JEE 2014 PET I Advanced Paper II Qns

♠ Brilliant Tutorials Pvt. Ltd. IIT/ELITE/PET/PCM(Adv)/P(II) - 1

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BRILLIANT’S

PROGRESSIVE EVALUATION TEST

FOR STUDENTS OF OUR ONE/TWO-YEAR POSTAL COURSES

TOWARDS

JOINT ENTRANCE EXAMINATION, 2014

QUESTION PAPER CODE

Time: 3 Hours Maximum Marks: 180

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

purpose.

INSTRUCTIONS:

A. General 1. This booklet is your Question Paper containing 60 questions. The booklet has 24 pages. 2. This question paper CODE is printed on the right hand top corner of this sheet and on

the back page (page no. 24) of this booklet. 3. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers, and

electronic gadgets in any form are not allowed to be carried inside the examination hall. 4. Fill in the boxes provided below on this page and also write your Name and Enrollment

No. in the space provided on the back page (page no. 24) of this booklet. 5. The answer sheet, a machine-readable Objective Response Sheet (ORS), is provided

separately, in which appropriate bubble for each question must be darkened with Black Ball Point Pen only.

6. DO NOT TAMPER WITH/MUTILATE THE ORS OR THE BOOKLET. 7. Do not break the seals of the question paper booklet before being instructed to do so by the

invigilators. B. Question paper format: Read the instructions printed on the back page (page no. 24) of this booklet. C. Marking scheme: Read the instructions on the back page (page no. 24) of this booklet.

Name: . Enrollment No.:

PHYSICS – CHEMISTRY – MATHEMATICS

1

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I have verified all the informations filled in by the Candidate.

………………………………… Signature of the Invigilator

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JEE 2014 PET I/PET IV/PCM/ADV (PII)/Qns 8’13

PAPER II

2


SECTION I

One or more options correct Type

This section contains 8 multiple choice questions. Each question has four choices (A),

(B), (C) and (D) out of which ONE OR MORE is/are correct.

1. Select which of the following statements are correct.

(A) The units expressed by (Megasec), (Parsec) and (Microsec) all belong to the same

physical quantity.

(B) The equivalence of the electrical unit of energy, expressed by (volt. ampere hour)

and mechanical unit of energy expressed by (joules) is established by the First

Law of Thermodynamics.

(C) The various units of energy expressed in the following statement are correctly

placed in the decreasing order of magnitude as indicated, where the units have

their normal values.

1 kilo calorie (KC) 1 BTU 1 KJ 1 a.m.u 1 MeV> > > >

(D) The dimensions of the physical quantity/quantities expressed by the units, HP

(horse-power) coulomb volt/hour, and kilo candela (KCd) are identical.

2. A particle of mass m is projected from a point O on a horizontal plane at an angle θ

to the horizontal with initial velocity 0v��

. Which of the following statements are true

for this motion. (Assume the air drag is negligible)?

(A) The change of linear momentum, P,∆

�� during the first t sec (< its time of flight)

of its motion will be P m g t.→ →

∆ = −

(B) The change of linear momentum P→

∆ during the first t sec (< its time of flight)

of its motion will be P m g t.→ →

∆ =

(C) The total change in its linear momentum during its motion will be

0v gP 2m

g

×∆ =

��

(D) The total change in its linear momentum during its motion will be

0P 2mv sin∆ = θ

��

PART A : PHYSICS

3


3. A river of uniform width d flows at a constant speed of u. A boat, which is rowed at

the speed of u

2 sets off at an angle φ to the direction of flow of the river. For the

motion of the boat, which of the following statements will be true?

(A) The drift of the boat down the river will be minimum when 120φ = °

(B) The total time t taken by the boat to reach the other bank and instantly starting

off at the same angle φ to come to its initial bank will also be minimum when

120.φ =

(C) If 90 ,φ = ° the drift of the boat down the river when it reaches the other bank

will be d

.2

(D) The drift of the boat down the river when the boat reaches the other bank can

never be less than d.

