test type : full syllabus test pattern : jee-main test

Test Type : FULL SYLLABUS Test Pattern : JEE-Main

TEST DATE : 23 - 03 - 2017

Paper Code : 1001CT102116065Form Number :

CLASSROOM CONTACT PROGRAMME(Academic Session : 2016 - 2017)E

NG

LIS

H

Corporate Office : CAREER INSTITUTE, “SANKALP”, CP-6, Indra Vihar, Kota (Rajasthan)-324005

+91-744-5156100 [email protected] www.allen.ac.in

Your Target is to secure Good Rank in JEE (Main) 2017

Important Instructions

Do not open this Test Booklet until you are asked to do so.

1. Immediately fill in the form number on this page of the Test Booklet with Blue/Black Ball PointPen. Use of pencil is strictly prohibited.

2. The candidates should not write their Form Number anywhere else (except in the specified space)on the Test Booklet/Answer Sheet.

3. The test is of 3 hours duration.

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

5. There are three parts in the question paper A,B,C consisting of Physics, Chemistry andMathematics having 30 questions in each part of equal weightage. Each question is allotted 4(four) marks for correct response.

6. One Fourth mark will be deducted for indicated incorrect response of each question. No deduction

from the total score will be made if no response is indicated for an item in the Answer Sheet.

7. Use Blue/Black Ball Point Pen only for writting particulars/marking responses on Side–1 andSide–2 of the Answer Sheet. Use of pencil is strictly prohibited.

8. No candidate is allowed to carry any textual material, printed or written, bits of papers, mobile

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

JEE (Main + Advanced)

LEADER COURSE (SCORE-I) & ENTHUSIAST COURSE (SCORE-II)

E-1/171001CT102116065

SPACE FOR ROUGH WORK

Leader Course (Score-I) & Enthusiast Course (Score-II)/23-03-2017

PART A - PHYSICS

BEWARE OF NEGATIVE MARKING

HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS

1. An optical fibre communication system works on a

wavelength of 1.3 m. The number of subscribers it

can feed if a channel requires 20 kHz are

(1) 2.3 1010 (2) 1.15 1010

(3) 1 105 (4) None of these

2. Velocity-displacement graph of a particle moving in

a straight line is as shown in figure:

S

V

(1) magnitude of acceleration of particle is constant.

(2) magnitude of acceleration of particle is increasing

(3) acceleration versus displacement graph is straight

line

(4) acceleration versus displacement graph is parabola

3. Velocity of a particle moving in a curvilinear path in

a horizontal X Y plane varies with time as2ˆv (2t i t j)

m/s. Here, t is in second. At t = 1 s.

(1) acceleration of particle is 8 m/s2

(2) tangential acceleration of particle is 4

5 m/s2

(3) radial acceleration of particle is 6

5m/s2

(4) radius of curvature to the path is 5 5

2m

4. A block of mass m slides down on a wedge of mass

M as shown in figure. Let 1a

be the acceleration of

the wedge and 2a

the acceleration of block w.r.t.

ground. N1 is the normal reaction between block and

wedge and N2 the normal reaction between wedge

and ground. Friction is absent everywhere. Select the

incorrect alternative

M

m

(1) N2< (M + m)g

(2) N1 = m(g cos – | 1a

|sin)

(3) N1 sin = M| 1a

|

(4) m 2a

= – M 1a

1001CT102116065E-2/17


Target : JEE (Main + Advanced) 2017/23-03-2017

5. In the adjoining figure if acceleration of M with respect

to ground is a, then:

mM

a

(1) acceleration of m with respect to M is 2a

(2) acceleration of m with respect to ground is

2a sin (/2)

(3) acceleration of m with respect to ground is a

(4) acceleration of m with respect to ground is a tan

6. Which of the following statement is incorrect for a

spherical body rolling without slipping on a rough

horizontal ground at rest?

(1) The acceleration of a point in contact with ground

is zero

(2) The acceleration of C.O.M. of the sphere may or

may not be zero.

(3) Friction force may or may not be zero .

(4) Work done by friction w.r.t. ground on the body is

zero .

7. The end B of the rod AB which makes angle with

the floor is being pulled with, a constant velocity v0

as shown. The length of the rod is l. At the instant

when = 37° theny

A

v0

BO x

(1) velocity of end A is 5

3 v0 downwards

(2) angular velocity of rod is 05 v

3 (3) angular velocity of rod is constant

(4) velocity of end A is constant

8. A solid sphere of radius R is rolled by a force F acting

at the top of the sphere as shown in the figure. The

sphere rolls without slipping on rough stationary

surface.Initially sphere is in the rest position then:

Rough

F

(1) work done by friction when the centre of mass

moves a distance S is 2FS.

(2) speed of the CM when CM moves a distance S

is 20 FS

7 M(3) work done by the force F when Centre of Mass

moves a distance S is FS


is 4RS

M

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9. A disc of mass M and radius R moves in the x-y plane

as shown in the figure. The angular momentum of

the disc at the instant shown is:

(1) 5

2mR2 along- z axis about O

(2) 5

2mR2 along + z axis about O

(3) zero about point A

(4) 4 mR2 along +Z axis about A

10. The figure shows a process AB undergone by 2 moles

of an ideal diatomic gas. The process AB is in such a

way that VT= constant. T1 = 300 K and T2 = 500 K.

(R = gas constant)

V

T

A

B

T1 T2

(1) The molar heat capacity of gas in the process

A B is R

52

J/mol–K


A B is R J/mol–K

(3) The work done by the gas is –400R J

(4) The work done by the gas is –200R J.

11. An ideal gas undergoes cyclic process as shown indensity pressure graph. During the process AB the

work done ABW = 70 J. During the process BC, thegas absorbs 150 J of heat. During the process CA,gas undergoes expansion and does 210 J of work.

P (pressure)

(kg/m3)

de

nsity

A

B 20

0

P0 2P0 4P0

C

N/m2

(1) The efficiency of cyclic process is 33 %(2) The efficiency of cyclic process is 66%(3)The process CA is adiabatic .(4) The process BC is isothermal .

12. Assuming all pulleys, springs and string massless.Consider all surface smooth. Choose the correctstatement(s).

K

m

K

K

(1) The angular frequency for small oscillation of

the system is K

3m(2) The angular frequency for small oscillation of

the system is 4K

33m(3) The elastic potential energy of system at

equilibrium is 2 233m g

4K(4) The elastic potential energy of system at


2K

1001CT102116065E-4/17



13. A small sphere of mass m = 0.5 kg carrying a

positive charge q = 110 C is connected with a light,

flexible and inextensible string of length r = 60 cm

and whirled in a vertical circle. If a vertically upwards

electric field of strength E = 105 NC–1 exists in the

space, The minimum velocity of sphere required at

highest point so that it may just complete the circle.

(g = 10 ms–2)

(1) 8 m/s

(2) 7m/s

(3) 6m/s

(4) 9 m/s

14. A particle of mass m having negative charge q move

along an ellipse around a fixed positive charge Q so

that its maximum and minimum distances from fixed

charge are equal to r1 and r2 respectively.

The angular momentum L of this particle is

(1) 1 2

0 1 2

mr r Qq

(r r ) (2)

1 2

0 1 2

mr r Qq

2 (r r )

(3) 1 2

0 1 2

mr r Qq

3 (r r ) (4)

1 2

0 1 2

mr r Qq

4 (r r )

15. Switch S of circuit shown in figure is in position 1 for

a long time. At instant t = 0, it is thrown from

position 1 to 2. The thermal power P1(t) generated in

resistance R1.

S

+ –

R 1

R 2

1

2

E

C

(1)

2 2

22t /(R R )C1

2

1 2

E R.e

(R R )

(2)

2 2

2t /(R R )C1

2

1 2

E R.e

(R R )

(3)

2 2

2t / 2(R R )C1

2

1 2

E R.e

(R R )

(4)

2 2

2t /(R R )C1

21 2

E R.e

2(R R )

E-5/171001CT102116065



16. In the figure the potentiometer wire of length

l =100 cm and resistance 9is joined to a cell of emf

E1 = 10V and internal resistance r1 = 1. Another

cell of emf E2 = 5 V and internal resistance r2 = 2 is

connected as shown. The galvanometer G will show

no deflection when the length AC is:

G

A BC

E = 10Vr = 1

1

1

E = 5Vr = 2

2

2

(1) 50 cm (2) 55.55 cm

(3) 52.67 cm (4) 54.33 cm

17. A cubical room is formed with 6 plane mirrors. An

insect moves along the diagonal of the floor with

uniform speed. The speed of its image in two adjacent

walls parallel to the walls is 202 cm/s. Then the speed

of the image formed on the roof with respect to ground

is :

(1) 20 cm/s (2) 40 cm/s

(3) 20 2 cm/s (4) 10 2 cm/s

18. A prism of refractive index 2 refracting angle A

produces minimum deviation Dm of a ray on one face

at an angle of incidence 45. The values of

A and Dm are respectively.

(1) 45, 45 (2) 45, 60

(3) 60, 30 (4) 60, 45

19. In young’s double slit experiment, the intensity of light

at a point on the screen where the path difference is

is k units; being the wavelength of light used. The

intensity at a point where the path difference is /4

will be

(1) k/4 (2) k/2

(3) k (4) zero

20. In the ideal double-slit experiment, when a glass-plate

(refractive index 1.5) of thickness t is introduced in the

path of one of the interfering beams (wave-length ),

the intensity at the position where the central

maximum occurred previously remains unchanged.

