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PHYSICS, CHEMISTRY & MATHEMATICS

SET - A CTY – PHASE – 4 QP CODE -

Time Allotted: 3 Hours Maximum Marks: 360

Do not open this Test Booklet until you are asked to do so. Please read the instructions carefully. You are allotted 5 minutes speci fically for this

purpose.

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2. The Answer Sheet is kept inside this Test Booklet. When you are directed to open the Test

Booklet, take out the Answer Sheet and fill in the particulars carefully. 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. Candidates will be awarded marks as stated above in instruction No.5 for correct response of each

question. ¼ (one fourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet.

7. There is only one correct response for each question. Filling up more than one response in any

question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 6 above.

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duty in the Room / Hall. However, the candidates are allowed to take away this Test Booklet with them.

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Enrolment Number :_________________________________________________________

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FIITJEE - JEE (Mains)

JEE MAINS



2

Section 1 PHYSICS

1. Identical particles of charge q and mass m are fixed at the corners of

a cube. One of the charges is released. Its kinetic energy when it is

far off from the rest of the charges is B

F

G

CD

A

E

H a

(A) 2

0

7q

4 a (B)

2

0

q 3 13

4 a 2 3

(C) 2

0

q 29

4 a 6

(D) none of the above.

2. A parallel plate capacitor (C1) is charged such that the potential difference between them is V1. A

second capacitor (C2) is charged to V2 and connected to the first, the negative plate of one being

connected to the positive of the other and vice versa. The potential difference between the plates

is

(A) V1 – V2 (B) 1 1 2 2

1 2

C V C V

C C

(C) 1 1 2 2

1 2

C V C V

C C

(D) 1 1 2 2

1 2

C V C V

C C

3. The resistance of a series combination of two resistances is S . When they are joined in parallel,

the resistance is P . The ratio S

P has a minimum value

(A) 2 (B) 1

(C) 4 (D) none of above, since there is no minimum.

Space for Rough Work

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4. An electric dipole is placed on the axis of a uniformly charged circular ring with its axis perpendicular to the axis of the ring. The torque on the dipole as a function of the distance from the centre of the ring looks like

(A)

O r

(B)

O r

(C)

O r

(D)

O r

. 5. The capacitor in the circuit is uncharged and the internal resistance

of the cell is negligible. The current (i) through the cell in the beginning is

(A) 11 A (B) 5A (C) infinite (D) none of the above.

P Q

A

B

2 4

2 F

3 6

18V

i

6. The charge on the capacitor shown in the figure reaches 63% of its

steady state value in (assume that it is initially uncharged)

(A) 50 s (B) 55 s

(C) 70 s (D) 32 s.

5 F

3

4 2

8

10 V


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7. In the circuit shown in the figure, the resistance R is

(A) zero (B) 5

(C) 2.5 (D) 7

3

2R

2A+

–F,C

8. The current through the 9 V battery is equal to

(A) 1A (B) 3A

(C) 2.5A (D) 5A.

5

4

2

3

9 V

6

CA

B

D

9. Null points were obtained at 160 cm and 180 cm on a potentiometer with a cell connected with a

resistance in parallel, in one case the resistance is 9 while in the other it is 4. The internal

resistance of the cell is

(A) 1 (B) 5

(C) 13 (D) none of these.


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10. Twelve identical wires each having a resistance R form a cube as

shown in the figure. An additional resistance R, is connected

between D and G. The resistance between A and C is (A)5 R/6

(B) 4 R/3

(C)2 R/3

(D)3 R/4

C

F

GH

A

D

B

E

11. A galvanometer of resistance 50 has a range of 10 mA. The resistance required to the be added

in parallel so that the range is increased to 100 mA is

(A)5 (B) 450

(C)500 (D)50

9

12. A point charge q is placed at a distance 2

a directly above the centre of a horizontal square of side

a while a second negative point charge, –q is placed at a distance a below one of its (the square’s)

corners. The electrostatic flux through the square is

(A)0

q

6 (B)

0

q

8

(C)0

q

24 (D)

0

5q

24.


