VITEEE SOLVED PAPER-2022
PART –I (PHYSICS)
1. The root mean square speed of smoke particles of mass 5 × 10−17 kg in their Brownian motion in air at NTP is approximately
[Given k = 1.38 × 10−23 JK−1]
(a) 60 mms−1
(b) 12 mms−1
(c) 15 mms−1
(d) 36 mms−1
2. The equation of a particle executing simple harmonic motion is given by At t = 1s, the speed of particle will be (Given : π = 3.14)
(a) 0 cms−1
(b) 157 cms−1
(c) 272 cms−1
(d) 314 cms−1
3. Following are expressions for four plane simple harmonic waves
The paris of waves which will produce destructive interference and stationary waves respectively in a medium, are
(a) (iii, iv), (i, ii)
(b) (i, iii), (ii, iv)
(c) (i, iv), (ii, iii)
(d) (i, ii), (iii, iv)
4. If a charge q is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be :
5. The electric potential V(x) in a region around the origin is given by V(x) = 4x2 The electric charge enclosed in a cube of 1 m side with its centre at the origin is (in coulomb)
6. A heater coil is cut into two equal parts and only one part is now used in the The heat generated will now be
(a) four times
(d) one fourth
7. In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a
(b) straight line
8. An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero?
(b) Potential energy
9. The self induced emf of a coil is 25 volts. When the current in it is changed at uniform rate from 10 A to 25 A in 1s, the change in the energy of the inductance is:
(a) 740 J
(b) 437.5 J
(c) 540 J
(d) 637.5 J
10. Alternating current can not be measured by D.C. ammeter because
(a) Average value of current for complete cycle is zero
(b) A.C. Changes direction
(c) A.C. can not pass through D.C. Ammeter
(d) D.C. Ammeter will get damaged.
11. The magnetic field of a plane electromagnetic wave is given by:
The amplitude of the electric field would be:
(a) 6 Vm−1 along x-axis
(b) 3 Vm−1 along z-axis
(c) 6 Vm−1 along z-axis
(d) 2 × 10−8 Vm−1 along z-axis
12. An ideal gas is expanding such that PT3 = constant. The coefficient of volume expansion of the gas is:
13. Two light beams of intensities in the ratio of 9 : 4 are allowed to interfere. The ratio of the intensity of maxima and minima will be:
(a) 2 : 3
(b) 16 : 81
(c) 25 : 169
(d) 25 : 1
14. The deBroglie wavelength of a proton and α-particle are equal. The ratio of their velocities is :
(a) 4 : 3
(b) 4 : 1
(c) 4 : 2
(d) 1 : 4
15. The recoil speed of a hydrogen atom after it emits a photon in going from n = 5 state to n = 1 state will be
(a) 4.34 m/s
(b) 2.19 m/s
(c) 4.17 m/s
(d) 3.25 m/s
16. Which of the following figure represents the variation of ln(R/R0) with ln A(If R = radius of a nucleus and A = its mass number)?
17. Zener breakdown occurs in a p-n junction having p and n both :
(a) lightly doped and have wide depletion layer
(b) heavily doped and have narrow depletion layer
(c) lightly doped and have narrow depletion layer
(d) heavily doped and have side depletion layer
18. If E and H represents the intensity of electric field and magnetizing field respectively, then the unit of E/H will be:
19. A stone of mass m, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is :
(a) the same throughout the motion
(b) minimum at the highest position of the circular path
(c) minimum at the lowest position of the circular path
(d) minimum when the rope is in the horizontal position
20. A particle is moving with a velocity where K is a constant. The general equation for its path is :
(a) y = x2 + constant
(b) y2 = x + constant
(c) y2 = x2 + constant
(d) xy = constant
21. A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation
Where F0 and T are constants. The force acts only for the time interval 2T. The velocity v of the particle after time 2T is:
22. The magnetic moment of an electron (e) revolving in an orbit around nucleus with an orbital angular momentum is given by:
23. Angular momentum of the particle rotating with a central force is constant due to
(a) constant torque
(b) constant force
(c) constant linear momentum
(d) zero torque
24. The escape velocity of a body depends upon mass as
25. A Potential energy as a function of r is given by where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be:
26. If two soap bubbles of different radii are connected by a tube
(a) air flows from the smaller bubble to the bigger
(b) air flows from bigger bubble to the smaller bubble till the sizes are interchanged
(c) air flows from the bigger bubble to the smaller bubble till the sizes become equal
(d) there is no flow of air.
