IPU CET 2027 Sample Paper B.Tech

SAMPLE PAPER

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

IPU CET 2027 (B.Tech)
Modelled on the actual exam pattern
.

QUESTIONS MAX MARKS TIME MARKING

150 600 150 Min +4 / −1

GENERAL INSTRUCTIONS

1. This paper contains 150 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 4 marks; 1 mark is deducted for each wrong answer.

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

IPU CET 2027 (B.Tech)
SAMPLE QUESTION PAPER

Questions 150 Max Marks 600 Time 150 Min Marking +4 / −1

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

PHYSICS

1. Choose the most appropriate option. An ideal fluid 2. Choose the most appropriate option. A solid cylinder
with pressure p flows through a horizontal pipe with of mass 20 kg rotates about its axis with angular speed
radius r. If the radius of the pipe is increased by a factor 100 rad s⁻¹. The radius of the cylinder is 0.25 m. What is
of 2, which of the following most likely gives the new the kinetic energy associated with the rotation of
pressure? cylinder? What is the magnitude of angular momentum of
cylinder about its axis?
(A) p

(B) 4p (A) 62.5 T-s

(C) 16p (B) 70.4 T-s

(D) The new pressure cannot be determined without more (C) 79.6 T-s

information (D) 60.5 T-s

3. Choose the most appropriate option. The resistance R 4. Choose the most appropriate option. If electrical force
of a conductor varies with temperature t as shown in between two charges is 200 N and we increase 10%
figure. If the variation is represented by R _ t = R _ 0 ( 1 + charge on one of the charges and decrease 10% charge
α t + β t ^ 2 ) . Then, on the other, then electrical force between them for the
same distance becomes
(A) α and β bothe negative

(B) α is positive and β is negative (A) 200 N

(C) α and β both are positive (B) 202 N

(D) α is negative and β is negative (C) 198 N

(D) 19 N

5. Choose the most appropriate option. An electric 6. Choose the most appropriate option. A beam of light
charge q is placed at the centre of a cube of side l. The (λ = 600 nm) from a distant source, falls on a single slit 1
electric flux through one of its faces will be mm wide and the resulting diffraction pattern is observed
on a screen 2 m away. The distance between the first
(A) q ε _ 0
dark fringes on either side of the central bright fringe is
(B) q 6 ε _ 0
(A) 1.2 cm
(C) q ε _ 0 l ^ 2
(B) 1.2 mm
(D) q 4 π ε _ 0 l ^ 2
(C) 2.4 cm

(D) 2.4 mm

7. Choose the most appropriate option. As given in the 8. Choose the most appropriate option. If a guitar string
figure a series circuit connected across a 200 V, 60 Hz is 0.5 m long, what is the wavelength of its third
line consists of a capacitor of capacitive reactance 30 Ω, harmonic?
a non-inductive resistor 44 Ω, a coil of inductive
(A) 0.25 m
reactance 9012 and another resistance of resistance 36
(B) 0.33 m
Ω. The power dissipated in the circuit is
(C) 0.5 m
(A) 320 W
(D) 1 m
(B) 176 W

(C) 144 W

(D) 0 W

9. Choose the most appropriate option. Two spherical 10. Choose the most appropriate option. An air bubble
conductors A and B of radii 1mm and 2mm are separated starts rising from the bottom of a lake. Its diameter is 3.6
by a distance of 5 cm and are uniformly charged. If the mm at the bottom and 4 mm at the surface. The depth of
spheres are connected by a conducting wire, then at the lake is 250 cm and the temperature at surface is
equilibrium condition, the ratio of the magnitude of the 40°C. What is the temperature at the bottom of the lake?
electric fields at the surface of spheres A and B is Given atmospheric pressure = 76 cm of Hg and g = 980
cm / s ^ 2
(A) 4:1

(B) 1:2 (A) 11°C

(C) 2:1 (B) 12.36°C

(D) 1:4 (C) 13°C

(D) 10.37°C

11. Choose the most appropriate option. If torques of 12. Choose the most appropriate option. If 10% of a
equal magnitudes are applied to a hollow cylinder and a radioactive substance decays in every 5 yr, then the
solid sphere both having the same mass and radius. The percentage of the substance that will have decayed in 20
cylinder is free to rotate about its standard axis of yrs, will be
symmetry and the sphere is free to rotate about an axis
(A) 40%
passing through its centre. Which of the two will acquire
(B) 50%
a greater angular speed after a given time?
(C) 65.6%
(A) ω _ 1 > ω _ 2
(D) 34.4%
(B) ω _ 1 = ω _ 2

(C) ω _ 2 > ω _ 1

(D) None of these

13. Choose the most appropriate option. The Young's 14. Choose the most appropriate option. An ideal gas is
modulus of brass and steel are 10 × 10 ^ 10 Nm ^ - 2 and taken through a cyclic thermodynamical process through
20 × 10 ^ 10 Nm ^ - 2 , respectively. A brass wire and four steps. The amounts of heat involved in these steps
steel wire of the same length are extended by 1 mm are Q _ 1 = 5960 J, Q _ 2 = -5585 J, Q _ 3 = -2980 J and Q _
under the same force. If the radii of the brass and steel A = 3645 J, respectively. The value of W _ 4 is
wires are R _ B and R _ S respectively, then
(A) 1315 J
(A) R _ S = R _ B 4 (B) 275 J
(B) R _ S = 4 R _ B (C) 765 J
(C) R _ s = √( 2 ) , R _ B (D) 675 J
(D) R _ S = R _ B √( 2 )

15. Choose the most appropriate option. A stretched 16. Choose the most appropriate option. A wire of
string of length 1 m fixed at both ends, when vibrated in arbitrary shape carries a current I = 2A. Consider the
one loop has a frequency 200 Hz. It is now plucked at a portion of wire between (0,0,0) and (4, 4, 4). A magnetic
point situated at 25 cm from one end. The stretched filled given by B = ( 1.2 × 10 ^ - 4 1 + 2 × 10 ^ - 4 j )
string would vibrate with a frequency of exists in the region. The force acting on the given portion
of the wire is
(A) 100 Hz

(B) 200 Hz (A) x = 10.25 sin (ot + o)

(C) 400 Hz (B) x = 10.25 sin (wt - )

(D) 800 Hz (C) X = 11.25 sin (wt + o)

(D) x = 11.25 sin (ot - 0)

