AMUEEE 2027 Sample Paper

SAMPLE PAPER

S A M P L E Q U E S T I O N P A P E R

AMUEEE 2027
Modelled on the actual exam pattern
.

QUESTIONS MAX MARKS TIME MARKING

135 135 150 Min +1 / 0

GENERAL INSTRUCTIONS

1. This paper contains 135 multiple-choice questions. All questions are compulsory.

2. Each question has four options — (A), (B), (C) and (D) — of which only one is correct.

3. Each correct answer carries 1 mark; there is no negative marking.

4. Total time allowed is 150 minutes. Manage your time across all sections.

5. Use of calculators, mobile phones or any electronic device is not permitted.

6. Attempt the paper first, then check your answers against the Answer Key at the end.

Candidate Name: Roll No.: Date:

SAMPLE PAPER

AMUEEE 2027
SAMPLE QUESTION PAPER

Questions 135 Max Marks 135 Time 150 Min Marking +1 / 0

Attempt all questions. Choose the one correct option for each.

PHYSICS

1. Two long straight wires vertically pierced the plane of
the paper at vertices of an equilateral triangle as shown
in figure. They each carry 2 A, out of the paper. The
magnetic field at the third vertex P has magnitude.

(A) 10 ^ - 5 T

(B) 14 × 10 ^ - 5 T

(C) 17 × 10 ^ - 5 T

(D) 0.85 × 10 ^ - 5 T

2. A piece of ice is tied using a string to the bottom of bucket A. The bucket is filled with water with ice completely
submerged in it.' Another bucket B is filled with water and a piece of ice is released in water. If floats on the surface of
water (see Fig.). What would be the impact on the level of water in the two buckets, when ice pieces melt away
completely?

(A) Level of water remain unchanged in both the buckets.

(B) Level of water will go down in bucket A, but will remain unchanged in bucket B.

(C) Level of water will go down in bucket, A but will go up in bucket B.

(D) Level of water will remain unchanged in bucket A, but will go up in bucket B.

3. Acceleration-time graph of a body moving in a straight 4. An alternating voltage V = 200 √( 2 ) ( 100 n ) volt is
line is as shown in figure. The body started its motion connected to a 1 μ F capacitor through an AC ammeter.
from rest. At what point is the body moving with the The reading of the ammeter
largest speed?
(A) 40 mA
(A) 1 (B) 20 √( 2 ) mA
(B) 2 (C) 20 mA
(C) 3 (D) 10 √( 2 ) mA
(D) 4

5. Figure shows three arrangements of electric field 6. One end of massless spring of spring constant 100
lines. In each arrangement, a proton is released from rest N/m and natural length 0.49 m is fixed and other end is
at point A and then i accelerated through point B by the connected to a body of mass 0.5 kg lying on a frictionless
electric field. Points A and B have equal separations in horizontal table. The spring remains horizontal. If the
the three arrangements. If p _ 1 , p _ 2 and p _ 3 are body is made to rotate at an angular velocity of 2 rad/s,
linear momentum of the proton at point B in the three then the elongation of the spring will be
arrangement respectively, then
(A) 2 cm
(A) p _ 1 > p _ 3 > p _ 2 (B) 1 cm
(B) p _ 1 > p _ 2 > p _ 3 (C) 0.5 cm
(C) p _ 2 > p _ 1 > p _ 3 (D) 0.25 cm
(D) ρ _ 1 = p _ 2 = ρ _ 3

7. Assume that the light of wavelength is 6000 Å coming 8. Two seconds after projection, a projectile is moving at
from a star. What is the time resolution of a telescope 30° above the horizontal, after one more second, it is
whose objective has a diameter of 100 inch? moving horizontally. The initial speed of the projectile is
(Take g = 10 ms ^ - 2 )
(A) 3.66 × 10 ^ - 7 rad

(B) 1.44 × 10 ^ - 7 rad (A) 10 m/s

(C) 2.9 × 10 ^ - 7 rad (B) 10/3 m/s

(D) 5.8 × 10 ^ - 7 rad (C) 20 m/s

(D) 2013 m/s

9. A rocket is moving at a speed of 200 m/s towards a 10. In a stack of three polarising sheets, the first and the
stationary target. While moving it emits a wave of third are crossed while the middle one has its axis at 45°
frequency 1000 Hz. Some of the sound reaching the to the axes of the other two. The fraction of intensity of
target gets reflected back to the rocket as an echo. The an incident unpolarised beam of light that is transmitted
frequency of the echo as detected by the rocket is by the stack is
(velocity of sound = 330 m/s)
(A) ½
(A) 1000 Hz (B) ⅓
(B) 1580 Hz (C) ¼
(C) 2540 Hz (D) ⅛
(D) 4080 Hz

11. The air pressure at sea level is 101325 Pa. At the 12. A small satellite is in elliptical orbit around the earth
centre of a rarefaction of a sound wave in air, the as shown in figure, L denotes the magnitude of its
pressure is 91000 Pa. Which is the most likely pressure at angular momentum and K denotes its kinetic energy. If 1
the centres of a compression of the same wave? and 2 denote two positions of the satellite, then

(A) 91000 Pa (A) L _ 2 = L _ 1 , K _ 2 = K _ 1

(B) 101000 Pa (B) L _ 2 = L _ 1 , K _ 2 > K _ 1

(C) 111650 Pa (C) L _ 2 > L _ · K _ 2 K _ 1

(D) 121000 Pa (D) L _ 2 = L _ 1 , K _ 2 K _ 1

13. A magnetic field cannot 14. A block is released from rest on a 45° smooth incline
and slide a distance d. The time taken to slide the same
(A) change the velocity of a charged particle.
distance is n times as much to slide on a 45° rough
(B) change the momentum of a charged particle.
incline than on the smooth incline. The coefficients of
(C) change the kinetic energy of a charged particle. friction for the rough incline is
(D) change the trajectory of a charged particle.
(A) √ 1 - 1 n ^ 2

