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Vidyamandir Classes

VMC/JEE Advanced 1 2014

JEE Advanced 2014 Paper 1 | Code 7

25 May, 2014 | 9:00 AM – 12 Noon

Answer key and solutions by Vidyamandir Classes

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PART-A PHYSICS

1. A light source, which emits two wavelengths 1 400= nmλ and 2 600= nm,λ is used in a Young’s

double slit experiment. If recorded fringe widths for 1λ and 2λ are 1β and 2β and the number of

fringes for them within a distance y on one side of the central maximum are m1 and m2, respectively,

then :

(A) 2 1>β β

(B) 1 2>m m

(C) From the central maximum, 3rd

maximum of 2λ overlaps with 5th minimum of 1λ

(D) The angular separation of fringes for 1λ is greater than 2λ

Answer

(ABC)

D y, m ,

d d

λ λβ = = θ =

β

As 1 2λ < λ option

⇒ 1 2β < β ⇒ option A is correct

⇒ 1 2m m> ⇒ option B is correct

⇒ 1 2θ < θ

Moreover, 3rd

max. of 22

3D

d

λλ =

5th

min. of 11

9

2

D

d

λλ =

and 2 13 9

2

D D

d d

λ λ= ⇒ option C is correct

2. A parallel plate capacitor has a dielectric slab of dielectric constant K between its plates that covers

1/3 of the area of its plates, as shown in the figure. The total capacitance of the capacitor is C while that

of the portion with dielectric in between is C1. When the capacitor is charged, the plate area covered by

the dielectric gets charge Q1 and the rest of the area gets charge Q2. The electric field in the dielectric is

E1 and that in the other portion is E2. Choose the correct option/options, ignoring edge effects.

(A) 1

2

1=E

E (B)

1

2

1=

E

E K

(C) 1

2

3=

Q

Q K (D)

1

2 +=

C K

C K

Answer

(AD)

1 2 1 2 1 2V V E d E d E E= ⇒ = ⇒ =

1 2

0 0 03 2 3

Q QQE

K A K A / A /= ⇒ =

∈ ∈ ∈

⇒ 1

2 2

Q K

Q=

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01

3

K AC

d

∈=

0 01 2

2

3 3

K A . AC C C

d d

∈ ∈= + = +

= ( ) 023

AK

d

∈+

⇒ 1

2C K

C K

+=

3. At time t = 0, terminal A in the circuit shown in the figure is connected to B by a key and an alternating

current I(t) = I0 cos ( ( )tω , with I0 = 1A and 1500 −= rad sω starts flowing in it with the initial

direction shown in the figure. 7

6=At t ,

π

ω the key is switched from B to D. Now onwards only A and D

are connected. A total charge Q flows from the battery to charge the capacitor fully. If

20=C F ,µ 10= ΩR and the battery is ideal with emf of 50 V, identify the correct statement(s).

(A) Magnitude of the maximum charge on the capacitor before 7

6=t

π

ω is 31 10−× C.

(B) The current in the left part of the circuit just before 7

6=t

π

ω is clockwise.

(C) Immediately after A is connected to D, the current in R is 10A.

(D) 32 10−= ×Q C.

Answer

(CD)

( )0 02

c c ci I cos t V I X cos tπ = ω ⇒ = ω −

( )0C

IV sin t

C= ω

ω

( ) ( )0 1

500

Iq CV sin t sin t= = ω = ω

ω

= ( )32 10 sin t−× ω

Max. charge = 32 10−×

00

37 7

6 6 2

Ii t I cos

π π = = ω × = − ω ω

Hence it is anticlockwise.

Just after connecting to D.

3 37

2 10 106

q sin− −π = × = −

.

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( )50 10 0q

ic

− − =

10i A=

Final charge = 31 10 C−×

( )3 3 31 10 1 10 2 10Q

− − −= × − − × = ×

4. Let E1 (r), E2(r) and E3 (r) be the respective electric field at a distance r from a point charge Q, an

infinitely long wire with constant linear charge density λ , and an infinite plane with uniform surface

charge density .σ If ( ) ( ) ( )1 0 2 0 3 0E r E r E r= = at a given distance r0, then :

(A) 204=Q rσπ (B) 0

2=r

λ

πσ

(C) ( ) ( )1 0 2 02 2 2=E r / E r / (D) ( ) ( )2 0 3 02 4 2=E r / E r /

Answer

(C)

1 204

QE

r=

π∈

202

Er

λ=

π∈

302

Eσ

=∈

At r = r0

1 2 020 00 0

224

QE E Q r

rr

λ= ⇒ = ⇒ = λ

π∈π∈ …(i)

2 3 00 0 0

22 2

E E rr

λ σ= ⇒ = ⇒ λ = π σ

π∈ ∈ …(ii)

