JEE Advanced 2014_Test 4 (Paper II) Code B

8/10/2019 JEE Advanced 2014_Test 4 (Paper II) Code B

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Space for Rough Work

Test - 4 (Paper-II) All India Aakash Test Series for JEE (Advanced)-2014

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PART - I : PHYSICS

SECTION - 1

Only One Option Correct Type

This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY

ONE is correct.

1. How long will it take sound waves to travel the distance of 70 m between two points Pand Qif the air temperature

between them varies linearly from 16C to 51C? Consider the air to be an ideal diatomic gas of molar mass

29.05 g/mole (Gas constant, R= 8.3 J/mol)

(A) 0.2 s (B) 0.5 s

(C) 0.12 s (D) 2.5 s

2. A point source emitting spherical waves is located between two points of position vectors1

r

and2

r

on the line

joining them. If damping of waves is negligible and the medium is homogeneous, amplitude of waves at two points

are found to beA1andA2respectively. The position vector of point source is

(A) 1 1 2 2

1 2

A r A r

A A

+

(B) 1 1 2 2

1 2

A r A r

A A

+

+

(C) 1 1 2 2

1 2

A r A r

A A

(D) 1 1 2 2

1 2

A r A r

A A

+

3. A wave pulse moving alongx-axis is represented by equation y=2

0.5m

1 ( 10 )x t+ , wherex, yare in metres and

tis in second. Height and speed of the pulse are respectively

(A) 0.5 m and 10 m/s

(B) 0.5 m and m/s

(C) 2 m and m/s

(D)1m

2and

10m/s

TEST - 4 (Paper - II)Time : 3 Hrs. MM : 186


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All India Aakash Test Series for JEE (Advanced)-2014 Test - 4 (Paper-II)

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4. The ends of a rod of length lare maintained at temperatures T1and T2(T1> T2). The thermal conductivity of the

rod at a point is given as k=a

Twhere Tis the temperature of rod at that point and a is a positive constant.

Temperature of rod at a distancexfrom the hotter end is

(A)

/

2

2

1

x l

TT

T

(B) /1 2(1 )x lT T e+

(C)

/

2

1

1

x l

TT

T

(D)

/

2

1

1

x l

TT

T

5. The relation between internal energy U, pressure Pand volume Vof an ideal gas in an adiabatic process is,

U= + PV, where and are constants. The ratio of specific heats CP: C

Vfor the gas is

(A)1

+

(B)1

1+

(C)

+ (D)

+

6. If the temperature of one mole of a gas varies with its volume asT= T0+ V2where T0and are positive constant.

The volume of gas, when its pressure is minimum, would be

(A) 0T

(B)

2

0T

(C) 0

1

T

(D) 0

( 1)

( 1)T

+

SECTION - 2

One or More Options Correct Type

This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONE

OR MORE are correct.

7. Two waves travel on the same string. It is possible for them to have

(A) Different frequencies (B) Different speeds

(C) Different wavelengths (D) The same frequency but different wavelengths


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8. A vibrating string 50.0 cm long is under a tension of 1.00 N. The

result from five successive stroboscopic pictures are shown in the

figure. The stroke rate is set at 6000 flashes per minute, and

observations revealed that the maximum displacement occurred at

flashes 1 and 5 with no other maxima in between.

(A) Frequency of vibration of string is 12.5 Hz

12

3

4

5 1

2

3

4

5

(B) Wavelength of waves on string is 0.5 m

(C) String vibrates in second overtone mode

(D) Mass of the string is 12.8 g

9. In a liquid of density 1300 kg/m3, longitudinal waves with frequency 400 Hz are found to be having a wavelength of

8.00 m.

(A) Bulk modulus of the liquid is 1.33 1010Pa

(B) Time taken by the wave to travel a distance of 6.4 km in the liquid is 2.00 s

(C) Liquid particles are displaced perpendicular to the direction of propagation of wave

(D) Velocity of the wave is increased when it is transmitted from the liquid to air at atmospheric pressure

10. A transverse displacement of a string (clamped at both ends) is given by ( ) 2

, 0.06 sin cos1203

xy x t t

= wherex,

yare in meters and t is in second. The length of string is 1.5 m and its mass is 3 10 2kg. Choose correct

options.

