Jee Test Paper 1

8/8/2019 Jee Test Paper 1

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thTest Series, Paper1 www.vidyadrishti.com

2 www.vidyadrishti.com An education portal for future IITians

PHYSICS

SECTION I (Single Correct Choice Type)This Section contains 8 multiple choice questions. Each question has four choices A), B), C) and D) out of

which ONLY ONE is correct.

1. A free point charge q and mass m is set at the origin as shown in the figure. A constant electric field

0 0E i E j+ and constant magnetic field ( )0B k is present in whole region. When this charge reaches atposition (2, 2, 0) its speed will be

(a) 08qEm

(b) 04qEem

(c) 0qEBm

(d) 2qBm

2. In a circuit shown, when the circuit is in the steady state, the plates of the parallel plate capacitor arepulled apart, so that the distance between the plates is doubled. The work done by the external force

is (in micro joule)

(a) Zero(b)25(c) 50(d) -50

SPACE FOR ROUGH WORK

1 F

10 Vr

0E j

0B

q, m

F

x

y

0E i
http://www.vidyadrishti.com/http://www.vidyadrishti.com/http://www.vidyadrishti.com/


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3. In the following regular hexagons, made up of wires of two different materials P and Q, current entersand leaves from pointsXand Y(lying at midpoints of the side) respectively. In which case the magnetic

field at its centre is not zero.

(a)

(b)

(c)

(d)

4. After the switch is closed, the work done by the cell is constant over time, Cin Fis(a) 400(b)800(c) 960(d)1250


25 mH

C

2

Q

X

Y

PQ

P

P

Q

Q

X

Y

QP

P

P

Q

X

Y

PQ

P

P

P

X

Y

PQ

P

Q


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5. Which of the following options is correct?(a)R = 400 , C= 0.5 F(b)R = 500 , C= 0.5 F(c)R = 400 , C= 1 F(d)R = 500 , C= 0.1 F

6. When an AC voltage, of variable frequency is applied to series LCR circuit, the current in the circuit isthe same at 4 kHz and 9 kHz. The current in the circuit is maximum at

(a) 2 kHz(b)3 kHz(c) 4.2 kHz(d)6 kHz

7. In given figure, a wire loop has been so that it has three segments: segment ab (a quarter circle), bc (asquare corner), and ca (straight). Here are three choices for a magnetic field through the loop

I. 1 3 7 5 B i j t k = + II. 2 5 4 15 B ti j k =

III. 3 2 5 12 B i t j k =

where B

is in milliteslas and tis in seconds. If the induced current in the loop due to 1 2,B B

and 3B

are i1, i2 and i3 respectively then

a) i1 > i2 > i3b) i2 > i1 > i3c) i3 > i2 > i1d) i1 = i2 = i3


100 V

0.2 A

R 2H

400 V 400 V

z

y

x

c

b

a


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8. For a post office box, the graph of galvanometer deflection versus R (resistance pulled out of theresistance arm) for the ratio of resistances in ratios arms equal to 100:1 is given as shown. A careless

student pulls out two non consecutive values ofR(320 and 326 ohm) as shown in the figure. Find thevalue of unknown resistance.

(a) 3.2 ohm(b)3.24 ohm(c) 3.206 ohm(d)None of these


R326

320-3

5

Deflection (in division)


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SECTION II (Multiple Correct Choice Type)

This section contains 4 multiple choice questions. Each question has four choices A), B), C) and D) out of

which ONE OR MORE may be correct.

9. P and Q are two co-axial circular rings and the region between them has a magnetic fieldB. Radius ofthe two rings are a and 2a respectively. The magnetic field B is such that the electron does not reach

the ring Q when it starts from P with a radial velocity ofv0, then

(a) the path of electron is complete circle(b)radius of the path of electron is 3

4

a

(c) the magnitude of the magnetic field is 043

mv

ae

(d)Net angular displacement of electron with respect to its initial radial path is 106o

10.IfVA VB = V0 and the value of each resistance isR, then(a) net resistance betweenAB is 2

3

R

(b)net resistance betweenAB is 35

R

(c) current through CD is 02

V

R

(d)current inEFis 023

V

R


B

aO

PQ

2 a

C

RBA

E F

D


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11.The figure shows, a graph of the current in a discharging circuit of a capacitor through a resistor ofresistance 10 .

