## VITEEE Examination Previous Year Question Paper 2022 With Answer Key

VITEEE SOLVED PAPER-2022

PART –I (PHYSICS)

1. The root mean square speed of smoke particles of mass 5 × 1017 kg in their Brownian motion in air at NTP is approximately

[Given k = 1.38 × 1023 JK1]

(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 cms1

(b)   157 cms1

(c)   272 cms1

(d)   314 cms1

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 :

(a)   zero

(b)   q/2ε0

(c)   q/4ε0

(d)   q/2πε0

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)

(a)   8ε0

(b)   −4ε0

(c)   0

(d)   −8ε0

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

(b)   doubled

(c)   halved

(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

(a)   helix

(b)   straight line

(c)   ellipse

(d)   circle

8. An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero?

(a)   Momentum

(b)   Potential energy

(c)   Acceleration

(d)   Force

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 Vm1 along x-axis

(b)   3 Vm1 along z-axis

(c)   6 Vm1 along z-axis

(d)   2 × 108 Vm1 along z-axis

12. An ideal gas is expanding such that PT3 = constant. The coefficient of volume expansion of the gas is:

(a)   1/T

(b)   2/T

(c)   4/T

(d)   3/T

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:

(a)   ohm

(b)   mho

(c)   joule

(d)   newton

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:

(a)   2F0T/M

(b)   F0T/2M

(c)   4F0T/3M

(d)   F0T/3M

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

(a)   m0

(b)   m1

(c)   m2

(d)   m3

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:

(a)   (A/B)1/5

(b)   (B/A)1/5

(c)   (2A/B)1/5

(d)   (B/2A)1/5

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 :

(a)

(b)   f = −r

(c)

(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 × 109 C

(b)   2.0 × 109 C

(c)   3.2 × 109 C

(d)   0.5 × 109 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 :

(a)   3c/v

(b)   v/3c

(c)   v/2c

(d)   2c/v

PART-II (CHEMISTRY)

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

(a)   NO

(b)   NO+

(c)   O2

(d)   NO

38. The oxidation number of phosphorus in Ba(H2PO2)2 is

(a)   +3

(b)   +2

(c)   +1

(d)   −1

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 × 103 The molar mass of protein will be

(R = 0.083 L bar mol1 K1)

(a)   51022 g mol1

(b)   122044 g mol1

(c)   31011 g mol1

(d)   61038 g mol1

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 mol2 The gas which can most easily be liquefied is :

(a)   O2

(b)   N2

(c)   NH3

(d)   CH4

46. Which one of the following does not have a pyramidal shape?

(a)   (CH3)3N

(b)   (SiH3)3N

(c)   P(CH3)3

(d)   P(SiH3)3

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?

(a)   Lactose

(b)   Fructose

(c)   Sucrose

(d)   Maltose

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:

(a)   polypropylene

(b)   polyvinyl chloride

(c)   polythene

(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

(a)   (E)-2-hepten-4-yne

(b)   (Z)-5-hepten-3-yne

(c)   (E)-5-hepten-3-yne

(d)   (Z)-2-hepten-4-yne

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

(a)   (CH3)2NH

(b)   (CH3)2N+

(c)   (CH3)3N+

(d)   (CH3)2N

63. Which of the following is not present in a nucleotide?

(a)   Guanine

(b)   Cytosine

(d)   Tyrosine

64. The shape of [Cu(NH3)4]2+ is

(a)   tetrahedral

(b)   square planar

(c)   pyramidal

(d)   octahedral

65. Heroin is a derivative of

(a)   cocaine

(b)   morphine

(c)   caffeine

(d)   nicotine

66. The limiting equivalent conductivity of NaCl, KCl and KBr are 126.5, 150.0 and 151.5 S cm2 eq1, respectively. The limiting equivalent ionic conductivity for Br is 78 Scm2eq1. The limiting equivalent ionic conductivity for Na+ ions would be :

(a)   128

(b)   125

(c)   49

(d)   50

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

(a)   At

(b)   Gd

(c)   Ac

(d)   Lw

70.  The form of iron obtained from blast furnace is:

(a)   Steel

(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?

(a)   35

(b)   48

(c)   60

(d)   22

72. Let R be a relation on the set N be defined by |(x, y)|x, y ∈ N, 2x + y = 41}. Then, R is

(a)   Reflexive

(b)   Symmetric

(c)   Transitive

(d)   None of these

73. The function f : R → R defined by f(x) = x2 + x is.

(a)   one-one

(b)   onto

(c)   many-one

(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

(d)   ±1/2

75. The modulus of  is

(a)   2

(b)   4

(c)   3√2

(d)   2√2

76. If α, β are the roots of the equation ax2 + bx + c = 0, then

(a)   2/a

(b)   2/b

(c)   2/c

(d)   −2/a

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:

(a)   20

(b)   19

(c)   18

(d)   17

79. The middle term in the expansion of  is

(a)   10C5

(b)   10C6

(c)

(d)   10C5x10

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

(c)

(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

(a)   2

(b)   5

(c)   7

(d)   3

84. For what value of k, does the equation

9x2 + y2 = k(x2 – y2 – 2x)

represent equation of a circle?