(B) 1 - 1 n ^ 2

(C) √ 1 - 1 2 n ^ 2

(D) 1 - 1 2 n ^ 2

15. In Young's double slit experiment using 16. Identify the correct statement(s) from among the
monochromatic light of wavelength λ, the intensity of following (i) The constancy of the binding energy per
light at a point on the screen where the path difference is nucleon in the range 30 < A < 170 is a consequence of
λ, is k units. The intensity of the light at a point, where the fact that the nuclear force is short ranged (ii) The
path difference is λ/3 is nuclear force does not depend on the charge of nucleons
(ii) The nuclear force is replusive when distance between
(A) k/2
two nucleons is less than 0.8 fm
(B) k/3
(A) (i) only
(C) k/4
(B) (i), (iii)
(D) 2k/3
(C) (i), (ii)

(D) (i), (i), (ii)

17. Consider the following statements about the four 18. The displacement of a body is given by x = 4 t + 5 t ^
fundamental forces in nature. (i) The strong nuclear force 3 where x is in metre and t is in second. The difference
binds protons and neutrons in a nucleus. (ii) The strong between the average velocity of the body in the time-
nuclear force is about 10 times the electromagnetic force interval t =1 s to t= 2 s and its instantaneous- velocity at
in strength. (iii) The weak nuclear force is the weakest of t=1s is
all the four fundamental forces. (iv) The range of the
(A) 20.0 m/s
weak nuclear is about 10 ^ - 16 m The correct
(B) 22.5 m/s
statement(s) is (are)
(C) 27.0 m/s
(A) (i) only
(D) 39.0 m/s
(B) (ii) and (ii)

(C) (iii) and (iv)

(D) (i), (ii) and (iv)

19. Four charges each equal to (-Q) are placed at the 20. An electron is placed on X-axis where the electric
four corners of a square and a charge q is placed at its potential depends on x as shown in figures (the potential
centre. If the system of charges is in equilibrium, the does not depend on y and z). What is the electric force on
value of q is the electron ?

(A) ( Q )/( 4 ) ( 2 √( 2 ) - 1 ) (A) 40 × 10 ^ - 18 N

(B) ( Q )/( 4 ) ( 2 √( 2 ) + 1 ) (B) 80 × 10 ^ - 16 N

(C) ( Q )/( 2 ) Q √( 2 ) - 1 ) (C) 3.2 × 10 ^ - 56 N

(D) ( Q )/( 2 ) R √( 2 ) + 1 (D) 40 × 10 ^ - 16 N

21. Consider the following thermodynamical variables (i) 22. The combination of gates shown in figure yields
Pressure (ii) Internal Energy (ii) Volume (iv) Temperature
(A) NAND gate
Out of these, the intensive variable(s) is (are)
(B) OR gate
(A) (i) only
(C) NOT gate
(B) (i), (iv)
(D) XOR gate
(C) (i), (ii)

(D) (i), (ii), (iv)

23. Different curves in the figures show the behaviour of 24. Figure represents the position-time graph of a body
gases (i) Curve I represent ideal gas behaviour (ii) Curves of mass 4 kg. Impulse ( k g m s ^ - 1 ) imparted to the
II, III and IV also represents ideal gas behaviour at body at t = 0 is
different temperatures T _ 2 , T _ 3 and T _ 4 (iii) Curves
(A) 6
II, III and IV represents behaviour of a real gas at
(B) 4
different temperatures T _ 2 , T _ 3 and T _ 4 (iv) T _ 2 > T
_ 3 > T _ 4 (v) T _ 2 T _ 3 T _ 4 The correct statements are (C) 3

(D) 0
(A) (i), (ii),(iv)

(B) (i). (iii), (iv)

(C) (i) (iii), (v)

(D) (i), (ii), (v)

25. The relation between time t and distance x for a 26. An alpha particle accelerated through V volts is fired
moving particle is t = a x ^ 2 + β x , where α and β are towards a nucleus. It distance of closest approach is r. If
constants. If v is the velocity at distance X, then the a proton accelerated through the same potential is fired
retardation of the particle is towards the same nucleus, its distance of closest
approach will be
(A) 20 v ^ 3

(B) 2 β v ^ 3 (A) r

(C) 2 α β v ^ 3 (B) 2r

(D) 2 β ^ 2 v ^ 2 (C) r/2

(D) r/4

27. In electromagnetic waves travelling in vacuum (i) The 28. When a beam of 10.6 eV photons of intensity 2.0 W /
electric field E is always perpendicular to the magnetic m ^ 2 falls on a metallic surface of area 1 × 10 ^ - 4 m ^
field B. (ii) The cross product Ex B always gives the 2 , 0.53 \% of the incident photons eject photoelectrons.
direction in which the waves travel. (iii) The field E and B What is the number of photoelectrons emitted per
vary sinusoidally. (iv) There is a phase difference of ( π second?
)/( 2 ) between E and B. The correct statement(s) (are)
(A) 1.18 × 10 ^ 16
(A) (i), (iii) (B) 6.25 × 10 ^ 11
(B) (i), (iii), (iv) (C) 6.25 × 10 ^ 13
(C) (i), (ii), (iii), (iv) (D) 6.25 × 10 ^ 15
(D) (i), (ii), (iii)

29. Consider the following (i) Submarine communications 30. An inverter battery operated on 24 V and has
(ii) A.M. radio (iii) Shortwave ratio (iv) Radar Arrange the negligible internal resistance. It is rated at 140 ampere-
above in increasing frequency of the waves associated hour. What external resistance would have to be
with them connected to the battery, if it were to be discharged in 14
hours.
(A) (iv), (iii), (ii), (i)