From (i) and (ii) ⇒ 202Q r= σπ

01 2 2

0 0 0 0

4

2 4

r Q QE

r r

= =

π∈ π∈

02

0 0 0 0

2

2 2

rE

r r

λ λ = = π∈ π∈

03

02 2

rE

σ = ∈

⇒ 0 01 22

2 2

r rE E

=

0 01 34

2 2

r rE E

=

0 02 32

2 2

r rE E

=

5. A student is performing an experiment using a resonance column and a tuning fork of frequency

1244 s− . He is told that the air in the tube has been replaced by another gas (assume that the column

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remains filled with the gas). If the minimum height at which resonance occurs is ( )0 350 0 005. . m,± the

gas in the tube is :

(Useful information : 1 2 1 2 1 2 1 2167 640 140 590/ / / /RT J mole ; RT J mole .− −= = The molar masses

M in grams are given in the options. Take the value of 10

Mfor each gas given there.)

(A) None 10 7

2020 10

M ,

= =

(B) Nitrogen10 3

2828 5

M ,

= =

(C) Oxygen 10 9

3232 16

M ,

= =

(D) Argon 10 17

3636 32

M ,

= =

Answer

(D)

1244f s−=

0 35 0 005min . .= ±ℓ

0 35 0 0054

. .λ

= ±

Using C f= λ

1000

244 0 35 4RT

.M

γ ×= × ×

For Monoatomic, 5

1 673

.γ = =

5 1000 10 10

167 6403

RTRT

M M M

×= × =

⇒ 10 244 0 35 4

0 533640

..

M

× ×= =

For diatomic, 7

1 45

.γ = =

7 1000 10 10

140 5905

RTRT

M M M

×= × =

⇒ 10 24 0 35 4

0 578590

..

M

× ×= =

6. One end of a taut string of length 3m along the x axis is fixed at x = 0. The Speed of the waves in the

string is 1100ms− . The other end of the string is vibrating in the y direction so that stationary waves are

set up in the string. The possible waveform(s) of these stationary waves is(are) :

(A) ( ) 50

6 3

x ty t Asin cos

π π= (B) ( ) 100

3 3

x ty t Asin cos

π π=

(C) ( ) 5 250

6 3

x ty t Asin cos

π π= (D) ( ) 5

2502

xy t Asin cos t

ππ=

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Answer

(ACD)

Equation of stationary wave will be.

y Asin kx cos t= ω

Possible values of λ are given by

32 4

nλ λ

+ = (n = 0, 1, 2,……)

( )2 1 34

nλ

+ =

⇒ ( ) ( )2 2 1 2 112 2

2 1 12 6

n n, K

n

π + π +πλ = = = =

+ λ

3 5 7

6 6 6 6K , , ,

π π π π= , ……..

7. A transparent thin film of uniform thickness and refractive index

1 1 4n .= is coated on the convex spherical surface of radius R at

one end of a long solid glass cylinder of refractive index

2 1 5n . ,= as shown in the figure. Rays of light parallel to the axis

of the cylinder traversing through the film from air to glass get

focused at distance 1f from the film, while rays of light

traversing from glass to air get focused at distance 2f from the

film. Then :

(A) 1 3f R= (B) 1 2 8f . R= (C) 2 2f R= (D) 2 1 4f . R=

Answer

(AC)

Refraction from the thin film will not matter hence

For air to glass

1

1 5 1 1 5 1. .

f R

−− =

∞

⇒ 1 3f R=

For glass to air

2

1 1 5 1 1 5. .

f R

−− =

∞ −

⇒ 2 2f R=

8. Heater of an electric kettle is made of a wire of length L and diameter d. It takes 4 minutes to raise the

temperature of 0.5 kg water by 40 K. This heater is replaced by a new heater having two wires of the

same material, each of length L and diameter 2d. The way these wires are connected is given in the

options. How much time in minutes will it take to raise the temperature of the same amount of water by

40 K?

(A) 4 if wires are in parallel (B) 2 if wires are in series

(C) 1 if wires are in series (D) 0.5 if wires are in parallel

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Answer

(BD)

0 2R

d

ρ

π=ℓ

( )2

0

4V

H minR

= ×

For the new wire

( )0

2 42

RR'

d= =

ℓρ

π

For series 0

2

RR =

( )2

0 2s

VH t

R /=

⇒ 2st min=

For parallel

0

8

RR =

( )2

0 8p

VH t

R /=

⇒ 0 5pt . min=

9. Two ideal batteries of emf V1 and V2 and three resistances R1, R2 and R3

are connected as shown in the figure. The current in resistance R2 would

be zero if :

(A) 1 2V V= and 1 2 3R R R= =

(B) 1 2V V= and 1 2 32R R R= =

(C) 1 22V V= and 1 2 32 2R R R= =

(D) 1 22V V= and 1 2 32R R R= =

Answer

(ABD)

If 2

0Ri =

⇒ VA = VB

⇒ 1 1 0V iR− = &

⇒ 1 2

1 3

V V

R V=

A, B, D satisfy the above criteria.