(A) Velocity of wave is 180 m/s (B) Tension in string is 648 N

(C) String is vibrating in its fundamental mode (D) String is vibrating in second harmonic

11. A thermodynamic system undergoes a cyclic process as shown in figure. The cycle consists of two loops : I and II.

P

V

I

II

(A) Over one complete cycle system does a positive work

(B) Over one complete cycle heat flows out of the system

(C) In each of the loop I and II net work done is positive

(D) In loop II heat flows into the system


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SECTION - 3

Paragraph Type

This section contains 2 paragraphs. Each describing theory, experiment, data etc. Four questions relate to two 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 Question Nos. 12 to 13

A spherical body of radius R, density , specific heat S, emissivity ehas an absolute temperature T. It receivesheat radiation at a rate of Iwatt/m2. (= Stefan's constant)

12. Maximum temperature attained by body is

(A)

1/4

I

S

(B)

1/4

I

R

(C)

1/4

I

(D)

1/4

I

13. Rate of change of temperature is inversely proportional to

(A)R (B)e

(C) (D) I


A transverse wave moving in a medium gets partially reflected and partially transmitted at the point of discontinuity

of the medium. The reflected wave changes its phase by radians if reflecting medium is denser, otherwise there

is no phase change in the reflected wave. In ideal cases, sum of energies of reflected and transmitted waves is

equal to the total energy of incident waves.

14. A transverse pulse travels along a string which is tied to another lighter string as shown in figure. Which of the

following pulse refers to a reflected pulse?

v

Heavierstring

Lighterstring

(A)

v

(B)

v

(C)

v

(D)

v


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15. If the amplitudes of reflected and incident waves areArandA

irespectively then in case of partial transmission, the

ratio Ai/A

r is

(A) Greater than 1 (B) Lesser than 1

(C) Lesser than equal to 1 (D) Greater than equal to 1

SECTION - 4

Matching Column Type

This section contains 2 multiple choice questions. Each question has matching Columns. The codes for the Columnshave choices (A), (B), (C) and (D) out of which ONLY ONEis correct.

16. Column I lists various laws related to thermal radiation and column II lists the related graphs. Match the columns.

Column I Column II

(P) Kirchhoff's law (1)

Temperature

Time

(Q) Stefan's law of radiation (2)

Rate ofradiation

Temperature

(R) Newton's law of cooling (3)

Temperature

Wavelength

(S) Wein's displacement law (4)

Emissivity

Absorptive power


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Codes :

P Q R S

(A) 2 1 4 3

(B) 3 2 1 4

(C) 4 2 1 3

(D) 4 2 3 1

17. A source of sound, an observer and the medium can move along thex-axis as shown in figure. vs, v0and vmare

velocities of source, observer and medium and +x-axis is considered positive direction. Column I lists various sets

of relative motion between source, observer and medium and column II lists apparent frequency heard by the observer.

If frequency of source is 350 Hz and speed of sound relative to medium is 340 m/s, then match the columns.

Column I Column II

Source Observer

vs

v0

xx

(P) vs= 20 m/s, v0= 10 m/s, vm= 0 (1) 320 Hz

(Q)vs= 10 m/s, v0= 20 m/s, vm= 0 (2) 331 Hz

(R) vs= 0 v0= 20 m/s, vm= 20 m/s (3) 361 Hz

(S) vs= 10 m/s, v0= 0, vm= +10 m/s (4) 371 Hz

Codes :P Q R S

(A) 3 2 4 1

(B) 3 1 2 4

(C) 3 2 1 4

(D) 2 4 3 1

SECTION - 5

Integer Value Correct Type

This section contains 3 questions. The answer to each of the question is a single digit integer, ranging from 0 to 9. The

appropriate bubbles corresponding to the respective question numbers in the ORS have to be darkened. For example,if the correct answers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of

bubbles will look like the following :

0

X

Y

Z 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9


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18. A tuning fork vibrating with frequency f0is dropped into a deep well at t= 0. The velocity of sound in air is v. The

frequency of sound heard by a man at the top of well at time tis 0

1

f

ngt

v+

. Find the value of n.

19. A tuning fork produces a sound of frequency f0and resonates with an air column of length l, closed at one end

vibrating in its fundamental mode at temperature T. If adiabatic exponent of the gas in column is , the molar mass

of gas is found to be 2 20

2

RT

l f

. Find the value of .

l, M

20. Assuming isothermal condition, height of centre of mass of a tall column of air in the earth's atmosphere above its

surface isnRT

Mg, where Tis temperature of air, Mis the average molar mass and Ris the gas constant. Find the

value of n.

PART - II : CHEMISTRY

SECTION - 1



ONE is correct.

