VITEEE 2027 Sample Paper

SAMPLE PAPER

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

VITEEE 2027
Modelled on the actual exam pattern
.

QUESTIONS MAX MARKS TIME MARKING

115 115 150 Min +1 / 0

GENERAL INSTRUCTIONS

1. This paper contains 115 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

VITEEE 2027
SAMPLE QUESTION PAPER

Questions 115 Max Marks 115 Time 150 Min Marking +1 / 0

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

PHYSICS

1. At what speed should the electron revolve around the 2. In an atom the two electrons move around the nucleus
nucleus of an hydrogen atom in order that it may not be in circular orbits of radii R and 4R. What is the ratio of
pulled into the nucleus by electrostatic attraction. Take the times taken by them to complete one revolution?
the radius of orbit of electron as 0.5Ẵ, mass of electron
(A) 1:8
as 9.1 x 10⁻³¹ kg and charge as 1.6 x 10⁻¹⁹C.
(B) 1:9
(A) 225 x 10⁴ m/s
(C) 12:13
(B) 225 x 10⁵ m/s
(D) 1:5
(C) 225 x 10⁶ m/s

(D) 225 10⁷ m/s

3. A liquid is kept in a cylindrical vessel which is rotated 4. Three identical magnetic north poles each of the pole
along its axis. The liquid rises at its sides. If the radius of strength 10 A-m are placed at the comers of an
vessel is 0.05m and the speed of rotation is 2rev/s, the equilateral triangle of side 10 cm. The net magnetic force
difference in the height of liquid at the centre of the on one of the pole is:
vessel and its sides is:
(A) 10⁻³ N
(A) 0.001m (B) √2 x 10⁻³ N
(B) 0.002m (C) √3 x10⁻³ N
(C) 0.01m (D) None of the above
(D) 0.02m

5. To get an output y = 1 in the given circuit, which of the 6. Some amount of a radioactive substance (half life = 10
following input is correct? days) is spreaded inside a room and consequently, the
level of radiation becomes 50 times the permissible level
(A) 1 0 0
for normal occupancy of the room. After how many days
(B) 1 0 1
will the room be safe for occupation?
(C) 1 1 0
(A) 20 days
(D) 0 1 0
(B) 34.8 days

(C) 56.4 days

(D) 62.9 days

7. An explosion breaks a rock into three parts in a 8. A thick rope of rubber of density 1.5x 10³ kg / m³ and
horizontal plane. Two of them go off at height at right Young's modulus Y = 5 x 10⁸ N/m², 8m in length is hung
angles to each other. The first part of mass 1 kg moves from the ceiling of a room. What is the increase in length
with a speed of 12 ms⁻¹ and the second part of mass 2 kg due to its own height?
moves with 8 ms⁻¹ speed. If the third part flies of with 4
(A) 9.6x 10⁻⁴ metre
ms-speed, then its mass is
(B) 10.05 x 10⁻⁵ metre
(A) 3 kg
(C) 10.01x 10⁻⁵ metre
(B) 5 kg
(D) 11.02x 10⁻⁵ metre
(C) 7 kg

(D) 17 kg

9. A particle of mass M at rest decays into two particles 10. A parallel plate capacitor of capacitance 100 pF is to
of masses m₁ and m₂ having : non-zero velocities. The be constructed by using paper sheets of 10 mm thickness
ratio of the de-broglie wavelengths of the particles λ₁/λ₂ as dielectric. If dielectric constant of paper is 4, the
is: number of circular metal foils of diameter 2 cm each
required for the purpose is:
(A) m₁/m₂

(B) m₂/m₁ (A) 40

(C) 1 (B) 20

(D) √m₂/√m₁ (C) 30

(D) 10

11. A uniform electric field and a uniform magnetic field 12. The magnetic flux through a circuit of resistance R
are produced, pointed in the same direction. An electron changes by an amount ΔΦ in a time Δt. Then the total
is projected with its velocity pointing in the same quantity of electric charge q that passes any point in the
direction. circuit during the time Δt is presented by

(A) The electrons will turn to its left (A) q = ( 1 )/( R ) ( Δ φ )/( Δ t )

(B) The electrons will turn to its right (B) q = ( Δ φ )/( R )