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10. In the figure, a ladder of mass m is shown leaning against a wall.

It is in static equilibrium making an angle θ with the horizontal

floor. The coefficient of friction between the wall and the ladder

is 1µ and that between the floor and the ladder is 2µ .

The normal reaction of the wall on the ladder is N1 and that of

the floor is N2. If the ladder is about to slip, then :

(A) 1 20 0µ µ= ≠ and 22

mgN tanθ = (B) 1 20 0µ µ≠ = and 1

2

mgN tanθ =

(C) 1 20 0µ µ≠ ≠ and 2

1 21

mgN

µ µ=

+ (D) 1 20 0µ µ= ≠ and 1

2

mgN tanθ =

Answer

(CD)

1 20 0,µ = µ ≠

( )1 0AN sin mg cos× θ = × θ τ =ℓ

12

mgN

tan=

θ

2N mg=

1 20 0,µ ≠ µ =

⇒ The rod can’t stay in equilibrium

1 20 0,µ ≠ µ ≠

[ ]2 2 2 02

BN cos N sin mg . cos× θ = µ θ + θ τ =ℓ

ℓ ℓ

[ ]2 22

N cos sin mg . cosθ − µ θ = θℓ

ℓ ℓ …(i)

2 1 1N N mg+ µ = …(ii)

1 2 2N N= µ …(iii)

From (ii) and (iii), 21 21

mgN =

+ µ µ

11. A rocket is moving in a gravity free space with a constant acceleration of 22ms− along + x direction

(see figure). The length of a chamber inside the rocket is 4m. A ball is thrown from the left end of the

chamber in + x direction with a speed of 10 3. ms− relative to the rocket. At the same time, another ball

is thrown in x− direction with a speed of 10 2. ms− from its right end relative to the rocket. The time in

seconds when the two balls hit each other is ___________.

A

B N1

N2

mg

θ

1µ

1 1 1f N=µ

2 2 2f N=µ2µ

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Answer

(2)

12. A galvanometer gives full scale deflection with 0.006 A current. By connecting it to a 4990Ω

resistance, it can be converted into a voltmeter of range 0 30V− . If connected to a 2

249

nΩ resistance,

it becomes an ammeter of range 0 1 5. A− . The value of n is __________.

Answer

(5)

Ig = 0.006A

For voltmeter conversion.

( )g g sV I R R= +

( )30 0 006 4990g. r= + …(i)

For ammeter conversion:

( )g g g sI R I I R= −

( )0 006 1 5 0 006g s. R . . R'= − …(ii)

From (i) and (ii)

10

5249

sR' n= ⇒ =

13. A horizontal circular platform of radius 0.5 m and mass 0.45 kg is free to rotate about its axis.

Two massless spring toy-guns, each carrying a steel ball of mass 0.05 kg are attached to the platform at

a distance 0.25 m from the centre on its either sides along its diameter (see figure). Each gun

simultaneously fires the balls horizontally and perpendicular to the diameter in opposite directions.

After leaving the platform, the balls have horizontal speed of 19 ms− with respect to the ground.

The rotational speed of the platform in 1rad s−

after the balls leave the platform is:

G I Ig

gI I−

R's

Ig Rs G

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Answer

(4)

From conservation of angular momentum.

( )( )( ) ( ) ( )20 5

0 05 9 0 25 2 0 452

.. . .× = ω

⇒ 4 rad / sω =

14. Consider an elliptically shaped rail PQ in the vertical plane with OP = 3

m and OQ = 4 m. A block of mass 1 kg is pulled along the rail from P to

Q with a force of 18 N, which is always parallel to line PQ (see the

figure given). Assuming no frictional losses, the kinetic energy of the

block when it reaches Q is (n × 10) Joules. The value of n is ______.

(Take acceleration due to gravity = 210 ms− ).

Answer

(5)

FdW F . dr=

= ( ) ( )ˆ ˆ ˆ ˆF cos i F sin j · dx i dy j− θ + θ +

3 4

5 5F

F FdW dx dy= − +∫ ∫ ∫ .

( ) ( )3 43 4

5 5F

F FW = − − + +

= 25 25 18

905 5

FJ

×= =

From energy conservation.

1 10 4 40FW U K K K= ∆ + ∆ = × × + ∆ = + ∆

⇒ 50 5K J n∆ = ⇒ =

15. A uniform circular disc of mass 1.5 kg and radius 0.5 m is initially at rest

on a horizontal frictionless surface. Three forces of equal magnitude

F = 0.5 N are applied simultaneously along the three sides of an

equilateral triangle XYZ with its vertices on the perimeter of the disc

(see figure). One second after applying the forces, the angular speed of

the disc in 1rad s− is _________.