The minimum thickness of the glass-plate is

(1) 2 (2) 2/3

(3) /3 (4)

21. In Young’s double slit experiment the two slits act as

coherent sources of equal amplitude A and of

wavelength . In another experiment with same set

up the two slits are sources of equal amplitude A and

wavelength , but are incoherent. The ratio of intensity

of light at the mid point of the screen in the first case

to that in the second case is

(1) 1 : 1 (2) 1 : 2

(3) 2 : 1 (4) 4 : 1

1001CT102116065E-6/17



22. A certain radioactive material can undergo three

different types of decay, each with a different decay

constant 1, 2 and 3. Then the effective decay

constant is

(1) 1 2 3

eff3

(2) eff 1 2 3

1 1 1 1

(3) eff 1 2 3

(4) eff 1 2 3

1 1 1 1 1

3

23. The wavelength of K line for an element of atomic

number 29is . Then the wavelength of K line for an

element of atomic no 15 is (Take mosley‘s

constant b = 1 for both elements)

(1)29

15 (2)

28

15

(3) 4 (4) 2

24 . In the given circuit, the current through 5mH indicator

in steady state is

(1) 4/3 Amp (2) 8/3 AMP

(3) 4 Amp (4) 2/3 Amp

25. In the circuit shown, the key (k) is closed at t = 0,

the current through the key at the instant

t = 10–3ln 2 sec. is

(1) 1.5 Amp (2) 2.5 Amp

(3) 4 Amp (4) 2/3 Amp

26. Two long parallel horizontal rails, a distance aparttand each has a resistance per unit length are joinedat one end by a resistance R. A perfectly conductingrod MN of mass m is free to slide along the rails withoutfriction. There is a uniform magnetic field of inductionB normal to the plane of paper and directed into thepaper. A variable force F is applied to the rod MNsuch that, as the rod moves, a constant current i flowsthrough P.

M

N

x x x x x

x x x x x

x x x x x

i

x

F

B

The applied force F as function of distance x of the

rod from R is

(1) 2

2 2

2m ii B (R 2 x)

B

(2) 2

2 2

4m ii B (R 2 x)

B

(3) 2

2 2

2m ii B (R 2 x)

B

(4) none of these

E-7/171001CT102116065



27. A small conducting loop of radius o and resistance r

is pulled with velocity v perpendicular to a long straight

conductor carrying a current i0. If a constant power P

is dissipated in the loop. The variation of velocity of

the loop as a function of x.Given that x >> 0.

a v

x

i0

(1)

2

2

0 0

2xPr

i a(2)

2

2

0 0

4xPr

i a

(3)

2

2

0 0

6xPr

i a(4) none of these

28. Two coaxial solenoids are made by winding thin

insulated wire over a pipe of cross-sectional area

A = 10 cm2 and length = 20 cm. If one of the

solenoids has 300 turns and the other 400 turns, their

mutual inductance is (0 = 4 × 10–7 T mA–1)

(1) 2.4 × 10–5 H (2) 4.8 × 10–4 H

(3) 4.8 × 10–5 H (4) 2.4 × 10–4 H

29. In the adjacent circuit, A and B represent two inputs

and C represents the output,

C

R2

A

B

The circuit represents

(1) NOR gate (2) AND gate

(3) NAND gate (4) OR gate

30. In the given circuit, a voltmeter ‘V’ is connected across

a bulb ‘B’. If the resistor ‘R’ is increased in value ?

VB

6V

R

(1) The voltmeter shows a lower voltage

(2) The voltmeter shows a higher voltage

(3) The voltmeter shows a same voltage

(4) The glow of bulb will increase

1001CT102116065E-8/17



PART B - CHEMISTRY31. The electronic spectrum of [Ti(H2O)6]

3+ gives a single

broad peak with a maxima at 20300 cm–1. The crystal

field stabilization energy is equal to

(1) 97 kJ mol–1 (2) 243 kJ mol–1

(3) 297 kJ mol–1 (4) None of these

32. Phenol condenses with phthalic anhydride in

presence of conc. H2SO4 to form

(1) methyl orange (2) phenolphthalein

(3) phenyl red (4) salicylic acid

33. At 298 K the equivalent conductivity of aniline

hydrochloride of 0.01 M solution is 122.5 but in

presence of sufficient excess of aniline to prevent of

hydrolysis it is 106.5. The equivalent conductivity of

HCl at infinite dilution is 426.0. The hydrolysis

constant of aniline is

(1) 0.05 (2) 2.63 × 10–5

(3) 4.86 × 10–5 (4) 2.18 × 10–8

34. Which of the following is not concentrated by

electromagnetic separation ?

(1) Copper pyrites (2) Pyrolusite

(3) Chromite (4) Cassiterite

35 The two substances A and B are in equilibrium with

C and D as

2A B 3C 2D

if the initial pressure of A and B in the ratio of 4 : 1

and at equilibrium partial pressure of A and D are

equal. Find the correct relation.

(1) pP 10 K (2) pP 0.4 K

(3) P = 0.4 Kp (4) P = 0.4 (Kp)2

36. Select the option containing correct order of the given

parameter.

(1) C > Si > Pb > Ge (Order of reactivity with alkali)

(2) C > Pb > Ge > Si (Order of reactivity with alkali)

(3) [CoCl3(NH3)3] > [CoCl(NH3)5]Cl2 >

[Co(NH3)6]Cl3 > [CoCl2(NH3)4]Cl

(order of electrical conductivity.)

(4) [Co(NH3)6]Cl3 > [CoCl(NH3)5]Cl2 >

[CoCl2(NH3)4]Cl > [CoCl3(NH3)3]


37.H

O

4 3LiAlH CH MgBr

35ºC ExcessA B

Identify B in the reaction :-

(1) H

O

(2) OH

(3) OH

(4) CH4

38. The wavelength of the electron emitted by a metal

sheet of work function 4 eV when photons from EMR

of wavelength 124 nm strike the metal plate.

(1) 10 nm

(2) 206.67 nm

(3) 50 nm

(4) 0.5 nm

E-9/171001CT102116065



39. Which of the following is paramagnetic ?

(1) O2[AsF6] (2) Al2O3

(3) C2 (4) Be2

40. Which of the following amino acids does not contain

asymmetric carbon ?

(1) Histidine (2) Glycine

(3) –Alanine (4) Threonine

41. Identify the correct option.

(I) AgCl is not soluble in H2O but soluble in KCN.

(II) Zn when reacts with cold v.v. dil HNO3 gives

NH4NO3.

(III) CuSO4 reacts with KI to form Cu2I2 + K2SO4.

(IV) 1000ºC4 2CuSO .5H O The gases liberated

are SO2 and O2.

(1) All statements are correct

(2) I, II and IV are correct

(3) II and III are incorrect statements

(4) Only I is incorrect.

42. Identify the correct option regarding surfacephenomenon.

(1) Colloidal solution of As2S3 can be prepared byPeptization.

(2) Out of KCl, BaCl2, AlCl3, Na3PO4 ; BaCl2 is most

effective in coagulation of sulphur sol.

(3) C H COOCH —C—CH OH15 31 2 2

CH OH2

CH OH2

is non–ionic

detergent.(4) On increasing concentration of

C2H5 SO3Na electrical conductance

will always increase

43. Which of the following is correct for the equilibrium ?

2CH3 C

O

O H H3C C

O

O H

H O

OC CH3

(Equilibrium constants for the reaction in water and

benzene are KWater KBenzene)

(1) KWater > KBenzene (2) KWater < KBenzene

(3) KWater = KBenzene (4) None of these

44. Which of the following options is incorrect ?

(1) Tailing of mercury can be used as test for Ozone.

(2) Carbon suboxide is amphoteric in nature and

carbon monoxide is neutral.

(3) Both Ni3B and FeB have no B–B bond.

(4) Both V3B2 and NaB15 have B–B bond.

45. 2 2 4H O / H SOA

Identify ‘A’ in the reaction.

(1)

OH

(2)

OH

(3)

OH

(4)

OH

1001CT102116065E-10/17



46. Which of the following statements is incorrect ?

(1) The specific heat capacity of substance is greater

in the solid state than in liquid state.

(2) The specific heat capacity of a substance is greater

in gaseous state than in the liquid state.

(3) The latent heat of vaporization of a substance is

greater than that of fusion.

(4) The internal energy of an ideal gas is a function of

its temperature.

47. The anode mud in the refining of silver

(1) Zn, Cu, Ag, Au

(2) Zn, Au

(3) Cu, Ag, Au

(4) Au

48. Identify the incorrect order of the given parameter.

(1) V > Ni > Mn (order of melting point)

(2) Co > Ni > Cu > Zn (order of melting point)

(3) Na2S > ZnS > CuS

(order of solubility in aqueous medium)

(4) CuS > ZnS > Na2S


49.

CHO OHC

CHO OHC

2

(i)NaOH(excess)

(ii)H / 2H O,0ºC

(1)

HO

OH HO

OH

(2)

HO

OH

O–

O

O–

O

(3)

O

O

O

O

(4)

COOH

O

OH HO

OOH

E-11/171001CT102116065



50. 5 milli-moles of a solid A was dissolved in 5 moles ofH2O. On adding to the solvent, A starts polymerisinginto another insoluble solid following zero orderkinetics. On adding 6 milli-moles of another solidsolute C (after 20 minute) the polymerisationcompletely stops. The insoluble solid polymer isremoved and the resulting solution was cooled to atemperature less than - 0.186°C (melting point ofsolution) to cause solidification of some liquidwater. Calculate the value of ‘X’ if rate constantfor polymerisation reaction is represented as10–X moles/minute. [Kf(H2O) = 1.86 K –Kg mole–1]

(1) 1 (2) 4 (3) 3 (4) 5

51. Silver has an atomic radius of 144 pm and the

density of silver is 10.6 g cm–3. Based on this

information identify the correct statement.