4. Two spherical bodies rotate about stationary mutually perpendicular intersecting

axes, OX and OY with constant angular velocities of 3.0 rad/s and 4.0 rad/s

respectively. Then

(A) The relative angular velocity of one body relative to the other is 5 rad/s

(B) The relative angular acceleration of one body relative to the other is zero

(C) The relative angular velocity of one body relative to the other is 12 rad/s

(D) The relative angular acceleration of one body relative to the other is 212 rad / s


(A) Experiments show that the temperature of the Earth’s crust increases about

1 C° for each 30 m of depth. Assume that the earth’s crust has a thermal

conductivity of 0.80 Wm/ºC. Then the amount of heat that flows out through the

Earth’s surface each second per square metre of area will be 22.4 mW / m

(B) A sphere of radius 3 cm, acts like a black body. It is in equilibrium with its

surroundings and absorbs 30 kW of power radiated to it from the surroundings.

The temperature of the body will be 2600 K [Assume 8 2 45.67 10 W / m K ]−σ = ×

4


(C) The thermodynamic states of 1 mole of an ideal diatomic gas are represented by

the four points A [3P, 2V], B [2P, 3V], C [2P, 6V] and D[4P, 2V] on the P – V

diagram. Nothing is known about the processes A → B, B → C and C → D. Then

no work will be done if the gas is taken along the process D → A.

(D) An air bubble is of diameter 4.0 m,µ when it is located in water at the depth

5.0 m. The pressure above the water surface is 1 atmos. Then the pressure inside

the air bubble will be 2.2.atmos (Surface tension of water 10.073 Nm .−

1 atmos 101.3 kPa= )


(A) Two mass points of masses 1m and 2m are located at a distance r from each

other. Assume all other objects are very far off. Then the gravitational potential

energy gE between the two masses will be 1 2g

Gm mE

r=

(B) Inside a uniform sphere of density ρ , there is a spherical cavity whose centre is

at a distance � from the centre of the sphere. All points within the cavity will

have the same gravitational potential.

(C) Two perfectly free rigid bodies A (mass 1m ) and B (mass 2 1m m> ) initially at

rest move under an identical constant force F��

acting on each of them. Soon

they undergo a perfectly elastic collision and separate. The total linear

momentum of the two bodies will be conserved during the collision even when

the force F��

continues to act on them after the collision.

(D) The temperature on the surface of water in an open vertical tank is 1.5 times the

temperature at its bottom. An air bubble just formed at the bottom of the tank

has a volume V. When the air bubble rises to the surface its volume is 2V.

Assume air to be an ideal gas. The height of the water in the tank will be 3.4 m.

7. A uniform sphere of mass M and radius R starts at t = 0 to roll down from rest at a

point O on an inclined plane inclined at angle α to the horizontal. The rolling is

perfect without any slip. At the pint P at instant t, its angular velocity is ω and its

linear acceleration is a. For this motion,

O

P a

RM

ω

α

5


(A) The angular momentum of the sphere relative to the point O at time t will be

L Rmgtsin= α

(B) The angular momentum of the sphere relative to the point P at time t will be

L I= ω where I is the moment of inertia of the sphere about its own axis

(C) The angular acceleration β of the sphere at the point P will be a

Rβ =

(D) The angular momentum of the sphere relative to the point O will not change if

the inclined plane had been perfectly smooth.

8. Three point masses m, 2m and 3m are placed at the vertices A, B and C respectively

of an equilateral triangle of side a. For this system,

(A) The centre of gravity of the three masses will be located at O, the centroid of the

triangle

(B) The centre of gravity of the three masses will lie on the medium line AO but not

at the point O

(C) If the mass m is given an initial velocity V in the direction OA,��

then the

smallest value 0V of V for which the mass m will escape from the gravitation

field of the two masses 2m and 3m will be given by 0V 10 GM / a=

(D) If the mass m be given the velocity V in the direction AO→

[instead of 0A→

] then

the least velocity needed for m to escape from the gravitation field of 2m and 3m

will be the same (viz) 0V as obtained in (C).