Answer

(2)

( )3 3 30Fr F R sinτ = =

Iτ = α

( )

2 2

3 30 3 0 5 0 5 0 5 2

2 1 5 0 5

F R sin . . .

I mR / . .

τ × × × ×α = = =

×

= 2 rad/s2

2 1 2t rad / sω = α = × =

P

Q

4m

3m

90

O

O

F

F

F

X

Y

Z

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16. Two parallel wires in the plane of the paper are distance X0 apart. A point charge is moving with speed

u between the wires in the same plane at a distance X1 from one of the wires. When the wires carry

current of magnitude I in the same direction, the radius of curvature of the path of the point charge is

R1. In contrast, if the currents I in the two wires have directions opposite to each other, the radius of

curvature of the path is R2. If 0

1

3x

x= , the value of 1

2

R

R is _______.

Answer

(3)

muR

qB=

If the current is in same direction

( )

0 01

1 0 12 2

I IB

x x x

µ µ= −

π π −

If the current is in opposite direction.

( )

0 02

1 0 12 2

I IB

x x x

µ µ= −

π π −

Give x0 = 3x1

⇒ B2 = 3B1

1 2

2 1

13

R BR

B R B∝ ⇒ = =

17. To find the distance d over which a signal can be seen clearly in foggy conditions, a railways engineer

uses dimensional analysis and assumes that the distance depends on the mass density ρ of the fog,

intensity (power/area) S of the light from the signal and its frequently f. The engineer finds that d is

proportional to 1 / nS . The value of n is __________.

Answer

(3)

Let a b cd s f= ρ

( ) ( ) ( ) ( )3 3 1a b C

L ML MT T− − −=

( ) ( ) ( ) ( )3 3a b a b cL M L T

+ − − −=

Equating Power.

3 1 1 3a a /− = ⇒ = −

0 1 3a b b a /+ = ⇒ = − =

⇒ 1 3 3/d s n∝ ⇒ =

18. Airplanes A and B are flying with constant velocity in

the same vertical plane at angles 300 and 60

0 with

respect to the horizontal respectively as shown in figure.

The speed of A is ms .−1100 3 At time t = 0s, an

observer in A finds B at a distance of 500 m.

This observer sees B moving with a constant velocity

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perpendicular to the line of motion of A. If at t = t0 ,

A just escapes being hit by B, t0 in seconds is _______.

Answer

(5)

BA B AV V V= −

At t = 0, AB = 500 m

If at t = t0 A just escapes being hit by B & is toBA AV V⊥

30B AV co s V=

⇒ 200BV m / s=

⇒ 500

530B

t s.V sin

= =

19. A thermodynamic system is taken from an initial state i with internal energy 100iU J= to the final state f

along two different paths and ,iaf ibf as schematically shown in the figure. The work done by the system along

the paths , andaf ib bf are 200 50 100, andaf ib bfW J W J W J= = = respectively. The heat supplied to the

system along the path , and are , andiaf ib bfiaf ib bf Q Q Q respectively. If the internal energy of the system in

the state b is 200 500and ,b iafU J Q J= = the ratio /af ibQ Q is _____.

Answer

(2)

100 200i bU J U J= , =

100 50 100af ib bfW J W W J= , = , =

500iafQ J=

( )∆ 200 100 50 150ib ib ibQ U W J= + = − + =

∆bf bf bfQ U W= +

Now

∆ ∆ 500 20 300ibf iaf iaf iaf iaf afU U Q W Q W J= = − = − = − =

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∆ ∆ 300ib bfU U+ =

⇒ ( )200 100 ∆ 300 ∆ 200bf bfU U− + = ⇒ =

⇒ 200 100 300bfQ J= + =

⇒ 300 150 2bf ibQ / Q /= =

20. During Searle’s experiment, zero of the Vernier scale lies between 23 20 10−×. m and

23 25 10−×. m of the main

scale. The 20th

division of the Vernier scale exactly coincides with one of the main scale divisions. When an

additional load of 2 kg is applied to the wire, the zero of the Vernier scale still lies between 23 20 10−×. m and

23 25 10−×. m of the main scale but now the 45th

division of Vernier scale coincides with one of the main scale

divisions. The length of the thin metallic wire is 2 m and its cross-sectional area is 7 28 10 .m−× The least count of

the Vernier scale is 51.0 10 .m−× The maximum percentage error in the Young’s modules of the wire is _____.

Answer

(8)

yAx

ω=ℓ

(x = elongation)

y x

y x

∆ ∆=

2 1x x x= −

45 20x L .C L .C= × − ×

= 525 25 1 10L .C m−× = × ×

52 1 2 2 10| x | | x | | x | L .C m−∆ = ∆ + ∆ = × = ×

⇒ 100 100y x

y x

∆ ∆× = ×

= 5

5

2 10100 8

25 10%

−

−

×× =

×

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PART-B CHEMISTRY

21. An ideal gas in a thermally insulated vessel at internal pressure = P1, volume = V1 and absolute

temperature = T1 expands irreversibly against zero external pressure, as shown in the diagram.