(B) (i), (ii), (iii), (iv) (A) 1.6 Ω

(C) (ii), (i), (iv), (iii) (B) 2.4 Ω

(D) (ii), (iii), (iv), (i) (C) 5.9 Ω

(D) 10.0 Ω -

31. Two identical conducting spheres A and B carry equal 32. A particle of mass m is moving with a constant
charge. They are initially separated by a distance much velocity along a line parallel to the positive direction of
larger than their diameters and the force between them X-axis. The magnitude of its angular momentum with
is F. A third identical conducting sphere C is uncharged. respect to the origin
Sphere C is first touched to A, then to C and removed. As
(A) is zero.
a result, the force between A and B now is
(B) goes on increasing as x increases.
(A) F/16
(C) goes on decreasing as x increases.
(B) F/4
(D) remains constant for all positions of the particle.
(C) 3F/8

(D) F/2

33. Figure shows a potentiometer. Length of the 34. In a certain mass spectrometer, an ion beam passes
potentiometer wire AB is 100 cm and its resistance is 100 through a velocity filter consisting of mutually
Ω . EMF of the battery E is 2V. A resistance R of 50 Ω perpendicular fields E and B. The beam then enters a
draws current from the potentiometer. What is the region of another magnetic field B’, perpendicular to the
voltage across R when the sliding contact C is at the mid- beam. The radius of curvature of the resulting ion beam
point of AB? is proportional to

(A) 2 / 3 v (A) EB’/B

(B) 1 V (B) EB/B’

(C) 4 / 3 V (C) BB’/E

(D) 3 / 2 V (D) E/BB’

35. In the circuit, the galvanometer G shows zero 36. A sample of an ideal gas undergoes an isothermal
deflection. If the batteries A and B have negligible process as shown by the curve AB in the pV diagram. If Δ
internal resistance, then the value of R is Q , Δ U and Δ W represent the amount of heat absorbed
the change in internal energy and the work done
(A) 100 Ω
respectively, then which of the following statement is
(B) 200 Ω
correct?
(C) 500 Ω
(A) Δ Q = + ve, Δ U = 0 , Δ W = - v e
(D) 1000 Ω
(B) Δ Q = + v θ , Δ U = 0 , Δ W = + v e

(C) Δ Q = + v θ , Δ U = 0 , Δ W = 0

(D) Δ Q = + v e , Δ U = + v e , Δ W = + v e

37. Figure shows a rectangular copper plate with is 38. The only force acting on a 2 kg body that is moving
centre of mass at the origin O and side AB = 2BC = 2 m. If in xy-plane has a magnitude of 5 N. The body initially has
a quarter part of the plate (shown as shaded) is removed, a velocity of 4 m/s in the positive x-direction. Some time
the centre of mass of the remaining plate would lie at later, the body has a velocity of 6 m/s in the positive y-
direction. The work done on the body by the 5 N force
(A) ( 1 )/( 12 ) m , ( 1 )/( 6 ) m
during this time is
(B) ( 1 )/( 6 ) m , ( 1 )/( 12 ) m
(A) 20 J
(C) ( 1 )/( 3 ) m , ( 1 )/( 6 ) m
(B) 40 J
(D) ( 1 )/( 3 ) m , ( 1 )/( 2 ) m
(C) 52 J

(D) 72 J

39. The angle of prism and refractive index of the 40. A man throws a ball of mass 3.0 kg with a speed of
material of the prism are A and ( A )/( 2 ) , respectively. 5.0 m/s. His hand is in contact with the ball for 0.2 s. If he
The angle of minimum deviation of the prism is throws 4 balls in 2 seconds, the average force exerted by
him in 1 second is:
(A) ( π )/( 2 ) - A

(B) π - A (A) 15 N

(C) π - ( A )/( 2 ) (B) 30 N

(D) π - 2 A (C) 150 N

(D) 75 N

41. The nearest star to our solar system is 4.3 light years 42. The time period of a physical pendulum is 2 π √( I / m
away. The distance of this star in Parsec is (Mean g d ) , where I is the moment of inertia of the pendulum
distance between the earth and the sun = 5 × 10 ^ 11 m about the axis of rotation . and d is perpendicular
and one light year = 9.46 × 10 ^ 15 m ) distance between the axis of rotation and the centre of
mass of the pendulum. A circular ring hängs from a nail
(A) 3
on a wall. The mass of the ring is 3 kg and its radius is 20
(B) 8.0
cm. If the ring is slightly displaced, the time of resulting
(C) 13.0 oscillations will be
(D) 33 × 10 ^ 4
(A) 1.0 s

(B) 1.3 s

(C) 1.8 s

(D) 2.1 s

43. A cyclotron’s oscillator frequency is 10 MHz. What 44. Sound waves from a loudspeaker reach a point P via
should be the operating magnetic field for accelerating two paths which differ in length by 1.8 m. When the
protons? (mass of the proton = 167 x 10-27 kg) frequency of sound is gradually increased, the resultant
intensity at P is found to be maximum the frequency is
(A) 0.33 T
1000 Hz. At what next higher frequency will a maximum
(B) 0.66 T
be detected? (velocity of sound= 360 m/s)
(C) 1.5 T
(A) 1200 Hz
(D) 3.0 T
(B) 1400 Hz

(C) 1600 Hz

(D) 1800 Hz

45. Two solid spheres of the same metal but of mass M
and 8 M fall simultaneously in a viscous liquid. If their
terminal velocities are v and nv, then the value of n will
be

(A) 16

(B) 8

(C) 4

(D) 2

CHEMISTRY

46. Products (X and Y) of the following reactions (I and 47. Catalytic converters are generally made from
II) are : 1. array l 2 NaOH + Cl _ 2 NaCl + X + H _ 2 O \
(A) transition metals
(Cold and di.) array 2. array l 6 NaOH + 3 Cl _ 2 NaCl + Y
(B) alkaline metals
+ 3 H _ 2 O \ ( Hot and conc. ) array
(C) carbon
(A) X = NaClO _ 3 and Y = NaOCl
(D) hydrogen
(B) X = N a C l O and Y = N a O C l _ 3