27. The focal length f is related to the radius of curvature r of the spherical convex mirror by :
(b) f = −r
(d) f = r
28. A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the gas from D to E to F will be
(a) −450 J
(b) 450 J
(c) 900 J
(d) 1350 J
29. A vertical electric field of magnitude 4.9 × 105 N/C just prevents a water droplet of a mass 0.1 g from falling. The value of charge on the droplet will be:
(Given g = 9.8 m/s2)
(a) 1.6 × 10−9 C
(b) 2.0 × 10−9 C
(c) 3.2 × 10−9 C
(d) 0.5 × 10−9 C
30. In the circuit shown in the figure, the total charge is 750 μC and the voltage across capacitor C2 is 20 V. Then the charge on capacitor C2 is :
(a) 450 μC
(b) 590 μC
(c) 160 μC
(d) 650 μC
31. For a transistor α and β are given as Then the correct relation between α and β will be:
32. A current I flows along the length of an infinitely long, straight, thin walled pipe. Then
(a) the magnetic field at all points inside the pipe is the same, but not zero
(b) the magnetic field is zero only on the axis of the pipe
(c) the magnetic field is different at different points inside the pipe
(d) the magnetic field at any point inside the pipe is zero
33. A Carnot engine has efficiency of 50%. If the temperature of sink is reduced by 40°C, its efficiency increases by 30%. The temperature of the source will be :
(a) 166.7 K
(b) 255.1 K
(c) 266.7 K
(d) 367.7 K
34. When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on
(a) Electromagnetic induction
(b) Resonance in ac circuits
(c) Mutual induction in ac circuits
(d) interference of electromagnetic waves
35. An electron moving with speed v and a photon moving with speed c, have same D-Broglie wavelength. The ratio of kinetic energy of electron to that of photon is :
36. Assuming fully decomposed, the volume of CO2 released at STP on heating 9.85 g of BaCO3 (Atomic mass, Ba = 137) will be
(a) 1.12 L
(b) 2.24 L
(c) 4.06 L
(d) 0.84 L
37. Among the following, the species having the smallest bond is
38. The oxidation number of phosphorus in Ba(H2PO2)2 is
39. The correct order of thermal stability of hydroxides is:
(a) Ba(OH)2 < Ca(OH)2 < Sr(OH)2 < Mg(OH)2
(b) Mg(OH)2 < Sr(OH)2 < Ca(OH)2 < Ba(OH)2
(c) Mg(OH)2 < Ca(OH)2 < Sr(OH)2 < Ba(OH)2
(d) Ba(OH)2 < Sr(OH)2 < Ca(OH)2 < Mg(OH)2
40. Which of the following has correct increasing basic strength?
(a) MgO < BeO < CaO < BaO
(b) BeO < MgO < CaO < BaO
(c) BaO < CaO < MgO < BeO
(d) CaO < BaO < BeO < MgO
41. Water sample is reported to be highly polluted if BOD (Biological Oxygen Demand) value of sample becomes
(a) more than 17 ppm.
(b) equal to 10 ppm.
(c) equal to 5 ppm.
(d) less than 5 ppm.
42. 200 mL of an aqueous solution of a protein contains its 1.26 g. The osmotic pressure of this solution at 300 K is found to be 2.57 × 10−3 The molar mass of protein will be
(R = 0.083 L bar mol−1 K−1)
(a) 51022 g mol−1
(b) 122044 g mol−1
(c) 31011 g mol−1
(d) 61038 g mol−1
43. Lyophilic sols are more stable than lyophobic sols because:
(a) the colloidal particles have positive charge
(b) the colloidal particles have negative charge
(c) the colloidal particles are solvated
(d) there is strong electrostatic repulsion between the colloidal particles
44. Which of the following is not permissible arrangement of electrons in an atom?
(a) n = 5, l = 3, m = 0, s = +1/2
(b) n = 3, l = 2, m = −3, s = −1/2
(c) n = 3, l = 2, m = −2, s = −1/2
(d) n = 4, l = 0, m = 0, s = −1/2
45. The value of van der Waals constant ‘a’ for gases O2, N2, NH3 and CH4 are 1.360, 1.390, 4.170 and 2.253 litre2 atm mol−2 The gas which can most easily be liquefied is :
46. Which one of the following does not have a pyramidal shape?
47. Boric acid is polymeric due to
(a) its acidic nature
(b) the presence of hydrogen bonds
(c) its monobasic nature
(d) its geometry
48. Which of the following order is not correct?
(a) MeBr > Me2CHBr > Me3CBr > Et3CBr(SN2)
(b) PhCH2Br > PhCHBrMe2 > PhCBrMePh(SN1)
(c) MeI > MeBr > MeCl > MeF (SN2)
(d) All are correct
49. A catalyst is a substance which :
(a) is always in the same phase as in the reaction
(b) alters the equilibrium in a reaction
(c) does not participate in the reaction but alters the rate of reaction
(d) participates in the reaction and provides an easier pathway for the same
50. Which of the following is a non-reducing sugar?
51. An ideal gas expands against a constant external pressure of 2.0 atmosphere from 20 litre to 40 litre and absorbs 10 kJ of heat from surrounding. What is the change in internal energy of the system?