(C) The electron velocity will increase in magnitude (C) q = ( Δ φ )/( Δ t )

(D) The electron velocity will decrease in magnitude (D) q = R ( Δ φ )/( Δ t )

13. Energy E of a hydrogen atom with principle quantum 14. The half life of a radioactive isotope X is 50 yr. It
number n is given by E = -13.6/n2 eV. The energy of a decays to another element Y which is stable. The two
photon ejected when the electron jumps from n = 3 state elements X and Y are found to be the ratio of 1 : 15 in a
to n = 2 state of hydrogen is approximately sample of a given rock. The age of the rock was
estimated to be
(A) 1.5 eV

(B) 0.85 eV (A) 200 yr

(C) 3.3 eV (B) 250 yr

(D) 1.9 eV (C) 100 yr

(D) 150 yr

15. A body of mass m₁ collides elastically with another 16. Identify the operation performed by the circuit given
body of mass m₂ at rest. If the velocity of m₁ after below
collision becomes 2/3 times its initial velocity, the ratio of
their masses is:

(A) 1:5

(B) 5:1

(C) 5:2

(D) 2:5 (A) NOT

(B) AND

(C) OR

(D) NAND

17. Current through the ideal diode as shown in the 18. In a single slit, Fraunhoffer diffraction experiment,
figure given alongside is: with decrease in the width of the slit, the width of the
central maximum
(A) zero

(B) 20A (A) remains the same

(C) (1/20)A (B) increase

(D) (1/50)A (C) decrease

(D) can be any of these depending on the intensity of the
source

19. A capillary tube of radius 0.25 mm is submerged 20. The refractive index of the material of a prism is √2
vertically in water so that 25 mm of its length is outside and its refracting angle is 30°. One of the refracting
water. The radius of curvature of the meniscus will be (ST surface of the prism is made a mirror inwards. A beam of
of water = 75 x 10⁻³ Nm⁻¹) monochromatic light entering the prism from the other
face will retrace its path after reflection from the
(A) 0.2 mm.
mirrored surface if its angle of incidence on the prism is
(B) 0.4 mm
(A) 45°
(C) 0.6 mm
(B) 60°
(D) 0.8 m
(C) 0°

(D) 30°

21. A block A of mass 100 kg rests on another block B of 22. A uniform magnetic field of induction B is confined in
mass 200 kg and is tied to a wall as shown in the figure. a cylindrical region of radius R. If the field is increasing
The coefficient of friction between A and B is 0.2 and that at a constant rate of dB/dt = αT/s, then the intensity of
between B and the ground is 0.3. The minimum force F the electric field induced at point P distant r from the
required to move the block B is axis as shown in the figure:

(A) 1/8r

(B) 1/8r

(C) 1/2rα

(D) r

(A) 900 N

(B) 200 N

(C) 1100 N

(D) 700 N

23. Consider the arrangement as shown in figure. The 24. If a shunt of 1/ 10th of the coil resistance is applied to
distance D is large compared to d. Minimum value of d so a moving coil galvanometer. Its sensitivity becomes
that there is a dark fringe at 0, is
(A) 10 folds

(B) 1/10 folds

(C) 11 folds

(D) 1/11 folds

(A) √( ( λ D )/( 2 ) )

(B) √( ( 2 )/( D λ ) )

(C) √( ( D )/( 2 λ ) )

(D) √( ( 2 λ )/( D ) )

25. The work functions of three metals A, B and C are W _ 26. In the given AC circuit, when switch S is at position 1,
A , Wв and Wc respectively. They are in the decreasing the source emf leads current by /6. Now, if the switch is
order. The correct graph between kinetic energy and
frequency v of incident radiation is:

(A)

(B)

(C)
at position 2, then
(D)

(A) current leads source emf by /3

(B) current leads source emf by /4

(C) source emf lead current by /4

(D) None of the above

27. In the given circuit, all diodes are ideal. The current 28. In the circuit shown in figure, the minimum current
required for the junction diode to be at/above the knee-
point is 2.0 mA, The knee point of the diode is 1.0 volt.
The maximum value of resistance R, so that voltage
across the diode above the knee point is:

(A) 100 Ω
through battery is
(B) 200 Ω

(C) 500 Ω
(A) 2A (D) 1k Ω
(B) 1A

(C) 3A

(D) 4 A

29. Calculate the maximum energy possessed by a β- 30.  A 5 kg stone falls from a height of 100 m and
particle in following decay ¹⁷⁶Lu — ¹⁷⁶Hf +β⁻ + ⊽ atomic penetrates 2 m in a layer of sand. The time of
mass of ¹⁷⁶Lu = 175.94269μ and of ¹⁷⁶Hf = 175.94142μ penetration is

(A) 1.921 MeV (A) 14.28 sec

(B) 2.923 MeV (B) 0.089 sec

(C) 1.182 MeV (C) 120 kg-m/s

(D) 10 MeV (D) 0.89 sec

31. The activity of ₇₉Au²⁰⁰ of mass 2.0 x 10⁻⁸ kg is 60 32. A ray of light passing through a prism of refractive
curie. Find the disintegration constant of ₇₉Au²⁰⁰. index √2 undergoes minimum deviation. It is found that
the angle of incidence is double the angle of refraction
(A) 3.7 x 10⁻⁵ s⁻¹
within the prism. The angle of prism is:
(B) 4.9 x 10⁻⁹ s⁻¹
(A) 60°
(C) 10 x 10⁻⁹ s⁻¹
(B) 90°
(D) 9.1 x 10⁻¹¹ s⁻¹
(C) 75°

(D) 30°

33. If prism' angle α = 1°, μ = 1.54, distance between 34. A black body of mass 34.38 g and surface area 19.2
screen and prism b = 0.7 m, distance between prism and cm2 is at an initial temperature of 400 K. It is allowed to
source a = 0.3m, λ = 180 π nm then in Fresnel biprism cool inside an evacuated enclosure kept at constant
find the value of β (fringe width) temperature of 300 K. The rate of cooling is 0.04°C/s.The
specific heat of body is:
(A) 10⁻⁴ m

(B) 10⁻³ mm (A) 2800 J/kg-K

(C) π x 10⁻⁴ m (B) 2100 J/kg-K

(D) π x 10⁻³ m (C) 1400 J/ kg-K

(D) 1200 J/kg-K

35. The period of oscillation of a magnet in a vibration
magnetometer is 8 s. The period of oscillation of magnet
whose magnetic moment is four time that of the first
magnet is

(A) 1s

(B) 4s

(C) 8s

(D) 16s

CHEMISTRY

36. Which of the following compound (s) will give 37. Give the IUPAC name of m-CICH₂C₆H₄CH₂C(CH₃)₃
butanone on oxidation with alkaline KMnO₄ solution?
(A) 1 - (3 - chloro-3-methylphenyl)-2, 2-diethyl propane
(A) Butan-1-ol (B) 2 - (3 - chloromethyl propyl)-2, 2-dimethyl propane
(B) Butan-2-0l (C) 1 - (3 - chloromethyl phenyl)-3, 3- dimethyl propane
(C) Both 1 and 2 (D) 1 - chloromethyl - 3- (2, 2 - dimethyl propyl) benzene
(D) None of the above

38. Which of the following act as an oxidising agent? 39. Which of the following reagent is used to identify
fructose?
(A) Np⁴⁺

(B) Sm²⁺ (A) Neutral FeCl₃

(C) Eu²⁺ (B) CHCH₃ / KOH(alco.)

(D) Yb²⁺ (C) Ammonical AgNO₃

(D) Iodine

40.  With what velocity should an α-particle travel 41. When 96.5 C of electricity is passed through a
towards the nucleus of a copper atom to arrive at a solution of silver nitrate (at wt. of Ag = 107.87≃108), the
distance of 10⁻¹³m from the nucleus of the copper atom? amount of silver deposited is
(K =9 x 10⁹Nm²/C² (Mass of α-particle = 6.64 x 10⁻²⁷kg)
(A) 5.8 mg
(A) 6.34 x 10⁻⁶ ms⁻¹ (B) 10.8 mg
(B) 6.34 x 10⁻⁵ ms⁻¹ (C) 15.8 mg
(C) 5.34 x 10⁶ ms⁻¹ (D) 20.8 mg
(D) 5.34 x 10⁵ ms⁻¹