17. Choose the most appropriate option. An electron of a 18. Choose the most appropriate option. If pressure of
stationary hydrogen atom passes from the fifth energy CO _ 2 (real gas) in a container is given by P = ( R T )/( 2 v
level to the ground level. The velocity that the atom - b ) - a 4 b ^ 2 , then mass of the gas in the container is
acquired as a result of photon emission will be
(A) 11 g
(A) ( 24 h R )/( 25 m ) (B) 22 g
(B) ( 25 h R )/( 24 m ) (C) 33 g
(C) ( 24 m )/( 25 h R ) (D) 44 g
(D) ( 25 m )/( 24 h R )

19. Choose the most appropriate option. When a piece of 20. Choose the most appropriate option. A child swings a
metal is illuminated by a monochromatic light of ball on a string in a circular motion. The ball moves in a
wavelength λ, then stopping potential is 3Vs When same plane vertical to the ground. If the sun is directly
surface is illuminated by light of wavelength 2λ, then overhead how does the shadow move?
stopping potential becomes Vs. The value of threshold
(A) In a circle
wavelength for photoelectric emission will be
(B) In an ellipse
(A) 4 λ
(C) In a figure 8 patterns
(B) 8 λ
(D) Back and forth along a straight line
(C) 4λ/3

(D) 6 λ

21. Choose the most appropriate option. The bob of a 22. Choose the most appropriate option. A tank is filled
pendulum is released from a horizontal position A as with a liquid upto a height H. A small hole is made at the
shown in the figure. If the length of the pendulum is 1.5 bottom of this tank. Consider t _ 1 be the time taken to
m, what is the speed with which the bob arrives at the empty first half of the tank and t _ 2 be the time taken to
lower most point B, given that it dissipated 5% of its empty rest half of the tank. Then, determine the ratio t _
initial energy against air resistance? 1t_2.

(A) 5 m/s (A) 1.33

(B) 5.5 m/s (B) 1.5

(C) 5.3 m/s (C) 2

(D) 4.4 m/s (D) 0.414

23. Choose the most appropriate option. A proton and an 24. Choose the most appropriate option. A ray of
electron are placed in a uniform electric field. Which of unpolarised light is incident on a glass plate at the
the following is correct? polarising angle of 57°. Now,

(A) The electric forces acting on them will be equal (A) both the reflected and transmitted rays will be

(B) The magnitude of the forces will be equal completely polarised

(C) Their accelerations will be equal (B) the reflected ray will be completely polarised and
transmitted ray will be partially polarised
(D) The magnitude of their accelerations will be equal
(C) the reflected ray will be partially polarised and
transmitted ray will be completely polarised

(D) both the reflected and transmitted rays will be partially
polarised

25. Choose the most appropriate option. A smooth 26. Choose the most appropriate option. The resistors in
inclined plane of length L having inclination θ with the the circuits below each represent a light bulb. If all three
horizontal inside a lift which is moving down with circuits use the same size battery, which circuit will
retardation α. The time taken by a body to slide down the produce the most light?
inclined plane, from rest, will be
(A) I only
(A) √( ( 2 L )/( g θ ) ) (B) II only
(B) √( ( 2 L )/( α θ ) ) (C) III only
(C) √( ( 2 L )/( ( g + α ) θ ) ) (D) I, II and III will produce the same amount of light
(D) √( ( 2 L )/( ( g - α ) θ ) )

27. Choose the most appropriate option. During an 28. Choose the most appropriate option. For constructive
adiabatic process, the pressure of a gas is found to be interference to take place between two monochromatic
proportional to the cube of its absolute temperature. The light waves of wavelength λ, the path difference should
ratio of C _ p C _ v for the gas is be

(A) 3/2 (A) ( 2 n - 1 ) ( λ )/( 4 )

(B) 5/3 (B) ( 2 n + 1 ) ( λ )/( 4 )

(C) 4/3 (C) ( 2 n - 1 ) ( λ )/( 5 )

(D) 2 (D) n λ

29. Choose the most appropriate option. A metallic ball 30. Choose the most appropriate option. A light ray falls
has spherical cavity at its centre. If the ball is heated, on a square glass slab as shown in the figure. The index
what happens to the cavity? of refraction of the glass, if total internal reflection is
occur at vertical face, is equal to
(A) Its volume increases

(B) Its volume decreases (A) ( √( 2 ) + 1 ) 2

(C) Its volume remains unchanged (B) √( ( 5 )/( 2 ) )

(D) Its volume may decrease or increase depending upon (C) ( 3 )/( 2 )

the nature of heating process (D) √( ( 3 )/( 2 ) )

31. Choose the most appropriate option. The potential 32.  Choose the most appropriate option. A ball is thrown
energy of gravitational interaction of a point mass m and from the ground to clear a wall 3 m high at a distance of
a thin uniform rod of mass M and length L, if they are 6 m and falls 18 m away from the wall, the angle of
located along a straight line at a distance a from each projection of ball is
other, is
(A) ^ - 1 ( ( 3 )/( 2 ) )
(A) U = ( G M m )/( a ) ( ( a + L )/( a ) ) (B) ^ - 1 ( ( 2 )/( 3 ) )
(B) U = G M m ( ( 1 )/( a ) - ( 1 )/( a + L ) ) (C) ^ - 1 ( ( 1 )/( 2 ) )
(C) U = - ( G M m )/( a ) (D) ^ - 1 ( ( 3 )/( 4 ) )
(D) U = - ( G M m )/( L ) ( ( a + L )/( a ) )

33. Choose the most appropriate option. Two identical 34. Choose the most appropriate option. Two liquid
thin plano-convex glass lenses (refractive index 1.5) each drops of equal radii are falling through air with the
having radius of curvature of 20 cm are placed with their terminal velocity v. If these two drops coalesce to form a
convex surfaces in contact at the center. The intervening single drop, its terminal velocity will be
space is filled with oil of refractive index 1.7. The focal
(A) √( 2 ) v
length of the combination is:
(B) 2v
(A) -20 cm
(C) √ [ 3 ] 4 v
(B) -25 cm
(D) √ [ 3 ] 2 v
(C) -50 cm