6


SECTION II

Paragraph Type

This section contains 4 paragraphs each describing theory, experiment, data, etc. Eight

questions relate to four paragraphs with two questions on each paragraph. Each question

of a paragraph has only one correct answer among the four choices (A), (B), (C) and (D).

Paragraph for Questions 9 and 10

O

T′

P

3 m

5 m3 m

A B

u 2 m / s=

C

A frictionless pulley P of mass 3m is suspended by a light massless thread from a

point O. Two masses A and B of mass 3m and 5m respectively are connected by a

light inextensible thread which runs over the pulley as shown in the diagram. The

point O along with the system is given a uniform vertically upward velocity of

=u 2m / s, and simultaneously the masses A and B are released to move freely.

=

2Take g 10m / s

9. Which of the following statements are true?

(a) The system of masses A&B is moving in an inertial frame of reference

(b) The acceleration of mass B relative to the pulley P will be 22.5 m / s vertically

down.

(c) The acceleration of mass A relative to the mass B will be 25 m / s vertically

upwards

(d) The pulley P remains at rest with respect to the point O.

Make the correct choice from:

7


(A) All the statements are true

(B) Only (a) and (b) are true

(C) Only (b) and (c) are true

(D) Only (a), (b) and (d) are true.


(a) The tension in the thread ′ =OP, T 11 mg upwards

(b) The tension in the thread OP, ( )′ =T 10.5 mg upwards

(c) The relative velocity of mass B (5m) relative to the point O, after 1 second of

motion will be 4.5 m/s vertically down.

(d) The relative velocity of A (3m) relative to the point O, after 1 second of motion

will be 2.5 m/s upwards.

Make the correct choice from:

(A) Only (a) and (d) are correct

(B) All the statements are correct

(C) The statements (b) and (d) only are correct

(D) The statements (a) (c) and (d) only are correct.

Paragraph for Questions 11and 12

T

S

1L ρ1

M

2L ρ2

1h

2h

T is a vertical tank containing two immiscible, non-reacting liquids 1 2L and L of

densities ρ ρ1 2and filled to the heights 1 2h and h in the tank as shown in the

figure. M is a wooden cylindrical body of length � floating at rest at the interlayer

between 1 2L and L with its length submerged in the ratio 11:9 in the liquids

1 2L and L respectively. The density of wood is ρ.

8


11. The difference of pressure ∆P between the upper and lower surfaces of the wooden

body is given by

(A) ∆ = �P mg / A where m is the mass of the wooden body and A the area of its

cross-section.

(B) 2 2 1 1P h h g10

ρ ∆ = ρ − ρ +

�

(C) ∆ = ρ�P g

(D) ρ

∆ = ρ − ρ +

�2 2 1 1P h h g

20

12. The wooden block is now removed and a small orifice S at the bottom of the tank is

opened so that the liquids flow out. Then the speed v of the liquid 2L flowing out of

S just when it is opened is given by

(A) ( )1 2v 2g h h= +

(B) 1 1 2 2

1 2

h hv 2g

ρ + ρ=

ρ + ρ

(C) 1 2

1 2

h hv 2g

h h

=

+

(D) 2v 2gh=


A thin uniform copper rod AB of length L and mass M rotates uniformly with an

angular velocity ω in a horizontal plane about a vertical axis AO through its

end A. The Young’s modulus of copper is E. Density of copper is ρ.

O

A BL

ω

ω

9


13. The tension T in the rod as a function of r the distance from the rotation axis will

be

(A) 2

2

2

rT M L 1

L

= ω −

(B)

2 2

2

M L rT 1

2 L

ω= −

(C) 2 2M r

TL

ω= (D)

2 2M rT

2L

ω=

14. The elongation ∆L of the rod will be

(A) ρω

∆ =

2 3LL

E (B)

ρω∆ =

2 3LL

2E

(C) ρω

∆ =

2 3LL

3E (D)

ρω∆ =

2 3LL

4E


A body of mass 1m experiences a perfectly elastic collision with another body of

mass 2m at rest in two ways.