42. Although zirconium belongs to 4d and hafnium 43. Glucose when treated with conc. HNO₃ gives
belongs to 5d transition series even they show similar
(A) acetic acid
physical and chemical properties because both
(B) saccharic acid
(A) belong to d-block
(C) gluconic acid
(B) have same number of electrons
(D) sorbitol
(C) belongs to the same group of the periodic table

(D) have similar atomic radius

44. Zinc oxide loses oxygen on heating according to the 45. Phenol is bifunctional compound because
reaction ZnO Heat Zn ^ 2 + + ( 1 )/( 2 ) O _ 2 + 2 e It
(A) It is acidic and contain ーOH
becomes yellow on heating because
(B) It reacts with Na to give phenoxide
(A) Zn²⁺ ions and electrons move too interstitial sites and F -
(C) It reacts with both Na and Zn to give phenoxide and
centres are created
benzene respectively
(B) Oxygen and electrons move at the crystal and ions
(D) both (a) and (c)
become yellow

(C) Zn²⁺ again combine with oxygen to give yellow oxide

(D) Zn²⁺ are replaced by oxygen

46. In dilute alkaline solution of MnO₄⁻ changes to 47. Which of the following has lowest boiling point ?

(A) MnO₄²⁻ (A) p-nitrophenol

(B) MnO₂ (B) m-nitrophenol

(C) Mn₂O₃ (C) o-nitrophenol

(D) MnO (D) Phenol

48. The final product of the following sequence of 49. Identify (D) in the following reaction series:
reaction is

(A) CH₃ーCH₂ーOH
(A)
(B)
(B)
(C) CH₃ーCH＝CH₂
(C)
(D) CH₃CH₂CH₂OH
(D)

50.  For a particular value of azimuthal quantum number, 51. What is the end product for the reaction?
the total number of magnetic quantum number values
are given by

(A) l = ( m + 1 )/( 2 )
(A)
(B) l = ( m - 1 )/( 2 )
(B)
(C) l = ( 2 m + 1 )/( 2 )
(C)
(D) m = ( 2 l + 1 )/( 2 )
(D)

52. What is the ratio of the velocities of CH₄ and O₂ 53. A solution of KMnO₄ is reduced to a various products
molecules so that they are associated with de-Broglie depending upon its pH At pH7, it is reduced to a
waves of equal wavelengths? colourless solution (A), at pH=7 it forms a brown
precipitate (B) and at pH>7, it gives a green solution (C).
(A) 1:2
(A), (B) and (C) are
(B) 2:1
(A) Mn²⁺ MnO₂ MnO₄²⁻
(C) 3:2
(B) MnO₂ Mn²⁺ MnO₄²⁻
(D) 1:3
(C) Mn²⁺ MnO₄²⁻ MnO₂

(D) MnO₄²⁻ Mn²⁺ MnO₂

55. An organic compound X is oxidised by using acidified
K₂Cr₂O₇. The product obtained reacts with phenyl
hydrazine, but does not answer silver mirror test. The
possible structure of X is
54.
(A) CH₃COCH₃

The main product (P) is (B) (CH₃)₂CHOH

(A) C₆H₅OC₂H₅ (C) CH₃CHO

(B) C₂H₅OC₂H₅ (D) CH₃CH₂OH

(C) C₆H₅OC₆H₅

(D) C₆H₅.I

56. The flame colours of metal ions are due to 57. Order of ease of decarboxylation of the following
acids is
(A) Schottky defect
(i) CH₃COOH
(B) Frenkel defect
(ii) CH₂＝CHーCH₂.COOH
(C) Metal excess defect (iii) CH₂(COOH)₂
(D) Metal deficient defect

(iv)

(A) i >ii > iii > iv

(B) iii > iv > ii > i

(C) iv > iii > ii > i

(D) i > iii > ii > iv

58. An aqueous solution of titanium chloride, when 59. Which of the following is a peptide linkage ?
subjected to magnetic measurement, show zero magnetic
(A) ーCOーNH
moment. The formula of complex in aqueous solution is
(B)
(A) [Ti(H₂O)₆] CI₄
(C)
(B) [Ti(H₂O)₆] CI₃
(D) ーCOーOーNH₄
(C) [Ti(H₂O)₅Cl] CI₂

