a : b :c 1 : 2 : 3=

18.( ) ( )

103 2

1/3 1/210

2/3 1/3 1/2 2/3 1/3 1/2

x 1 x 1x 1 x 1

x x 1 x x x x 1 x x

+ + = + +

( )10

1/3 1/ 2x x=

For term independent of x ,10 r r

03 2

=

r =4

10

4C 210=

20. 1 1 1 1 12

2y x z2 tan y tan x tan z tan tan

1 xz1 y

+= + =

2y xz= also 2y x z= +

x z y = = ( )x, y, z are in A.P. and G.P.

21. By Newton & Libnitz rule

dyx 2

dx= = x 2=

At x 2= , y 2= equation of tangent ( )y 2 2 x 2 =

At x 2= , y 2= equation of tangent ( )y 2 2 x 2+ = + So, x intercept 1=

23. By family of point circle & line S L 0 + =

( )2 2x 3 y y 0 + + =

5 = 2 2x y 6x 5y 9 0+ =

Which is satisfied by (5, 2)

25. By Chain rule

( )1y sec tan x=

( ) ( )1 1 2dy 1

sec tan x .tan tan x .dx 1 x

=+

x 1

dy 1 12 . 1.

dx 2 2= = =


33/33


26.2 2tan A cot A tan A 1 1 cot A

tanA 1 1 tanA tan A 1 tan A 1

++

( )1 cot A

tan A 1tanA 1

= + +

( )

sin A cos A cos Atan A 1 .

sin A cos A sinA

= + +

tan A cot A 1= + +

sec A. cos ecA 1= +

28. By Binomial Probability

1 2p q x 5

3 3= = =

( ) ( ) ( )p x 4 P x 4 P x 5 = = + = 4 5

5 5

4 5

1 2 1C C

3 3 3

= +

( )51 10 13= +

5

11

3=

30.( ) ( )

x 0

1 cos2x 3 cos xlim

xtan4x

+

Divide by2x in Numerator and denominator

( )2

2

x 0

2

sin x2 3 cos x

xlimxtan4x

x

+

( )2

x 0

sinx2 3 cos x

xlim

tan4x4

4x

+

( )22 1 3 14 1

+=

jee mains mock test 1-29-03 14

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