(1) It has FCC crystal lattice.

(2) It has BCC crystal lattice.

(3) Approximately 0.24 fraction of edge is not

covered by atoms.

(4) None of the statement is true.

52. Which of the following is least biodegradable ?

(1) C17H35COONa

(2) CH3(CH2)11SO3Na

(3) SO3NaCH(CH2)9

CH3

H3C

(4) CH3—CH—(CH2—CH)2—CH2—CH—CH3

CH3 CH3

SO3Na

53. + 3 4H PO3 2CH CH CH A

2 2 4O dil.H SO

heatB C D

A, C and D are

(1)

CH2CH2CH3

,

OH

, CH3COCH3

(2)

CHH3C CH3

,

OH

, CH3COCH3

(3)

CHH3C CH3

,

COCH3

, CH3COCH3

(4)

CHH3C CH3

,

OH

, CH3—CH—CH3

OH

54. How many moles of H2O (per mole of Cl2 evolved)

will be formed when KMnO4 is added to HCl solution?

(1) 5/4 (2) 4/5

(3) 5/8 (4) 8/5

1001CT102116065E-12/17



55. The densities of air at 25ºC and 100ºC are 1.2 gL–1

and 0.9 g L–1 respectively. Assuming that the air obey’s

Charle’s law, the value of absolute zero of

temperature in degree Celsius is

(1) –273ºC (2) 200ºC

(3) –200ºC (4) 0ºC

56. Which of the following order is correct w.r.t.

magnitude of enthalpies of formation for alkali metal

halides ?

(1) Iodide > Bromide > Chloride > Fluoride

(of same metal)

(2) CsCl > RbCl > NaCl > LiCl

(3) NaF > CsF > RbF > KF

(4) LiI > NaI > RbI > CsI

57. For the reaction : N2 (g) + 3H2(g) 2NH3(g),

H = –24 Kcal at 427ºC and 200 atm. Calculate

magnitude of internal energy change (in Kcal U), if

168 gm N2 gas and 30 gm H2 gas are allowed to

react completely (100 % reaction yield) to form NH3

gas at 427ºC and 200 atm.

(1) –106 Kcal

(2) –24 Kcal

(3) –21.2 Kcal

(4) – 120 kcal

58.

NH2

2 2NaNO HCl H O

0 5ºC boilA B

2 2Br / H O Zn

dustC D

Compound ‘D’ is

(1)

OH

Br

BrBr

(2)

OH

(3)

Br

BrBr

(4)

OH

HO OH

59. Calculate solubility (in moles/litre) of a saturated

aqueous solution of Ag3PO4 if the vapour pressure of

the solution becomes 750 torr at 373 K.

(1) 2

15(2)

1

30(3)

10

54(4)

20

27

60. It is found that for every 10º rise in temperature, the

rate of the reaction doubles itself. This is mainly

because

(1) The speed of the reactants doubles for every 10º

rise in temperature.

(2) The fraction of the molecules forming the

activated complex doubles itself.

(3) The concentration doubles itself.

(4) The collision frequency doubles itself.

E-13/171001CT102116065



PART C - MATHEMATICS

61. If the lines ax + y + 1 = 0, x + by + 1 = 0 andx + y + c = 0 (where a, b & c are distinct anddifferent from 1) are concurrent, then the value of

1 1 1

1 a 1 b 1 c

(1) –1 (2) 1 (3) 0 (4) 2

62. Domain of the function

x

1f x

x 1 e 1 x 4 x 5 x 6

(1) , 5 1, 4 6,

(2) , 5 1, 0 0, 4 6,

(3) 5, 1 0, 4 6,

(4) , 5 1, 4 6,

63. 1 2

2 2

0 0

1 sinx ax bx c dx 1 sin x ax bx c dx .

So, location of the roots of 2ax bx c 0 is

(1) At least one real root between (1, 2)


(3) At most one real root between (0, 2)

(4) Can’t say exactly about the roots

64. If the sum of first n terms of an A.P. is cn(n – 1), wherec 0, then sum of the squares of these terms is

(1) 22 2c n n 1

(2) 22c n n 1 2n 1

3

(3) 22c n n 1 2n 1

3

(4) 2 2

2c nn 1

3

65. The maximum value of sin cos(tanx) is

(1) 3

2(2) sin1

(3) 1 (4) sin (cos1)

66. The interval of the values of ‘a’ for which the line

x y 0 bisect 2 distinct chords drawn from a

point 1 2a 1 2a

, 2 2

to the circle

2 22x 2y 1 2a x 1 2a y 0

(1) a , 0 2,

(2) a , 0 0,

(3) a 2,

(4) a , 2 2,

67. The vector ˆ ˆ ˆxi yj zk makes with the plane of the

two vectors (2, 3, –1) and (1, –1, 2) an acute

angle 1cot 2 . Then,

(1) y x z zx (2) z x y xy

(3) x y z yz (4) x y z xyz

68. If from a point P (a, b, c) perpendiculars PA, PB aredrawn to yz and zx plane, then the equation of theplane OAB (where O is origin) is:(1) bcx + cay + abz = 0(2) bcx + cay – abz = 0(3) bcx – cay + abz = 0(4) –bcx + cay + abz = 0

69. If sin 2sin 3sin 0 and

cos 2cos 3cos 0 , then the value of

cos 3 8 cos3 27cos 3 (1) cos (3 + 3 + 3) (2) 18 cos ( + + )(3) 6 cos ( + + ) (4) 36 cos ( + + )

1001CT102116065E-14/17



70. If , are the roots of the equation 2x 2x 4 0 ,

then the value of n n is :

(1) n n2 cos

3

(2) n 1 n

2 cos3

(3) n n

2 sin3

(4)

n 1 n2 sin

3

71. If n 2 n 1

1 1 1s 1 .......

2 2 2 , then the least

integral value of n such that n

12 s

100 is

(1) 7 (2) 9

(3) 8 (4) 6

72. Statement-1: Any function f (x) is even function,when f (– x) = f (x) over its specified domain.

Statement-2: 2

2

1 x x 1f x

41 x

,

where [.] is greatest integer function. Function f(x) is

even function.

(1) Statement-1 is true, statement-2 is true

but statement-1 is not the correct explanation

for statement-2

(2) Statement-1 is true, statement-2 is false

(3) Statement-1 is false, statement-2 is true

(4) Both statements are true, and statement-1 is the

true explanation of statement-2

73. Statement-1: If two tangents are drawn to an

ellipse from a single point and if they are perpendicu-

lar to each other, then locus of that point is always a

circle.

Statement-2: For an ellipse 2 2

2 2

x y1

a b , locus of

that point from which two perpendicular tangents

are drawn, is 22 2x y a b .



for statement-2





74. Consider a system of equations ax + by = 0,

cx + dy = 0, where a, b, c, d, {0, 1}.

Statement-1: The probability that system of

equations has a solution is 1.

Statement-2: The probability that the system of

equations has a unique solution is 3

8.



for statement-2





E-15/171001CT102116065



75. In a ABC, if two sides b & c and an angle B aregiven.Statement-1: Let b = 5 cm, c = 3 cm andB = 60o. Total number of possible triangles are 2.Statement-2: If c sin B < b < c and B is an acuteangle, then there are two possible values of C.(1) Statement-1 is true, statement-2 is true

but statement-1 is not the correct explanationfor statement-2

(2) Statement-1 is true, statement-2 is false(3) Statement-1 is false, statement-2 is true(4) Both statements are true, and statement-1 is the

true explanation of statement-276. For a series S = 1 – 2 + 3 – 4 … n terms,

Statement-1: Sum of series always dependent onthe value of n, i.e. whether it is even or odd.