(given : 1 atm-litre = 101.3 J)
(a) 4052 J
(b) 5948 J
(c) 14052 J
(d) 9940 J
52. The polymer used for optical lenses is:
(b) polyvinyl chloride
(d) polymethyl methacrylate
53. Which of the following arrangements represents the increasing order (smallest to largest) of ionic radii of the given species O2−, S2−, N3−, P3−?
(a) O2− < N3− < S2− < P3−
(b) O2− < P3− < N3− < S2−
(c) N3 < O2− < P3− < S2−
(d) N3− < S2− < O2− < P3−
54. The IUPAC name of the following compound is
55. In CsCl type structure, the co-ordination number of Cs+ and Cl− respectively are
(a) 6, 6
(b) 6, 8
(c) 8, 8
(d) 8, 6
56. Which one of the following reactions will not result in the formation of carbon-carbon bond?
(a) Reimer-Tiemann reaction
(b) Friedel Craft’s acylation
(c) Wurtz reaction
(d) Cannizzaro reaction
57. Water is :
(a) more polar than H2S
(b) more or less identical in polarity with H2S
(c) less polar than H2S
(d) None of these
58. Carboxylic acids are more acidic than phenol and alcohol because of
(a) intermolecular hydrogen bonding
(b) formation of dimers
(c) highly acidic hydrogen
(d) resonance stabilization of their conjugate
59. The order of increasing sizes of atomic radii among the elements O, S, Se and As is:
(a) As < S < O < Se
(b) Se < S < As < O
(c) O < S < As < Se
(d) O < S < Se < As
60. Bauxite ore is generally contaminated with impurity of oxides of two elements X and Y. Which of the following statement is correct?
(a) X is a non-metal and belongs to the third period while Y is a metal and belongs to the fourth period.
(b) One of two oxides has three-dimensional polymeric structure.
(c) Both (a) and (b) are correct.
(d) None of the above
61. The partial pressure of CH3OH(g), CO(g) and H2(g) in equilibrium mixture for the reaction, CO(g) + 2H2(g) ⇌ CH3OH(g) are 2.0, 1.0 and 0.1 atm respectively at 427° The value of Kp for the decomposition of CH3OH to CO and H2 is
(a) 102 atm
(b) 2 × 102 atm−1
(c) 50 atm2
(d) 5 × 10−3 atm2
62. The conjugate base of (CH3)2NH2+ is
63. Which of the following is not present in a nucleotide?
64. The shape of [Cu(NH3)4]2+ is
(b) square planar
65. Heroin is a derivative of
66. The limiting equivalent conductivity of NaCl, KCl and KBr are 126.5, 150.0 and 151.5 S cm2 eq−1, respectively. The limiting equivalent ionic conductivity for Br− is 78 Scm2eq−1. The limiting equivalent ionic conductivity for Na+ ions would be :
67. Rate of dehydration of alcohols follows the order:
(a) 2° > 1° > CH3OH > 3°
(b) 3° > 2° > 1° > CH3OH
(c) 2° > 3° > 1° > CH3OH
(d) CH3OH > 1°> 2° > 3°
68. An alkene having molecular formula C7H14 was subjected to ozonolysis in the presence of zinc dust. An equimolar amount of the following two compounds was obtained
The IUPAC name of the alkene is
(a) 3, 4-dimethyl-3-pentene
(b) 3, 4-dimethyl-2-pentene
(c) 2, 3-dimethyl-3-pentene
(d) 2, 3-dimethyl-2-pentene
69. Lanthanoid contraction can be observed in
70. The form of iron obtained from blast furnace is:
(b) Cast Iron
(c) Pig Iron
(d) Wrought Iron
PART – III (MATHEMATICS)
71. A class has 175 students. The following data shows the number of students opting one or more subjects. Maths-100, Physics-70, Chemistry-40, Maths and Physics-30, Maths and Chemistry-28, Physics and Chemistry-23, Maths, Physics and Chemistry-18. How many have offered Maths alone?