21. A compound which leaves behind no residue on heating is

(A) Cu(NO3)2

(B) KNO3

(C) NH4NO

3(D) CaCO

3

22. In the contact process, the impurities of arsenic are removed by

(A) Fe2O3(Anhydrous) (B) Fe

2O3(Hydrated)

(C) Al(OH)3

(D) Cr(OH)3


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23. The hydride which does not act as a reducing agent due to the oxidation of hydrogen

(A) NH3 (B) CaH2

(C) NaH (D) LiAlH4

24. A metal which reacts with N2 is

(A) Li (B) Ca

(C) Mg (D) All of these

25. In ring test the formula of compound involves in formation of ring is

(A) [Fe(H2O)5NO2]2+ (B) [Fe(H2O)5NO]

2+

(C) [Fe(H2O)5NO]3+ (D) [Fe(H2O)5NO2]

3+

26. Which of the following does not exist as ionic lattice in solid state?

(A) PF5 (B) PBr5

(C) PI5 (D) PCl5

SECTION - 2

One or More Options Correct Type

This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONE

OR MORE are correct.

27. Which of the following compound/s of potassium and oxygen is/are known?

(A) K2O (B) K2O2

(C) KO2 (D) KO3

28. Which of the following is/are exit in liquid state at room temperature?

(A) Cl2O7 (B) Cl2O6

(C) ClO2 (D) Cl2O

29. The used organic solvent in industrial preparation of H2O2must

(A) Dissolve quinol (B) Dissolve quinone

(C) Resist oxidation (D) Be immiscible with water

30. Which of the following is/are intermediate hydride?

(A) CuH (B) ZnH2

(C) CdH2 (D) NaH

31. In which of the following compound none of the angle is 180?

(A) SF2(OCH3)2 (B) BrF3

(C) PF5 (D) XeF2


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SECTION - 3

Paragraph Type



(A), (B), (C) and (D).


A yellowish-white, deliquescent substance (A) reacts quickly with water by forming a solution B. A sample of B

gave a curdy white precipitate of (C) on adding AgNO3solution but this readily dissolved on addition of dilute NH4OH,

through gelatinous precipitate (D) was formed in its place. "D" dissolves in a conc. NaOH and on passing CO 2through solution reprecipitation of D results.

Also compound (A) dissolved unchanged in dry ether and when this solution was reacted with excess of LiH, a

new compound E was formed.

32. The compound (A) is

(A) AlCl3 (B) ZnCl2

(C) MgCl2 (D) SnCl2

33. Compound "E" on reaction BCl3form compound "F" containing boron, which of the following is not true for "F"?

(A) "F" on reaction with NH3(excess) at high temperature form inorganic benzene

(B) "F" is a non-planar molecule

(C) "F" is a Lewis acid

(D) "F" is gas at room temperature


White solid (A) on heating with NaOH gives an alkaline gas (B) and solid (C). Both (A) and (C) give ring test while

(C) gives golden yellow flame. (A) on strong heating it decomposed to give a gas (D) and H2O. (D) is a neutral

oxide. (D) on heating at 920C which gives two gases (E) and (F). The gas (E) when mixed with hydrogen at high

temperature and pressure under catalyst gives gas (B). Gas (F) is essential for living system.34. What is compound (A)?

(A) N3H (B) NH4NO2

(C) (NH4)2Cr2O7 (D) NH4NO3

35. The compound (D) is

(A) N2O (B) N2

(C) CO (D) O2


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SECTION - 4


This section contains 2 multiple choice questions. Each question has matching Columns. The codes for the Columns

have choices (A), (B), (C) and (D) out of which ONLY ONEis correct.

36. In Column I compounds are given and there solubility order from left to right are given in Column II. Match Column

I with Column II.

Column I Column II

(P) LiF, NaF, KF, RbF, CsF (1) Increases then decreases

(Q) LiCl, NaCl, KCl, RbCl, CsCl (2) Decreases and continue to decrease

(R) BeSO4, MgSO4, CaSO4, SrSO4 (3) Decreases then increases

(S) MgCl2, CaCl2, SrCl2, BaCl2 (4) Increases and continue to increase

Codes :

P Q R S

(A) 3 4 1 2

(B) 2 3 4 1

(C) 4 3 2 1

(D) 4 3 1 2

37. In Column (I) couple of compounds are given and the property exhibited by both of the compounds is given in

Column II. Match Column I with Column II.