(C) X = NaHClO _ 3 and Y = NaOCl

(D) X = NaClO _ 3 and Y = NaHClO _ 3

48. The EAN value y [ Ti ( σ - C _ 6 H _ 5 ) _ 2 ( π - C _ 5 H _ 49. The K _ sp of PbCO _ 3 and MgCO _ 3 , are 1.5 × 10 ^ -
5 ) _ 2 ] ^ ° is 15 and 1 × 10 ^ - 15 respectively at 298 K. The
concentration of Pb ^ 2 + ions in a saturated reactants
(A) 32
solution containing M g C O _ 3 and PbCO _ 3 is
(B) 33
(A) 1.5 × 10 ^ - 4 M
(C) 34
(B) 3 × 10 ^ - 8 M
(D) 35
(C) 2 × 10 ^ - 8 M

(D) 2.5 × 10 ^ - 8 M

50. Which of the following is an example of 51. A β - hydroxy carbonyl compound is obtained by the
thermosetting polymers? action of NaOH on

(A) Bakelite (A) R _ 3 CCHO

(B) PVC (B) C _ 6 H _ 5 CHO

(C) Nylon 6, 6 (C) CH _ 3 CHO

(D) Buna-S (D) HCHO

52. Which of the following structures represents a chiral 53. Which of the following radioactive element is used in
compound? the treatment of cancer?

(A) (A) Uranium

(B) (B) Thorium

(C) (C) Cerium

(D) (D) Plutonium

54. Structure anions of acids HNO _ 3 , H _ 3 PO _ 4 and H 55. The strongest base in the following is
_ 2 SO _ 4 are, respectively
(A)
(A) tetrahedral, tetrahedral and trigonal bipyramidal (B)
(B) angular, tetrahedral and trigonal bipyramidal (C)
(C) tetrahedral, tetrahedral and angular (D)
(D) planar, tetrahedral and tetrahedral

56. An ideal gas initially at temperature, pressure and 57. Which of the following structures contain sp-
volume, 27 ^ ° C , 1.00 bar and 10 L respectively is hybridised carbon atom(s)?
heated at constant volume until pressure is 10.0 bar ,it
(A) I, II and III
then undergoes a reversible isothermal expansion until
(B) I, III and IV
pressure is 1.00 bar what is the total work W during the
process? (C) II, III and IV

(D) I, II and IV
(A) - 23.02 × 10 ^ 3 J

(B) - 14.0 × 10 ^ 3 J

(C) 14.0 × 10 ^ 3 J

(D) Zero

58. A compound C _ 5 H _ 10 O ( A) forms a phenyl 59. The reaction quotient (Q) for the reduction of O _ 2 to
hydrazone and gives negative Tollen's test and a positive H _ 2 O in acid solution, O _ 2 ( g ) + 4 H ^ + ( a q ) + 4 e
Iodoform reaction. It also gives n-pentane on reduction. ^ - 2 H _ 2 O ( l ) is, [where, α _ H ^ + = activity of H ^ + ,
The compound ( A) is p _ O _ 2 = pressure of O _ 2 , when it is present in the
reaction, p ^ 0 = pressure of O _ 2 at standard state)].
(A) pentanal

(B) 2-pentanone (A) Q = p ^ ° α _ H ^ + ^ 4 + p _ 0 _ 2

(C) 3-pentanone (B) Q = P _ O _ 2 α _ H ^ + ^ 4 + ρ ^ °

(D) allyl alcohol (C) Q = α _ H ^ + ^ 4 + ρ _ 0 _ 2 p ^ °

(D) Q = α _ H ^ + ^ 4 + p ^ 0 p _ 0 _ 2

60. The intermediate product (X) formed in the following 61. For the reaction, ( 1 )/( 2 ) H _ 2 ( g ) + ( 1 )/( 2 ) Cl _ 2
reaction is B _ 2 H _ 6 + 6 NH _ 3 arrow 3 X Heat 2 B _ 3 N ( g ) H ^ + ( a q ) + Cl ^ - ( a q ) Δ G _ recation ^ ° = -
_ 3 H _ 6 + 12 H _ 2 131.23 kJ mol ^ - 1 The value of Δ G _ formation ^ ° of Ag
^ + ( a q ) shall be given by ,(if Δ G _ f ^ δ ( H ^ + a q ) =
(A) [ BH ( NH _ 3 ) _ 3 ] ^ + [ BH _ 4 ] ^ -
0
(B) [ BH _ 2 OH _ 3 ) _ 4 ] ^ + [ BH _ 4 ]
(A) - 54.12 kJ mol ^ - 1
(C) [ BH ( NH _ 3 ) _ 4 ] ^ + [ BH _ 4 ]
(B) - 131.23 kJ mol ^ - 1
(D) [ BH _ 2 ( NH _ 3 ) _ 2 ] ^ + · [ BH _ 4 ]
(C) + 77.11 kJ mol ^ - 1

(D) + 5412 k J mol ^ - 1

62. An example of non-stoichiometric hydride is 63. The following reactions show the H _ 2 O _ 2
behaviour in I and II reactions as: 1. array r PbS ( s ) + 4
(A) sodium hydride
H _ 2 O _ 2 ( a q ) PbSO _ 4 ( s ) \ + 4 H _ 2 O ( l ) array 2.
(B) beryllium hydride
HOCl + H _ 2 O _ 2 H _ 3 O ^ + + Cl ^ - + O _ 2
(C) lanthanum hydride
(A) Oxidising in acidic medium and reducing in basic
(D) diborane
medium