1. In a head-on collision, the two bodies fly apart in exactly opposite direction with

equal speeds.

2. In a non-head-on collision, the two bodies after collision fly apart symmetrically to

the initial direction of the first body before collision, with an angle of divergence of

60º between their directions after collision.

15. For the head on collision, the ratio of the masses 1m and 2m will be

(A) =1 2m m (B) =1

2

m 1

m 2

(C) =1

2

m 1

m 3 (D) =

1

2

m 1

m 4

16. For the non-head-on collision the ratio of the masses 1 2m and m will be

(A) =1 2m m (B) =1

2

m2

m

(C) =1

2

m 2

m 3 (D) 1 2

3m / m

2=

10


SECTION III

Matching List Type

This section contains 4 multiple choice questions. Each question has matching lists.

The codes for the lists have choices (A), (B), (C) and (D) out of which ONLY ONE is correct

17.

S

P

2

4 3

2

1

4

3

1

In the diagram, S is a spool of thread resting on a horizontal rough table top, such

that it can roll without any slipping at the point P. While the spool is resting, the

loose end of the thread is pulled gently when the thread is leaving the spool at the

points 1, 2, 3 and 4 of the spool. The directions of the pull are → → → →

11, 22, 33 and 44

respectively. As a result the spool will roll to the right or left, winding or unwinding

the thread or remain stationary. These are shown in a jumbled way in list II

corresponding to the pulls shown in list I. Use the code below to select the correct

motions of the spool from the choices A, B, C and D.

List I List II

P. →

11

1.Remains stationary

Q. →

22

2. Rolls clockwise winding the thread

R. →

33

3. Rolls counter clockwise unwinding the thread

S. →

44

4. Rolls clockwise unwinding the thread.

11


Code

P Q R S

(A) 1 2 3 4

(B) 2 1 4 3

(C) 2 4 1 3

(D) 1 3 2 4

18. An ideal gas of ratio of specific heats γ , undergoes a general polytropic process

given by the equation =nPV constant where n is a constant. For specific values, or

range of values of n, the gas has characteristic value or range of values for its molar

specific heat C for the process expressed in terms of the gas constant R. List I gives

the chosen values for n for which the molar specific heat is shown in List II in a

jumbled way. Use the code given below to select the correct values from amongst the

choices A, B, C and D. The gas is given to be a diatomic gas.

List I List II

P. n = 1.2 1. =R

C2

Q. n = 1.3 2. C is negative

R. n = 1.5 3. = −5R

C2

S. n = 0 4. =7R

C2

Code

P Q R S

(A) 1 2 3 4

(B) 2 3 4 1

(C) 4 1 2 3

(D) 3 2 1 4

12


19. Conservation of total linear/angular momenta and total mechanical energy of a

system are important principles occurring in physical events. Four situations may

arise which are categorised as follows:

Category 1 (C1) → Total linear/angular momenta and total energy are both

conserved separately

Category 2 (C2) → Total linear/angular momenta are conserved, but total energy

is not.

Category 3 (C3) → Total energy is conserved but not total linear/angular

momentum

Category 4 (C4) → Total linear/angular momenta and total energy are both NOT

conserved.

Four events are mentioned below (List I) for which the above categories are given in

List II in a jumbled manner. Use the code given below to select the correct categories

from among choices A, B, C and D.

Event Category

(List I) (List II)

P. A body falls freely under gravity 1. C4

Q. The Earth moves around the sun in elliptic orbit 2. C3

R. Two bodies undergo an oblique inelastic collision 3. C1

S. An insect climbs up a vertical wooden pole 4. C2

Code:

P Q R S

(A) 2 3 4 1

(B) 1 4 3 2

(C) 1 2 3 4

(D) 2 3 1 4

13


20. A composite body is made up of a solid sphere of radius R of material of uniform

density ρ2 covered by another concentric solid spherical shell of inner radius R and

outer radius 2R of another material of uniform density ρ.