(D) [Ti(H₂O)₆] CI

60. In an amino acid, the carboxyl group ionises at pkₐ₁= 61. A black powder when heated with conc. HCl gives a
2.34 and ammonium, ion at pkₐ₂ = 9.6. The isoelectric greenish yellow gas. The gas acts as an oxidising and a
point of the amino acid is at pH bleaching agent. When it is passed are slaked lime, a
white powder is formed which is a ready source of gas.
(A) 5.97
The black powder and white powder respectively are
(B) 11.94
(A) KCIO₃ and NaClO₃
(C) 2.34
(B) MnO₂ and CaCOCl₂
(D) 9.60
(C) MnO₂ and KCIO₃

(D) MnCl and COCI₂

62. Which of the following ion is diamagnetic? 63. A compound (A) C₄H₈Cl₂ on alkaline hydrolysis to give
compound (B) C₄H₈0 which gives an oxime and positive
(A) Nd³⁺
Tollen's reagent test. What is the structure of (A)?
(B) La³⁺
(A) CH₃CH₂CH₂CHCl₂
(C) Tb³⁺
(B) CH₃CCl₂CH₂CH₃
(D) Er³⁺
(C) CH₃CH(CI)CH(CI)CH₃

(D) CH₂CICH₂CH₂CH₂CI

64. In a set of reactions m - bromobenzoic acid gave a 65. What is the conjugate base of OH⁻?
product D. Identify the product D.
(A) O₂
(A) (B) H₂O
(B) (C) O⁻
(C) (D) O²⁻
(D)

66. An oxide of a non-metal has the following properties 67. What are the species (A) and (B) in the following
(i) It acts both as proton donor as well as proton acceptor
(ii) It reacts readily with basic and acidic oxides
(ii) It oxidies Fe at its boiling point. The oxide may be
(A) H₂CrO₄, H₂Cr₂O₇
(A) P₂O₅
(B) H₂Cr₂O₇, Cr₂O₃
(B) SiO₂
(C) CrO₄²⁻, CrO₇²⁻
(C) H₂O
(D) H₂CrO₄, CrO₄²⁻
(D) CO₂

68. The rate constant for the reaction 2N₂O₅ ⟶ 4NO₂ + 69. In the reaction 2FeCl₃ + H₂S ⟶ 2FeCl₂ + 2HCl + S The
O₂, is 3.0 x 10⁻⁵s⁻¹. If rate is 2.40 x 10⁻⁵, then correct statement is
concentration of N₂O₅(in mol/L) is
(A) FeCl₃ acts as an oxidising agent
(A) 1.4 (B) H₂S and FeCl₃ both act as an oxidising agent
(B) 1.2 (C) FeCl₂ get oxidised while H₂S get reduced
(C) 0.04 (D) H₂S acts as an oxidising agent
(D) 0.8

70. The order of reactivity of the following alcohol is

(A) 1 > 2 >3 > 4

(B) 1 > 3 > 2 > 4

(C) 4 > 3 > 2 > 1

(D) 4 > 3 >1 > 2

MATHEMATICS

71. If a and b are two vectors, such that a.b 0 and | a · b | 72. If from a point P(a,b,c) perpendiculars PA and PB are
= | a × b | then the angle between vectors a and b is drawn to YZ and ZX-planes, then the equation of the
plane OAB is
(A) 3π/4

(B) π/4 (A) bcx + cay + abz = 0

(C) π (B) bcx + cay – abz = 0

(D) 7π/4 (C) - bcx + cay + abz = 0

(D) bcx-cay+abz=0

73. Let a, b and c be positive real numbers. The following 74. Which of the following function is not differentiable at
system of equations in x, y and z, x ^ 2 a ^ 2 + y ^ 2 b ^ x = 1?
2-z^2c^2=1,x^2a^2-y^2b^2+z^2c^2
(A) f ( x ) = ( | x - 1 | ) + | x - 1 |
= 1 and - x ^ 2 a ^ 2 + y ^ 2 b ^ 2 + z ^ 2 c ^ 2 = 1 has
(B) f ( x ) = ( | x - 1 | ) - | x - 1 |
(A) finitely many solutions
(C) f ( x ) = ( x ^ 2 - 1 ) | ( x - 1 ) ( x - 2 ) |
(B) no solution
(D) None of the above
(C) unique solution