(B) Reducing in acidic medium and oxidising in basic
medium

(C) Oxidising in acidic medium and reducing in acidic
medium

(D) Reducing in acidic medium and oxidising in acidic
medium

64. The best reducing agent among the following is 65. The crystal field splitting energy (CFSE) for [ CoCl _ 6
] ^ 4 - is about 18000 cm ^ - 1 What would be the CFSE
(A) NH _ 3
value of [ CoCl _ 4 ] ^ 2 - ?
(B) SbH _ 3
(A) 18000 cm ^ - 1
(C) P H _ 3
(B) 8000 cm ^ - 1
(D) AsH _ 3
(C) 16000 cm ^ - 1

(D) 2000 cm ^ - 1

66. Which one acts as refrigerant? 67. Which of the following has the maximum vapour
pressure?
(A) CF _ 2 Cl _ 2

(B) CF _ 4 (A) HCI

(C) CFCl _ 3 (B) HBr

(D) CF _ 3 Cl (C) Hf

(D) HI

68. Which of the following is most soluble in water? 69. The rate constant, the activation energy and the
Arrhenius parameter of a chemical reaction at 25 ^ ° C
(A) CsClO _ 4
are 3.0 × 10 ^ - 4 s ^ - 1 , 104.4 kJ mol ^ - 1 and 6.0 × 10
(B) NaClO _ 4
^ 14 s ^ - 1 respectively. The value of the rate constant
(C) k Cl O _ 4 at T arrow ∞ is
(D) LiClO _ 4
(A) 2.0 × 10 ^ 18 s ^ - 1

(B) 60 × 10 ^ 14 s ^ - 1

(C) 3.6 × 10 ^ 30 s ^ - 1

(D) Infinity

70. Which one of the following set of metals deposits an 71. The difference between C _ p and C _ V is [ C _ p and
anode mud during the process of electrolytic refining of C _ V signify molar quantities]
copper?
(A) larger in case of gases in comparison to solids and
(A) Sn and Ag liquids

(B) Pb and Zn (B) larger in case of liquids in comparison to gases and

(C) Ag and Au solids

(D) Fe and Ni (C) larger in case of solids in comparison to gases liquids

(D) equal in solids, liquids and gases

72. Which of the following metal ions is expected to be 73. Aspartame is an
coloured?
(A) alkaloid
(A) Zn ^ 2 + (B) insecticide
(B) Ti ^ 3 + (C) artificial sweetener
(C) Sc ^ 3 + (D) antiseptic
(D) Ti ^ 4 +

74. Which of the following cations has the strongest 75. For the reaction A + B arrow P = - ( d [ A ] )/( d t ) = -
tendency towards complex formation? ( d [ B ] )/( d t ) = k [ A ] [ B ] k t = 1 [ A ] _ 0 - [ B ] _ 0 [ A
] [ B ] _ 0 [ B ] [ A ] _ 0 when , [ A ] _ 0 ≠ [ B ] _ 0 and
(A) Sm ^ 3 +
when, [ A ] _ 0 ≠ [ B ] _ 0 . If, [ A ] _ 0 = [ B ] _ 0 then the
(B) L u ^ 3 +
integrated rate law will be
(C) Gd ^ 3 +
(A) k t = ( [ A ] )/( [ B ] )
(D) Yb ^ 3 +
(B) ( 1 )/( [ B ] ) = 1 [ A ] _ 0 + k t

(C) ( 1 )/( [ A ] ) = 1 [ B ] _ 0 + k t

(D) ( 1 )/( [ A ] ) = 1 [ A _ b . + k t or ( 1 )/( [ B ] ) = 1 [ B ] _
0+kt

76. What will be the pH of solution formed by mixing 10 77. Amongst the following interhalogen compounds
mL 0.1 M NaH _ 2 PO _ 4 and 15 mL 0.1 M Na _ 2 HPO _ 4 . which one is used for the production of UF _ 6 during ^
[Given: p K _ 1 = 2.12 , p K _ 2 = 7.2 ] 235 U enrichment process?

(A) 7.0 (A) ClF _ 3

(B) 6.9 (B) ClF _ 5

(C) 7.4 (C) IF _ 3

(D) 7.5 (D) IF _ 5

78. Which of the following compounds is (S)-4-chloro-1- 79. Which one of the following is not the use of SO _ 2 ?
methylcyclohexene?
(A) Preservative
(A) (B) Anti-chlor
(B) (C) Disinfectant
(C) (D) Insecticide
(D)

80. The most reactive to nucleophilic attack at the 81. The ratio of the half-life time ( t _ 1 / 2 ) to the three
carbonyl group is quarter life-time, ( t _ 3 / 4 ) , for a reaction that is second
order
(A)

(B) (A) depends directly on concentration of reactants

(C) (B) is independent of concentration of reactant

(D) (C) depends inversely on the concentration of reactants

(D) depends directly to the square of concentration of
reactants

82. The standard emf of the cell ( E _ cell ^ ° and 83. The solubility of pure oxygen in water at 20°C and
equilibrium constant ( K _ eq ) of the following reaction of 1.0 atmosphere pressure is 138 × 10 ^ - 3 mol/litre. What
298 K Cd ^ 2 + + 4 NH _ 3 leftharpoons Cd ( NH _ 3 ) _ 4 ^ will be the concentration of oxygen at 20°C and partial
2+ pressure of 0.21 atmosphere?