(D) 50 cm

35. Choose the most appropriate option. The wavelength 36. Choose the most appropriate option. In a car race,
of the de-Broglie wave associated with a thermal neutron car A takes a timet less than car B at the finish and
of mass m at absolute temperature T is given by (here, K passes the finishing point with speed v more than that of
is the Boltzmann constant) the car B. Assuming that both the cars starts from rest
and travel with constant accelerations a _ 1 , and a _ 2
(A) h √( m K T )
respectively. So, the value of v will be
(B) h √( 2 m k T )
(A) ( √ a _ 1 / a _ 2 ) t
(C) h √( 3 m k T )
(B) ( √ a _ 2 / a _ 1 ) t
(D) h 2 √( m k T )
(C) ( a _ 1 √ a ^ 2 ) t

(D) ( √ a _ 1 a _ 2 ) t

37. Choose the most appropriate option. A liquid is 38. Choose the most appropriate option. The image seen
poured into a vessel at rest with the hole in a wall closed in a flat bathroom mirror is a
by a valve. It is filled to height H. The distance of hole
(A) real image that appears behind the mirror
from the top surface is h. What is the horizontal
(B) real image that appears in front of the mirror h on
acceleration required to move the vessel so that the
liquid does not come out when the valve is opened (C) virtual image that appears behind the mirror

(given, 1 = length of the base)? (D) virtual image that appears in front of the mirror

(A) 2 gh

(B) g

(C) l/gH

(D) 2gh/l

39. Choose the most appropriate option. If the escape 40. Choose the most appropriate option. The coefficient
speed of a projectile on Earth's surface is 11.2 kms ^ - 1 of volume expansion of glycerine is 49 × 10 ^ - 5 K ^ - 1 .
and a body is projected out with thrice this speed, then What is the fractional change in its density for a 30°C rise
determine the speed of the body far away from the Earth. in temperature?

(A) 56.63 kms ^ - 1 (A) 1.5 × 10 ^ - 2

(B) 33 kms ^ - 1 (B) 2 × 10 ^ - 4

(C) 39 kms ^ - 1 (C) 3.5 × 10 ^ - 3

(D) 31.7 kms ^ - 1 (D) 2.5 × 10 ^ - 2

41. Choose the most appropriate option. Average energy 42. Choose the most appropriate option. Electrons are
in one time period of a simple harmonic oscillator whose accelerated through a potential difference Vₒ and protons
amplitude is A, angular velocity ω and mass m , is are accelerated through a potential difference of 4 V. The
de-Broglie wavelengths are λ _ e and λ _ p for electrons
(A) ( 1 )/( 4 ) m ω ^ 2 A ^ 2
and protons, respectively. The ratio of λ _ e λ _ p is given
(B) ( 1 )/( 2 ) m ω ^ 2 A ^ 2
by (given, me is mass of electrons and mₚ is mass of
(C) m ω ^ 2 A ^ 2 proton)
(D) ( 1 )/( 3 ) m ω ^ 2 A ^ 2
(A) λ _ e λ _ p = √ m _ p m _ e

(B) λ _ e λ _ p = √ m _ e m _ p

(C) λ _ e λ _ p = ( 1 )/( 2 ) √ m _ e m _ p

(D) λ _ e λ _ p = 2 √ m _ p m _ e

43. Choose the most appropriate option. A drop of liquid 44. Choose the most appropriate option. A body takes 5
of density p is floating half-immersed in a liquid of min for cooling from 50°C to 40°C. Its temperature comes
density d. If σ is the surface tension, then the diameter down to 33.33°C in next 5 min. Temperature of the
of the drop of the liquid is surroundings is

(A) √( ( σ )/( g ( 2 ρ - d ) ) ) (A) 15°C

(B) √( ( 2 σ )/( g ( 2 ρ - d ) ) ) (B) 20°C

(C) √( ( 8 σ )/( g ( 2 ρ - d ) ) ) (C) 18°C

(D) √( ( 12 σ )/( g ( 2 ρ - d ) ) ) (D) 17°C

45. Choose the most appropriate option. Two identical 46. Choose the most appropriate option. A capacitor of
wires A and B have the same length L and carry the same capacitance 5 μ F is connected as shown in the figure.
current I. Wire A is bent into a circle of radius R and wire The internal resistance of the cell is 0.5 Ω . The amount
B is bent to form a square of side a. If B₁ and B₂ are the of charge on the capacitor plate is
values of magnetic induction at the centre of the square
(A) Zero
respectively, then the ratio is B _ 1 B _ 2 is
(B) 5 μ C
(A) ( π ^ 2 8 )
(C) 10 μ C
(B) ( π ^ 2 8 √( 2 ) )
(D) 25 μ C
(C) ( π ^ 2 16 )

(D) ( π ^ 2 16 √( 2 ) )

47. Choose the most appropriate option. A block of mass 48. Choose the most appropriate option. Velocity of
mis in contact with the cart C as shown in the figure. The sound in a gaseous medium is 330 m s ^ - 1 . If the
coefficient of static friction between the block and the pressure is increased by 4 times without change in
cart is u. The acceleration a of the cart that will prevent temperature, the velocity of sound in the gas is
the block from falling satisfies.
(A) 330 m s ^ - 1
(A) α > ( m g )/( μ ) (B) 660 m s ^ - 1
(B) α > ( g )/( 2 μ ) (C) 156 m s ^ - 1
(C) α ≥ ( g )/( μ ) (D) 990 m s ^ - 1
(D) α ( g )/( μ )

49. Choose the most appropriate option. Consider the
analogy between an oscillating spring-body system and
an oscillating L-C-R circuit. Then, the correspondence
between the two systems that is NOT correct is

(A) charge q corresponds to displacement x of the body

(B) inductance L corresponds to mass m of the body

(C) capacitance C corresponds to spring constant k

(D) magnetic energy corresponds to kinetic energy of the
body

50. Choose the most appropriate option. Although waves in the open ocean propagate in all directions, waves
washing into any shore usually move nearly perpendicular to the shore. Which of the following best explains the
reason for this phenomenon?