Column I Column II

(P) SO3, H2O2 (1) Do not hydrolyse

(Q) CaCO3, KClO3 (2) Decomposes on heating

(R) P4O10, Cl2O7 (3) Has p-dlinkage

(S) NF3, SF6 (4) Acts as oxidizing agent

Codes :

P Q R S

(A) 2 4 1 3

(B) 4 2 3 1

(C) 4 3 2 1

(D) 2 1 3 4


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SECTION - 5



appropriate bubbles corresponding to the respective question numbers in the ORS have to be darkened. For example,

if the correct answers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of


0

X

Y

Z 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

38. In CHxBry, the value of 'y' at which dipole moment is highest is _______.

39. How many s-block elements from period 2 to period 5 do not give flame test?

40. What is the basicity of the metaphosphoric acid, form when P4O10is hydrolysed?

PART - III : MATHEMATICS

SECTION - 1



ONE is correct.

41. The condition that the parabolas y2= 4axand y2= 4c(x b) have a common normal other than x-axis (a, b, c

being distinct positive real numbers) is

(A) 1 2b

a c<

(C) 1b

a c<

(D) 1 1

b

a c < 0

(C) A pair of hyperbolas if < 0

(D) A pair of straight lines and a hyperbola if < 0 and 0


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48. For different values of k, the circlex2+ y2+ (8 + k)x+ (8 + k)y+ (16 + 12k) = 0, always passes through two fixed

points Pand Q. For k= k1, the tangents at Pand Qintersect at the origin. Which of the following is/are correct?

(A) The mid point of Pand Qis (6, 6) (B) The sum of ordinates of Pand Qis 12

(C) k1may be equal to32

9

(D) k1may be equal to

8

3

49. Given line L: xcos + 2ysin = 4

(A) Minimum area of triangle formed by the line Land axes in the first quadrant is 4 units

(B) If triangle formed by the line Land axes is isosceles, then equation of altitude corresponding to the line Lmay

be y+ x= 0

(C) If triangle formed by line Land axes is isosceles, then slope of an angle bisector may be 2 1+

(D) Locus of mid-point of the intercept of line Lbetween the coordinate axes is 2 24 1

1x y

+ =

50. Auxillary circle Cto the hyperbola with parametric equation ( 4 2 s ec , 3 2 tan ) and centre Ois drawn. From avariable point Pon the hyperbola in first quadrant, foot of perpendicular onx-axis is Q. From Q, tangent lying in 1st

quadrant is drawn to circle Cto meet it at R. Ris joined with Oand PSis drawn parallel to OR, where Slies on

x-axis. Mark the quantities that do not vary with position of point P.

(A)PQ

QR(B)

PS

OQ

(C) SQ (D) OS

51. A ray along L1 : x + y= 2 strikes the curve 8 cosx= , y= 2 sin ; 0 at Aand gets reflected. The

reflected ray L2strikes the curve x= 4t, y= 2t2, tRat Band gets reflected. The reflected ray is L

3. Which of

the following is/are correct?

(A) The coordinates ofAare (0, 2) and L2is alongx y= 2

(B) The coordinates ofAare (0, 2) and L2is along y x= 2

(C) The coordinates of Bare (4 4 2, 2 4 2) + and L3is alongx= 4 4 2

(D) The coordinates of Bare (4 4 2, 6 4 2 )+ + and L3is along 4 4 2x= +


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SECTION - 3

Paragraph Type



(A), (B), (C) and (D).


Given two fixed pointsAand Bin a plane and a positive real number knot equal to unity. Introduce a rectangular

Cartesian coordinate system by choosing mid point ofABas origin and the positive direction of x-axis is chosen

fromAto B. The locus of points Mfor which the equationMA

kMB

= holds is a circle Ck.

52. If the circles1

kC and

2 1 2

(0 1,0 1)k

C k k< < , are symmetric to each other with respect to the perpendicular

bisector of segmentAB, then

(A) k1 = k2 (B)k1k2< 1

(C) k1k2> 1 (D) k1k2= 1

53. An arbitrary circle passes through pointsAand Bintersects the circle Ckat an angle

(A)4

(B) Nothing can be said

(C)2

(D)


A family of rays having the equation (3 + 4)x+ (4 )y 7 = 0 is incident on an ellipse E1and the reflected

family of rays has the equation (3 + 4)x+ (4 3)y+ 7 + = 0. The point source of the incident family of rays

and point of convergence of reflected family of rays lie on axis of the ellipse. The foot of perpendicular drawn from

(1, 1) to any tangent of the ellipse (E1) lies onx2+ y2= 4. E2is another concentric ellipse that passes through the

foci of the first ellipse and also its foci lie on the first ellipse (E1).