The final internal pressure, volume and absolute temperature of the gas are 2 2 2P , V and T , respectively.

For this expansion,

(A) q = 0 (B) 2 1T T= (C) 2 2 1 1P V P V= (D) 2 2 1 1P V P Vγ γ=

Answer

(ABC)

q = 0 (∵ Vessel is thermally insulated)

extw P V 0= − ∆ =

U q ( w) 0∆ = − − = T 0⇒ ∆ = (Hence T2 = T1)

Now for ideal gas PV = nRT is always valid.

⇒ 1 1 2 2

1 1 2 2 2 11 2

P V P VP V P V ( T T )

T T= ⇒ = =∵

Note : 1 21 2P V P Vγ γ≠ (∵ the process has been carried out irreversibly)

22. Hydrogen bonding plays a central role in the following phenomena:

(A) Ice floats in water

(B) Higher Lewis basicity of primary amines than tertiary amines in aqueous solutions

(C) Formic acid is more acidic than acetic acid

(D) Dimerisation of acetic acid in benzene

Answer

(ABD)

23. Upon heating with 2Cu S , the reagent(s) that give copper metal is(are)

(A) CuFeS2 (B) CuO (C) Cu2O (D) 4CuSO

Answer

(BCD)

2 2 2Cu S Cu O Cu SO+ → +

2 2Cu S 2CuO 4Cu SO+ → +

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24. The correct combination of names for isomeric alcohols with molecular formula 4 10C H O is(are) :

(A) tert-butanol and 2-methylpropan-2-ol (B) tert-butanol and 1, 1-dimethylethan-1-ol

(C) n-butanol and butan-1-ol (D) Isobutyl alcohol and 2-methylpropan-1-ol

Answer

(A,C,D)

3

3

3

CH|

H C C OH|CH

− − 3 2 2 2H C CH CH CH OH− − − − 3 2

3

H C C CH OH|CH

− − −

Trivial name (tert butanol) n-butanol isobutyl alcohol

IUPAC name 2 methyl propan-2-ol Butan-1-ol 2-methyl propan-1-ol

∴Only correct combination is (A,C,D).

25. The reactivity of compound Z with different halogens under appropriate conditions is given below:

The observed pattern of electrophilic substitution can be explained by :

(A) The steric effect of the halogen

(B) The steric effect of the tert-butyl group

(C) The electronic effect of the phenolic group

(D) The electronic effect of the tert-butyl group

Answer

(ABC)

)

As the size of halogens decreases, poly-halogenation can take place.

Though t-Butyl also activates the ring via +I effect but it is the steric effect of t-Butyl group which is more

dominant and causes crowding at ortho positions. Hence, in the given molecule the directing property is

being controlled by the OH group which exerts +M effect (o-p directing effect)

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26. The pair(s) of reagents that yield paramagnetic species is(are) :

(A) Na and excess of 3NH (B) K and excess of 2O

(C) Cu and dilute 3HNO (D) 2O and 2-ethylanthraquinol

Answer

(ABC)

( ) ( ) ( ) ( ) ( ) ( ) ( )3 3 3x y

Paramagnetic (Blue solution)

Na s x y NH l Na NH am. e NH am.−+ + + → +

2 2Paramagnatic

K O KO+ →

( ) ( )3 3 2 ParamagneticCu HNO dil Cu NO NO+ → +

2 2 2(not Paramagnetic)

O 2 ethylanthraquinol H O+ − →

27. The correct statement(s) for orthoboric acid is(are) :

(A) It behaves as a weak acid in water due to self ionization

(B) Acidity of its aqueous solution increases upon addition of ethylene glycol

(C) It has a three dimensional structure due to hydrogen bonding

(D) It is a weak electrolyte in water

Answer

(BD)

28. In the reaction shown below, the major product(s) formed is(are) :

(A) (B)

(C) (D)

Answer

(A)

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Since lone pairs of amide is involved in conjugation

∴ There is very less possibility of the lone pairs taking part in the reaction as a nucleophile.

29. In a galvanic cell, the salt bridge :

(A) Does not participate chemically in the cell reaction.

(B) Stops the diffusion of ions from one electrode to another.

(C) is necessary for the occurrence of the cell reaction.

(D) Ensures mixing of the two electrolytic solutions.