Statement-2: Sum of series is n

2 when value of

n is any even integer.(1) Statement-1 is true, statement-2 is true




77. 2 2 2 2 2 2n

n 1 n 2 n 3 1lim ........

nn 1 n 2 n 3

(1) ln 24

(2) ln 2

4

(3) 1

ln24 2

(4)

1ln2

4 2

78. The area bounded by the curve x1y e

2

is

(1) 2 1 ln2 (2) 1

1 ln 22

(3) 2 ln2 1 (4) 1

1 ln 22

79. If 0

A1 1

and 1 0

B5 1

, then the value of

for which 2A B is

(1) 1 (2) –1

(3) 4 (4) No real values

80. If n 2 3 n0 1 2 3 n1 x c c x c x c x ....... c x ,

then the value of

n0 1 2 nc 3c 5c ........ 1 2n 1 c is :

(1) nn 1 .2 (2) 0

(3) n 11 2n .2 (4) n1 n .2

81. For what value of k to the following system ofequations possess a non-trivial solution ?

x ky 3z 0

3x ky 2z 0

2x 3y 4z 0

(1) 11

14(2)

33

2 (3)

33

20(4)

33

2

82. The mean and variance of a binomial variable X are2 and 1 respectively. Then, the probability that X takesvalues greater than 1 is

(1) 15

16(2)

11

16(3)

5

16(4)

1

16

83. The curve for which the intercept cut off by anytangent on y-axis is proportional to the square of theordinate of the point of tangency is

(1) 2

1

cc x 1

y (2)

12

cc y 1

x

(3) 1 2c c

1x y (4) 2 3

1 2c y c x y

(where c1 and c

2 are arbitrary constants)

1001CT102116065E-16/17



84. Evaluate x

dxx

(1) 2

(2)

2

(3) 2

(4)

2

85. The angle between the lines joining the origin to the

points of intersection of the straight line y 3x 2

with the curve 2 2x 2xy 3y 4x 8y 11 0 is

(1) 1tan 2 (2) 1 2

tan3

(3) 1 4

tan3

(4)

1 2 2tan

3

86. The tangents to the parabola y2 = 4ax makes angle

1 and

2 with the positive x-axis. Then, the locus of

their point of intersection if cot 1 + cot

2 = c is

(1) y = ac (2) x = ac

(3) xy = ac2 (4) xy = a

c

87. If two points P and Q on the hyperbola2 2

2 2

x y1

a b , whose centre is C, are such that CP

is perpendicular to CQ, ( a b ), then value of

2 2

1 1

CP CQ

(1) 1

ab(2) 2 2

1 1

a b

(3) 2 2

1 1

a b (4) 2 2

1

a b

88. Tangent is drawn to ellipse 2

2xy 1

27 at

3 3 cos , sin (where 0, 2

). Then, the

value of such that sum of intercepts on the axes

made by this tangent is minimum, is

(1) 3

(2)

6

(3) 8

(4)

4

89. Solution of the equation

x 3 4 x 1 x 8 6 x 1 1 is

(1) x 4, 9 (2) x 3, 8

(3) x 5, 10 (4) x 4, 7

90. Let 2A : 2cos sin 2 and

3B :

2 2

, then A B is

(1) 3

: , 2

(2) 7

: , 2 6

(3) : , 2 6

(4) 5 3

: , , 2 6 2

E-17/171001CT102116065




Paper Code : 1001CT102116065Form Number :

CLASSROOM CONTACT PROGRAMME(Academic Session : 2016 - 2017)

HIN

DI

Corporate Office : CAREER INSTITUTE, “SANKALP”, CP-6, Indra Vihar, Kota (Rajasthan)-324005

+91-744-5156100 [email protected] www.allen.ac.in

Your Target is to secure Good Rank in JEE (Main) 2017

Important Instructions

Do not open this Test Booklet until you are asked to do so.

1. Immediately fill in the form number on this page of the

Test Booklet with Blue/Black Ball Point Pen. Use of pencil

is strictly prohibited.

2. The candidates should not write their Form Number

anywhere else (except in the specified space) on the Test

Booklet/Answer Sheet.

3. The test is of 3 hours duration.

4. The Test Booklet consists of 90 questions. The maximum

marks are 360.

5. There are three parts in the question paper A,B,C

consisting of Physics, Chemistry and Mathematics

having 30 questions in each part of equal weightage.

Each question is allotted 4 (four) marks for correct

response.

6. One Fourth mark will be deducted for indicated incorrect

response of each question. No deduction from the total

score will be made if no response is indicated for an item

in the Answer Sheet.

7. Use Blue/Black Ball Point Pen only for writting

particulars/marking responses on Side–1 and Side 2 of

the Answer Sheet.

Use of pencil is strictly prohibited.

8. No candidate is allowed to carry any textual material,

printed or written, bits of papers, mobile phone any

electronic device etc, except the Identity Card inside the

examination hall/room.

9. Rough work is to be done on the space provided for this

purpose in the Test Booklet only.

10. On completion of the test, the candidate must hand over

the Answer Sheet to the invigilator on duty in the Room/

Hall. However, the candidate are allowed to take away

this Test Booklet with them.

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

Sheet.

1.

2.

3. 3 4. 90360

5. A, B, C 30 4

6.

7.

8.

9.

10.

11.

Test Type : FULL SYLLABUS Test Pattern : JEE-Main

TEST DATE : 23 - 03 - 2017

JEE (Main + Advanced)

LEADER COURSE (SCORE-I) & ENTHUSIAST COURSE (SCORE-II)

H-1/331001CT102116065


PART A - PHYSICS

BEWARE OF NEGATIVE MARKING

HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS

1. 1.3 m 20 kHz

(1) 2.3 1010 (2) 1.15 1010

(3) 1 105 (4)

2.

S

V

(1)

(2)

(3)

(4)

1. An optical fibre communication system works on a

wavelength of 1.3 m. The number of subscribers it

can feed if a channel requires 20 kHz are

(1) 2.3 1010 (2) 1.15 1010

(3) 1 105 (4) None of these

2. Velocity-displacement graph of a particle moving in

a straight line is as shown in figure:

S

V

(1) magnitude of acceleration of particle is constant.

(2) magnitude of acceleration of particle is increasing

(3) acceleration versus displacement graph is straight

line

(4) acceleration versus displacement graph is parabola

1001CT102116065H-2/33


3. Velocity of a particle moving in a curvilinear path in

a horizontal X Y plane varies with time as2ˆv (2t i t j)

m/s. Here, t is in second. At t = 1 s.

(1) acceleration of particle is 8 m/s2

(2) tangential acceleration of particle is 4

5 m/s2

(3) radial acceleration of particle is 6

5m/s2

(4) radius of curvature to the path is 5 5

2m

4. A block of mass m slides down on a wedge of mass

M as shown in figure. Let 1a

be the acceleration of

the wedge and 2a

the acceleration of block w.r.t.

ground. N1 is the normal reaction between block and

wedge and N2 the normal reaction between wedge

and ground. Friction is absent everywhere. Select the

incorrect alternative

M

m

(1) N2< (M + m)g

(2) N1 = m(g cos – | 1a

|sin)

(3) N1 sin = M| 1a

|

(4) m 2a

= – M 1a

3. X-Y

2ˆv (2t i t j)

m/s

t t = 1s

(1) 8 m/s2

(2) 4

5 m/s2

(3) 6

5m/s2

(4) 5 5

2m

4. M M

1a

2a

N1 N2

M

m

(1) N2< (M + m)g

(2) N1 = m(g cos – | 1a

|sin)

(3) N1 sin = M| 1a

|

(4) m 2a

= – M 1a

H-3/331001CT102116065


5. In the adjoining figure if acceleration of M with respect

to ground is a, then:

mM

a

(1) acceleration of m with respect to M is 2a

(2) acceleration of m with respect to ground is

2a sin (/2)

(3) acceleration of m with respect to ground is a

(4) acceleration of m with respect to ground is a tan

6. Which of the following statement is incorrect for a

spherical body rolling without slipping on a rough

horizontal ground at rest?

(1) The acceleration of a point in contact with ground

is zero

(2) The acceleration of C.O.M. of the sphere may or

may not be zero.

(3) Friction force may or may not be zero .

(4) Work done by friction w.r.t. ground on the body is

zero .

5. M a

mM

a

(1) M m 2a

(2) m 2a sin (/2)

(3) m a

(4) m a tan

6.

(1)

(2)

(3)

(4)

1001CT102116065H-4/33


7. The end B of the rod AB which makes angle with

the floor is being pulled with, a constant velocity v0

as shown. The length of the rod is l. At the instant

when = 37° theny

A

v0

BO x

(1) velocity of end A is 5

3 v0 downwards

(2) angular velocity of rod is 05 v

3 (3) angular velocity of rod is constant

(4) velocity of end A is constant

8. A solid sphere of radius R is rolled by a force F acting

at the top of the sphere as shown in the figure. The

sphere rolls without slipping on rough stationary

surface.Initially sphere is in the rest position then:

Rough

F

(1) work done by friction when the centre of mass

moves a distance S is 2FS.


is 20 FS

7 M(3) work done by the force F when Centre of Mass

moves a distance S is FS


is 4RS

M

7. AB B v0 l = 37°

y

A

v0

BO x

(1) A 5

3v0

(2) 05 v

3

(3) (4) A

8. R F

Rough

F

(1) S 2FS

(2) S

20 FS

7 M

(3) S F FS

(4) S

4RS

M

H-5/331001CT102116065


9. A disc of mass M and radius R moves in the x-y plane

as shown in the figure. The angular momentum of

the disc at the instant shown is:

(1) 5

2mR2 along- z axis about O

(2) 5

2mR2 along + z axis about O

(3) zero about point A

(4) 4 mR2 along +Z axis about A

10. The figure shows a process AB undergone by 2 moles

of an ideal diatomic gas. The process AB is in such a

way that VT= constant. T1 = 300 K and T2 = 500 K.

(R = gas constant)

V

T

A

B

T1 T2


A B is R

52

J/mol–K

(2) The molar heat capacity of gas in the processA B is R J/mol–K

(3) The work done by the gas is –400R J

(4) The work done by the gas is –200R J.

9. M R x-y

(1) O –z 5

2mR2

(2) O +z 5

2mR2

(3) A

(4) A +Z 4 mR2

10. AB AB VT= T1 = 300 K T2 = 500 K. (R = )

V

T

A

B

T1 T2

(1) A B R

52

J/mol–K

(2) A B R J/mol–K

(3) –400R J (4) –200R J

1001CT102116065H-6/33


11. An ideal gas undergoes cyclic process as shown indensity pressure graph. During the process AB the

work done ABW = 70 J. During the process BC, thegas absorbs 150 J of heat. During the process CA,gas undergoes expansion and does 210 J of work.