(A) The shallow water decreases the speed of the waves causing them to refract

(B) The shallow water increases, the speed of the waves causing them to refract

(C) The shallow water decreases the speed of the waves causing them to diffract

(D) The shallow water increases the speed of the waves causing them to diffract

CHEMISTRY

51. Choose the most appropriate options. The ozone 52. Choose the most appropriate option. The atomic
layer forms naturally by radius of Ne is

(A) the interaction of CFC with oxygen. (A) greater than Ar

(B) the interaction of UV radiations with oxygen. (B) less than Ar

(C) the interaction of IR radiations with oxygen (C) same as Ar

(D) the interaction of water vapour and oxygen. (D) cannot be determined

53. Choose the most appropriate options. Which of the 54. Choose the most appropriate option. Compared to an
following is used as a food preservative? electron with a principal quantum number of 1, an
electron with a principal quantum number of 2 will have a
(A) Sodium benzoate

(B) Potassium chloride (A) lower energy

(C) Sodium bicarbonate (B) higher energy

(D) b and c both (C) negative spin

(D) positive spin

55. Choose the most appropriate options. Rate of 56. Choose the most appropriate options. Among [ Ni (
dehydration of alcohols follows the order CN ) _ 4 ] ^ 2 - , [ NiCl _ 4 ] ^ 2 - and [ Ni ( CO ) _ 4 ]

(A) 2 ^ ° > 1 ^ ° CH _ 3 OH > 3 ^ ° (A) [ NiC _ 4 ] ^ 2 - is square planar and [ Ni ( CN ) _ 4 ] ^ 2

(B) 3 ^ ° > 2 ^ ° > 1 ^ ° > CH _ 3 OH - Ni ( CO ) _ 4 are tetrahedral

(C) 2 ^ ° > 3 ^ ° > 1 ^ ° > CH _ 3 OH (B) Ni ( CO ) _ 4 is square planar and [ Ni ( CN ) _ 4 ] ^ 2 - [
NiCl _ 4 ] ^ 2 - are tetrahedral
(D) CH _ 3 OH > 1 ^ 8 > 2 ^ ° > 3 ^ °
(C) N i ( CN _ 4 ] ^ 2 - is square planar [ NiCl _ 4 ] ^ 2 - Ni (
CO ) _ 4

(D)

57. Choose the most appropriate option. What is the 58. Choose the most appropriate options. If the dipole
total heat needed to change 1g of water from -10°C to moment of HBr is 2.60 × 10 ^ - 30 Cm and the
110°C at 1 atm? ( Δ H _ fusion = 80 cal / g , Δ H _ interatomic spacing is 1.41 Å, then the percent ionic
vaporisation = 540 cal / g . specific heat of ice and steam character of HBr is
are 0.5 cal/g °C)
(A) 16.23%
(A) -730 cal (B) 13.21%
(B) -630 cal (C) 11.50%
(C) 630 cal (D) 15.81%
(D) 730 cal

59. Choose the most appropriate option. An imaginary 60. Choose the most appropriate options. Consider the
metal crystallises in a cubic lattice. The unit cell edge following reactions, C ( s ) + O _ 2 ( g ) CO _ 2 ( g ) , Δ H =
length is 100 pm, (1 pm = 10 ^ - 12 m ). The density of - 94 kcal 2 CO ( g ) + O _ 2 2 CO _ 2 ( g ) Δ H = - 135.2 kcal
this metal is 200 g / cm ^ 3 . The atomic mass of the Then, the heat of formation of CO (g) is .: CI
metal is 2 g/mol. How many of these metal atoms are
(A) 26.4 kcal
there within a unit cell?
(B) - 26.4 kcal
(A) 1
(C) 41.2 kcal
(B) 2
(D) - 41.2 kcal
(C) 4

(D) 6

61. Choose the most appropriate option. Immediately, 62. Choose the most appropriate option. A 25 mL sample
upon bringing a hot piece of metal into a room, the heat of hard water is titrated with a 0.001 M solution of EDTA,
is felt from 5 m away. The type of heat transfer is and the end point of the titration is reached at 50 mL of
probably EDTA added.What is the concentration of Ca ^ 2 + and
Mg ^ 2 + ions in solution?
(A) convection

(B) transduction (A) 0.0005 M

(C) radiation (B) 0.001 M

(D) conduction (C) 0.002 M

(D) 0.006 M

63. Choose the most appropriate option. H _ 2 can be 64. Choose the most appropriate option. Which of the
added to ethylene in the presence of a heterogeneous following changes to a reaction will always increase the
catalyst such as solid What might account for the initial rate constant for that reaction?
attraction between the hydrogen molecules and the solid
(A) Decreasing the temperature
platinum?
(B) Increasing the temperature
(A) Hydrogen bonding
(C) Increasing the concentration of the reactants
(B) Metallic bonding
(D) Increasing the concentration of the catalyst
(C) Van der Waals' attractions

(D) The plasma continuum effect

65. Choose the most appropriate option. NH _ 3 has a K _ 66. Choose the most appropriate option. For the
b of 1.8 × 10 ^ - 3 . Which of the following has a 5.6 × 10 isoelectronic series S ^ 2 - , Cl ^ - , A r , K ^ + and v ,
^ - 10 ? which species requires the least energy to remove an
outer electron?
(A) NH _ 3

(B) NH _ 4 ^ + (A) S ^ 2-

(C) NH _ 2 ^ - (B) Cl ^ -

(D) H ^ + (C) Ar

(D) K ^ +

67. Choose the most appropriate options. The metallic 68. Choose the most appropriate option. Which of the
sodium dissolved in liquid ammonia to form a deep blue following choices represents ( 239 )/( 94 ) Pu producing a
colour solution.The deep blue colour is due to the position?
formation of
(A) _ 94 ^ 239 Pu _ 94 ^ 235 Pu + _ 2 ^ 4 He
(A) solvated electrons, e ^ - ( NH _ 3 ) _ x (B) _ 94 ^ 239 Pu _ - 1 ^ 0 e + _ 93 ^ 29 Np
(B) solvated atomic sodium Na ( NH _ 3 ) _ 4 (C) _ 94 ^ 239 Pu _ - 1 ^ 0 e _ 94 ^ 239 Np
(C) ( Na ^ + + Na ) (D) _ 94 ^ 239 Pu ^ 239 Np + _ + 1 ^ 0 e
93
(D) ( NaNH _ 2 + H _ 2 )

69. Choose the most appropriate options. On reduction 70. Choose the most appropriate options. The correct
of glycolic acid with HI, the product formed is increasing order of solubility of sulphates in water

(A) acetic acid (A) BeSO _ 4 > MgSO _ 4 > CaSO _ 4 > SrSO _ 4 > BaSO _ 4

(B) iodo acetic acid (B) BaSO _ 4 > SrSO _ 4 > CaSO _ 4 > MgSO _ 4 > BeSO _ 4

(C) formic acid (C) H _ 2 SO _ 3 , NO _ 2 and SO _ 2

(D) None of these (D) SO _ 2 , NO _ 2 and H _ 2 O

71. Choose the most appropriate options. Which one of 72. Choose the most appropriate options. When 'Z'
the following electrolytes is most effective for the grams of calcium carbonate completely burnt in air gives
coagulation of Fe ( OH ) _ 3 sol? 28g of a solid compound. The mass of calcium carbonate
halogens is correct? used will be
(A) NaCl