(a) The initial potential difference across the capacitor is 100 volt.(b)The capacitance of the capacitor is 1

10ln2F

(c) The total heat produced in the circuit will be 500ln 2

joules

(d)The thermal power in the resistor will decrease with a time constant 12ln2

second

12.In series LCR circuit voltage drop across resistance is 8 volt, across inductor is 6 volt and acrosscapacitor is 12 volt. Then

(a) voltage of the source will be leading current in the circuit(b)voltage drop across element will be less than the applied voltage(c) power factor of circuit will 43 (d)none of these


t2s

2.5A

10A

i


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SECTION III (Assertion Reason Type)

This question contains 5 reasoning type questions. Each question has 4 choices (a), (b), (c) and (d), out of


13.Statement I: Electron in an electron beam emerge through a narrow hole, with all electrons havingsame speed and making small angles with the beam direction. These electrons can be focused, almost

to a points on the screen by the application of an appropriate magnetic field a shown, in the space

between the screen and electron gun.

Statement II: Magnetic field corrects the small angle which the direction of velocities of electrons

make with the beam direction and makes all of them move in the direction of the beam.

a) Statement-I is true, Statement-II is true; Statement-II is a correct explanation for Statement I.b) Statement-I is true, Statement-II is true; Statement-II is not a correct explanation for Statement-I.c) Statement-I is true, Statement-II is falsed) Statement-I is false, Statement-II is true

14.Statement I: Force acting on a closed current carrying loop in a uniform magnetic field is zero,whatever be the orientation of the loop in the field.

Statement II: Length element d I

is a vector and 0.d I =

.



B

Screen

d

12

B


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15.Statement I: Electric field produced by changing magnetic field is nonconservative.Statement II: For the electric field E

induced by a changing magnetic field, . 0.E dt=


16.Statement I: The free electrons in a conducting wire are in constant thermal motion. If such a wire isplaced in a magnetic field, there is a magnetic force on the wire.

Statement II: There is a magnetic force on each free electron due to constant thermal motion.


17.Statement I: A magnetic field can be produced by moving charges or electric currents.Statement II: The magnetic field at the origin due to a current element idl

placed at a position r

is

0

34

idl r

r

.




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SECTION-IV (Linked Comprehension Type)

This section contains 3 paragraphs. Based upon the each paragraph has 3 multiple choice questions. Each of

these questions has four choices A), B), C) and D) out ofWHICH ONLY ONE CORRECT.

Comprehension for questions 18 to 20

A positively charged particle, having charge q, and mass m is accelerated by a potential difference

V. This particle moving alongx-axis enters a region (at the origin) where an electric field Eexists

The direction of the electric field is along positive y-axis. The electric field exists in the region

bounded by the linesx = 0 andx = a. Beyond the line x = a (i.e., in the regionxa) there exists a

magnetic field of strengthB, directed along the positivey-axis.

18.Yco-ordinate of the point where the particle meets the linex = a is-(a) 2

4Ea

V

(b) 2EaV

(c) 22

Ea

V

(d)None of the above19.The pitch of the helix formed after the particle enters the region x a is

(a)2

Ea m

B qV

(b)2

Ea m

B qV

(c) 22

Ea m

B qV

(d) 22

Ea m

B qV


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20.Let the particle cross the line x = a at time t= 0. TheZco-ordinate of the particle at time mBq

will be-

(a) 2 2VmB q

(b)1 2Vm

B q

(c) 1 22

Vm

B q

(d)None of these.


x = a

B

q

Ox

y

E

m


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Two parallel vertical metallic railsAB and CD are separated bt 1 m. They are connected at the two ends by

resistacesR1 andR2 as shown in the figure. A horizontal metallic bar L of mass 0.2 kg slides without friction,

vertically down the rails under the action of gravity. There is a uniform horizontal magnetic field of 0.6 T

perpendicular to the plane of the rails. It is observed that when the terminal velocity is attained, the powers

dissipated inR1 andR2 are 0.76 Wand 1.2 Wrespectively (g = 0.8 m/s2)

21.The terminal velocity of the barL will be(a) 2 m/s(b)3 m/s(c) 1 m/s(d)None of these

22.The value ofR1 is(a) 0.47 (b)0.82 (c) 0.12 (d)None of these

23.The value ofR2 is(a) 0.6 (b)0.5 (c) 0.4 (d)0.3


L

D

1m

C

R1

R2B

A


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A 6 V battery of negligible internal resistance is connected across a uniform wire AB of length 100 cm. The positive

terminal of another battery of emf 4 V and internal resistance 1 is joined to point A as shown in figure. Take the

potential at B to be zero.