(D) infinitely many solutions

75. The parametric coordinates of any point on n the 76. Given f ( x ) = ( ( 1 + x )/( 1 - x ) ) and g ( x ) = 3 x + x
parabola whose focus is (0, 1) and the directrix is x+2=0, ^ 3 1 + 3 x ^ 2 then log (x) equals
are
(A) [ f ( x ) ] ^ 3
(A) ( t ^ 2 - 1,2 t + 1 ) (B) -f(x)
(B) ( t ^ 2 + 1,2 t + 1 ) (C) 3f(x)
(C) ( t ^ 2 , 2 t ) (D) none of these
(D) ( t ^ 2 + 1,2 t - 1 )

77. ∫ _ 0 ^ x | t | d t and x ( 2 n π , ( 2 n + 1 ) π ) , n N is 78. The foci of a hyperbola are (-5, 18) and (10, 20) and it
equal to touches the Y-axis. The length of its transverse axis is

(A) 4n-1-cosx (A) 100

(B) 4n-sinx (B) √89/2

(C) 4n-cosx (C) √89

(D) 4n+1-cosx (D) √50

79. The equation of the curve in which the portion of the 80. The mean and the variance of a binomial distribution
tangent included between the coordinate axes is bisected are 4 and 2, respectively. Then, the probability of 2
at the point of contact, is success is

(A) a parabola (A) 28/256

(B) an ellipse (B) 219/256

(C) a circle (C) 128/256

(D) a hyperbola (D) 37/256

81. Let A = [ array c c c 1 & - 1 & 1 \ 2 & 1 & - 3 \ 1 & 1 & 1 82. Let ω be the complex number ( 3 )/( 2 π ) + i ( 3 )/( 2 π
array ] and 10 B = [ array c c c 4 & 2 & 2 \ - 5 & 0 & α \ 1 & ) Then, the number of distinct complex number z
- 2 & 3 array ] .If b is the inverse of A then �� is satisfying | array c c c z + 1 & ω & ω ^ 2 \ ω & z + ω ^ 2 &
1 \ ω ^ 2 & 1 & z + ω array | = 0 is equal to
(A) 5

(B) -2 (A) 1

(C) 1 (B) 0

(D) -1 (C) 2

(D) 3

83. The combined equation of the asymptotes of the 84. The degree of the differential equation satisfying √(1-
hyperbola 2 x ^ 2 + 5 x y + 2 y ^ 2 + 4 x + 5 y = 0 x²) + √(1-y²) = a (x - y), is

(A) 2 x ^ 2 + 5 x y + 2 y ^ 2 + 4 x + 5 y - 2 = 0 (A) 1

(B) 2 x ^ 2 + 5 x y + 2 y ^ 2 = 0 (B) 2

(C) 2 x ^ 2 + 5 x y + 2 y ^ 2 + 4 x + 5 y + 2 = 0 (C) 3

(D) . None of the above (D) None of these.

85. If d= a×b+b×c+c× a is a non−zero vector and 86.  The normal at (a, 2a) on y ^ 2 = 4 a x meets the
|(d⋅c)(a×b)+(d⋅a)(b×c)+(d⋅b)(c×a)|=0 then curve again at ( a t ^ 2 , 2 a t ) , then the value of t is

(A) | a | + | b | + | c | = | d | (A) -1

(B) | a | = | b | = | c | (B) 1

(C) a, b and c are coplanar (C) -3

(D) None of the above (D) 3

87. The equation of the ellipse with its centre at (1,2), 88. If A = [ array c c c 0 & 1 & - 1 \ 2 & 1 & 3 \ 3 & 2 & 1
one locus at (6, 2) and passing through (4, 6) is array ] then ( A ( adj A ) A ^ - 1 ) A is equal to

(A) 45 ( x - 1 ) ^ 2 + 20 ( y - 2 ) ^ 2 = 1 (A) 2 [ array l l l 3 & 0 & 0 \ 0 & 3 & 0 \ 0 & 0 & 3 array ]