P (pressure)

(kg/m3)

de

nsity

A

B 20

0

P0 2P0 4P0

C

N/m2

(1) The efficiency of cyclic process is 33 %

(2) The efficiency of cyclic process is 66%

(3)The process CA is adiabatic.

(4) The process BC is isothermal.12. Assuming all pulleys, springs and string massless.

Consider all surface smooth. Choose the correctstatement(s).

K

m

K

K

(1) The angular frequency for small oscillation of

the system is K

3m(2) The angular frequency for small oscillation of

the system is 4K

33m(3) The elastic potential energy of system at


4K(4) The elastic potential energy of system at


2K

11. AB

ABW = 70 J BC 150 J CA 210 J

P (pressure)

(kg/m3)

de

nsity

A

B 20

0

P0 2P0 4P0

C

N/m2

(1) 33 % (2) 66% (3) CA (4) BC

12.

K

m

K

K

(1) K

3m

(2) 4K

33m

(3) 2 233m g

4K

(4) 2 23m g

2K

H-7/331001CT102116065


13. A small sphere of mass m = 0.5 kg carrying a

positive charge q = 110 C is connected with a light,

flexible and inextensible string of length r = 60 cm

and whirled in a vertical circle. If a vertically upwards

electric field of strength E = 105 NC–1 exists in the

space, The minimum velocity of sphere required at

highest point so that it may just complete the

circle. (g = 10 ms–2)

(1) 8 m/s

(2) 7m/s

(3) 6m/s

(4) 9 m/s

14. A particle of mass m having negative charge q move

along an ellipse around a fixed positive charge Q so

that its maximum and minimum distances from fixed

charge are equal to r1 and r2 respectively.

The angular momentum L of this particle is

(1) 1 2

0 1 2

mr r Qq

(r r ) (2)

1 2

0 1 2

mr r Qq

2 (r r )

(3) 1 2

0 1 2

mr r Qq

3 (r r ) (4)

1 2

0 1 2

mr r Qq

4 (r r )

13. r = 60 cm

m = 0.5 kg q = 110 C

E = 105 NC–1

( g = 10 ms–2)

(1) 8 m/s

(2) 7m/s

(3) 6m/s

(4) 9 m/s

14. q m

Q

r1 r2

L

(1) 1 2

0 1 2

mr r Qq

(r r ) (2)

1 2

0 1 2

mr r Qq

2 (r r )

(3) 1 2

0 1 2

mr r Qq

3 (r r ) (4)

1 2

0 1 2

mr r Qq

4 (r r )

1001CT102116065H-8/33


15. Switch S of circuit shown in figure is in position 1 for

a long time. At instant t = 0, it is thrown from

position 1 to 2. The thermal power P1(t) generated in

resistance R1.

S

+ –

R 1

R 2

1

2

E

C

(1)

2 2

22t /(R R )C1

2

1 2

E R.e

(R R )

(2)

2 2

2t /(R R )C1

21 2

E R.e

(R R )

(3)

2 2

2t / 2(R R )C1

2

1 2

E R.e

(R R )

(4)

2 2

2t /(R R )C1

21 2

E R.e

2(R R )

15. S

1 t = 0, 1 2

R1 P1(t)

S

+ –

R 1

R 2

1

2

E

C

(1)

2 2

22t /(R R )C1

2

1 2

E R.e

(R R )

(2)

2 2

2t /(R R )C1

21 2

E R.e

(R R )

(3)

2 2

2t / 2(R R )C1

21 2

E R.e

(R R )

(4)

2 2

2t /(R R )C1

21 2

E R.e

2(R R )

H-9/331001CT102116065


16. In the figure the potentiometer wire of length

l =100 cm and resistance 9is joined to a cell of emf

E1 = 10V and internal resistance r1 = 1. Another

cell of emf E2 = 5 V and internal resistance r2 = 2 is

connected as shown. The galvanometer G will show

no deflection when the length AC is:

G

A BC

E = 10Vr = 1

1

1

E = 5Vr = 2

2

2

(1) 50 cm (2) 55.55 cm

(3) 52.67 cm (4) 54.33 cm

17. A cubical room is formed with 6 plane mirrors.

An insect moves along the diagonal of the floor with

uniform speed. The speed of its image in two adjacent

walls parallel to the walls is 202 cm/s. Then the

speed of the image formed on the roof with respect

to ground is :

(1) 20 cm/s (2) 40 cm/s

(3) 20 2 cm/s (4) 10 2 cm/s

16. =100 cm 9 E1 = 10V r1 = 1 E2 = 5 V r2 = 2 G AC

G

A BC

E = 10Vr = 1

1

1

E = 5Vr = 2

2

2

(1) 50 cm (2) 55.55 cm

(3) 52.67 cm (4) 54.33 cm

17. 6

202 cm/s

(1) 20 cm/s (2) 40 cm/s

(3) 20 2 cm/s (4) 10 2 cm/s

1001CT102116065H-10/33


18. A prism of refractive index 2 refracting angle A

produces minimum deviation Dm of a ray on one face

at an angle of incidence 45. The values of

A and Dm are respectively.

(1) 45, 45 (2) 45, 60

(3) 60, 30 (4) 60, 45

19. In young’s double slit experiment, the intensity of light

at a point on the screen where the path difference is

is k units; being the wavelength of light used. The

intensity at a point where the path difference is /4

will be

(1) k/4 (2) k/2

(3) k (4) zero

20. In the ideal double-slit experiment , when a

glass-plate (refractive index 1.5) of thickness t is

introduced in the path of one of the interfering beams

(wave-length ), the intensity at the position where

the central maximum occurred previously remains

unchanged. The minimum thickness of the glass-plate

is

(1) 2 (2) 2/3

(3) /3 (4)

21. In Young’s double slit experiment the two slits act as

coherent sources of equal amplitude A and of

wavelength . In another experiment with same set

up the two slits are sources of equal amplitude A and

wavelength , but are incoherent. The ratio of intensity

of light at the mid point of the screen in the first case

to that in the second case is

(1) 1 : 1 (2) 1 : 2

(3) 2 : 1 (4) 4 : 1

18. 2 A 45° Dm A Dm (1) 45, 45 (2) 45, 60(3) 60, 30 (4) 60, 45

19.

k ;

/4

(1) k/4 (2) k/2

(3) k (4) zero

20. t

1.5

(1) 2 (2) 2/3

(3) /3 (4)

21. A A (1) 1 : 1 (2) 1 : 2

(3) 2 : 1 (4) 4 : 1

H-11/331001CT102116065


22. A certain radioactive material can undergo three

different types of decay, each with a different decay

constant 1, 2 and 3. Then the effective decay

constant is

(1) 1 2 3

eff3

(2) eff 1 2 3

1 1 1 1

(3) eff 1 2 3

(4) eff 1 2 3

1 1 1 1 1

3

23. The wavelength of K line for an element of atomic

number 29is . Then the wavelength of K line for

an element of atomic no 15 is (Take mosley‘s constant

b = 1 for both elements)

(1)29

15 (2)

28

15

(3) 4 (4) 2

24 . In the given circuit, the current through 5mH indicator

in steady state is

(1) 4/3 Amp (2) 8/3 AMP

(3) 4 Amp (4) 2/3 Amp

22. 1, 2 3

(1) 1 2 3

eff3

(2) eff 1 2 3

1 1 1 1

(3) eff 1 2 3

(4) eff 1 2 3

1 1 1 1 1

3

23. 29 K 15 K b = 1

(1)29

15 (2)

28

15

(3) 4 (4) 2

24. 5mH

(1) 4/3 Amp (2) 8/3 AMP

(3) 4 Amp (4) 2/3 Amp

1001CT102116065H-12/33


25. In the circuit shown, the key (k) is closed at t = 0,

the current through the key at the instant

t = 10–3ln 2 sec. is

(1) 1.5 Amp (2) 2.5 Amp

(3) 4 Amp (4) 2/3 Amp

26. Two long parallel horizontal rails, a distance aparttand each has a resistance per unit length are joinedat one end by a resistance R. A perfectly conductingrod MN of mass m is free to slide along the rails withoutfriction. There is a uniform magnetic field of inductionB normal to the plane of paper and directed into thepaper. A variable force F is applied to the rod MNsuch that, as the rod moves, a constant current i flowsthrough P.