24.The potentials at point A and C are(a) 6 V and 2 V respectively(b) 4 V and 0 V respectively(c) 6 V and 0 V respectively(d) 4 V and 6 V respectively

25.The point D of the wire AB at which the potential is equal to the potential at point C is such that(a) AD = 33.3 cm(b) AD = 66.7 cm(c) AD = 50 cm(d) AD = 100 cm

26. If the points C & D are connected by a wire, the current through 1 resistor is(a) 2 A(b) 4 A(c) 6 A(d) zero


C

D

6V

4V


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CHEMISTRY

SECTION I (Single Correct Choice Type)This Section contains 8 multiple choice questions. Each question has four choices A), B), C) and D) out of


1. cis-2-butene ( ) ( )2CHCl Br/base ;A A is

(a) (b)

(c) (d)


H

Cl

H

Br

Me Me

H

Cl

Me

Br

Me H

H

Cl

H

Cl

Me Me

H

Cl

Me

Cl

Me H


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2. Reaction oftrans-2-phenyl-1-bromocyclopentane with alcoholic KOH produces(a) 4-phenyl cyclopentene(b)2-phenyl cyclopentene(c) 1-phenyl cyclopentene(d)3-phenyl cyclopentene

3. EtBr on reaction with LiAlH4 gives ethane gas while Me3C Br on same treatment gives hydrogen gasbecause

(a) H- is a strong nucleophile but not a strong base(b)H- is a strong base but not a strong nucleophile(c) Me3C+ is more stable than Et+(d) In EtBr, SN2 occurs while in Me3C Br, E2 occurs

4. ( ){ } ozonolysisalkene 2,2 dimethylpropanal + methanalA (A)+ dil H2SO4major product (B), (B) is

(a) 3, 3-dimethylbutan-2-ol(b)3, 3-dimethylbutan-1-ol(c) 2, 3-dimethylbutan-2-ol(d)2, 3-dimethylbutan-1-ol



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5. Maximum amount of heat is evolved in(a) CH3CH2CH = CH2 + H2

(b) C = C + H2

(c) C = C + H2

(d)CH2 = CH CH = CH2 + H2

6. Minimum amount of heat is evolved in(a) CH3CH2CH = CH2 + H2

(b) C = C + H2

(c)

C = C + H2

(d)CH2 = CH CH = CH2 + 2H2


CH3

H3C H

H

H

H3C CH3

H

CH3

H3C H

H

H

H C CH3

H


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7. IdentifyA andB in the following reaction sequence.( ) ( )

2 5

2 5

C H O3 2 C H OHCH CH CH CH HBr A B

= +

(a)A = (CH3)2C CH2 CH3,B = CH3 C = CH CH3

(b)A = (CH3)2CH CH CH3,B = (CH3)2 CH - CH = CH2

(c)A = (CH3)2C CH2 CH3,B = H2C = C CH2 CH3

(d)A = (CH3)2CH CH CH3,B = (CH3)2 CH - CH = CH2


CH3

Br

CH3Br

Br

CH3

Br


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8. In the radical chlorination of methane, one propagation step is shown as4 3

Cl CH HCl CH+ +

Why do we eliminate the possibility that this step goes as shown below?

4 3Cl CH CH Cl H+ +

(a) Because in the next propagation step, H would have to react with CH4 to form CH3 and HCl; thisreaction is not feasible.

(b)Because this alternative step is more endothermic than the first.(c) Because free hydrogen atoms cannot exist.(d)Because this alternative step is not consistent with the photochemical efficiency of this reaction.



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SECTION II (Multiple Correct Choice Type)

This section contains 4 multiple choice questions. Each question has four choices A), B), C) and D) out of


9. Which of the following is/are correct forCH2 = CH2 + H2CH3 CH3

(a) G is ve at low temperature(b)His ve(c) S is ve(d)G is +ve at high temperature and the reaction has low activation energy.