72. Let R be a relation on the set N be defined by |(x, y)|x, y ∈ N, 2x + y = 41}. Then, R is
(d) None of these
73. The function f : R → R defined by f(x) = x2 + x is.
(d) None of these
74. If 12 cot2 θ – 31 cosec 0 + 32 = 0, then the value of sin θ is
(a) 3/5 or 1
(b) 2/3 or −2/3
(c) 4/5 or 3/4
75. The modulus of is
76. If α, β are the roots of the equation ax2 + bx + c = 0, then
77. The solution set of the inequality 37 – (3x + 5) ≥ 9x – 8 (x – 3) is
(a) (−∞, 2)
(b) (−∞, −2)
(c) (−∞, 2]
(d) (−∞, −2]
78. If n+2C8 : n – 2 P4 = 57 : 16, then the value of n is:
79. The middle term in the expansion of is
80. The fourth, seventh and tenth terms of a GP. Are p, q, r respectively. then :
(a) p2 = q2 + r2
(b) q2 = pr
(c) p2 = qr
(d) pqr + pq + 1 = 0
81. The point (t2 + 2t + 5, 2t2 + t – 2) lies on the line x + y = 2 for
(a) All real values of t
(b) Some real values of t
(d) None of these
82. The equations of the lines which cuts off an intercept −1 from y-axis and equally inclined to the axes are
(a) x – y + 1 = 0, x + y + 1 = 0
(b) x – y – 1 = 0, x + y – 1 = 0
(c) x – y – 1 = 0, x + y + 1 = 0
(d) None of these
83. The distance between the parallel lines 3x – 4y + 7 = 0 and 3x – 4y + 5 = 0 is a/b. Value of a + b is
84. For what value of k, does the equation
9x2 + y2 = k(x2 – y2 – 2x)
represent equation of a circle?
85. A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at
(a) (0, 2)
(b) (1, 0)
(c) (0, 1)
(d) (2, 0)
86. Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (−3, 1) and has eccentricity is
(a) 5x2 + 3y2 – 48 = 0
(b) 3x2 + 5y2 – 15 = 0
(c) 5x2 + 3y2 – 32 = 0
(d) 3x2 + 5y2 – 32 = 0
87. The co-ordinates of the point which divides the join of the points (2, −1, 3) and (4, 3, 1) in the ratio 3 : 4 internally are given by :
(a) (2/7, 20/7, 10/7)
(b) (10/7, 15/7, 2/7)
(c) (20/7, 5/7, 15/7)
(d) (15/7, 20/7, 3/7)
88. The relationship between a and b, so that the function f defined by
is continuous at x = 3, is
(a) a = b + 2/3
(b) a – b = 3/2
(c) a + b = 2/3
(d) a + b = 2
89. at x = 0 is
(a) continuous as well as differentiable
(b) differentiable but not continuous
(c) continuous but not differentiable
(d) neither continuous nor differentiable
90. The variance of the data 2, 4, 6, 8, 10 is
(d) None of these
91. Find the probability of getting the sum as a perfect square number when two dice are thrown together.
(d) None of these
92. The principal value of is
93. If the system of linear equations
x + ky + 3z = 0
3x + ky – 2z = 0
2x + 4y – 3z = 0
Has a non-zero solution (x, y, z), then xz/y2 is equal to :
94. The value of definite integral
95. The area enclosed between the graph of y = x3 and the lines x = 0, y = 1, y = 8 is
(d) None of these
96. The total number of 3-digit numbers, the sum of whose digits is even, is equal to
97. To fill 12 vacancies, there are 25 candidates of which five are from scheduled caste. If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all, then the number of ways in which the selection can be made
(a) 5C3 × 22C9
(b) 22C9 – 5C3
(c) 22C3 + 5C3
(d) None of these
98. are in A.P. then,
(a) p, q, r are in A.P.