(a)   1

(b)   2

(c)   −1

(d)   4

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

(a)   8

(b)   7

(c)   6

(d)   None of these

91. Find the probability of getting the sum as a perfect square number when two dice are thrown together.

(a)   5/12

(b)   7/18

(c)   7/36

(d)   None of these

92. The principal value of  is

(a)   −5π/3

(b)   5π/3

(c)   −π/3

(d)   4π/3

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 :

(a)   10

(b)   −30

(c)   30

(d)   −10

94. The value of definite integral

(a)   0

(b)   π/4

(c)   π/2

(d)   π

95. The area enclosed between the graph of y = x3 and the lines x = 0, y = 1,  y = 8 is

(a)   45/4

(b)   14

(c)   7

(d)   None of these

96. The total number of 3-digit numbers, the sum of whose digits is even, is equal to

(a)   450

(b)   350

(c)   250

(d)   325

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)   22C95C3

(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

(a)   3

(b)   4

(c)   2

(d)   6

103. The eccentricity of the curve 2x2 + y2 – 8x – 2y = 0 is :

(a)   1/2

(b)   1/√2

(c)   2/3

(d)   3/4

104. The equation of the hyperbola with vertices at (0, ±6) and e = 5/3 is

105. is equal to:

(a)   0

(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

(a)   1

(b)   2

(c)   3

(d)   0

108. Value of  is

(a)   π/2

(b)   −π/2

(c)   π/4

(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

(a)   1/10

(b)   3/10

(c)   3/5

(d)   1/2

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?

(a)   448

(b)   580

(c)   470

(d)   74.67

112. What is the average marks obtained by these seven students in History? (rounded off to two digits)

(a)   72.86

(b)   27.32

(c)   24.86

(d)   29.14

113. How many students have got 60% or more marks in all the subjects?

(a)   One

(b)   Two

(c)   Three

(d)   Four

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, _____?

(a)   122

(b)   217

(c)   120

(d)   153

115. In a certain code BANKER is written as LFSCBO. How will CONFER be written in that code?

(a)   GFSDPO

(b)   FGSDOP

(c)   GFSEPO

(d)   FHSDPO

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?

(a)   South-West

(b)   South

(c)   North-West

(d)   South-East

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?

(a)   144°

(b)   150°

(c)   168°

(d)   180°

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.

Statements:

All utensils are spoons.

All bowls are spoons.

Conclusions:

(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.

(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:

PART-V (ENGLISH)

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:

(a)   sore-bet

(b)   sore-bay

(c)   sore-bye

(d)   shore-bay

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

## VITEEE Examination Previous Year Question Paper 2021 With Answer Key

VITEEE SOLVED PAPER-2021

PART –I (PHYSICS)

1. The distance of the centres of moon and earth is D. The mass of earth is 81 times the mass of the moon. At what distance from the centre of the earth, the gravitational force will be zero?

(a)   D/2

(b)   2D/3

(c)   4D/3

(d)   9D/10

2. Two wires A and B are of the same material. Their lengths are in the ratio of 1 : 2 and the diameter are in the ratio 2 : 1. If they are pulled by the same force, then increase in length will be in the ratio of

(a)   2 : 1

(b)   1 : 4

(c)   1 : 8

(d)   8 : 1

3. If x = at + bt2, where x is the distance travelled by the body in kilometers while t is the time in seconds, then the unit of b is

(a)   km/s

(b)   kms

(c)   km/s2

(d)   kms2

4. A soap bubble of radius r1 is placed on another soap bubble of radius r2(r1 < r2). The radius R of the soapy film separating the two bubbles is

5. A charge q is moving with a velocity v parallel to a magnetic field B. Force on the charge due to magnetic field is

(a)   q v B

(b)   q B/v

(c)   zero

(d)   B v/q

6. Two spheres A and B of masses m and 2m and radii 2R and R respectively are placed in contact as shown. The COM of the system lies

(a)   inside A

(b)   inside B

(c)   at  the point of contact

(d)   None of these

7. Identify the correct statement.

(a)   Static friction depends on the area of contact

(b)   Kinetic friction depends on the area of contact

(c)   Coefficient of kinetic friction is more than the coefficient of static friction