Answer

(AB)

30. For the reaction:

3 2 4 2 4I ClO H SO Cl I HSO− − − −+ + → + +

The correct statement(s) in the balanced equation is(are) :

(A) Stoichiometric coefficient of 4HSO− is 6 (B) Iodide is oxidized

(C) Sulphur is reduced (D) 2H O is one of the products

Answer

(ABD)

3 2 4 4 2I ClO H SO Cl HSO I− − − −+ + → + +

22I I 2e 3− −→ + ×

3 26H ClO 6e Cl 3H O 1+ − − −+ + → + ×

3 2 2ClO 6I 6H 3I Cl 3H O− − + −+ + → + +

3 2 4 2 2 4ClO 6I 6H SO 3I Cl 3H O 6HSO− − − −+ + → + + +

31. The total number(s) of Stable conformers with non-zero dipole moment for the following compound is(are)

Answer

(3)

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Now the stable conformers of the given molecule are

32. Among 2 2 3 2PbS, CuS, HgS, MnS, Ag S, NiS, CoS, Bi S and SnS , the total number of BLACK coloured.

sulphides is _________.

Answer

(7)

2 2 3PbS, CuS, HgS, Ag S, NiS, CoS and Bi S are the black colour sulphides.

33. A list of species having the formula 4XZ is given below :

( ) [ ]224 4 4 4 4 3 44

XeF ,SF ,SiF , BF , BrF , [Cu NH ] , FeCl ,−− − +

[ ] [ ]2 2

4 4CoCl and PtCl .− −

Defining shape on the basis of the location of X and Z atoms, the total number of species having a square planar

shape is ______.

Answer

(4)

2 24 4 3 4 4XeF , BrF [Cu(NH ) ] and [PtCl ]− + − are square planar species

34. Consider all possible isomeric ketones, including stereoisomers of MW = 100. All these isomers are independently

reacted with NaBH4 (NOTE: stereoisomers are also reacted separately). The total number of ketones that give a

racemic product (s) is(are) ______.

Answer

(5)

4NaBH3 2 2 2 3

O||

CH CH CH CH C CH− − − − − → Racemic Mixture

4* NaBH

3 2 3|

3

O||

CH CH C H C CH

CH

− − − − → Diastereomeric Mixture

(2 isomers)

4NaBH3 2 3

|

3

O||

CH C H CH C CH

CH

− − − − → Racemic Mixture

4

3| ||

NaBH3 3

|

3

CH O

CH C C CH

CH

− − − → Racemic Mixture

4NaBH3 2 2 2 3

O||

CH CH CH C CH CH− − − − − → Racemic Mixture

Vidyamandir Classes


4NaBH3 2 3

|

3

O||

CH C H C CH CH

CH

− − − − → Racemic Mixture

35. Consider the following list of reagents:

Acidified K2Cr2O7, Alkaline 4, 4 2 2 2 3 3 3 2 2 3KMnO CuSO , H O , Cl ,O , FeCl , HNO and Na S O .

The total number of reagents that can oxidise aqueous iodide to iodine is _____.

Answer

(7)

2 2 7K Cr O2I I− → ……….1

4KMnO / OH OH2 3I I I IO− − −→ → +

22 2 2I Cu Cu I I− ++ → + ……....2

2 2 2 3 3 3H O | Cl | O | FeCl | HNO2

3 4 5 6 7I I− →

2 22 2 3 4 6I S O I S O− − −+ → +

36. A compound H2X with molar weight of 80 g is dissolved in a solvent having density of 0.4 1gml− .

Assuming no change in volume upon dissolution, the molality of a 3.2 molar solution is _______.

Answer

(8)

Molarity = 3.2 M

Volume of solvent = 1000 ml

∴ weight of solvent = 400 g

∴ molality = 3.2

1000 8400

× =

37. In an atom, the total number of electrons having quantum numbers n = 4, 1 sm 1 and m 1/ 2= = −

is _______.

Answer

(6)

n = 4

l = 0,1, 2, 3

4s, 4p, 4d, 4f

1m 1=

1m 1⇒ = ±

Subshell l m

4s 0 0

4p 1 –1, 0, +1

4d 2 –2, –1, 0, 1, 2

4f 3 –3, –2, –1, 0, 1, 2, 3

Vidyamandir Classes


38. MX2 dissociates into 2M + and X− ions in an aqueous solution, with a degree of dissociation ( α ) of

0.5. The ratio of the observed depression of freezing point of the aqueous solution to the value of the

depression of freezing point in the absence of ionic dissociation is

Answer

(2)

22MX M 2X+ −+

1 0 0

1-α α 2α

i = 1+2α = 2

Therefore the ratio of observed depression of freezing point of the aqueous solution to the value of the

depression of freezing point in the absence of ionic dissociation is 2 : 1.

39. The total number of distinct naturally occurring amino acids obtained by complete acidic hydrolysis

of the peptide shown below is ________.

Answer

(1) Total number of distinct amino acids obtained is 4.

Out of the four distinct products formed only glycine exists naturally.

Vidyamandir Classes


40. If the value of Avogadro number is 23 16.023 10 mol−× and the value of Boltzmann constant is

23 11.380 10 JK− −× , then the number of significant digits in the calculated value of the universal gas

constant is

Answer

(4)

The value of R calculated from the given values will be written upto 4 significant digits.