(A) E _ cell ^ ° = 1.0 V , K _ eq = 1.26 × 10 ^ 7 (A) 2.9 × 10 ^ - 4 mol/litre

(B) E _ cell ^ ° = 0.21 V , K _ eq = 1.26 × 10 ^ 7 (B) 5.8 × 10 ^ - 4 mol/litre

(C) E _ cell ^ ° = 1.0 V _ 1 K _ eq = 6.60 × 10 ^ 33 (C) 7.6 × 10 ^ - 4 mol/litre

(D) E _ cell ^ ° = 021 V , K _ eq = 6.60 × 10 ^ 33 (D) 11.6 × 10 ^ - 4 mol/litre

84. What are 'X' and 'Y ? 85. Which of the following complexes is optically active?

(A) (A) [ Co ( NH _ 3 ) _ 5 Cl ] ^ +

(B) (B) [ Co ( NH _ 3 ) C _ 5 ] ^ 3 -

(C) in both cases (C) c i s - [ Co ( en ) _ 2 Cl _ 2 ]

(D) in both cases (D) tans - [ Co ( en ) _ 2 Cl _ 2 ]

86. Which of the following carbocations is most stable? 87. For the given pV isotherms, which of the following is
correct for T _ 1 , T _ 2 , T _ 3 ?
(A) I

(B) II (A) T _ 1 T _ 2 T _ 3

(C) III (B) T _ 3 T _ 2 T _ 1

(D) IV (C) T _ 2 T _ 3 T _ 1

(D) T _ 1 T _ 3 T _ 2

88. 0.002 M solution of a weak acid has an equivalent 89. On heating an aldehyde with Fehling's reagent, a
conductance ( Λ ) 60 ohm ^ - 1 cm ^ 2 eq ^ - 1 What will reddish brown precipitate is obtained due to the
be the pH ? (Given Λ ^ ° = 400 ohm ^ - 1 cm ^ 2 eq ^ - 1 ] formation of
)
(A) R C O O ^ -
(A) 3.52 (B) CuO
(B) 2.52 (C) Cu _ 2 O
(C) 1.87 (D) R CH _ 2 OH
(D) 2.7

90. If χ _ 1 and χ _ 2 represent the mole fractions of a
component A in the vapour phase and liquid mixture
respectively, and p _ A ^ 0 and | p _ B ^ ° . represent
vapour pressures of pure A and pure B, then total vapour
pressure of liquid mixture is

(A) p _ A ^ ° χ _ 1 χ _ 2

(B) p _ A ^ ° x _ 2 χ _ 1

(C) p _ B ^ ° χ _ 1 χ _ 2

(D) p _ B ^ ° χ _ 2 χ _ 1

MATHEMATICS

91. y = acos(log x) + bsin(log x) is a solution of the 92. The solution of the inequality | x ^ 2 - 4 x | 5 is
differential equation
(A) (-1,5)
(A) x ^ 2 d ^ 2 y d x ^ 2 + x ( d y )/( d x ) + y = 0 (B) (-4,5)
(B) x d ^ 2 y d x ^ 2 + ( d y )/( d x ) + y = 0 (C) (-5,4)
(C) d ^ 2 y d x ^ 2 + ( d y )/( d x ) + y = 0 (D) (- 1,4)
(D) x d ^ 2 y d x ^ 2 + x ^ 2 ( d y )/( d x ) + y = 0

93. If ^ - 1 ( √( α ) ) - ^ - 1 ( √( α ) ) = x then sin x is equal 94. If g ( x ) = x ^ 2 + x - 2 and ( 1 )/( 2 ) ( g o f ) x = 2 x
to ^ 2 - 5 x + 2 then f(x) is equal to

(A) ^ 2 ( α / 2 ) (A) 2x-3

(B) ^ 2 ( α / 2 ) (B) 2x + 3

(C) α (C) 3x -2

(D) ( α / 2 ) (D) 2x-2

95. If four whole numbers taken at random are 96. If both roots of the equation x ^ 2 - 2 ( a - 1 ) x + ( 2
multiplied together, then the probability that the last a + 1 ) = 0 are positive, where a is a real number, then
digit in the product is 1, 3, 7, or 9, is
(A) a ( 4 , ∞ )
(A) 81/625 (B) a ( - ∞ , 0 ] [ 4 , ∞ ]
(B) 8/625 (C) a ( 1 , ∞ )
(C) 32/625 (D) a [ 4 , ∞ )
(D) 16/625

97. If ∫ _ 0 ^ ∞ [ 3 e ^ - x ] d x = l where [.] denotes the 98. A straight line has its extremities on two fixed
greatest integer function, then the value of l is straight lines and cuts off from them a triangle of
constant area C ^ 2 .Then the locus of the middle point of
(A) 0
the line is
(B) In3
(A) 2 x y = C ^ 2
(C) e ^ 3
(B) x y + C ^ 2 = 0
(D) 3 e ^ - 1
(C) 4 x ^ 2 y ^ 2 = C

(D) None of these

99. Let * be a binary operation on the set R of real 100. Which of the following is an incorrect statement?
numbers defined by a ^ * b = ( 3 a b )/( 7 ) then the
(A) n ^ 3 + 3 n ^ 2 + 5 n + 3 is divisible by 3 for all ne IN
identity element in R for ‘*’ is
(B) n ( n + 1 ) ( 2 n + 1 ) is divisible by 6 for all ne IN
(A) 3/7
(C) n ^ 2 - n + 41 is a prime number for all ne IN
(B) 3/14
(D) 7 ^ n - 3 ^ n is divisible by 4 for all ne IN where IN
(C) 2/3 denotes the set of all natural numbers.
(D) None of these

101. Leta, be the rth term of an AP, whose first term is a 102. If A = ( array l l l 0 & 1 & 2 \ 1 & 2 & 3 \ 3 & α & 1
and common difference is d. If for some positive integers array ) A ^ - 1 = ( array c c c ( 1 )/( 2 ) & - ( 1 )/( 2 ) & ( 1
m , n , m ≠ n , α _ m = ( 1 )/( n ) and α _ n = ( 1 )/( m ) )/( 2 ) \ - 4 & 3 & β \ ( 5 )/( 2 ) & - ( 3 )/( 2 ) & ( 1 )/( 2 )
then a – d equals array ) then