(B) Na _ 2 SO _ 4 (A) 200g

(C) Na _ 3 PO _ 4 (B) 100g

(D) As _ 2 S _ 3 (C) 56 g

(D) 50 g

73. Choose the most appropriate options. An aqueous 74. Choose the most appropriate option. Name the given
solution of 2% (wt/wt) non volatile solute exerts a compound : Cu ( ClO _ 4 ) _ 2
pressure of 1.004 bar at the boiling point of solvent.
(A) Copper (I) chlorate
What is the remove acidic impurities in metallurgical
(B) Copper (II) perchlorite
molecular mass of the solute?
(C) Copper (III) chlorate
(A) 0.3655
(D) Copper (II) perchlorate
(B) 36.55

(C) 41.34

(D) 40.16

75. Choose the most appropriate option. 20 g of NaCl is 76. Choose the most appropriate option. Which of the
poured into a coffee cup calorimeter containing 250 mL following statements is most likely true concerning the
of water. If the temperature inside the calorimeter drops given reaction? 2A(g) + B(g) → 2C(g) + D(s)
1°C by the time, the NaCl is totally dissolved, what is the
(A) Entropy of system is decreasing
heat of solution for NaCl and water? (specific heat of
(B) Entropy of system is increasing
water is 4.18 J/g °C.)
(C) The reaction is spontaneous
(A) -3 kJ/mol
(D) The reaction is non spontaneous
(B) – 1 kJ/mol

(C) 1 kJ/mol

(D) 3 kJ/mol

77. Choose the most appropriate options. Arrange the 78. Choose the most appropriate option. Which of the
following compounds in the increasing order of their following transition of an electron in H-atom will emit
reactivity towards HCN I. Acetaldehyde II. Acetone III. Di- maximum energy?
tert-butyl ketone
(A) n _ 6 n _ 5
(A) II I > II > IV > I (B) n _ 1 n _ 2
(B) II > I > IV > II (C) n _ 3 n _ 2
(C) IV > III > II > I (D) n _ 4 n _ 3
(D) II > IV > I > I

79. Choose the most appropriate options. Toluene reacts 80. Choose the most appropriate option. Which of the
with excess of Cl, in the presence of sunlight to give a following demonstrates non-ideal behaviour of a gas?
product which on hydrolysis followed by reaction with
(A) Some of the molecules move more rapidly than others
NaOH gives
(B) Condensation occurs at low temperatures
(A)
(C) The gas exerts a force on the walls of its container
(B)
(D) The average speed of the molecules in the gas is
(C) directly proportional to the square root of the absolute
(D) temperature.

81. Choose the most appropriate option. A metal rod is 82. Choose the most appropriate option. As temperature
in thermal contact with the two heat reservoirs both at is increased, the equilibrium of a gaseous reaction will
constant temperature one at 100K and the other at 200K always
. The rod conducts 1000 J of heat from the warmer to the
(A) shift to the right
colder reservoir .If no energy is exchanged with the
(B) shift to the left
surrounding what is the total change of entropy?
(C) remains constant
(A) - 5 J / K
(D) the answer cannot be determined from the given
(B) 0 J / K
information
(C) 5 J / K

(D) 10 J / K

83. Choose the most appropriate options. Arrange the 84. Choose the most appropriate option. The values of all
following in the decreasing order of basic character . I. p- of the following are reversed when a reaction is reversed
toluidine II. N,N-dimethyl-p-toluidine III. p-nitroaniline IV. except
Aniline
(A) enthalpy
(A) II > III > I > IV (B) Gibbs energy
(B) I > II > III > IV (C) rate constant
(C) II > I > IV > III (D) reaction potential. .
(D) IV > III > I > II

85. Choose the most appropriate options. Terylene is a 86. Choose the most appropriate options. Which of the
condensation polymer of ethylene glycol and following statement is applicable for tyndall effect ?

(A) benzoic acid (A) The diameter of the dispersed particle is much smaller

(B) phthalic acid than the wavelength of the light used

(C) salicylic acid (B) The diameter of the dispersed phase is much smaller
than the wavelength of the light used
(D) terephthalic acid
(C) The refractive indices of the dispersed phase is much
smaller than the wavelength of the light used

(D) The refractive indices of the dispersed phase and the
dispersion medium must differ greatly in

87. Choose the most appropriate option. What is the 88. Choose the most appropriate options. NH _ 3
minimum power required for heat engine to lift a 80 kg molecule attract H ^ + ion towards itself to form
mass 5 m in 20 s if it releases 1000 J of heat energy from ammonium ion ( NH _ 4 ^ + ) through
its exhaust each second?
(A) electrovalent bond
(A) 200 w (B) metallic bond
(B) 500 w (C) co-ordinate bond
(C) 1200 w (D) hydrogen bonding.
(D) 3000 w

89. Choose the most appropriate option. Which of the 90. Choose the most appropriate options. On combustion
following would be the most soluble in water? of x-g of ethanol in bomb calorimeter, y-joules of heat
energy is produced. The heat of combustion of ethanol (
(A) Carbon tetrachloride
Δ H _ comb ) is
(B) Methane
(A) Δ H _ comb = - x · J
(C) Octane
(B) Δ H _ comb = - y J
(D) Ethyl alcohol
(C) Δ H _ comb = - ( x )/( y ) × 44 Jmol ^ - 1

(D) Δ H _ comb = - ( y )/( x ) × 44 J mol ^ - 1

91. Choose the most appropriate option. What type of 92. Choose the most appropriate options. Among all the
intermolecular bonding occurs in gaseous CH _ 4 ? given compounds, which will have D-configuration?

(A) Covalent (A) 5 and 15

(B) lonic (B) 5 and 16 have D-configuration?

(C) Hydrogen (C) 0

(D) Van der Waals’ (D)

93. Choose the most appropriate option. The product 94. Choose the most appropriate option. Gas A
formed by the condensation reaction of alcohols is decomposed according to the following reaction A ( g )
leftharpoons B ( g ) + C ( g ) A student conducted an
(A) alcohol
experiment and determined that the equilibrium pressure
(B) carboxylic acid
of gas A was 0.20 P, where P was the total pressure of
(C) ester the system. What is the equilibrium constant Kₚ for this
(D) ether reaction?