2

R

C

2R

3R

A

B

P

The common centre of the composite body is C. Four points, C, A, B and P are located as shown in the diagram, the point P being at distance PC = 3R from C. The

gravitational potentials C A BV , V , V and PV (only magnitudes) at the points C, A,

B and P respectively are listed in List II in a jumbled way against the points in List I. Select the correct values of the gravitational potentials (only magnitudes being taken) against each of the points C, A, B and P using the code that shows only

one of the choices (A), (B), (C) and (D) being correct [Take π ρ =3

04

R m ]3

(List I) (List II)

P. → CC V 1.

0Gm3

R

Q. → AA V 2.

0Gm13

2 R

R. → BB V 3.

0Gm9

2 R

S. → PP V 4.

0Gm13

2 R

Code:

P Q R S

C(V ) A(V ) B(V ) P(V )

(A) 2 4 1 3

(B) 1 2 4 3

(C) 4 2 3 1

(D) 4 3 1 2

14


m

SECTION I


This section contains 8 multiple choice questions. Each question has four choices

(A), (B), (C) and (D) out of which ONE OR MORE is/are correct.

21. An oxalate salt (0.15 g) dissolved in 100 mL of water required 45 mL of N/20

4KMnO solution for complete oxidation. The percent of oxalate ion in the sample is

(A) 76% (B) 86% (C) 66% (D) 46%

22. A solution is saturated with respect to 3SrCO and 2SrF . The −23[CO ] was found

to be −×

31.5 10 M. The concentration of −F ions in the solution is about

Given: −= ×

10 3sp 3K (SrCO ) 7 10 M ; −

= ×10 3

sp 2K (SrF ) 7.9 10 M

(A) −×

24.1 10 M (B) ×24.1 10 M

(C) −×

21.4 10 M (D) ×21.4 10 M

23. The equilibrium − −+ ��⇀↽��2 3I I I is set up in aqueous solution. When started with

one mole of 2I and 0.5 mole of −I in a 2L flask, at equilibrium, addition of excess

3AgNO gave 0.25 mole of yellow precipitate. The value of equilibrium constant is

(A) 1.33 (B) 2.66 (C) 3.33 (D) 4.44


(A) The ratio of mean velocity of RMS velocity of a given gas is independent of

temperature.

(B) Square of mean velocity of 2O molecules is equal to the square of RMS velocity

of 2SO molecules at 20ºC.

(C) Mean K.E. of gas molecules at any given temperature is independent of the

mean velocity of the gas molecules.

(D) The difference between RMS velocity and mean velocity at any temperature for

different gases decreases as larger the molar masses of gases.

25. Liquation process is employed for the purification of the metals

(A) Pb (B) Sn (C) Bi (D) Mg

PART B : CHEMISTRY

15


26. Which of the following thermodynamic relationships are correct?

(A) ∆

∆ = − P

d GS

dT (B)

∆ ∆ = −

T

d GV

dP

(C)

∆ = P

dES nF

dT (D)

∆ ∆ =

P

d GH nF

dS

27. Which of the following statements are correct?

(A) At critical state, the value for compressibility factor is 0.375

(B) If a gas is allowed to expand below its inversion temperature cooling effect is

caused.

(C) For triatomic gases =P

V

C1.44.

C

(D) At constant temperature, the collision frequency is proportional to 2P .

28. Which of the following statements are correct?

(A) Among halogens oxidizing nature increases down the group.

(B) Helium has the least ionization potential among the inert gases.

(C) Size of the species increases in the order + + −< < < �

2Mg Na F A

(D) The correct order of electron affinities is > > >O C B N

SECTION – II

Paragraph Type


questions relate to four paragraphs with two questions on each paragraph. Each question



In the case of molecular orbitals, they are obtained by combining atomic orbitals of

comparable energy. These molecular orbitals are more stable and have complex

shapes and represented by ∗ ∗σ σ π π, , , etc as bonding and antibonding.