54. What is the length of major axis of E2?

(A) 4 (B) 2

(C) 2 (D) 4 2

55. The number of common tangents to the circlex2+ y2= 1 and the ellipse E1is

(A) 0 (B) 1

(C) 2 (D) 4


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SECTION - 4


This section contains 2 multiple choice questions. Each question has matching Columns. The codes for the Columns

have choices (A), (B), (C) and (D) out of which ONLY ONEis correct.

56. A circle is given with centre Cand radius a> 0. Fixed points Sand S1lie on a diameter line of this circle and are

symmetric about C. Variable line segments SM are drawn so that Mlies on the circle. SMis produced to Hso that

SM= MH. Pis the point of intersection of line S1

Hand the perpendicular bisector of segment SH. Match conditions

given in column I with corresponding nature of locus of point Pgiven in column II.

Column I Column II

(P) Sand S1do not coincide and lie inside the circle (1) Circle

(Q)Sand S1coincide with C (2) Ellipse

(R) Sand S1do not coincide and lie on the circle (3) Single point

(S)Sand S1do not coincide and lie outside the circle (4) Hyperbola

Codes :

P Q R S

(A) 1 2 4 3

(B) 1 3 2 4

(C) 2 1 3 4

(D) 2 3 4 1

57. Match the following

Column I Column II

(P) The locus of middle points of the chords of the parabola (1) 16y2 9x2= 4x2y2

y2= 4xthat passes through the point (1, 4) lies on

(Q) The locus of middle point of chords of the parabola y2= 4x (2) y2 2x+ 8 = 0

which subtend a right angle at the vertex, lies on

(R) The locus of middle points of the portions of the tangents to (3)

2

28 41

23 9

x y + = 2 2

116 9

x y = , included between axis, lies on

(S) Consider the ellipse

2 2

116 9

x y+ = , the normal at any point (4) y2 4y 2x+ 2 = 0

Pof the ellipse cuts the major axis at N. The locus of

middle point of PN, lies on


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Codes :

P Q R S

(A) 4 1 2 3

(B) 2 4 3 1

(C) 1 3 4 2

(D) 4 2 1 3

SECTION - 5



appropriate bubbles corresponding to the respective question numbers in the ORS have to be darkened. For example,

if the correct answers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of


0

X

Y

Z 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

58. One of the diameters of the circle circumscribing the rectangleABCDisx 2y+ 1 = 0. VerticesAand Blie on the

line 3x+ y 2 = 0 and mid point of ABis (1, 1). Let is the area of the rectangle. If the diameter of circle is

12 5 units, then value of1120 2

is equal to ________.

59. A circle touches two sides PQand PSof a rectangle PQRSat Aand Brespectively, and passes through the

vertex R. If area of the triangle ABRis 5ABsq. units and if area of the rectangle PQRSis 'a' sq. units, then the

value of

' '

20

a

is equal to _______.

60. Lines ax2+ 2hxy ay2= 0 and 5x+ 12y= 13 form an isosceles triangle, then area of triangle is _______.


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Test - 3 (Paper - II) (Answers & Hints) All India Aakash Test Series for JEE (Advanced)-2014

TEST - 3 (Paper - II)

PHYSICS

1. (D)

2. (B)

3. (D)

4. (D)

5. (D)

6. (C)

7. (C, D)

8. (A, B, C)

9. (A, D)

10. (A, D)

11. (A, B, C, D)

12. (D)

13. (A)

14. (A)

15. (C)

16. (A)

17. (C)

18. (6)

19. (6)

20. (3)

CHEMISTRY

21. (C)

22. (C)

23. (C)

24. (D)

25. (D)

26. (B)

27. (A, B, C, D)

28. (A, B, C)

29. (B, C)

30. (A, B)

31. (A, B, C, D)

32. (B)

33. (D)

34. (A)

35. (B)

36. (B)

37. (B)

38. (8)

39. (5)

40. (3)

MATHEMATICS

41. (D)

42. (C)

43. (B)

44. (A)

45. (C)

46. (C)

47. (A, D)

48. (B, D)

49. (A, B, C, D)

50. (A, B, D)

51. (A, B, C, D)

52. (C)

53. (B)

54. (A)

55. (B)

56. (A)

57. (C)

58. (0)

59. (2)

60. (5)

ANSWERS

JEE Advanced 2014_Test 4 (Paper II) Code B

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Transcript of JEE Advanced 2014_Test 4 (Paper II) Code B