Vidyamandir Classes


PART-C MATHEMATICS

41. Let : (0, )f ∞ → ℝ be given by

1

1( )tx t

x

dtf x e

t

− + = ∫

Then :

(A) ( )f x is monotonically increasing on [ )1, ∞

(B) ( )f x is monotonically decreasing on (0, 1)

(C) 1

( ) 0f x fx

+ =

, for all (0, )x∈ ∞

(D) (2 )xf is an odd function of x onℝ

Answer

42. Let M and N be two 3 3× matrices such that MN = NM. Further, if 2M N≠ and

2 4M N= , then

(A) Determinant of 2 2( )M MN+ is 0

(B) There is a 3 3× non-zero matrix U such that 2 2( )M MN+ U is the zero matrix

(C) Determinant of 2 2( ) 1M MN+ ≥

(D) For a 3 3× matrix U, if 2 2( )M MN U+ equals the zero matrix then U Is the zero matrix

Answer

Vidyamandir Classes


43. Let a∈ℝ and let :f →ℝ ℝ be given by :

5( ) 5f x x x a= − +

Then :

(A) ( )f x has three real roots if a > 4

(B) ( )f x has only one real root if a > 4

(C) ( )f x has three real roots if a < -4

(D) ( )f x has three real roots if –4 < a < 4

Answer

Vidyamandir Classes


44. From a point ( , , )P λ λ λ , perpendiculars PQ and PR are drawn respectively on the lines , 1y x z= = and

, 1y x z= − = − . If P is such that QPR∠ is a right angle, then the possible value(s) ofλ is(are) :

(A) 2 (B) 1 (C) 1− (D) 2−

Answer

45. Let M be a 2 2× symmetric matrix with integer entries. Then M is invertible if :

(A) The first column of M is the transpose of the second row of M

(B) The second row of M is the transpose of the first column of M

(C) M is a diagonal matrix with nonzero entries in the main diagonal

(D) The product of entries in the main diagonal of M is not the square of an integer

Vidyamandir Classes


Answer

46. Let ,x y and z

be three vectors each of magnitude 2 and the angle between each pair of them is 3

π.

If a

is a nonzero vector perpendicular to x and y z and b×

is a nonzero vector perpendicular to

y and z x×

, then :

(A) ( . )( )b b z z x= −

(B) ( . )( )a a y y z= −

(C) . ( . )( . z)a b a y b= −

(D) ( . )( )a a y z y= −

Answer

47. For every pair of continuous functions [ ]0 1 →ℝf , g : , such that max

[ ] [ ] ( ) : 0,1 max ( ) : 0.1 ,∈ = ∈f x x g x x the correct statement(s) is (are):

(A) 2 2( ( )) 3 ( ) ( ( )) 3 ( ) for some [0,1]+ = + ∈f c f c g c g c c

(B) 2 2( ( )) ( ) ( ( )) 3 ( ) for some [0,1]+ = + ∈f c f c g c g c c

(C) 2 2( ( )) 3 ( ) ( ( )) ( ) for some [0,1]+ = + ∈f c f c g c g c c

(D) 2 2( ( )) ( ( )) for some [0,1]= ∈f c g c c

Vidyamandir Classes


Answer

48. Let :[ , ] [1, )→ ∞f a b be a continuous function and let : →ℝ ℝg be defined as

0 if ,

( ) ( ) if ,

( ) if .

<

= ≤ ≤

>

∫

∫

x

a

b

a

x a

g x f t dt a x b

f t dt x b

Then :

(A) g(x) is continuous but not differentiable at a

(B) g(x) is differentiable on ℝ

(C) g(x) is continuous but not differentiable at b

(D) g(x) is continuous and differentiable at either a or b but not both

Answer

Vidyamandir Classes


49. Let :2 2

− →

ℝf ,

π π be given by f (x) = ( )( )3

log +sec x tan x .

Then :

(A) f (x) is an odd function (B) f (x) is a one-one function

(C) f (x) is an onto function (D) f (x) is an even function

Answer

50. A circle S passes through the point (0, 1) and is orthogonal to the circles ( )2 21 16− + =x y and

2 2 1+ =x y . Then :

(A) Radius of S is 8 (B) Radius of S is 7

(C) Centre of S is ( )7 1− , (D) Centre of S is ( )8 1− ,

Answer

Vidyamandir Classes


51. Let 2n ≥ be an integer. Take n distinct points on a circle and join each pair of points by a line

segment. Colour the line segment joining every pair of adjacent points by blue and the rest by red. If the

number of red and blue line segments are equal, then the value of n is _______.

Answer

52. The value of ( )2 51

3 2

204 1

dx x dx

dx

−

∫ is _______.