10.When nitrobenzene is treated with Br2 in presence of FeBr3, the major product formed is mbromonitrobenzene. The statements which are related to obtain the m-isomer are

(a) the electron density on meta carbon is more than at ortho andpara-positions(b)the intermediate carbonium ion formed after initial attack of Br+ at the meta-position is least

destabilized

(c) loss of aromaticity when Br+ attacks at the ortho and para positions and not at m-position(d)easier loss ofH+ to region aromaticity from the meta-position than from ortho andpara-positions.

11.Alkene may be converted into alcohols by various ways like acid catalysed hydration,solvomercuration-demercuration method, hydroboration oxidation method etc. Which of the following

statements is/are correct?

(a) 3-methyl-butene on acid catalysed hydration gives 3-methyl- 2-butanol(b)3-methyl-butene on acid catalysed hydration gives 2-methyl- 2-butanol(c) 3-methyl-1-butene on solvomercuration-demercuration gives 3-methyl-2-butanol(d)3-methyl-1-butene on hydroboration oxidation gives 3-methyl-1-butanol



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12. ( )4KMnO PhenolH

ProductA B+

Which of the following is correct regarding productB?

(a) B is colourless in acidic(b) B is pink colour in basic medium(c) B has benzenoid form in basic medium(d) B exists in ionic form in basic medium


CH3

CH3


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13.Statement I: The conjugated dienes are more stable than the corresponding alkenes containing onedouble bond or even the dienes containing two isolated doubled bonds.

Statement II: Conjugated dienes are regarded as hybrids of several contributing structures.


14.Statement I: All the hydrogen atoms in CH2 = C = CH2 lie in one plane.Statement II: All the carbon atoms in it are sp2 hybridised.


15.Statement I:IUPAC name of is 1, 2, 3, 4, - tetramethyl cyclopentyl cyclopropane.

Statement II: Five membered ring is a parent chain.




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16.Statement I: 1-Butene on reaction with HBr in the presence of a peroxide produces 1-bromobutane.Statement II: It involves the formation of a primary radical.


17.Statement I: Cyclopropanone is more reactive than cyclopentanone towards nucleophillic additionreaction.

Statement II: Reaction of Cyclopropanone relieves its strain considerably.




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Ozonolysis is one of the important methods of determination of olefinic bonds in a compound. It is a cleavage

reaction in which double bond is completely broken and alkene molecule is converted into two or more

smaller molecules depending on the number of olefinic bonds with a carbonyl group. Ozonolysis is carried out

in two stages. First is addition of ozone to give ozonide, second step involving hydrolysis of ozonide in

presence of reducing agent (usually zinc) to give product of reductive ozonolysis. In presence of zinc it yields

aldehydes and ketones while in presence of Ag2O, H2O or peracids form acids and/or ketones. Further

ozonides of alkynes yield carboxylic acid by cleavage through diketone which is oxidized. Acetylene gives

however mixture of glyoxal as well as formic acid.

18.An organic C6H6 (M.F.) on reductive ozonolysis gives 2 moles ofCHOCH2CHO. The possible structurewill be

(a)

(b)

(c) H3C

(d)

CH2

H2C

CH3


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19.An alkene on reductive ozonolysis produces glyoxal (CHOCHO) and 2 moles of methanol. Theprobable structure of alkene is

(a) CH3 CH = CH CH = CH2(b)CH2 = CH CH = CH2(c) CH3 C = C CH3(d)CH2 = CH C = CH

20.

On oxidative ozonolysis (H2O) (assume benzene ring not affected) the above compound produces

(a) benzoic acid and 2 moles of

(b)benzoic acid, and CH3CO2H

(c) benzoic acid and 2 moles of

(d)benzoic acid, and CH3CO2H


CH3

CHO

CO2H

CHO

CO2H

CO2H

CO2H

CO2H

CO2H


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Carbonyl compounds react with sodium bisulphate to form a white crystalline precipitate of sodiumsulphite addition product. The reaction is a nucleophillic addition on carbon-oxygen double bond.

The nucleophile in the reaction being bulky, sterically hindered ketones do not respond to this

reaction. The bisulphate addition product is unstable to mineral acid and it gets revert back tooriginal carbonyl upon treatment with mineral acid.