(b) p2, q2, r2 are in A.P
(c) 1/p, 1/q, 1/r are in A.P
(d) p + q + r are in A.P
99. The sum of the first n terms of the series 12 + 2.22 + 32 + 2.42 + 52 + 2.62 + … is when n is even. When n is odd the sum is
100. The locus of a point that is equidistant from the lines x + y – 2√2 = 0 and x + y – √2 = 0 is
(a) x + y – 5√2 = 0
(b) x + y – 3√2 = 0
(c) 2x + 2y – 3√2 = 0
(d) 2x + 2y – 5√2 = 0
101. The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is
(a) (3, −4)
(b) (−3, 4)
(c) (−3, −4)
(d) (3, 4)
102. For the parabola y2 = −12x, equation of directrix is x = a. The value of ‘a’ is
103. The eccentricity of the curve 2x2 + y2 – 8x – 2y = 0 is :
104. The equation of the hyperbola with vertices at (0, ±6) and e = 5/3 is
105. is equal to:
(b) 12 cos2x − 10 sin2x
(c) 12 cos2x – 10 sin2x – 2
(d) 10 sin 2x
106. The function is
(a) differentiable at x = 2
(b) not differentiable at x = 2
(c) continuous at x = 2
(d) None of these
107. The local minimum value of the function f given by f(x) = 3 + |x|, x ∈ R is
108. Value of is
(d) None of these
109. The equation of the plane which bisects the angle between the planes 3x – 6y + 2z + 5 = 0 and 4x – 12y + 3z – 3 = 0 which contains the origin is
(a) 33x – 13y + 32x + 45 = 0
(b) x – 3y + z – 5 =0
(c) 33x + 13y + 32x + 45 = 0
(d) None of these
110. An urn contains five balls. Two balls are drawn and found to be white. The probability that all the balls are white is
PART-IV (APTITUDE TEST)
Directions (Qs. 111-113): Study the following table to answer the given questions:
111. What is the total marks obtained by Meera in all the subject?
112. What is the average marks obtained by these seven students in History? (rounded off to two digits)
113. How many students have got 60% or more marks in all the subjects?
114. A series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series.
5, 11, 24, 51, 106, _____?
115. In a certain code BANKER is written as LFSCBO. How will CONFER be written in that code?
116. Kailash faces towards north. Turnings to his right, he walks 25 metres. He then turns to his left and walks 30 metres. Next, he moves 25 metres to his right. He then turns to the right again and walks 55 metres. Finally, he turns to the right and moves 40 metres. In which direction is he now from his starting point?
117. An accurate clock shows 8 O’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 O’clock in the afternoon?
118. Two statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
All utensils are spoons.
All bowls are spoons.
(I) No utensil is a bowls.
(II) Some utensils are bowls
(III) No spoon is a utensil.
(a) Only conclusions I follows
(b) Conclusions I and III follow
(c) Either conclusion I or II follows
(d) Only conclusion III follows
Directions (Qs. 119-120) : Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.
Read both the statements and Give answer
(a) if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
(b) If the data in statement II alone are sufficient to answer the question, while the data is statement I alone are not sufficient to answer the question.
(c) if the data in both the statements I and II together are not sufficient to answer the question.
(d) if the data in both the statements I and II together are necessary to answer the question.
119. What was the ratio between the ages of P and Q four years ago?
(I) The ratio between the present ages of P and Q is 3:4.
(II) The ratio between the present ages of Q and R is 4:5.
120. What was the cost price of the suitcase purchased by Samir?
(I) Samir got 25 percent concession on the labeled price.
(II) Samir sold the suitcase for Rs. 2000 with 25 percent profit on the labeled price:
121. Read the following passage and answer the question that follows. Choose the correct answer.
His instrument struck against something hard, dangerously near the kidney…. “ It is not quite at the kidney my friend,” Sadao murmured…. “My friend,” he always called his parents and so he did now, forgetting that this was his enemy.
To whom does Sadao attend to in the lines above?
(a) A relative
(b) His friend
(c) His enemy
(d) A patient
122. Choose the correct pronunciation for the word ‘sorbet’ from the following options:
123. What is the correct syllable division of the word ‘indomitable’?
(a) in – do – mit – able
(b) in – dom-i – t – ble
(c) in – do – mo – ta – be
(d) in – dom – i – table
124. Read the following passage and the question below. Choose the correct answer.
Gandhi never contented himself with large political or economic solutions. He saw the cultural and social backwardness in the Champaran villages and wanted to do something about it immediately. He appealed to teachers.
Which of the following statements is true about the passage?
(a) Gandhi was dissatisfied with political or economic solutions
(b) Gandhi was interested in the welfare of teachers of Champaran villages
(c) Gandhi was happy about the cultural and social backwardness of Champaran villages
(d) Gandhi was hopeful that teachers could save villages from cultural and social backwardness
125. Choose the correct meaning of the idiom ‘a bolt out of the blue’ from the given options:
(a) Something totally unexpected
(b) Lightning and thunderstorm
(c) To do something kind
(d) To mourn after someone