29. Relative stabilities and bond dissociation energies are in the order

(A) + − −> > >

22 2 2 2O O O O (B)

− +−> > >

22 2 2 2O O O O

(C) + − −> > >

22 2 2 2O O O O (D) 2

2 2 2 2O O O O− − +> > >

30. Following are some species

(i) 2C (ii) 2N (iii) 2B (iv) 2Be

Diamagnetic species amongst them are

(A) (i) and (ii) (B) ii, iii, iv (C) iii and i (D) All

16



The rate constant for the I order decomposition of a certain reaction is given by the

equation − ×= −�

41 1.3 10

n k (s ) 15.0T

31. The energy of activation for the reaction is

(A) 58.2 k.cal (B) 25.8 k.cal (C) 100 k.cal (D) 852 k.cal

32. The rate constant at 500 K is,

(A) −×

51.66 10 (B) ×56.16 10 (C) ×

51.66 10 (D) ×32.77 10


Nucleophilic substitution reactions are those substitution reactions involving the

attack of a nucleophile. These are usually written as SN. They follow two

mechanisms via unimolecular and bimolecular.

33. The incorrect statement regarding NS 1 reactions is

(A) These are first order reactions

(B) Rearrangement is possible

(C) Order of reactivity of alkyl halides is Allyl > ° > ° > ° > �31 2 3 CH C .

(D) Favoured by polar solvents.

34. Which one of the following is not a nucleophile?

(A) − 2R NH (B) − −R O R (C) −

3 2CH COCH (D) +

2R N


The uncertainty of movement of position x∆ and the uncertainty of momentum

∆ ∆p or mv are related to Heisenberg’s relationship as ∆ ⋅ ∆ ≥

π

hx p .

4 i.e.,

∆ ⋅ ∆ ≥

π

hx mv .

4 For an electron of mass −

= ×28m 9.10 10 g the product of

uncertainties is quite large.

−

−×∆ ⋅ ∆ ≥ =

π

2716.624 10

x v 0.57 sec. g .4 m

35. The uncertainty in the position of a particle when the uncertainty in the momentum

is zero is

(A) zero (B) infinity

(C) −×

3 11 10 g cm sec (D) cannot be calculated

17


36. Find the uncertainty in the velocity of a ball (in −1m sec ) of mass 0.15 kg, if its

uncertainty in position is of the order of °

1A .

(A) −×

246.62 10 (B) −×

248.0 10 (C) −×

243.51 10 (D) −×

2410.0 10

SECTION III

Matching List Type


The codes for the lists have choices (A), (B), (C) and (D) out of which ONLY ONE is correct

37.

List I List II

P. Reduction by Mg 1. Zr

Q. Reduction by Al 2. PbO

R. Reduction by C 3. �4TiC

S. Van Arkel method 4. 2 3Fe O .

Codes:

P Q R S

(A) 1 2 3 4

(B) 3 4 2 1

(C) 3 2 4 1

(D) 2 4 3 1

38.

P. Boyle’s law 1. = +PV RT Pb

Q. Charles law 2. =1 2

2 1

r d

r d

R. Helium gas 3. = +log V log T constant

S. Graham’s law 4. = − +log P log V constant

Codes:

P Q R S

(A) 1 2 3 4

(B) 4 3 2 1

(C) 4 3 1 2

(D) 1 3 4 2

18


39.

Units for k

P. zero order 1. 1 1mol L s− −

Q. first order 2. 1s −

R. second order 3. 1 1L mol s− −

S. nth order 4. − − −1 1 n 1(mol L ) s

Codes:

P Q R S

(A) 1 2 4 3

(B) 3 4 2 1

(C) 4 3 2 1

(D) 1 2 3 4

40.