M

N

x x x x x

x x x x x

x x x x x

i

x

F

B

The applied force F as function of distance x of the

rod from R is

(1) 2

2 2

2m ii B (R 2 x)

B

(2) 2

2 2

4m ii B (R 2 x)

B

(3) 2

2 2

2m ii B (R 2 x)

B

(4) none of these

25. t = 0 (k) t = 10–3n 2 sec

(1) 1.5 Amp (2) 2.5 Amp

(3) 4 Amp (4) 2/3 Amp

26. R m MN

B F MN P i R x F

M

N

x x x x x

x x x x x

x x x x x

i

x

F

B

(1) 2

2 2

2m ii B (R 2 x)

B

(2) 2

2 2

4m ii B (R 2 x)

B

(3) 2

2 2

2m ii B (R 2 x)

B

(4)

H-13/331001CT102116065


27. A small conducting loop of radius o and resistance r

is pulled with velocity v perpendicular to a long straight

conductor carrying a current i0. If a constant power P

is dissipated in the loop. The variation of velocity of

the loop as a function of x.Given that x >> 0.

a v

x

i0

(1) 2

2

0 0

2xPr

i a(2)

2

2

0 0

4xPr

i a

(3) 2

2

0 0

6xPr

i a(4) none of these

28. Two coaxial solenoids are made by winding thin

insulated wire over a pipe of cross-sectional area

A = 10 cm2 and length = 20 cm. If one of the

solenoids has 300 turns and the other 400 turns, their

mutual inductance is (0 = 4 × 10–7 T mA–1)

(1) 2.4 × 10–5 H

(2) 4.8 × 10–4 H

(3) 4.8 × 10–5 H

(4) 2.4 × 10–4 H

27. a r I0 v P x x >> 0.

a v

x

i0

(1) 2

2

0 0

2xPr

i a(2)

2

2

0 0

4xPr

i a

(3) 2

2

0 0

6xPr

i a(4)

28. A = 10 cm2

= 20 cm

300 400

(0 = 4 × 10–7 T mA–1)

(1) 2.4 × 10–5 H

(2) 4.8 × 10–4 H

(3) 4.8 × 10–5 H

(4) 2.4 × 10–4 H

1001CT102116065H-14/33


29. In the adjacent circuit, A and B represent two inputs

and C represents the output,

C

R2

A

B

The circuit represents

(1) NOR gate (2) AND gate

(3) NAND gate (4) OR gate

30. In the given circuit, a voltmeter ‘V’ is connected across

a bulb ‘B’. If the resistor ‘R’ is increased in value ?

VB

6V

R

(1) The voltmeter shows a lower voltage

(2) The voltmeter shows a higher voltage

(3) The voltmeter shows a same voltage

(4) The glow of bulb will increase

29. A B C

C

R2

A

B

(1) NOR (2) AND

(3) NAND (4) OR

30. ‘V’ ‘B’‘R’

VB

6V

R

(1)

(2)

(3)

(4)

H-15/331001CT102116065


PART B - CHEMISTRY31. [Ti(H2O)6]

3+ 20300 cm–1 (1) 97 kJ mol–1 (2) 243 kJ mol–1

(3) 297 kJ mol–1 (4)

32. H2SO4 (1) (2) (3) (4)

33. 298 K 0.01 M 122.5 106.5 HCl 426.0

(1) 0.05 (2) 2.63 × 10–5

(3) 4.86 × 10–5 (4) 2.18 × 10–8

34. (1) (2) (3) (4)

35 A B, C D 2A B 3C 2D

A B 4 : 1

A D

(1) pP 10 K (2) pP 0.4 K

(3) P = 0.4 Kp (4) P = 0.4 (Kp)2

31. The electronic spectrum of [Ti(H2O)6]3+ gives a single

broad peak with a maxima at 20300 cm–1.

The crystal field stabilization energy is equal to

(1) 97 kJ mol–1 (2) 243 kJ mol–1

(3) 297 kJ mol–1 (4) None of these

32. Phenol condenses with phthalic anhydride in

presence of conc. H2SO4 to form

(1) methyl orange (2) phenolphthalein

(3) phenyl red (4) salicylic acid

33. At 298 K the equivalent conductivity of aniline

hydrochloride of 0.01 M solution is 122.5 but in

presence of sufficient excess of aniline to prevent of

hydrolysis it is 106.5. The equivalent conductivity of

HCl at infinite dilution is 426.0. The hydrolysis

constant of aniline is

(1) 0.05 (2) 2.63 × 10–5

(3) 4.86 × 10–5 (4) 2.18 × 10–8

34. Which of the following is not concentrated by

electromagnetic separation ?

(1) Copper pyrites (2) Pyrolusite

(3) Chromite (4) Cassiterite

35 The two substances A and B are in equilibrium with

C and D as

2A B 3C 2D

if the initial pressure of A and B in the ratio of 4 : 1

and at equilibrium partial pressure of A and D are

equal. Find the correct relation.

(1) pP 10 K (2) pP 0.4 K

(3) P = 0.4 Kp (4) P = 0.4 (Kp)2

1001CT102116065H-16/33


36. Select the option containing correct order of the given

parameter.

(1) C > Si > Pb > Ge (Order of reactivity with alkali)

(2) C > Pb > Ge > Si

(Order of reactivity with alkali)

(3) [CoCl3(NH3)3] > [CoCl(NH3)5]Cl2 >

[Co(NH3)6]Cl3 > [CoCl2(NH3)4]Cl


(4) [Co(NH3)6]Cl3 > [CoCl(NH3)5]Cl2 >



37.H

O

4 3LiAlH CH MgBr

35ºC ExcessA B

Identify B in the reaction

(1) H

O

(2) OH

(3) OH

(4) CH4

38. The wavelength of the electron emitted by a metal

sheet of work function 4 eV when photons from EMR

of wavelength 124 nm strike the metal plate.

(1) 10 nm (2) 206.67 nm

(3) 50 nm (4) 0.5 nm

36. (1) C > Si > Pb > Ge ()(2) C > Pb > Ge > Si ()(3) [CoCl3(NH3)3] > [CoCl(NH3)5]Cl2 >

[Co(NH3)6]Cl3> [CoCl2(NH3)4]Cl

()

(4) [Co(NH3)6]Cl3 > [CoCl(NH3)5]Cl2 >


()

37.H

O

4 3LiAlH CH MgBr

35ºC ExcessA B

B

(1) H

O

(2) OH

(3) OH

(4) CH4

38. EMR124 nm

4 eV

(1) 10 nm (2) 206.67 nm

(3) 50 nm (4) 0.5 nm

H-17/331001CT102116065


39. Which of the following is paramagnetic ?

(1) O2[AsF6] (2) Al2O3

(3) C2 (4) Be2

40. Which of the following amino acids does not containasymmetric carbon ?(1) Histidine (2) Glycine(3) –Alanine (4) Threonine

41. Identify the correct option.

(I) AgCl is not soluble in H2O but soluble in KCN.

(II) Zn when reacts with cold v.v. dil HNO3 givesNH4NO3.

(III) CuSO4 reacts with KI to form Cu2I2 + K2SO4.

(IV) 1000ºC4 2CuSO .5H O The gases liberated

are SO2 and O2.

(1) All statements are correct

(2) I, II and IV are correct

(3) II and III are incorrect statements

(4) Only I is incorrect.

42. Identify the correct option regarding surfacephenomenon.

(1) Colloidal solution of As2S3 can be prepared by

Peptization.

(2) Out of KCl, BaCl2, AlCl3, Na3PO4 ; BaCl2 is most

effective in coagulation of sulphur sol.

(3) C H COOCH —C—CH OH15 31 2 2

CH OH2

CH OH2

is non–ionic

detergent.(4) On increasing concentration of

C2H5 SO3Na electrical conductance

will always increase

39. (1) O2[AsF6] (2) Al2O3

(3) C2 (4) Be2

40. (1) (2) (3) – (4)

41. (I) AgCl, H2O KCN (II) HNO3 Zn, NH4NO3 (III) CuSO4, KI Cu2I2 + K2SO4 (IV) 1000ºC

4 2CuSO .5H O SO2

O2 (1) (2) I, II IV (3) II III (4) I

42. (1) As2S3

(2) KCl, BaCl2, AlCl3, Na3PO4 BaCl2

(3) C H COOCH —C—CH OH15 31 2 2

CH OH2

CH OH2

(4) C2H5 SO3Na

1001CT102116065H-18/33


43. Which of the following is correct for the equilibrium ?

2CH3 C

O

O H H3C C

O

O H

H O

OC CH3

(Equilibrium constants for the reaction in water and

benzene are KWater KBenzene)



44. Which of the following options is incorrect ?

(1) Tailing of mercury can be used as test for Ozone.

(2) Carbon suboxide is amphoteric in nature and

carbon monoxide is neutral.

(3) Both Ni3B and FeB have no B–B bond.

(4) Both V3B2 and NaB15 have B–B bond.

45. 2 2 4H O / H SOA

Identify ‘A’ in the reaction.

(1)

OH

(2)

OH

(3)

OH

(4)

OH

43.

2CH3 C

O

O H H3C C

O

O H

H O

OC CH3

( KWater KBenzene )



44. (1) Tailing of mercury

(2)

(3) Ni3B FeB B–B (4) V3B2 NaB15 B–B

45. 2 2 4H O / H SOA

‘A’

(1)

OH

(2)

OH

(3)

OH

(4)

OH

H-19/331001CT102116065


46. Which of the following statements is incorrect ?

(1) The specific heat capacity of substance is greater

in the solid state than in liquid state.

(2) The specific heat capacity of a substance is greater

in gaseous state than in the liquid state.

(3) The latent heat of vaporization of a substance is

greater than that of fusion.

(4) The internal energy of an ideal gas is a function of

its temperature.

47. The anode mud in the refining of silver

(1) Zn, Cu, Ag, Au

(2) Zn, Au

(3) Cu, Ag, Au

(4) Au

48. Identify the incorrect order of the given parameter.

(1) V > Ni > Mn (order of melting point)

(2) Co > Ni > Cu > Zn (order of melting point)





46.

(1)

(2)

(3)

(4)

47.

(1) Zn, Cu, Ag, Au

(2) Zn, Au

(3) Cu, Ag, Au

(4) Au

48.

(1) V > Ni > Mn ()

(2) Co > Ni > Cu > Zn ()


()


()

1001CT102116065H-20/33


49.

CHO OHC

CHO OHC

2

(i)NaOH(excess)

(ii)H / 2H O,0ºC

(1)

HO

OH HO

OH

(2)

HO

OH

O–

O

O–

O

(3)

O

O

O

O

(4)

COOH

O

OH HO

OOH

49.