(A) ( 1 )/( m n ) (A) α = 2 , β = - ( 1 )/( 2 )

(B) 1 (B) α = 1 , β = - 1

(C) 0 (C) α = - 1 , β = 1

(D) ( 1 )/( m ) + ( 1 )/( n ) (D) α = ( 1 )/( 2 ) , β = ( 1 )/( 2 )

103. If Sand S' are the foci of the ellipse x ^ 2 25 + y ^ 2 104. The graph y ^ 2 + 2 x y + 50 | x | = 625 divides the
26 = 1 and P is any point on it then range of values of plane into regions. Then, the area of bounded regions is
SP.S'P is
(A) 500 sq units
(A) 9 ≤ f ( θ ) ≤ 16 (B) 1250 sq units
(B) 9 ≤ f ( θ ) ≤ 25 ) (C) 2500 sq units
(C) 16 ≤ f ( θ ) ≤ 25 (D) 800 sq units
(D) 1 ≤ f ( θ ) ≤ 16

105. The distance of the point of intersection of the line x 106. The area bounded by the curve y = \ array c l x ^ 1 /
- 3 = (1/2)(y - 4) = (1/2)(z - 5) and the plane x + y + z=17 x & x ≠ 1 \ e , & x = 1 array . and y = | x - e | is
from the point (3,4,5) is
(A) e ^ 2 / 2
(A) 2 (B) e ^ 2
(B) 3 (C) 2 e ^ 2
(C) 1/3 (D) 1
(D) 1/2

107. The angle between the line x - 2 y + z = 0 = x + 2 y - 108. If _ x arrow 0 | x | ^ | x | = 1 where [.] denotes the
2 z and the plane 5x – 2y – 2 +17 = 0 is greatest integer function, then the value of l is

(A) 30° (A) 1

(B) 60° (B) -1

(C) 90° (C) 0

(D) 0° (D) does not exist

109. If R is the set of real numbers and f:R → R is a 110. The shortest distance between the parabolas 2 y ^
function defined by f(x) = sin x, then f ^ - 1 ( [ - 1,1 ] ) is 2 = 2 x - 1,2 x ^ 2 = 2 y - 1

(A) {x{ x = nt, n is an integer} (A) 2 √( 2 )

(B) {xl x = 1/2 + 2nt, n is an integer} (B) 1 2 √( 2 )

(C) R (C) 4

(D) null set φ (D) √( ( 36 )/( 5 ) )

111. If A = [ array l l k & l \ m & n array ] and k.n ≠ lm, 112. A fair coin is tossed n times. Let the random
then the value of A ^ 2 - ( k + n ) A + ( k n - l m ) I equals variable X denote the number of times the head occurs. If
P[X = 1], P[X = 2) and P[X = 3] are in arithmetic
(A) The zero matrix of order 2 x 2
progression (AP), then the number n of independent trial
(B) A
is
(C) -A
(A) 7
(D) 2A where l is the identify matrix of order 2 x 2
(B) 10

(C) 12

(D) 14

113. Let A be an event that a family has children of both 114. The solution of the differential equation ( d y )/( d x
sexes and B be the event that the family has at most one )=2xy-y^22xy-x^2,
boy. If the family has 3 children then the events A and B
(A) x y ( x + y ) = C
are
(B) x y ( x - y ) = C
(A) dependent
(C) x ^ 2 y ( x - y ) = C
(B) independent
(D) x ^ 3 y ( x - y ) = C
(C) mutually exclusive

(D) None of these

115. The minimum value of z = 2 x _ 1 + 3 x _ 2 subject to 116. Let 0 α π , 0 β π and α + β - ( α + β ) = ( 3 )/( 2 )
the constraints 2 x _ 1 + 7 x _ 2 ≥ 22 x _ 1 + x _ 2 ≥ 6,5 x _ .Then the relation between α and β will be
1 + x _ 2 ≥ 10 and x _ 1 , x _ 2 ≥ 0 is
(A) α = β
(A) 14 (B) α > β
(B) 20 (C) α β
(C) 10 (D) α = ( β )/( 3 )
(D) 16

117. A five-digit number divisible by 3 is to be formed 118. The equation | | x | + | ( x )/( x - 1 ) | = x ^ 2 | x - 1 |
using the numbers 0, 1, 3, 4 and 5 without repetition. The will be always true for x, belonging to
total number of ways this can be done is
(A) [ 0,1 )
(A) 216 (B) \ 0 \ ( 1 , ∞ )
(B) 600 (C) ( - 1,1 )
(C) 240 (D) ( - ∞ , ∞ )
(D) 3125

119. The function ( x ^ 2 - 9 ) | x ^ 2 - 7 x + 12 | + ( | x | ) 120. The points z _ 1 = x + i y and z _ 2 = ( 1 )/( - x + i y )
is not differentiable at in the complex plane lie on

(A) 4 (A) a circle with centre origin

(B) 3 (B) a straight line through origin

(C) -3 (C) axis of X

(D) 0 (D) axis of Y

121. Let ( ( θ - α ) )/( ( θ - β ) ) = ( a )/( b ) , ( ( θ - α ) )/( ( 122. Area of one loop formed by | y | = | x | is
θ - β ) ) = ( c )/( d ) .Then the value of ( α - β ) equals
(A) 0
(A) ( a c - b d )/( a d + b c ) (B) 2
(B) ( a c + b d )/( a d + b c ) (C) 4
(C) ( a c + b d )/( a b + c d ) (D) 2π
(D) ( a c - b d )/( a b + c d )

123. The value of ( 2 ^ - 1 0.8 ) is 124. If a,b,c are the integers between 1 and 9 and a51,
b41, c31 are three-digit numbers and the value of
(A) 0.96
determinant D = | array c c c 5 & 4 & 3 \ a 51 & b 41 & c
(B) 0.80
31 \ a & b & i array | is zero, then a,b,c are
(C) 0.64
(A) in GP
(D) 0.18
(B) in AP