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13. The inner and outer surfaces of a spherical shell are maintained at potentials of V1 and V2,

respectively. The radii of the surfaces are R1 and R2 while the material of the shell has resistivity

. The current density near the outer surface, radially outward, is (assume V1 > V2 > 0)

(A) 2

2

V

R (B) 1 2

2

V V

R

(C) 1 2

2 1

V V

(R R )

(D) 1 2 1

2 1 2

V V R

(R R ) R

.

14. The magnetic field existing in a region is given by B = B0 k̂

x1

A square loop of edge and carrying current i, is placed with its edges parallel to the x-y axis.

Find the magnitude of the net magnetic force experienced by the loop.

(A) 2B0i (B) B0i0 /2 (C) B0i (D) Bi /3

15. A conductor of length and mass m is placed along the east-west line on a table. Suddenly a

certain amount of charge is passed through it and it is found to jump to a height h. The earth's

magnetic induction is B. The charge passed through the conductor is – (B is horizontal)

(A)Bmgh

1 (B)

mB

gh2

(C)

mB

gh

(D)

B

gh2m

16. Two long parallel wires are at a distance 2d apart. They carry steady equal currents flowing out of the

plane of the paper, as shown. The variation of the magnetic field B along the XX ' the given by-

(A)

B

X' X

d d

(B)

B

X' X

d d

(C)

B

X' X

d d

(D)

B

X' X

d d


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17. A current carrying square loop is placed near an infinitely long current carrying wire as shown in

figure. The torque acting on the loop is

(a)

22

210 aii

(b)

2

210 aii

(c) )2ln(2

210

aii (d) Zero

18. The sensitivity of a galvanometer of resistance 8722 is decreased by 90 times. The shunt used is

(A) 88 (B) 90 (C) 94 (D) 98 . 19. A magnet suspended vertically makes 5 oscillations per minute due to horizontal component of

earth’s magnetic field (H=0.3 gauss). By what amount should the horizontal component of field be increased so that the magnet may make 10 oscillations per minute?

(A) 0.3 gauss (B) 0.6 gauss (C) 0.9 gauss (D) 1.2 gauss 20. Hysteresis curve for two materials are shown as below : Choose the correct option

(A) ‘A’ is suitable for making permanent magnet (B) ‘B’ is suitable for making permanent magnet (C) Both ‘A’ & ‘B’ are suitable for making permanent magnet (D) Neither is suitable as both are paramagnetic material


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21.. Charges +q and – q are kept just outside dielectric, of dielectric constant k. Magnitude of force on 2 due to 1 will be

(A) 2

2

0

q

4 kd (B)

2

2

0

kq

4 d

(C) 2

2

0

q

4 d (D) None of these

22. A spherical conductor is given a charge q and a rod with linear charge density is place near the

spherical conductor as shown in the figure. The mid point of the rod is at a distance r from center of sphere. the electric potential energy of system is [Ignore self electric potential energy]

(A) kqL

r

(B) 2r L

kq n2r L

(C) 2

2

kqL

ry

(D) None of these

23. Charge + q is uniformly distributed on a wire of length . charge – q is placed at a distance d from it as shown. Find the dipole moment of the system.

(A) qd,along CO (B) qd,along OC

(C) 2

2

0

q

4 d (D) q ,along OC

2


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24. The diagram shows three infinitely long uniform line charges

2, 3 and placed on the X, Y and Z axis respectively. The work done in moving a unit positive charge from (1, 1, 1) to (0, 1,1) is equal to

(A) 0

n2

2

(B)

0

n2

(C) 0

3 n2

2

(D) none

Y

X

Z

(0, 0, 0)

3

25. A cylindrical conductor of length and inner radius

R1 and outer radius R2 has specific resistance . A

cell of emf is connected across the two lateral faces of the conductor. Find the current drown from the cell.