(A) 0.10 P

(B) 0.20 P

(C) 0.40 P

(D) 0.80 P

95. Choose the most appropriate options. Beryllium 96. Choose the most appropriate options. Sulphur(s)
gives a compound X with the following percentage when react with HNO _ 3 ( conc )Green mainly gives
composition : Be - 6.1 \% N - 37.8 \% , C 1 - 48 \% , H - 8.1
(A) H _ 2 SO _ 4 , NO _ 2 and H _ 2 O
\% Molecular weight of X is 148 g mol ^ - 1 and that of Be
(B) H _ 2 S , N _ 2 O _ 5 and SO _ 2
is 9 g mol ^ - 1 . The molecular formula of the compound
is (C) H _ 2 SO _ 3 , NO _ 2 and SO _ 2

(D) SO _ 2 , NO _ 2 and H _ 2 O
(A) BeN _ 4 Cl _ 2 H _ 12

(B) BeN _ 2 ClH _ 6

(C) BeN _ 4 Cl _ 2 H _ 6

(D) BeN _ 4 ClH _ 8

97. Choose the most appropriate option. A 13 g gaseous 98. Choose the most appropriate option. A man
sample of an unknown hydrocarbon occupies a volume of straightens up his room. His action does not violate the
11.2 L at STP. What is the hydrocarbon? second law of thermodynamics because

(A) CH (A) the entropy of his roam increaæd

(B) C _ 2 H _ 4 (B) energy of the universe was conserved

(C) C _ 2 H _ 2 (C) tle entropy increases by the breakdown of nutrients in

(D) C _ 3 H _ 3 his body is greater than the entropy decreases by the
straightening of his room

(D) his action violates the second law of

99. Choose the most appropriate option. What is the 100. Choose the most appropriate option. Which of the
conjugate base of H _ 2 SO _ 4 ? following is true for an acid-base concentration cell such
as the one used by the pH meter?
(A) H _ 2 O

(B) OH ^ - (A) Current always flows towards the more acidic solution

(C) HSO _ 4 ^ - (B) Current always flows towards the more basic solution

(D) SO _ 4 ^ 2 - (C) Current always flows towards the more neutral solution

(D) Current always flows away from the more neutral
solution

MATHEMATICS

101. Choose the most appropriate option. On the sphere 102. Choose the most appropriate options. If f ( x ) = \
( x - 1 ) ^ 2 + ( y + 2 ) ^ 2 + ( z - 3 ) ^ 2 = 25 compute the array c c 1 - x ( π - 2 x ) ^ 2 · x ( 1 + π ^ 2 - 4 π x + x ^ 2 )
distance from the point M _ 0 to the plane 3 x - 4 z + 19 \ k , x = ( π )/( 2 ) array . x ≠ ( π )/( 2 ) is continuous at x
= ( π )/( 2 ) then k is equal to
(A) 1

(B) 2 (A) - ( 1 )/( 16 )

(C) 3 (B) - ( 1 )/( 32 )

(D) 4 (C) - ( 1 )/( 64 )

(D) - ( 1 )/( 28 )

103. Choose the most appropriate options. The value of _ 104. Choose the most appropriate option. Find the real
x arrow 0 ∫ _ 0 ^ x ^ 2 ^ 2 t d t x x is solution of the system of equations x ^ 4 + y ^ 4 - x ^ 2 y
^ 2 = 13 And x ^ 2 - y ^ 2 + 2 x y = 1 Satisfying the
(A) 0
condition x y ≥ 0
(B) 3
(A) ( x = 1 , y = - 2 ) ; ( x = - 1 , y = 2 )
(C) 2
(B) ( x = 2 , y = 1 ) ; ( x = - 2 , y = - 1 )
(D) 1
(C) ( x = 1 , y = 2 ) ; ( x = - 1 , y = - 2 )

(D) ( x = 1 , y = - 2 ) ; ( x = - 1 , y = - 2 )

105. Choose the most appropriate option. _ x arrow 0 √( 106. Choose the most appropriate options. The value of
1 + x ) - √( 1 - x ) x is equal to ^ 40 C _ 0 + ^ 40 C _ 1 + ^ 40 C _ 2 + ⋯ + ^ 40 C _ 20 is

(A) 0 (A) 2 ^ 40 + 40 ! ( 20 ! ) ^ 2

(B) 1 (B) 2 ^ 39 - ( 1 )/( 2 ) × 40 ! ( 20 ! ) ^ 2

(C) -1 (C) 2 ^ 39 + ^ 40 C _ 20

(D) ∞ (D) none of these

107. Choose the most appropriate options. Negation of 108. Choose the most appropriate options. Let f ( x ) = (
the statement ( p r ) arrow ( r q ) is x ^ 3 + 2 ) ^ 30 .If f ^ n ( x ) is a polynomial of degree 20
where f ^ n ( x ) denotes the n + h order derivative of f(x)
(A) ( p r ) ( - r ≠g q )
with respect to x then the value of n is
(B) - ( ρ r ) arrow ( r q )
(A) 60
(C) - ( p r ) arrow - ( r q )
(B) 40
(D) ( p r ) ( r q )
(C) 70

(D) 50

109. Choose the most appropriate options. The standard 110. Choose the most appropriate options. The number
deviation of a data is 6, when each observation is of real roots of ( 6 - x ) ^ 4 + ( 8 - x ) ^ 4 = 16
increased by 1, then the standard deviation of new data
(A) 0
is
(B) 2
(A) 5
(C) 4
(B) 7
(D) 6
(C) 6

(D) 8

111. Choose the most appropriate options. The function 112. Choose the most appropriate options. If A(2,3) and
f:[0,3] → [1,29) defined by f ( x ) = 2 x ^ 3 - 15 x ^ 2 + 36 B(-2, 1) are two vertices of a triangle and third vertex
x + 1 is moves on the line 2x + 3y =9, then the locus of the
centroid of the new set of observations will be the
(A) one-one and onto
triangle is
(B) onto but not one one
(A) 2x + 3y =1
(C) one-one but not onto
(B) 2x + y = 3
(D) neither one-one nor onto
(C) 2x - 3y = 1