(d)   Coefficient of kinetic friction is less than the coefficient of static friction

8. The distance travelled by a particle starting from rest and moving with an acceleration 4/3 ms2, in the third second is:

(a)   6m

(b)   4m

(c)   10/3 m

(d)   19/3 m

9. Photoelectric work function of a metal is 1 eV. Light of wavelength λ = 3000 Å falls on it. The photo electrons come out with a maximum velocity of :

(a)   10 metres/sec

(b)   102 metres/sec

(c)   104 metres/sec

(d)   106 metres/sec

10. The coefficient of apparent expansion of mercury in a glass vessel is 153 × 106/°C and in a steel vessel is 144 × 106/° If α for steel is 12 106/°C, then that of glass is

(a)   9 × 106/°C

(b)   6 × 106/°C

(c)   36 × 106/°C

(d)   27 × 106/°C

11. A step-up transformer operates on a 230 V line and supplies a load of 2 ampere. The ratio of the primary and secondary windings is 1 : 25. The current in the primary is

(a)   15 A

(b)   50 A

(c)   25 A

(d)   12.5 A

12. Two bodies of same mass are projected with the same velocity at an angle 30° and 60° The ratio of their horizontal ranges will be

(a)   1 : 1

(b)   1 : 2

(c)   1 : 3

(d)   2 : √2

13. Two point charges +3 μC and +8 μC repel each other with a force of 40 N. If a charge of −5 μC is added to each of them, then the force between them will become

(a)   −10N

(b)   +10N

(c)   +20N

(d)   −20N

14. A sphere rolls down on an inclined plane of inclination θ. What is the acceleration as the sphere reaches the bottom?

15. A given ray of light suffers minimum deviation in an equilateral prism P. Additional prisms Q and R of identical shape and of same material as that of P are now combined as shown in figure. The ray will now suffer

(a)   greater deviation

(b)   no deviation

(c)   same deviation as before

(d)   total internal reflection

16. The current in the 1Ω resistor shown in the circuit is

(a)   2/3 A

(b)   3 A

(c)   6 A

(d)   2 A

17. The root mean square velocity of hydrogen molecules at 300 K is 1930 metre/sec. Then the r.m.s velocity of oxygen molecules at 1200 K will be

(a)   482.5 metre/sec

(b)   965 metre/sec

(c)   1930 metre/sec

(d)   3860 metre/sec

18. Lenz’s law gives

(a)   the magnitude of the induced e.m.f.

(b)   the direction of the induced current

(c)   both the magnitude and direction of the induced current

(d)   the magnitude of the induced current

19. A parallel plate capacitor with air between the plates has a capacitance of 8 pF. Calculate the capacitance if the distance between the plates is reduced by half and the space between them is filled with a substance of dielectric constant. (k = 6)

(a)   72 pF

(b)   81 pF

(c)   84 pF

(d)   96 pF

20. For a particle executing S.H.M. the displacement x is given by x = A cos ω Identify the graph which represents the variation of potential energy (P.E.) as a function of time t and displacement x.

(a)   I, III

(b)   II, IV

(c)   II, III

(d)   I, IV

21. A radioactive sample contains 103 kg each of two nuclear species A and B with half-life 4 days and 8 days respectively. The ratio of the amounts of A and B after a period of 16 days is

(a)   1 : 2

(b)   4 : 1

(c)   1 : 4

(d)   2 : 1

22. A string of 7 m length has a mass of 0.035 kg. If tension in the string is 60.5 N, then speed of a wave on the string is

(a)   77 m/s

(b)   102 m/s

(c)   110 m/s

(d)   165 m/s

23. The following circuit represents

(a)   OR gate

(b)   AND gate

(c)   NAND gate

(d)   None of these

24. A straight section PQ of a circuit lies along the X-axis from x = −a/2 to x = a/2 and carries a steady current i. The magnetic field due to the section PQ at a point = +a will be

(a)   proportional to a

(b)   proportional to a2

(c)   proportional to 1/a

(d)   zero

25. A source producing sound of frequency 170 Hz is approaching a stationary observer with a velocity 17 ms1. The apparent change in the wavelength of sound heard by the observer is (speed of sound in air = 340 ms1)

(a)   0.1 m

(b)   0.2 m

(c)   0.4 m

(d)   0.5 m

PART-II (CHMISTRY)

26. Consider the following reactions:

NaCl + K2Cr2O7 (Conc.) → (A) + Side products

(A) + NaOH → (B) + Side products

(B) + H2SO4 (dilute) + H2O2 → (C) + Side products

The sum of the total number of atoms in one molecule each of (A), (B) and (C) is ______.