(A) I =

1

2

R

Rln

2 l (B) I =

2

1ln

2

R

R

l

(C) I = 2

1

2ln

2

R

R

l

(D) I =

1

2ln

2

R

R

R2

R1

26. Consider the circuit in the adjacent figure. What will be potential difference between A and B in

steady state? (All resistance = R)

(a)

(b) 2/

(c) 3/ (d) zero


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27. The temperature coefficient of resistance of a conductor varies as . If is

resistance at T =0 and R be the resistance at T then

(A) R= (6T +2) (B) R= (2T +3)

(C) R = (1+ + ) (D) R = (1-T+ + )

28. A uniform charge density is given to a non conducting uniform thin circular disc. Of radius r.

No other data is available. Potential at a point on the circumference of the disc is

(A) 0

r

2

(B)

0

2 r

(C) 0

r

(D)

0

2 r

29. A particle of mass m and charge +q approaches from a very large distance

towards a uniformly charged ring of radius R and charge, mass same as that

of particle, with initial velocity v0 along the axis of the ring as shown in the

figure. What is the closest distance of approach between the ring and the

particle? Assume the space to be gravity free and frictionless.

(A) 4

2

2 2 2 4

0 0

qR

m v

(B)

42

2 2 2 4

0 0

3qR

2 m v

(C) 2 4

20

2 4 2

0

m vR

2 q

(D)

42

2 2 2 4

0 0

qR

4 m v

30. In a meter bridge, the null point is found at a distance of 40 cm from A. If

now a resistance of 12 is connected in parallel with S, the null point

occurs at 60 cm from A. Determine the value of R.

(A) 15 (B) 12

(C) 10 (D) 5

Smooth

Ring

+q

Meter Scale

G

B

R S

100–

E k

A C


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Section 2 CHEMISTRY

1. An organic compound, C3H6O does not give a precipitate with 2, 4-dinitrophenylhydrazine

reagent and does not react with metallic sodium. It could be

(a) CH3 – CH2 – CHO (b) CH2 = CH – CH2OH (c) CH3 – CO – CH3 (d) CH2 = CH – O – CH3

22. CH3 CH2 Cl

CH3

OH Ag+ (aq.)

?

The major product formed is

CH3 C CH2 CH3

O

(a)

CH3 C CH2 OH

OH

CH3

(b)

CH3 C

CH3

H O

(c)

CH3 C CH2

CH3

HO

CH3(d)

3. Which products of the following reactions give iodoform test ?

(a) Ph – C CH 2

2

/?

H O H

Hg

(b) 4

||/

3 2

OPd BaSOCH C Cl H

(i) CH3MgBr

(c)CN

(ii) H3O+ ?

(d) All of them

2.


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4. In the given reaction:

C CH2CH3 CH2 CH2 CH2 Cl

OCH3MgBr

(P)

(P) will be :

(a)O

CH3

CH3

(b)

O

CH3

CH3

(c) CH3 C

MgBr

CH3

CH2 CH2 CH2 CH2Cl

(d) CH3 C

OH

CH3

CH2 CH2 CH2 CH2 Cl

5. Which of the following is not a resonating form of benzaldehyde ?

C OH

(a)

C O+

H

(b)

C OH

(c)+

C OH

(d)

+

6. How will you convert butan-2-one to propanoic acid ?

(a) Tollen’s reagent (b) Fehling solution

(c) (i)NaOH/I2 (ii) H+ (d) (i)NaOH/HI (ii) H+


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27.CH3

OC2H5

O

O

(A)

(B)

NaBH4

LiAlH4

A & B are respectively

(a)

CH3

OC2H5

O

OH

and CH3

OH

OH

+ C2H5OH

(b)

CH3

OH

OH

CH3

OC2H5

O

OH

and

(c)

CH3

OC2H5

OH

OH

andCH3

OC2H5

O

OH

(d) None

8. Ph – C C – CH3 2+ +Hg /HA, A is:

(a) Ph

CH3

O

(b)

Ph

CH3

O

(c)Ph

CH3

OH

(d)Ph

CH3

OH

7.