(D) x - y=1

113. Choose the most appropriate options. The solution 114. Choose the most appropriate option. In a class,
of the differential equation ( x ^ 2 - y x ^ 2 ) ( d y )/( d x ) there are 10 boys and 8 girls. When 3 students are
+ y ^ 2 + x y ^ 2 = 0 is selected at random, the probability that 2 girls and 1 boy
are selected, is
(A) ( ( x )/( y ) ) = ( 1 )/( x ) + ( 1 )/( y ) + C

(B) ( ( y )/( x ) ) = ( 1 )/( x ) + ( 1 )/( y ) + C (A) ( 35 )/( 102 )

(C) ( x y ) = ( 1 )/( x ) + ( 1 )/( y ) + C (B) ( 15 )/( 102 )

(D) ( x y ) + ( 1 )/( x ) + ( 1 )/( y ) = C (C) ( 55 )/( 102 )

(D) ( 25 )/( 102 )

115. Choose the most appropriate option. ∫ _ 0 ^ 1 x e ^ 116. Choose the most appropriate option. ( 1 + 2 i ) ^ 6
2 x d x is equal to is equal to

(A) e ^ 2 - 1 (A) None of these

(B) ( 1 )/( 4 ) ( e ^ 2 - 1 ) (B) - 177 + 44 j

(C) 2 e ^ 2 + 1 (C) 177 + 44 j

(D) ( 1 )/( 4 ) ( e ^ 2 + 1 ) (D) 177 - 44 i

117. Choose the most appropriate option. What is the 118. Choose the most appropriate option. Solve for x ( x
equation of the curve in which point M performs its > 0 ) _ 3 x ( ( 3 )/( x ) ) + _ 3 ^ 2 x = 1
motion, if the sum of the distances from this point to the
(A) x = 1 and there are infinitely more solutions .
points A(-1, -1) and B (1, 1) remains constant is equal to
(B) x _ 1 = 1 , x _ 2 = ( 1 )/( 3 ) only two solutions
2 √( 3 ) ?
(C) x _ 1 = 1 , x _ 2 = 3 only two solutions
(A) 2 x ^ 2 - 2 x y + 2 y ^ 2 - 3 = 0
(D) x _ 1 = 1 , x _ 2 = 3 , x _ 3 = ( 1 )/( 3 ) only three
(B) 2 x ^ 2 + 2 x y - 2 y ^ 2 - 3 = 0
solutions
(C) 2 x ^ 2 - 2 x y - 2 y ^ 2 + 3 = 0

(D) 2 x ^ 2 + 2 x y + 2 y ^ 2 + 3 = 0

119. Choose the most appropriate options. For real x, let 120. Choose the most appropriate options. If y =
f ( x ) = x ^ 3 + 5 x + 1 , then sec(tan⁻¹x), then y at x =1 is equal to term is the sum of
two preceding terms. Then, the common ratio of the G.P.
(A) f is one-one but not onto R
is
(B) f is onto R but not one-one
(A) 1 √( 2 )
(C) f is one-one and onto R
(B) ( 1 )/( 2 )
(D) f is neither one-one nor onto R
(C) 1

(D) √( 2 )

121. Choose the most appropriate option. If y ^ ( 1 )/( m 122. Choose the most appropriate options. Every term of
) + x ^ ( 1 )/( m ) = 2 x then G.P. is positive and also every term is the sum of two
preceding terms. Then, the common ratio of the G.P. is
(A) ( x ^ 2 + 1 ) d ^ 2 y d x ^ 2 + x ( d y )/( d x ) - m ^ 2 y
=0 (A) 1 - √( 5 ) 2

(B) ( x ^ 2 - 1 ) d ^ 2 y d x ^ 2 + x ( d y )/( d x ) + m ^ 2 y (B) √( 5 ) + 1 2
=0 (C) √( 5 ) - 1 2
(C) ( x ^ 2 - 1 ) d ^ 2 y d x ^ 2 + x ( d y )/( d x ) - m ^ 2 y = (D) 1
0

(D) ( x ^ 2 + 1 ) d ^ 2 y d x ^ 2 - x ( d y )/( d x ) + m ^ 2 y
=0

123. Choose the most appropriate options. For all n N , 7 124. Choose the most appropriate options. If θ + θ = 2
^ 2 n - 48 n - 1 is divisible by then the value of ^ 10 θ + ^ 10 θ

(A) 25 (A) 2

(B) 26 (B) 2 ^ 4

(C) 1234 (C) 2 ^ 8

(D) 2304 (D) 2 ^ 10

125. Choose the most appropriate options. The value of 126. Choose the most appropriate options. If the line x-
the integral ∫ _ 0 ^ 0.9 [ x - 2 [ x ] ] d x where [.] denotes 1=0 is the directrix of the parabola y ^ 2 - k x + 8 = 0
the greatest integer function, then one of the value of k is

(A) 0.9 (A) 1/8

(B) 0 (B) 8

(C) 1.8 (C) 4

(D) -0.9 (D) ¼

127. Choose the most appropriate option. Solve for x ( a 128. Choose the most appropriate options. If the
≠0)√[3](a+x)^2+4√[3](a-x)^2=5√[3]a arithmetic mean of the following data is 7 then a+b=
^2-x^2
(A) 4
(A) x _ 1 = ( 43 )/( 45 ) a, x _ 2 = ( 63 )/( 65 ) a (B) 2
(B) x _ 1 = ( 43 )/( 45 ) a , x _ 2 = 0 (C) 3
(C) x _ 1 = ( 63 )/( 65 ) a , x _ 2 = 0 (D) cannot be determined
(D) x _ 1 = - ( 63 )/( 65 ) a , x _ 2 = 0

129. Choose the most appropriate option. _ x arrow ∞ x x 130. Choose the most appropriate options. ∫ x ^ 2 - 2 x ^
^ m is equal to point 3 √ x ^ 2 - 1 d x equal to

(A) 0 (A) x ^ 2 √ x ^ 2 - 1 + C

(B) 1 (B) - x ^ 2 √ x ^ 2 - 1 + C

(C) - ( 1 )/( 2 ) (C) √ x ^ 2 - 1 x ^ 2 + C

(D) ∞ (D) - √ x ^ 2 - 1 x ^ 2 + C

131. Choose the most appropriate option. _ x arrow 0 ( 2 132. Choose the most appropriate option. Given ε _ k = (
x )/( 2 x ) is equal to ( 2 π k )/( n ) ) + i ( ( 2 π k )/( n ) ) find the Π _ k = 0 ^ n -
1(ε_k^2-2ε_kθ+1)
(A) 0