P. α − rays 1. −×

271.66 10 kg

Q. positron 2. positive electron

R. γ − rays 3. He nucleus

S. 1 amu 4. Electromagnetic radiation

Codes:

P Q R S

(A) 3 1 4 2

(B) 1 2 3 4

(C) 3 2 4 1

(D) 4 3 2 1

19


SECTION I


This section contains 8 multiple choice questions. Each question has four choices

(A), (B), (C) and (D) out of which ONE OR MORE is/are correct.

41. If a, b, c, x are positive and not equal and if a, b, c are in G.P, then

a b clog x, log x, log x are not in

(A) A.P (B) H.P (C) G.P (D) None of these

42. If the number of solutions of the equation 2 2sin x cos x16 16 10+ = 0 x≤ ≤ π , and

x 2π < ≤ π are m and n respectively, then

(A) m < n (B) m = n (C) m = 4 (D) n < m

43. If 2 2x ax b 0 and bx x a 0+ + = + + = have a common root and the first equation

has equal roots, then the value of 2a 2b+ is

(A) 0 (B) 2 (C) − 2 (D) 1

44. The locus of a point in a plane sum of whose distances from two perpendicular lines

in the plane is 2 is

(A) a circle (B) a rectangle (C) a square (D) None of these

45. An equation of a tangent to the hyperbola 2 216x 25y 96x 100y 356 0− − + − =

which makes an angle 4

π with the transverse axis is

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

46. If ( )1 1 1f x sin x cos x tan x− − −

= + + then

(A) Domain of ( ) ( )= − ∞ ∞f x ,

(B) Domain = [− 1, 1]

(C) Range = [ ]0, π

(D) Range = 3

,4 4

π π

PART C : MATHEMATICS

20


47. The minimum value of 2 23 sec 12 cosec 15θ + θ − is

(A) − 12 (B) 12

(C) 0 (D) − 3

48. The sum to n terms of the series 7 + 77 + 777 + …… is

(A) ( )n10

10 181

− (B) ( )n70

10 181

−

(C) n 110 +< (D) ( )

n70 7n10 1

81 9− −

SECTION II

Paragraph Type


Questions relate to four paragraphs with two questions on each paragraph. Each question



The equation of a curve is represented by 2 29x 4y 36x 8y 4 0+ − + + =

49. Which of the following is a focus of the curve?

(A) ( )2, 5 (B) ( )2, 5− (C) ( )5 1, 2− (D) ( )2, 5 1−

50. The equation of a directrix of the curve is

(A) 5x 3 5 5= − (B) 5y 3 5 5= −

(C) 5y 9 5 5= − (D) None of these


In ABC,∆ the sides a, b, c are in A.P.

51. Then A B C

tan , tan , tan2 2 2

are in

(A) A.P (B) G.P (C) H.P (D) None of these

52. A B C

cot cos A, cot cos B, cot cos C2 2 2

are in

(A) A.P (B) G.P (C) H.P (D) None of these

21



Let n ncos x sin x 1− = where n is a natural number.

53. When x− π ≤ ≤ π and n is an even integer the number of values of x satisfying the

equation is

(A) 1 (B) 2 (C) 0 (D) 3

54. When 0 x 2≤ ≤ π and n is an odd integer > 1 then the number of values of x

satisfying the equation is

(A) 1 (B) 2 (C) 3 (D) 0


In ABC, A∆ is a right angle and the smallest side is b = 17 units.

55. The value of 1 1b ctan tan

c a a b

− −+

+ + equals

(A) 2

π (B)

3

π (C)

4

π (D)

3

4

π

56. The perimeter of the triangle ABC is

(A) 306 units (B) 289 units (C) 324 units (D) 342 units

SECTION III

Matching List Type


The codes for the lists have choice (A), (B), (C) and (D) out of which ONLY ONE is correct.

57.