21.The nucleophile in the reaction between carbonyl compound and sodium bisulphate is(a) SO-3Na(b)SO3-H(c) SO32-(d)SO3

22.1-propanol upon treatment with PCC gives propanol. The product propanol can be purified by(a) treatment with NaHSO3 followed by filtration and subsequent acid catalysed hydrolysis(b)simple crystallisation(c) fraction crystallisation(d) filtration of its aqueous solution


SO3Na

White crystalline solid

OH

O + NaHSO3


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23.Which of the following compounds will not react with NaHSO3?(a) CH3CHO(b)PhCHO

(c) H3C

(d)


O

CH3

O

CH3

CH3

CH3

CH3


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An ordinary D (+) glucose has melting point 160oC and specific rotation []

25D = + 112

o. One another form ofD

(+) glucose has melting point 150oC and specific rotation []

25D = + 18.7

o. The two forms have significantly

different optical rotations but when an aqueous solution of either form is allowed to stand, its rotation varies

differently with other. The specific rotation of one form decreases and rotation of other increases, until both

solution show the same value e.g., + 52.7o. This change in rotation towards an equilibrium value is called

mutarotation.

24.Mutarotation is a characteristic of(a) epimers(b)enantiomers(c) anomers(d)ring-chain isomers

25.Two siginificant forms which exhaibit mutarotation are assigned and -forms. For mannose, themutarotation can be shown in brief as follows:

Which form of mannose exists predominantly in the aqueous form?

(a) - form(b)-form(c) Open chain form(d)None of these

OH

O

OH

OH

OH

OH OH

O

OH

OH

OH

OH

OH

O

OH

OH

OH

OH OH

H

OH

CHO

HO

OH

H

H

CH2OH

H

OH

O

OH

OH

OH

OH


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26.What percentage of-D-(+) glucopyranose is found at equilibrium in the aqueous solution?(a) 50%(b) 100%(c) 36%(d)64%



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MATHEMATICS

SECTION I (Single Correct Choice Type)

This Section contains 8 multiple choice questions. Each question has four choices A), B), C) and D) out of


1. The polynomialf(x) =x4 + ax3 + bx2 + cx + dhas real coefficients andf(2i) =f(z + i) = 0. The value of (a +b + c + d) equals

(a) 1(b)4(c) 9(d)10

2. In an increasing A.P., it is given that S(r1) = S(r2) where S(r) represent the sum of first rterms of theA.P. If a and d represent the first term and common difference of the A.P. then

(a) Max ( )1 2 2, ar rd

<

(b)Max ( )1 2 2, 1 ar rd

<

(c)

Max ( )1 22

, 2

a

r r d<

(d)Max ( )1 2 2, 1 ar rd

>

3. A rectangle of maximum area is inscribed in the circle |z 3 4i| = 1. If one vertex of the rectangle is 4+ 4i, then another adjacent vertex of this rectangle can be

(a) 3 + 4i or 4 3i(b)3 + 5i or 3 + 3i(c) 3 5i or 3 + 3i(d)3 4i or 4 + 3i



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4. Let g is the inverse function of ( )( )

10

2& ' .

1

x f f x

x=

+Ifg(2) = a then g(2) is equal to

(a) 105

2

(b) 210

1 a

a

+

(c) 1021

a

a+

(d) 102

1 a

a

+

5. The function f(x) = ex + x, being differentiable and one to one, has a differentiable inverse f-1(x). Thevalue of ( )1

df

dx

at the pointf(ln 2) is

(a) 12ln

(b) 13

(c) 14

(d)None6. A function f(x) satisfies the condition, f(x) = f(x) + f(x) + f(x) + . where f(x) is a differentiable

function indefinitely and dash denotes the order of derivative. Iff(0) = 1. Thenf(x) is:

(a) 2xe (b) xe (c) 2xe (d) 4xe



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7. Let f: [I, I + 1) [I, I + 1), where ( ) [ ] { }. f x x x= + Here [.] denotes the G.I.F and {.} denotesfractional part ofx. Then the expression forf

-1(x) is

(a)f-1(x) =I+ (x +I)2(b)f-1(x) = -I+ (x +I)2(c)f-1(x) =I+ (x I)2(d)f-1(x) = -I+ (x I)2

8. let ( ) { }min 1 tan ,1 sin ,1 , ,2 2

n n n f x x x x x

=

where nN, then the left derivative of the

function at .4x

=

(a) -2n(b) -2(n+ 1)(c) 1

4

n

n

(d) 14

n

n



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SECTION II (Multiple Correct Choice Type)This section contains 4 multiple choice questions. Each question has four choices A), B), C) and D) out of