Answer

53. Let 1 2 3 4 5n n n n n< < < < be positive integer such that 1 2 3 4 5 20n n n n n+ + + + = . Then the number of

such distinct arrangements ( )1 2 3 4 5n ,n ,n ,n ,n is _______.

Vidyamandir Classes


Answer

Alternate approach/solution

Consider

2 1

3 2 11

4 3 1

5 4 1

, , , , 0

n n a

n n b n a bhere n a b c d

n n c n a b c

n n d n a b c d

= + = + = + + >

= + = + + + = + = + + + +

Given Equation reduces to

15 4 3 2 20n a b c d+ + + + =

Number of Solution will be

= Coeff. of 20x in (Integral Solutions)

Vidyamandir Classes


5 10 4 8 12 3 6 9 2 4 6 8 2 3 4 5 6( ) ( ) ( ) ( ) ( )x x x x x x x x x x x x x x x x x x+ × + + × + + × + + + × + + + + +

=Coeff. of 20x in

15 5 4 8 3 6 2 4 6 2 3 4 5 (1 )(1 ) (1 ) (1 ) (1 )x x x x x x x x x x x x x x× + + + × + + × + + + × + + + + +

=Coeff. of 5x in

5 4 8 3 6 2 4 6 2 3 4 5(1 ) (1 ) (1 )(1 ) (1 )x x x x x x x x x x x x x+ × + + × + + + + + × + + + + +

=7

54. Let anda, b c

be three non-coplanar unit vectors that the angle between every pair of them is 3

π.

If a b b c pa qb rc ,× + × = + +

where andp, q r are scalars, then the value of 2 2 2

2

2p q r

q

+ +

is _______.

Answer

55. The slope of the tangent to the curve ( ) ( )2 25 21y x x x− = + at the point (1, 3) is

Answer

Vidyamandir Classes


56. Let [ ] [ ]0 4 0→f : , ,π π be defined by f (x) = ( )1−cos cos x . The number of points [ ]0 4∈x , π satisfying

the equation ( )10

10

−=

xf x is :

Answer

57. Let a, b, c be positive integers such that b

a is an integer. If a, b, c are in geometric progression and the

arithmetic mean of a, b, c is 2+b , then the value of

2 14

1

+ −

+

a a

a is _______.

Answer

58. The largest value of the non-negative integer a for which( )

( )

1

1

1

1 1

1 1 4

x

x

x

ax sin x alim

x sin x

−

−

→

− + − + =

+ − − is ______.

Vidyamandir Classes


Answer

59. Let : and :f g→ →ℝ ℝ ℝ ℝ be respectively given by ( ) ( ) 21 and 1f x x g x x= + = + .

Define :h →ℝ ℝ by ( )( ) ( ) ( ) ( )

0

0

max f x , g x if x ,h x

min f x , g x if x .

≤=

>

The number of points at which ( )h x is not differentiable is _______.

Answer

Vidyamandir Classes


60. For a point P in the plane, let ( ) ( )1 2andd P d P be the distances of the point P from the lines

0 and 0x y x y− = + = respectively. The area of the region R consisting of all points P lying in the first

quadrant of the plane and satisfying ( ) ( )1 22 4d P d P ,≤ + ≤ is _______.

Answer

Q.No. 1 A,B,C Q.No.21 A,B,C Q.No.41 A,C,D

Q.No. 2 A,D Q.No.22 A,B,D Q.No.42 A,B

Q.No. 3 C,D Q.No.23 B,C,D Q.No.43 B,D

Q.No. 4 C Q.No.24 A,C,D Q.No.44 C

Q.No. 5 D Q.No.25 A,B,C Q.No.45 C,D

Q.No. 6 A,C,D Q.No.26 A,B,C Q.No.46 A,B,C

Q.No. 7 A,C Q.No.27 B,D Q.No.47 A,D

Q.No. 8 B,D Q.No.28 A Q.No.48 A,C

Q.No. 9 A,B,D Q.No.29 A,B Q.No.49 A,B,C

Q.No. 10 C,D Q.No.30 A,B,D Q.No.50 B,C

Q.No. 11 2 Q.No.31 3 Q.No.51 5

Q.No. 12 5 Q.No.32 7 Q.No.52 2

Q.No. 13 4 Q.No.33 4 Q.No.53 7

Q.No. 14 5 Q.No.34 5 Q.No.54 4

Q.No. 15 2 Q.No.35 7 Q.No.55 8

Q.No. 16 3 Q.No.36 8 Q.No.56 3

Q.No. 17 3 Q.No.37 6 Q.No.57 4

Q.No. 18 5 Q.No.38 2 Q.No.58 2

Q.No. 19 2 Q.No.39 1 Q.No.59 3

Q.No. 20 8 Q.No.40 4 Q.No.60 6

JEE Advanced 2014

Paper 125 May 2014 | 9:00AM - 12:00 PM

Code - 7

Answer keyPHYSICS CHEMISTRY MATHS

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