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9

When m-chloro benzaldehyde is treated with 50% KOH solution; the product(s) obtained is (are)

(a)

OH

COO

+

OH

CH2OH

(b)

Cl

COO

+

Cl

CH2OH

(c)

Cl

CH CH

OH OH

OH

(d)

OH

CH CH

OH OH

OH

30.

MgBr

(i) CO2

(ii) H3

+OP

In the above reaction, product P is

CHO

(a)

COOH

(b)

(c)

OH

(d) C6H5CC6H5

O

11. Which of the following statement is correct about Bakelite ?

(a) It is condensation Polymer (b) It is synthetic polymer

(c) It is thermosetting polymer (d) All of above are correct

12. Which of the following functional group will NOT be found in products ?

2

2

( ) ( )

3 2 3 ( )?

i AlH i Bu

ii H OCH CH CH CH COOCH

(a) Alcohol (b) Alkene (c) Aldehyde (d) Carboxylic acid

13. 0.2 percent solution of phenol is ?

(a) Antiseptic (b) Detergent (c) disinfectant (d) Antibiotic

10.


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14. Catalyst used in formation of High density polythene is ?

(a) TiCl4 + Al(OEt)3 (b) TiCl4 + Al(Et)3 (c) SnCl4 + Al(OEt)3 (d) SnCl4 + Al(Et)3

15. Which of the following is/are the correct representation of β -D-Fructose

(B)(A)

O

OH

OHOH

H

H

OHOH

OH

O

OH

OHOH

H

H

OHH

OH

(D)(C)

O

OH

OHOH

H

H

OHOH

OH

O

H

OHH

H

H

OHOH

OH

16. Which of the following pairs of structures represents final Product ?

3 32

2 3

/ ( )( ) /

3 ( ) ( )( ) ( ) ( ) Pr

H O heat i CH MgBri Cl red P PCC

ii H O ii H OCH CN X Y Z oduct

(a) OH C H

COOH

CH3

and H C OH

CH3

COOH

(b) CH3 C OH

H

COOH

and HO C CH3

COOH

H

(c) H C CH3

COOH

OH

and CH3 C H

OH

COOH

(d) HOOC C OH

CH3

H

and HOOC C H

OH

CH3

17. What is (Z), the final product of the reaction 2 /.

2 5 ( ) ( ) ( )H NiPCC aq NaOHC H OH X Y Z

(a) diethyl ether (b) Ethanal (c) Butane (d) butan-1-ol


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18. On heating glycerol with excess amount to HI, the product formed is– (a) Allyl iodide (b) Isopropyl iodide (c) Propylene (d) 1,2,3–tri–iodopropane

19. When ethyl bromide is treated with moist Ag2O, main product is: (a) Ethyl ether (b) Ethanol (c) Ethoxy ethane (d) All of the above

20. HC CH 2HCl P (Major product) What is Major Product ?

(a) CH3 – CHCl2 (b) Cl CH2 – CH2 – Cl

(c) CH2 = CH – Cl (d) CH3 – CH2 – Cl

21. Which of the following does not give canizarro reaction :

CHO(a)

CH2CHO(b)

CHOCH3(c)

CHOO2N(d)

22. The product(s) obtained via oxymercuration (HgSO4 + H2SO4) of 1-butyne would be

(a) CH3CH2COCH3 (b) CH3CH2CH2CHO (c) CH3CH2CHO + HCHO (d) CH3CH2COOH + HCOOH


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23. In the Cannizaro’s reacting given below:

2Ph – CHO OH Ph - CH2OH + PhCO2

The slowest step is:

(a) the attack of OH at the carbonyl group

(b) the transfer of hydride to the carbonyl group

(c) the abstraction of proton from the carboxylic acid

(d) the deprotonation of Ph-CH2OH

24. Which of the following will react with water to form stable hydrate

(a) HCOOH (b) Cl3C.CHO (c) CCl4 (d) CH3CHO

25. Compound A (molecular formula C3H8O) is treated with acidified potassium dichromate to form

a product B (molecular formula C3H6O). B forms a shining silver mirror on warming with

ammonical silver nitrate. B when treated with an aqueous solution of H2NCONHNH2 and

sodium acetate gives a product C. Identify the structure of C:

(a) CH3CH2CH = N.NHCONH2 (b)

3

3 2|

CH

CH C N.NHCONH

(c)

3

3 2|

CH

CH C N.CONHNH (d) CH3CH2CH = N.CONHNH2

26. Which of the following is inert towards SN-1 reaction ?

(a) Ethyl chloride (b) Isopropyl chloride

(c)

Cl (d)

Cl


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27.

dil KMnO4A B

(CH3 COO)4 PbThe product

(a)

O

O

(b) CH2 COOH

CH2 COOH

(c) OH

OH

(d) OH

OH

C N

+Ether

AH3O

+

B.

MgBr

31.

C

O

(a)

C

N- MgBr

(b)

C

N - H

(c)

C

N- OH

(d)

29. Below conversion can be achieved by :

C

O

CH3

CH2 CH2 NMe3

CH2 CH3

CH2 CH2 NMe3

++

(a) Wolff-Kishner reduction (b) Clemmensen reduction (c) LiAlH4 (d) NaBH4

28.

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NH2

CH3OH

NaNO2 + HCl

?33.

The product formed is

(a)

O

CH3OH

(b)

OCH3

(c)

COOH

CH2NH2

(d)

CH3 OH

O

30.


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Section 3 MATHEMATICS

1.

2 4 5

7 6 50

sin tan 1 cos 2lim

7 tan sin 2sinx

x x x x

x x x

isequal to

(A) 0 (B) 1 (C) 1/2 (D) 2

2. Let f(x)= 32 6x where is G.I.F.Then number of point in (1,2) where f is

Discontinuous is

(A)5 (B) 7 (C) 13 (D) 12

3. Let f(x)= 5 2

4 3 2

2 8 11( )

4 8 8 4

x xf x

x x x x

then A= : , , ,x f iscontinuous at x is equal to

(A) R (B) 0R (C) 1R (D) 1, 2R

4. If g(x) be the inverse function of f(x) & '

5

1( )

1f x

x

then

2

2( )

dg x

dx is

(A)

5

1

1 g x (B)

4 5

5 1g x g x

(C)

'

5

1

g x

g x (D)

4'

5

5

1

g x

g x

5. Let y be the implicit function of x defined by 2 2 cot 1 0x xx x y then ' 1y equal to

(A) log2 (B) –log2 (C) -1 (D) 1

6. The value of k for which equation 3 12 0x x k has distinct roots in 0,2 is

(A) 4 (B) 2 (C) -2 (D) NONE

7. An equation of tangent line at point of inflection of 4 3 2( ) 6 12 8 3f x x x x x is

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


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8. The shortest distance of the line y-x=1 from 2x y is

(A) 3/8 (B) 3 2

4 (C) 3 /4 (D)

3 2

8

9. Extremum value of the 3 3

1 1sin cosf x x x ,-1<x<1 is

(A) 37

8

(B)

3

8

(C)

3

32

(D)

3

16

10. Minimum value of ( ) 3 2 5f x x x x is

(A) 0 (B) 7 (C) 8 (D) 10

11. Let T=

log2 3 2

3 2

0

2 1

1

x x

x x x

e edx

e e e

then Te is

(A) 7/4 (B) 7/2 (C) 11/2 (D) 11/4

12. The value of /2

0

sin 5

sin

xdx

x

is equal to

(A) 0 (B) 2

(C) (D) 2

13. The value of

1

3 61 1 1

dx

x x equal to

(A) 2 (B) 1 (C) 1 /2 (D) 2

14. The value of definite integral /2

10

0

cos sin12x xdx

equal to

(A) 1/ 10 (B) 1 /11 (C) 1/ 12 (D) 1/ 22

15. If

/3 2

2

/6

3tan 6 tan 11

1 tan 6

x x kdx

x

then k is equal to

(A) 10 (B) 12 (C) 14 (D) 16


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16. The value of

1 2 2 3 3 3 4 4 4

25 5 5

1 2 ... 1 2 ... 1 2 ..lim

1 2 ..n

n n n

n

is

(A) 4/5 (B) 3/ 5 (C) 2 /5 (D) 1 /5

17. The value of definite integral 1

1

log 1 2 3 6x x x xx dx

(A) log 2 log3

2

(B)