(C) equal

(D) None of the above

125. The length of perpendicular from the point i + 2 j + 126. Let a _ 1 , a _ 2 , a _ 3 , … . . a _ n be in AP. If 1 a _ 1
3 k to the line ( x - 6 )/( 3 ) = ( y - 7 )/( 2 ) = ( z - 7 )/( - 2 ) a_n+1a_2a_n-1+…+1a_na_1=Ka_1+a_n
[ 1 a _ 1 + 1 a _ 2 + … + 1 a _ n ] then K is equal to
(A) 6

(B) 7 (A) 1

(C) √17 (B) 2

(D) √14 (C) 3

(D) 5

127. A region in the xy-plane is bounded by the curve y = 128. A ray of light passing through the point (1, 2)
√ 25 - x ^ 2 and the line y = 0. If the point (a, a + 1) lies reflects on the X-axis at point A and the reflected ray
in the interior of the region, then passes through the point (5, 3). The coordinate of A is

(A) a ( - 4,3 ) (A) ( ( 5 )/( 13 ) , 0 )

(B) a ( - ∞ , - 1 ) ( 3 , ∞ ) (B) ( ( 13 )/( 5 ) , 0 )

(C) a ( - 1,3 ) (C) ( ( - 5 )/( 13 ) , 0 )

(D) None of these (D) ( ( - 13 )/( 5 ) , 0 )

129. The amplitude of the complex number 1 + α - i α is 130. The solution set of the in equality _ ( x / 3 ) ( x ^ 2 -
3 x + 2 ) ≥ 2 is
(A) π/4

(B) α - ( π )/( 4 ) (A) ( ( 1 )/( 2 ) , 2 )

(C) ( α )/( 2 ) - ( π )/( 4 ) (B) [ ( 1 )/( 2 ) , 2 ] )

(D) ( π )/( 4 ) - α (C) [ ( 1 )/( 2 ) , 1 ) ( 2 , ( 5 )/( 2 ) ]

(D) ( ( 1 )/( 2 ) , ( 5 )/( 2 ) )

131. The coefficient of x ^ 53 in the expansion Σ _ m = 0 132. The unit vector which is orthogonal to the vector i +
^ 100 10 ^ 0 C _ m ( x - 3 ) ^ 100 - m · 2 ^ m j + k and is coplanar with vectors i + 2 j - k and 2 i + j + 3
k , is
(A) ^ 100 C _ 47

(B) ^ 10 C _ 53 (A) i + 5 j - 6 k √( 62 )

(C) - 100 C _ 53 (B) i + 3 j - k √( 11 )

(D) - 100 C _ 100 (C) i + 7 i √( 50 )

(D) i + 2 j + k √( 6 )

133. Consider the following relations in the real numbers 134. Let f ( x ) = x ^ 3 + x , then the equation ( 2 )/( y - f
R _ 1 = \ ( x , y ) | x ^ 2 + y ^ 2 ≤ 25 \ R _ 2 = \ ( x , y ) y ≥ ( 2 ) ) + ( 3 )/( y - f ( 3 ) ) + ( 4 )/( y - f ( 4 ) ) = 0 , has
4 x ^ 2 9 \ then the range of R _ 1 R _ 2 is
(A) both roots lying in (f(2), f(3))
(A) [0,5] (B) exactly one root lying in (f(3), f(4))
(B) [-3,3] (C) exactly one root lying in ( - ∞ , f ( 2 ) )
(C) [-5,5] (D) exactly one root lying in ( f ( 4 ) , ∞ )
(D) [-3,5]

135. If A and B are disjoint sets, then B A ^ ′ where A' is
complement of A is equal to

(A) A

(B) B

(C) A'

(D) B’

ANSWER KEY

1. (C) 2. (B) 3. (B) 4. (C) 5. (B) 6. (B) 7. (C)

8. (D) 9. (D) 10. (D) 11. (C) 12. (B) 13. (C) 14. (B)

15. (C) 16. (D) 17. (A) 18. (A) 19. (B) 20. (D) 21. (B)

22. (B) 23. (B) 24. (A) 25. (A) 26. (A) 27. (A) 28. (B)

29. (B) 30. (B) 31. (C) 32. (D) 33. (A) 34. (D) 35. (A)

36. (B) 37. (B) 38. (A) 39. (D) 40. (B) 41. (A) 42. (B)

43. (B) 44. (A) 45. (C) 46. (B) 47. (A) 48. (A) 49. (B)

50. (A) 51. (C) 52. (D) 53. (B) 54. (D) 55. (A) 56. (A)

57. (D) 58. (B) 59. (A) 60. (D) 61. (B) 62. (C) 63. (C)

64. (B) 65. (B) 66. (A) 67. (A) 68. (D) 69. (B) 70. (C)

71. (A) 72. (B) 73. (C) 74. (B) 75. (D) 76. (C) 77. (A)

78. (A) 79. (D) 80. (B) 81. (B) 82. (B) 83. (A) 84. (B)

85. (C) 86. (B) 87. (A) 88. (A) 89. (C) 90. (B) 91. (A)

92. (A) 93. (A) 94. (A) 95. (D) 96. (D) 97. (B) 98. (A)

99. (D) 100. (C) 101. (C) 102. (A) 103. (C) 104. (B) 105. (B)

106. (B) 107. (D) 108. (A) 109. (C) 110. (B) 111. (A) 112. (A)

113. (B) 114. (B) 115. (A) 116. (A) 117. (A) 118. (B) 119. (A)

120. (B) 121. (B) 122. (C) 123. (A) 124. (B) 125. (B) 126. (B)

127. (C) 128. (B) 129. (C) 130. (C) 131. (C) 132. (A) 133. (A)

134. (B) 135. (B)