9. If ( ) ( )2/2

2

0

ln 1 sin, 0

sin

xf x d x

+= then:

(a) ( ) ( )1 1 f t t = + (b) ( )'

2 1f t

t

=

+

(c)f(x) cannot be determined(d)None of these

10.The function ( )( )

sin

sin

x a

x b

+

+has no maxima or minima if:

(a) b a = n, n I(b)b a (2n + 1), nI(c) b a = 2n, n I(d)none of these



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11.Let ( ) ( ) ( )2 21 12 1 1 ,4 2

g x f x f x x R= + wheref(x) > 0 xR then g(x) is

(a) Decreasing in 2 2,3 3

(b)Decreasing in 2 2, 0,3 3

(c) Increasing in 2 2, ,3 3

(d) Increasing in 2 2,0 ,3 3

12.The functionf(x) satisfying the equationf2(x) + 4f(x).f(x) + [f(x)]2 = 0.(a) ( ) ( )2 3. x f x c e = (b) ( ) ( )2 3. x f x c e += (c) ( ) ( )3 2. x f x c e = (d) ( ) ( )2 3. x f x c e +=



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13.Statement I:f(x) = sin (cos (cosec (tanx + cotx))) sin (cos (cosec (tanx cotx))) is periodic functionwith fundamental period

2

Statement II: product of two periodic functions is always periodic


14.Statement I: Equation of tangent of curve ( )131y x= at the point x = 1 isStatement II: Function ( )

1f x

x= is not differentiable atx = 0 because ( )

2

1'f x

x

= is not defined at

x = 0


15.Statement I: Iff: R R,f(x) = 1 x3 then point of intersection off(x) with its inverse will be threeStatement II: It is not necessary thatf(x) and its inverse will intersect each other on y =x line if they

are intersecting




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16.Statement I: There is no value ofa for which the equation x3 3x + a = 0 has two distinct roots in(0, 1).

Statement II: Iff(x) is continuous is an interval [a, b] and satisfying the condition f(a).f(b) < 0 andf(x) 0 in (a, b), then there will be exactly one root in (a, b) off(x).


17.Statement I: The functionf(x) = (x3 + 3x 14) (x2 + 3x 10) has a local extremum atx = 2Statement II:f(x) continuous & differentiable andf(2) = 0




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Let f(x) be defined as, f(x) = max {a, b, c}, where( )

1

sin coslim lim ,

n n

n nn

x xa

+

+=

+

( )1

sin coslim lim

n n

n nn

x xb

+=

+and

( )cos 1lim 1 cos ...

2 2 2n

nc

n n n

= + + +

. Then

18.The functionf(x) is continuous for(a)

( )2 1 4R n

+

(b)R {n}(c)R(d)None of these

19.The functionf(x) is differentiable for(a) ( )2 1

4R n

+

(b)R {n}(c)R(d)None of these

20.The area bounded byf(x) = max {a, b, c} andx-axis,x = 0 andx= , is(a) 2 (b) 1

2

(c) 2 2 (d) 4 2



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Let2 2 11,

2 + = + = andf(x) be a continuous function such thatf(x) +f(2 +x) = 2 x [0, 2] and

( )4

0

4, p f x dx q

= = . On the basis of this information answer the following question.

21.The value ofq equals(a) 1(b) 1

2

(c) 2(d) -2

22.The value ofp equals(a) 1(b)0(c) 2(d)None of these

23.The least positive integral value of a for which the equation ax2 bx + c = 0 has both roots lie betweenp & q when a, b, cNis

(a) 14

(b) 116

(c) 5(d)4



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In a game of chess between two playersA andB, eitherA wins,B wins or game ends in a draw. Probability

of winning the game by A and B are1

2and

1

3respectively. They agree to play a chess tournament

consisting of 3 games.

24.The probability that 2 games end in a draw, equals(a) 5

36

(b) 572

(c) 2572

(d) 5236

25.The probability thatA and B win alternately, equals(a) 5

36

(b) 572

(c) 2572

(d) 2536



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26.The probability thatB wins at least 1 game, equals(a) 5

9

(b) 1927

(c) 1136

(d) 2572



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Jee Test Paper 1

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