CHO OHC

CHO OHC

2

(i)NaOH(excess)

(ii)H / 2H O,0ºC

(1)

HO

OH HO

OH

(2)

HO

OH

O–

O

O–

O

(3)

O

O

O

O

(4)

COOH

O

OH HO

OOH

H-21/331001CT102116065


50. 5 milli-moles of a solid A was dissolved in 5 moles ofH2O. On adding to the solvent, A starts polymerisinginto another insoluble solid following zero orderkinetics. On adding 6 milli-moles of another solidsolute C (after 20 minute) the polymerisationcompletely stops. The insoluble solid polymer isremoved and the resulting solution was cooled to atemperature less than - 0.186°C (melting point ofsolution) to cause solidification of some liquidwater. Calculate the value of ‘X’ if rate constantfor polymerisation reaction is represented as10–X moles/minute. [Kf(H2O) = 1.86 K –Kg mole–1]

(1) 1 (2) 4 (3) 3 (4) 5

51. Silver has an atomic radius of 144 pm and the density

of silver is 10.6 g cm–3. Based on this information

identify the correct statement.

(1) It has FCC crystal lattice.

(2) It has BCC crystal lattice.

(3) Approximately 0.24 fraction of edge is not

covered by atoms.

(4) None of the statement is true.

52. Which of the following is least biodegradable ?

(1) C17H35COONa

(2) CH3(CH2)11SO3Na

(3) SO3NaCH(CH2)9

CH3

H3C


CH3 CH3

SO3Na

50. A 5 5 A (20 ) C 6 – 0.186°C () 10–X x [Kf(H2O)=1.86K –Kg mole–1]

(1) 1 (2) 4 (3) 3 (4) 5

51. 144 pm 10.6 g cm–3 (1) FCC (2) BCC (3) 0.24 fraction covered

(4)

52. (1) C17H35COONa

(2) CH3(CH2)11SO3Na

(3) SO3NaCH(CH2)9

CH3

H3C


CH3 CH3

SO3Na

1001CT102116065H-22/33


53. + 3 4H PO3 2CH CH CH A

2 2 4O dil.H SO

heatB C D

A, C and D are

(1)

CH2CH2CH3

,

OH

, CH3COCH3

(2)

CHH3C CH3

,

OH

, CH3COCH3

(3)

CHH3C CH3

,

COCH3

, CH3COCH3

(4)

CHH3C CH3

,

OH

, CH3—CH—CH3

OH

54. How many moles of H2O (per mole of Cl2 evolved)

will be formed when KMnO4 is added to HCl solution?

(1) 5/4 (2) 4/5

(3) 5/8 (4) 8/5

53. + 3 4H PO3 2CH CH CH A

2 2 4O dil.H SO

heatB C D

A, C D

(1)

CH2CH2CH3

,

OH

, CH3COCH3

(2)

CHH3C CH3

,

OH

, CH3COCH3

(3)

CHH3C CH3

,

COCH3

, CH3COCH3

(4)

CHH3C CH3

,

OH

, CH3—CH—CH3

OH

54. KMnO4 HCl H2O

(Cl2 )

(1) 5/4 (2) 4/5

(3) 5/8 (4) 8/5

H-23/331001CT102116065


55. The densities of air at 25ºC and 100ºC are 1.2 gL–1

and 0.9 g L–1 respectively. Assuming that the air obey’s

Charle’s law, the value of absolute zero of

temperature in degree Celsius is

(1) –273ºC (2) 200ºC

(3) –200ºC (4) 0ºC

56. Which of the following order is correct w.r.t.

magnitude of enthalpies of formation for alkali metal

halides ?


(of same metal)




57. For the reaction : N2 (g) + 3H2(g) 2NH3(g),

H = –24 Kcal at 427ºC and 200 atm. Calculate

magnitude of internal energy change (in Kcal U), if

168 gm N2 gas and 30 gm H2 gas are allowed to

react completely (100 % reaction yield) to form NH3

gas at 427ºC and 200 atm.

(1) –106 Kcal

(2) –24 Kcal

(3) –21.2 Kcal

(4) – 120 kcal

55. 25ºC 100ºC 1.2 gL–1

0.9 g L–1

(1) –273ºC (2) 200ºC

(3) –200ºC (4) 0ºC

56.


(of same metal)




57. N2 (g) + 3H2(g) 2NH3(g) 427ºC

200 atm H = –24 Kcal

U (Kcal ) ,

427ºC 200 atm 168 gm N2 30 gm

H2

NH3

(1) –106 Kcal

(2) –24 Kcal

(3) –21.2 Kcal

(4) – 120 kcal

1001CT102116065H-24/33


58.

NH2

2 2NaNO HCl H O

0 5ºC boilA B

2 2Br / H O Zn

dustC D

Compound ‘D’ is

(1)

OH

Br

BrBr

(2)

OH

(3)

Br

BrBr

(4)

OH

HO OH

59. Calculate solubility (in moles/litre) of a saturated

aqueous solution of Ag3PO4 if the vapour pressure of

the solution becomes 750 torr at 373 K.

(1) 2

15(2)

1

30(3)

10

54(4)

20

27

60. It is found that for every 10º rise in temperature, the

rate of the reaction doubles itself. This is mainly

because

(1) The speed of the reactants doubles for every 10º

rise in temperature.

(2) The fraction of the molecules forming the

activated complex doubles itself.

(3) The concentration doubles itself.

(4) The collision frequency doubles itself.

58.

NH2

2 2NaNO HCl H O

0 5ºC boilA B

2 2Br / H O Zn

dustC D

‘D’

(1)

OH

Br

BrBr

(2)

OH

(3)

Br

BrBr

(4)

OH

HO OH

59. Ag3PO4 373 K 750 torr

(1) 2

15(2)

1

30(3)

10

54(4)

20

27

60. 10º

(1) 10º

(2) fraction

(3)

(4)

H-25/331001CT102116065


PART C - MATHEMATICS

61. ax + y + 1 = 0, x + by + 1 = 0 x + y + c = 0 ( a, b & c

1 1 1

1 a 1 b 1 c

(1) –1 (2) 1 (3) 0 (4) 2

62. x

1f x

x 1 e 1 x 4 x 5 x 6

(1) , 5 1, 4 6,

(2) , 5 1, 0 0, 4 6,

(3) 5, 1 0, 4 6,

(4) , 5 1, 4 6,

63. 1 2

2 2

0 0


2ax bx c 0 (1) (1, 2) (2) (0, 1) (3) (0, 2) (4)

64. A.P. n cn(n – 1) ,c 0, (1) 22 2c n n 1

(2) 22c n n 1 2n 1

3

(3) 22c n n 1 2n 1

3

(4) 2 2

2c nn 1

3

61. If the lines ax + y + 1 = 0, x + by + 1 = 0 andx + y + c = 0 (where a, b & c are distinct anddifferent from 1) are concurrent, then the value of

1 1 1

1 a 1 b 1 c

(1) –1 (2) 1 (3) 0 (4) 2

62. Domain of the function

x

1f x

x 1 e 1 x 4 x 5 x 6

(1) , 5 1, 4 6,

(2) , 5 1, 0 0, 4 6,

(3) 5, 1 0, 4 6,

(4) , 5 1, 4 6,

63. 1 2

2 2

0 0


So, location of the roots of 2ax bx c 0 is



(3) At most one real root between (0, 2)

(4) Can’t say exactly about the roots

64. If the sum of first n terms of an A.P. is cn(n – 1), wherec 0, then sum of the squares of these terms is

(1) 22 2c n n 1

(2) 22c n n 1 2n 1

3

(3) 22c n n 1 2n 1

3

(4) 2 2

2c nn 1

3

1001CT102116065H-26/33


65. The maximum value of sin cos(tanx) is

(1) 3

2(2) sin1

(3) 1 (4) sin (cos1)

66. The interval of the values of ‘a’ for which the line

x y 0 bisect 2 distinct chords drawn from a

point 1 2a 1 2a

, 2 2

to the circle

2 22x 2y 1 2a x 1 2a y 0

(1) a , 0 2,

(2) a , 0 0,

(3) a 2,

(4) a , 2 2,

67. The vector ˆ ˆ ˆxi yj zk makes with the plane of the

two vectors (2, 3, –1) and (1, –1, 2) an acute

angle 1cot 2 . Then,



68. If from a point P (a, b, c) perpendiculars PA, PB aredrawn to yz and zx plane, then the equation of theplane OAB (where O is origin) is :

(1) bcx + cay + abz = 0

(2) bcx + cay – abz = 0

(3) bcx – cay + abz = 0

(4) –bcx + cay + abz = 0

69. If sin 2sin 3sin 0 and

cos 2cos 3cos 0 , then the value of

cos 3 8 cos3 27cos 3

(1) cos (3 + 3 + 3) (2) 18 cos ( + + )

(3) 6 cos ( + + ) (4) 36 cos ( + + )

65. sin cos(tanx)

(1) 3

2(2) sin1

(3) 1 (4) sin (cos1)

66. ‘a’ x y 0

2 22x 2y 1 2a x 1 2a y 0

1 2a 1 2a

, 2 2

(1) a , 0 2,

(2) a , 0 0,

(3) a 2,

(4) a , 2 2,

67. ˆ ˆ ˆxi yj zk , (2, 3, –1) (1, –1, 2)

1cot 2



68. P (a, b, c) yz zx PA, PB OAB O ) (1) bcx + cay + abz = 0(2) bcx + cay – abz = 0(3) bcx – cay + abz = 0(4) –bcx + cay + abz = 0

69. sin 2sin 3sin 0 cos 2cos 3cos 0 cos 3 8 cos3 27cos 3 (1) cos (3 + 3 + 3) (2) 18 cos ( + + )(3) 6 cos ( + + ) (4) 36 cos ( + + )

H-27/331001CT102116065


70. If , are the roots of the equation 2x 2x 4 0 ,

then the value of n n is :

(1) n n2 cos

3

(2) n 1 n

2 cos3

(3) n n

2 sin3

(4)

n 1 n2 sin

3

71. If n 2 n 1

1 1 1s 1 .......