(B) 20 ( x - 1 ) ^ 2 + 45 ( y - 2 ) ^ 2 = 1 (B) [ array c c c 0 & 1 / 6 & - 1 / 6 \ 2 / 6 & 1 / 6 & 3 / 6 \ 3 / 6

(C) 45 ( x + 1 ) ^ 2 + 20 ( y + 2 ) ^ 2 = 1 & 2 / 6 & 1 / 6 array ]

(D) None of the above. (C) [ array c c c - 6 & 0 & 0 \ 0 & - 6 & 0 \ 0 & 0 & - 6 array ]

(D) none of these

89. If ∫ _ 0 ^ ∞ 1 + x ^ 2 ( 1 + x ^ 2 ) dx = k ∫ _ 0 ^ 1 1 + x 90. If A = {x:x² - 5x+6=0}, B = {2,4}, C = {4,5), then A x
^ 2 ( 1 + x ) dx, then k is equal to (B∩C) is

(A) 4 (A) {(2, 4), (3, 4)}

(B) 8 (B) {(4,2), (4,3)}

(C) π (C) {(2, 4), (3, 4), (4,4)}

(D) 2π (D) {(2, 2), (3, 3), (4,4) (5,5)}

91. The principal amplitude of (sin 40° + i cos 40°)⁵ is 92. If A = ( 1 )/( 3 ) [ array c c c 1 & 2 & 2 \ 2 & 1 & - 2 \ a
& 2 & b array ] is an orthogonal matrix, then
(A) 70°

(B) - 110° (A) a = 2, b=1

(C) 110° (B) a = -2, b=-1

(D) - 70° (C) a = 2, b=-1

(D) a= -2, b = 1

93. The differential equation of all parabolas each of 94. If there is an error of K % is measuring the edge of a
which has a latus rectum 4a and whose axes are parallel cube, then the percent error in estimating its volume is
to the Y-axis is
(A) k
(A) of order 1 and degree 2 (B) 3k
(B) of order 2 and degree 3 (C) k/3
(C) of order 2 and degree 1 (D) None of these
(D) of order 2 and degree 2

95. Let u, v and w be such that |u| = 1, |v| = 2 and |w| =3. 96. Let X and Y be two events such that P(X/Y) = 1/2, P(Y
If the projection of v along u is equal to that of w along u / X) = 1/3 and P(X ∩ Y)=1/6. Which of the following is
and vectors v and w are perpendicular to each other, incorrect?
then |u-v+w| equals
(A) P(X U Y) = ⅔
(A) 2 (B) X and Y are independent
(B) √( 7 ) (C) P( X ^ c ∩ Y) = 1/6
(C) √( 14 ) (D) X and Y are not independent
(D) 14

97. Let A be a non-singular square matrix. Then, | adj A | 98. The area between the curve y = 2x⁴ – x², the X-axis
is equal to and the ordinates of two minima of the curve is

(A) | A | ^ n (A) 7/120

(B) | A | ^ n - 1 (B) 9/120

(C) | A | ^ n - 2 (C) 11/120

(D) None of these. (D) 13/120

99. If the relation between direction ratios of two lines 100. The equation of the plane through the intersection
are given by a+b+c = 0 and 2ab + 2ac – bc = 0, then the of the planes x + y + z = 1 and 2x + 3y - z + 4 = 0 and
angle between the lines is parallel to X-axis, is

(A) π (A) y - 3z + 6 = 0

(B) 2π/3 (B) 3y - z + 6 = 0

(C) π/2 (C) y + 3z + 6 = 0

(D) π/3 (D) 3y - 2z + 6 = 0

101. The range of the function f(x) = tan √ 9 π ^ 2 - x ^ 2 102. Let E' denote the complement of an event E. Let E, F,
is G be pairwise independent events such that P(G) > 0 and
P(E∩F∩G)=0. Then, P(E'∩F'/G) equals
(A) [0, √3]

(B) (0, √3) (A) P(E') + P(F')

(C) [0, √3) (B) P(E') - P(F')

(D) (0, √3] (C) P(E')- P(F)

(D) P(E)- P(F')