log 2 log3

3

(C) log2 log3 (D)

log 2 log3

4

18. If 3( ) 3 4f x x x then value of 1 4

1

1 0

f x dx f x dx

equal to

(A) 4 (B) 17 /4 (C) 21 /4 (D) 23 /4

19.

4 3 21

23 2

0

3 4 3

4 3 2 1

x x x dx

x x x

equal to

(A) 1/ 100 (B) 1/ 10 (C) 1 /20 (D) 0

20. sin .cos .cos2 .cos4 .cos8 .cos16x x x x x xdx equal to

(A) sin16

1024

xc (B)

cos32

1024

xc

(C)

cos32

1096

xc (D)

cos32

1096

xc

21.

3/2

2

2 1

4 1

x dx

x x

=

(A)

3

3/22 4 1

xc

x x

(B)

1/2

2 4 1

xc

x x

(C)

2

1/22 4 1

xc

x x

(D)

1/2

2

1

4 1c

x x


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22.

2 3 1

1 2 3 1

x dxC

x x x x f x

where f(x) is of the form 2ax bx c then

value of (a+b+c) is equal to

(A) 4 (B) 5 (C) 6 (D) none

23. 2

sin

cos cos 2

xdx

x x

(A) 21 tanc x (B)

21 tanc x (C) 21 cosc x (D)

21 sinc x

24. 49sin51 (sin )x x dx =

(A) 50sin 50 (sin )

50

x xc (B)

50cos50 (sin )

50

x xc

(C) 50cos50 (cos )

50

x xc (D)

51sin 50 (sin )

51

x xc

25. Range of 3 2( ) sin 6sin 11sin 6f x x x x has

(A) 24,2 (B) 24,0 (C) 0,24 (D) none

26.

3

sin6

( )

x x

f xx

then period of f(x) is

(A) not defined (B) f(x) is not periodic (C) 2 (D) 1

27.

2 2

1 1

5 6 60 77 160

sin cos10 10

( )x xC C

x x x x

x x

f x

where , denotes G.I.F. fractional part

then domain of f(x) is

(A) : ,0 10x x I x (B) 0,1,2,3,4,9

(C) 0,1,2,3,4,9,10 (D) 0,1,2,3,9,10


JEE MAINS



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28.

5 3( 5 4 )sin

120( )

x x x

f xx

then range of f(x) is

(A) 0 (B) I (C) Q (D) R

29. If g is the inverse function of f and f(x) = sinx, then g(x) is equal to

(A) sin(g(x)) (B) cosec(g(x))

(C) tan(g(x)) (D) none of these.

30. Let f(x) be a real valued bijective function such that 2f (x) sin {sin(x 1)} and f(0) =3 .

The value of 1f (3) will be

(A)2

1

cos (cos4)

(B)2 cos (sin 4) sin4

(C)2

1

sin (sin1) (D)

2

1

cos (sin1)


JEE MAINS



25

ANSWERS IIT MAINS

SET - A

SR. NO

PHYSICS CHEMISTRY MATHS

1. B D C

2. D A C

3. C D A

4. C B B

5. A B C

6. A C D

7. B C D

8. C A D

9. A B C

10. D B B

11. D D D

12. D D B

13. D A B

14. C B B

15. D B D

16. B B B

17. D D B

18. D B D

19. C B B

20. B A B

21. C B B

22. B A B

23. A B A

24. B B A

25. A A B

26. D C D

27. C A D

28. C A A

29. A B B

30. C B C

FIITJEE JEE (Mains)JEE MAINS FIITJEE Ltd., 142, New Civic Centre, Bhilai (C.G.) 490006 Ph:...

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