P. The solution set of

( ) ( )2

10 10log x 25 log x 5− ≤ + is 1. ( )2, ∞

Q. The solution set of

( ) ( )0.2 0.04log x 1 log x 1− < − is 2. ( )− ∞ −, 1

R. The values of x such that

( )2

1

10

x log x x 1 0+ + > lies in 3. (2, 5)

S. If x satisfies ( )−1

3

log x 1

( )+ +1

3

log x 1 ( )3log 5 x 1+ − <

then x lies in 4. (5, 6]

22


Codes:

P Q R S

(A) 4 3 2 1

(B) 4 1 2 3

(C) 2 3 4 1

(D) 1 4 3 2

58.

P. The incentre of the triangle formed by the coordinate axes

and the line 4x + 3y – 12 = 0 is

1. (6, 5)

Q. A circle with its centre on the focus of the parabola 2y 8x=

touches the directrix of the parabola. Then the point of

intersection of the parabola and the circle is

2. (6, 6)

R. The coordinates of the point from which the tangents to the

ellipse 2 2x 8y 64+ = are perpendicular are

3. (2, 4)

S. One of the foci of the conic 2 29x 16y 18x 160y 535 0− − + − = is

4. (1, 1)

Codes:

P Q R S

(A) 4 3 2 1

(B) 2 4 3 1

(C) 1 4 2 3

(D) 1 2 3 4

59.

P. The value of

2

cos cos100 100

π π+

3 99cos .... cos

100 100

π π+ + + =

1. 2

Q. In ABC,∆ a = 3, b = 4, c = 5 then

( )2 r R+ equals

(r – in radius

R – circum radius)

2. 3

R. In an equilateral triangle, R

..........r

= 3. 0

S. If 2 cos A + cos B + cos C = 2 in ABC,∆ then B C

cot cot2 2

equals

4. 7

23


Codes:

P Q R S

(A) 4 1 2 3

(B) 1 2 4 3

(C) 3 4 1 2

(D) 3 4 2 1

60.

P. If ,α β are the roots of 2x x 1 0− + = then the equation

whose roots are 3 3andα β is

1. 2x 19x 120 0+ − =

Q. If one root of the equation 2x ax 6 0− + = is the

smallest even prime number and one root of

2x ax b 0+ + = is the smallest odd prime number then

the equation whose roots are a and b is

2. 2x 8x 209 0− − =

R. If ,α β are the roots of 2x 7x 15 0+ + = then the

equation whose roots are ( )2 2 2andα − β α + β is ….

3. 25x 24x 32 0− + =

S. If ,α β are the roots of 2x 4x 5 0− + = then the

equation whose roots are 1

α +

α

and 1

β +

β

is

4. 2x 2x 1 0+ + =

Codes:

P Q R S

(A) 2 4 3 1

(B) 1 3 4 2

(C) 4 3 2 1

(D) 4 1 2 3

24


Name: . QUESTION PAPER CODE:

Enrollment No.:

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

purpose.

B. Question paper format

8. The question paper consists of 3 parts (Part A: Physics, Part B: Chemistry and Part C:

Mathematics). Each part has 3 sections.

9. Section I contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and

(D) for its answer, out of which one or more is/are correct.

10 Section II of each part contains 4 paragraphs with two questions on each paragraph.

Each question has 4 choices (A), (B), (C) and (D), out of which only one is correct.

11. Section III contains 4 multiple choice questions. Each question has matching list. The codes

for the lists have choices (A), (B), (C) and (D) out of which only one is correct.

C. Marking scheme

12. For each question in Section I, you will be awarded 3 marks if you darken the bubble(s)

corresponding to the correct choice(s) for the answer, and zero mark if no bubble is

darkened. In case of bubbling of incorrect answer, minus one (−−−−1) mark will be awarded.

13. For each question in Section II, you will be awarded 3 marks if you darken only the

bubble corresponding to the correct answer and zero mark if no bubble is darkened. In case

of bubbling of incorrect answer, minus one (–1) mark will be awarded.

14. For each question in Section III, you will be awarded 3 marks in which you have darkened

the bubble corresponding to the correct answer. In case of bubbling of incorrect answer,

minus one (−−−−1) mark will be awarded.

1

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JEE 2014 PET I Advanced Paper II Qns