103. If the distance between the plane Ax - 2y + z = d 104. If a, b, c are three non-zero vectors which are
and the plane containing the lines ( 2 )/( x - 1 ) = ( 3 )/( y - pairwise non-collinear. Also, a + 3b is collinear with c and
2 ) = ( 4 )/( z - 3 ) and ( 3 )/( x - 2 ) = ( 4 )/( y - 3 ) = ( 5 )/( b + 2c is collinear with a, then a + 3b + 6c is
z - 4 ) is √6, then | d | is equal to
(A) c
(A) 3 (B) 0
(B) 4 (C) a + c
(C) 6 (D) a
(D) 1

105. If the lines ( 2 )/( x - 1 ) = (3 )/( y + 2 ) = ( 4 )/( z - 1 ) 106. If the direction cosines of two lines are connected by
and ( 1 )/( x - 3 ) = ( 2 )/( y - k ) = ( 1 )/( z ) intersect, then the equations l+m+n=0, l ^ 2 + m ^ 2 - n ^ 2 = 0 , then
the value of k is the angle between the lines is

(A) 3/2 (A) π/4

(B) 7/2 (B) π/6

(C) -2/7 (C) π/2

(D) - 3/2 (D) π/3

107.  If the slope of the curve y = ( b - x )/( a x ) at the 108. The value of [ √( 2 ) \ ( 56 ^ ° 15 ^ ′ ) + i ( 56 ^ ° 15 ^
point (1, 1) is 2, then ′ ) \ ] ^ 8 is

(A) a = 1, b=-2. (A) - 16 i

(B) a = -1, b=2 (B) 16 i

(C) a = 1, b = 2 (C) 8 i

(D) None of these (D) 4 i

109. The relation on the set A = \ x : | x | 3 , x Z \ is 110. The order of the differential equation whose general
defined by R = \ ( x , y ) : y = | x | , x ≠ - 1 \ .Then, the solution is given by y = ( C _ 1 + C _ 2 ) ( x + C _ 3 ) - C _ 4
number of elements in the power set of R is e^x+C_5

(A) 8 (A) 2

(B) 16 (B) 3

(C) 32 (C) 4

(D) 64 (D) 5

ENGLISH

111. Mountaineers climb as a team because 112. Fill in the blank. Pradeep's face spoke ............. for
the happiness he was feeling.
(A) the height is too much for one individual

(B) the competition is between the team and the Peak (A) elegantly

(C) they have to rely on each other for safety (B) tons

(D) there is no competition among them (C) volumes

(D) much

113. Choose the word which best expresses the meaning 114. Which one of the following is not true about the
of the underlined word in the sentence. His conjecture status of English language across the world?
was better than mine.
(A) English as a native language
(A) guess (B) English as a heritage language
(B) fact (C) English as a foreign language
(C) surprise (D) English as a second language
(D) doubt

115.

Choose the correct answers from the given Paragraph.

Mountaineering is now looked upon as the king of sports. But men have lived amongst the mountains since pre-
historic times and in some parts of the world, as in the Andes and Himalayas, difficult mountain journeys have
inevitably been part of their everyday life. However, some of the peaks were easily accessible from most of the cities
of Europe. It is quite interesting that while modem mountaineers prefer difficult routes for the greater enjoyment of
sport, the early climbers looked for the easiest ones, for the summit was the prize they all set their eyes on. Popular
interest in mountaineering increased considerably after the ascent of the Alpine peak Of Matterhorn in 1865 and
Edward Whimpers dramatic account of the climb and fatal accident which occurred during the descent.

In the risky sport of mountaineering element of competition between either individuals or teams is totally absent.
Rather one can say that the competition is between the team and the peaks themselves. The individuals making up a
party must climb together as a team, for they depend upon another for their safety. Mountaineering can be dangerous
unless reasonable precautions are taken. However, the majority of fatal accidents happen to parties which are
inexperienced or not properly equipped. Since many accidents are caused by bad weather. the safe climber is the man
who knows when it is time to turn back, however tempting it may be to press on and try to reach the summit.

Mountaineering is different from other sports because

(A) it is risky and dangerous

(B) it can be fatal

(C) it is most thrilling and exciting, there is no competition between individuals

(D) None of the above

ANSWER KEY

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

113. (A) 114. (B) 115. (C)