2 2 2 , then the least

integral value of n such that n

12 s

100 is

(1) 7 (2) 9

(3) 8 (4) 6

72. Statement-1: Any function f (x) is even function,when f (– x) = f (x) over its specified domain.

Statement-2: 2

2

1 x x 1f x

41 x

,

where [.] is greatest integer function. Function f(x) is

even function.



for statement-2





70. , 2x 2x 4 0 n n

(1) n n2 cos

3

(2) n 1 n

2 cos3

(3) n n

2 sin3

(4)

n 1 n2 sin

3

71. n 2 n 1

1 1 1s 1 .......

2 2 2 , n

n

12 s

100

(1) 7 (2) 9

(3) 8 (4) 6

72. -1: f (x) f (– x) = f (x)

-2: 2

2

1 x x 1f x

41 x

,

[.] f (x)

(1) -1 -2 ; -2-1

(2) - 1 - 2

(3) - 1 - 2

(4) -1 -2 -2-1

1001CT102116065H-28/33


73. Statement-1: If two tangents are drawn to an

ellipse from a single point and if they are perpendicular

to each other, then locus of that point is always a

circle.

Statement-2: For an ellipse 2 2

2 2

x y1

a b , locus of

that point from which two perpendicular tangents

are drawn, is 22 2x y a b .



for statement-2





74. Consider a system of equations ax + by = 0,

cx + dy = 0, where a, b, c, d, {0, 1}.

Statement-1: The probability that system of

equations has a solution is 1.

Statement-2: The probability that the system of

equations has a unique solution is 3

8.



for statement-2





73. -1:

-2: 2 2

2 2

x y1

a b

22 2x y a b

(1) -1 -2 ; -2-1

(2) - 1 - 2

(3) - 1 - 2

(4) -1 -2 -2-1

74. ax + by = 0, cx + dy = 0 a, b, c, d, {0, 1}.

-1:

-2: 3

8

(1) -1 -2 ; -2-1

(2) - 1 - 2

(3) - 1 - 2

(4) -1 -2 -2-1

H-29/331001CT102116065


75. In a ABC, if two sides b & c and an angle B aregiven.Statement-1: Let b = 5 cm, c = 3 cm andB = 60o. Total number of possible triangles are 2.Statement-2: If c sin B < b < c and B is an acuteangle, then there are two possible values of C.(1) Statement-1 is true, statement-2 is true



true explanation of statement-276. For a series S = 1 – 2 + 3 – 4 … n terms,

Statement-1: Sum of series always dependent onthe value of n, i.e. whether it is even or odd.

Statement-2: Sum of series is n

2 when value of

n is any even integer.(1) Statement-1 is true, statement-2 is true




77. 2 2 2 2 2 2n

n 1 n 2 n 3 1lim ........

nn 1 n 2 n 3

(1) ln 24

(2) ln 2

4

(3) 1

ln24 2

(4)

1ln2

4 2

78. The area bounded by the curve x1

y e2

is

(1) 2 1 ln2 (2) 1

1 ln 22

(3) 2 ln2 1 (4) 1

1 ln 22

75. ABC b & c B -1: b = 5 cm, c = 3 cm B = 60o. -2: csin B < b < c B C (1) -1 -2 ; -2

-1 (2) - 1 - 2 (3) - 1 - 2 (4) -1 -2 -2

-1 76. S = 1 – 2 + 3 – 4 … n ,

-1: n n,

-2: n n

2

(1) -1 -2 ; -2-1

(2) - 1 - 2 (3) - 1 - 2 (4) -1 -2 -2

-1

77. 2 2 2 2 2 2n

n 1 n 2 n 3 1lim ........

nn 1 n 2 n 3

(1) ln 24

(2) ln 2

4

(3) 1

ln24 2

(4)

1ln2

4 2

78. x1y e

2

(1) 2 1 ln2 (2) 1

1 ln 22

(3) 2 ln2 1 (4) 1

1 ln 22

1001CT102116065H-30/33


79. If 0

A1 1

and 1 0

B5 1

, then the value of

for which 2A B is

(1) 1 (2) –1

(3) 4 (4) No real values

80. If n 2 3 n0 1 2 3 n1 x c c x c x c x ....... c x ,

then the value of

n0 1 2 nc 3c 5c ........ 1 2n 1 c is :

(1) nn 1 .2 (2) 0

(3) n 11 2n .2 (4) n1 n .2

81. For what value of k to the following system ofequations possess a non-trivial solution ?

x ky 3z 0

3x ky 2z 0

2x 3y 4z 0

(1) 11

14(2)

33

2 (3)

33

20(4)

33

2

82. The mean and variance of a binomial variable X are2 and 1 respectively. Then, the probability that X takesvalues greater than 1 is

(1) 15

16(2)

11

16(3)

5

16(4)

1

16

83. The curve for which the intercept cut off by anytangent on y-axis is proportional to the square of theordinate of the point of tangency is

(1) 2

1

cc x 1

y (2)

12

cc y 1

x

(3) 1 2c c

1x y (4) 2 3

1 2c y c x y

(where c1 and c

2 are arbitrary constants)

79. 0

A1 1

1 0

B5 1

,

2A B (1) 1 (2) –1

(3) 4 (4)

80. n 2 3 n0 1 2 3 n1 x c c x c x c x ....... c x

n0 1 2 nc 3c 5c ..... 1 2n 1 c

(1) nn 1 .2 (2) 0

(3) n 11 2n .2 (4) n1 n .2

81. k x ky 3z 0

3x ky 2z 0

2x 3y 4z 0

(1) 11

14(2)

33

2 (3)

33

20(4)

33

2

82. X 2 1 X

(1) 15

16(2)

11

16(3)

5

16(4)

1

16

83. y-

(1) 21

cc x 1

y (2) 1

2

cc y 1

x

(3) 1 2c c

1x y (4)

2 31 2c y c x y

(c1 c

2 )

H-31/331001CT102116065


84. Evaluate x

dxx

(1) 2

(2)

2

(3) 2

(4)

285. The angle between the lines joining the origin to the

points of intersection of the straight line y 3x 2

with the curve 2 2x 2xy 3y 4x 8y 11 0 is

(1) 1tan 2 (2) 1 2

tan3

(3) 1 4

tan3

(4)

1 2 2tan

3

86. The tangents to the parabola y2 = 4ax makes angle

1 and

2 with the positive x-axis. Then, the locus of

their point of intersection if cot 1 + cot

2 = c is

(1) y = ac (2) x = ac

(3) xy = ac2 (4) xy = a

c

87. If two points P and Q on the hyperbola2 2

2 2

x y1

a b , whose centre is C, are such that CP

is perpendicular to CQ, ( a b ), then value of

2 2

1 1

CP CQ

(1) 1

ab(2) 2 2

1 1

a b

(3) 2 2

1 1

a b (4) 2 2

1

a b

84.x

dxx

(1) 2

(2)

2

(3) 2

(4)

2

85. 2 2x 2xy 3y 4x 8y 11 0 y = 3x+2

(1) 1tan 2 (2) 1 2

tan3

(3) 1 4

tan3

(4)

1 2 2tan

3

86. y2 = 4ax x-1

2 cot

1 + cot

2 = c

(1) y = ac (2) x = ac

(3) xy = ac2 (4) xy = a

c

87. 2 2

2 2

x y1

a b P Q C,

CP, CQ ( a b ) ,

2 2

1 1

CP CQ

(1) 1

ab(2) 2 2

1 1

a b

(3) 2 2

1 1

a b (4) 2 2

1

a b

1001CT102116065H-32/33


88. Tangent is drawn to ellipse 2

2xy 1

27 at

3 3 cos , sin (where 0, 2

). Then, the

value of such that sum of intercepts on the axes

made by this tangent is minimum, is

(1) 3

(2)

6

(3) 8

(4)

4

89. Solution of the equation

x 3 4 x 1 x 8 6 x 1 1 is

(1) x 4, 9 (2) x 3, 8

(3) x 5, 10 (4) x 4, 7

90. Let 2A : 2cos sin 2 and

3B :

2 2

, then A B is

(1) 3

: , 2

(2) 7

: , 2 6

(3) : , 2 6

(4) 5 3

: , , 2 6 2

88. 2

2xy 1

27 3 3 cos , sin

( 0, 2

)

(1) 3

(2)

6

(3) 8

(4)

4

89. x 3 4 x 1 x 8 6 x 1 1

(1) x 4, 9 (2) x 3, 8

(3) x 5, 10 (4) x 4, 7

90. 2A : 2cos sin 2

3B :

2 2

, A B

(1) 3

: , 2

(2) 7

: , 2 6

(3) : , 2 6

(4) 5 3

: , , 2 6 2

H-33/331001CT102116065


test type : full syllabus test pattern : jee-main test

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