(B) 1 (A) 2 ( 1 - n θ )

(C) ( 1 )/( 2 ) (B) 2 ( 1 + n θ )

(D) ∞ (C) ( 1 - n θ ) ^ 2

(D) 1 + ^ 2 n θ

133. Choose the most appropriate option. There are 3 134. Choose the most appropriate option. On the sphere
true coins and 1 false coin with 'head' on both sides. A ( x - 1 ) ^ 2 + ( y + 2 ) ^ 2 + ( z - 3 ) ^ 2 = 25 find the
coin is chosen at random and tossed 4 times. If 'head' point M _ 0 to the plane 3 x - 4 z + 19
occurs all the 4 times, then the probability that the false
(A) ( 7 , - 2 , - 2 )
coin has been chosen and used is
(B) ( 2 , - 2,7 )
(A) ( 15 )/( 19 )
(C) ( - 2 , - 2,7 )
(B) ( 14 )/( 19 )
(D) ( - 2,7 ; - 2 )
(C) ( 13 )/( 19 )

(D) ( 16 )/( 19 )

135. Choose the most appropriate option. The value of 136. Choose the most appropriate option. ∫ _ - 2 ^ 2 3 x
the integral ∫ _ - 3 ^ 5 | x - 3 | d x is ^ 7 - 2 x ^ 5 + x ^ 3 - 3 x ^ 4 + 3 x ^ 2 + 1 d x is equal to

(A) 20 (A) does not exist

(B) 21 (B) 3

(C) 18 (C) 1/e

(D) 22 (D) ∞

137. Choose the most appropriate options. The number 138. Choose the most appropriate option. For any two
of solutions of the equation 3 ^ 2 x - 7 x + 2 = 0 in the vectors u and v , if | u + v | = | u - v | then the angle
interval [ 0,5 π ] is between them is equal to

(A) 0 (A) ( π )/( 4 )

(B) 5 (B) ( π )/( 3 )

(C) 6 (C) ( π )/( 2 )

(D) 10 (D) π

139. Choose the most appropriate options. If A and B are 140. Choose the most appropriate options. If a = i + j , b
independent events such that P ( B ) = ( 2 )/( 7 ) , P ( A B = 2 j - k and r × a = b × a r × b = a × b then a unit vector
) = 0.8 then P(A)= in the direction of r is

(A) 0.1 (A) 1 √( 11 ) ( i + 3 j - k )

(B) 0.2 (B) 1 √( 11 ) ( i - 3 + k )

(C) 0.3 (C) 1 √( 3 ) ( i + j + k )

(D) 0.4 (D) None of these

141. Choose the most appropriate option. The solution of 142. Choose the most appropriate options. If the tangent
the differential equation d ^ 2 y d x ^ 2 + 3 y = - 2 x is at (1,1) on y ^ 2 = x ( 2 - x ) ^ 2 meets the curve again at
P, then P is
(A) c _ 1 √( 3 ) x + c _ 2 √( 3 ) x - ( 2 )/( 3 ) x

(B) c _ 1 √( 3 ) x + c _ 2 √( 3 ) x - ( 4 )/( 5 ) (A) (4,4)

(C) c _ 1 √( 3 ) x + c _ 2 √( 3 ) x - 2 x ^ 2 + ( 4 )/( 9 ) (B) (-1,2)

(D) c _ 1 √( 3 ) x + c _ 2 √( 3 ) x - ( 2 )/( 3 ) x ^ 2 + ( 4 )/( 9 ) (C) (9/4,3/8)

(D) None of these

143. Choose the most appropriate option. The line y = 144. Choose the most appropriate option. _ x arrow 1 ( x
mx +C will be tangent to the ellipse x ^ 2 9 + y ^ 2 4 = 1 - 1 ) ( π x )/( x ) is equal to
if c is equal to
(A) 0
(A) ( 3 )/( m ) (B) - ( 1 )/( π )
(B) √ 9 m ^ 2 + 4 (C) - ( 2 )/( π )
(C) √ 1 + m ^ 2 (D) - ( 3 )/( π )
(D) √ 4 m ^ 2 + 9

145. Choose the most appropriate options. _ x arrow 0 ( ( 146. Choose the most appropriate options. Let P = \ θ : θ
1 - 2 x ) ( 3 + x ) )/( x 4 x ) is equal to - θ = √( 2 ) θ \ and, Q = \ θ θ + θ = √( 2 ) θ \ be two sets.
Then,
(A) 4

(B) 3 (A) P Q and Q - P ≠ φ

(C) 2 (B) Q P

(D) ½ (C) P Q

(D) P = Q

147. Choose the most appropriate option. Find the 148. Choose the most appropriate options. If α and β are
component of the vector a (-1,2,0) perpendicular to the non-real numbers satisfying x ^ 3 - 1 = 0 , then the value
plane of the vectors e _ 1 [ 1,0,1 ) and e _ 2 ( 1,1,1 ) . of | array c c c λ + 1 & α & β \ α & λ + β & 1 \ β & 1 & λ + α
array | is
(A) ( - ( 1 )/( 2 ) · ( 1 )/( 2 ) , 0 )

(B) ( 0 , - ( 1 )/( 2 ) , ( 1 )/( 2 ) ) (A) 0

(C) ( - ( 1 )/( 2 ) , 0 , ( 1 )/( 2 ) ) (B) λ ^ 3

(D) ( ( 1 )/( 2 ) , 0 , ( - 1 )/( 2 ) ) (C) λ ^ 3 + 1

(D) λ ^ 3 - 1

149. Choose the most appropriate option. ∫ _ - π / 2 ^ π / 150. Choose the most appropriate option. A die is thrown
2 | x | d x equals to twice and the sum of the numbers appearing is 6. Then,
the conditional probability that the number 4 has
(A) 0
appeared at least once is
(B) 1
(A) ( 1 )/( 5 )
(C) -1
(B) ( 4 )/( 5 )
(D) 2
(C) ( 2 )/( 5 )

(D) ( 2 )/( 36 )

ANSWER KEY

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

113. (A) 114. (A) 115. (D) 116. (A) 117. (A) 118. (C) 119. (C)

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

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

134. (C) 135. (A) 136. (A) 137. (C) 138. (C) 139. (C) 140. (A)

141. (A) 142. (C) 143. (B) 144. (A) 145. (C) 146. (D) 147. (C)

148. (B) 149. (D) 150. (C)