(a)   18

(b)   15

(c)   21

(d)   20

27. Xenon hexafluoride on partial hydrolysis produces compounds ‘X’ and ‘Y’. Compounds ‘X’, ‘Y’ and the oxidation state of Xe are respectively :

(a)   XeOF4(+6) and XeO3(+6)

(b)   XeO2(+4) and XeO3 (+6)

(c)   XeOF4(+6) and XeO2F2(+6)

(d)   XeO2F2(+6) and XeO2(+4)

28. The edge length of unit cell of a metal having molecular weight 75 g/mol is 5 Å which crystallizes in cubic lattice. If the density is 2g/cc then find the radius of metal atom. (NA = 6 × 1023). Give the answer in pm.

(a)   217 pm

(b)   210 pm

(c)   220 pm

(d)   205 pm

29. Consider the following statements :

(I) Increase in concentration of reactant increases the rate of a zero order reaction.

(II) Rate constant k is equal to collision frequency A if Ea = 0.

(III) Rate constant k is equal to collision frequency A if Ea = ∞.

(IV) In k vs T is a straight line.

(V) In k vs 1/T is a straight line.

Correct statements are

(a)   I and IV

(b)   II and V

(c)   III and IV

(d)   II and III

30. To deposit 0.634 g of copper by electrolysis of aqueous cupric sulphate solution, the amount of electricity required (in coulombs) is

(a)   1930

(b)   3960

(c)   4825

(d)   9650

31. In the following skew conformation of ethane, Hʹ−C−C−Hʹʹ dihedral angle is :

(a)   58°

(b)   149°

(c)   151°

(d)   120°

32. What is the product of following reaction?

33. In the following sequence of reactions,

the compound D is

(a)   propanal

(b)   butanal

(c)   n-butyl alcohol

(d)   n-propyl alcohol.

34. Which of the following reactions can produce aniline as main product?

(a)   C6H5NO2 + Zn/KOH

(b)   C6H5NO2 + Zn/NH4Cl

(c)   C6H5NO2 + LiAlH4

(d)   C6H5NO2 + Zn/HCl

35. Secondary structure of protein refers to

(a)   mainly denatured proteins and structure of prosthetic groups

(b)   three-dimensional structure, especially the bond between amino acid residues that are distinct from each other in the polypeptide chain

(c)   linear sequence of amino acid residues in the polypeptide chain

(d)   regular folding patterns of continuous portions of the polypeptide chain

36. The increasing order for the values of e/m (charge/mass) is

(a)   e, p, n, α

(b)   n, p, e, α

(c)   n, p, α, e

(d)   n, α, p, e

37. In which of the following pairs both the ions are coloured in aqueous solutions?

(a)   Sc3+, Ti3+

(b)   Sc3+, Co2+

(c)   Ni2+, Cu+

(d)   Ni2+, Ti3+

38. The total number of possible isomers for square-planar [Pt(Cl)(NO2)(NO3)(SCN)]2 is:

(a)   16

(b)   12

(c)   8

(d)   24

39. For the reaction,

2SO2(g) + O2(g) ⇌ 2SO3(g),

∆H = −57.2 kJ mol1 and Kc = 1.7 × 1016

Which of the following statement is INCORRECT?

(a)   The equilibrium constant is large suggestive of reaction going to completion and so no catalyst is required.

(b)   The equilibrium will shift in forward direction as the pressure increases.

(c)   The equilibrium constant decreases as the temperature increases.

(d)   The addition of inert gas at constant volume will not affect the equilibrium constant.

40. The half-life of a reaction is inversely proportional to the square of the initial concentration of the reactant. Then the order of the reaction is

(a)   0

(b)   1

(c)   2

(d)   3

41. A galvanic cell is set up from electrodes A and B

Electrode A : Cr2O72/Cr3+, E°red = +1.33 V

Electrode B : Fe3+/Fe2+, E°red = 0.77 V

Which of the following statements is false?

(a)   Standard e.m.f of the cell is 0.56 V

(b)   Current will flow from electrode A to B in the external circuit

(c)   A will act as cathode and have positive polarity

(d)   None of these

42. Keto-enol tautomerism is observed in :

43. In a set of reactions, ethylbenzene yield a product D.

44. What will be the final product in the following reaction sequence –

(a)   CH3CH2CONH2

(b)   CH3CH2COBr

(c)   CH3CH2NH2

(d)   CH3CH2CH2NH2

45. In a set of reactions acetic acid yielded a product D.

The structure of (D) would be –

46. In fructose, the possible optical isomers are

(a)   12

(b)   8

(c)   16

(d)   4

47. The position of both, an electron and a helium atom is known within 1.0 nm. Further the momentum of the electron is known within 5.0 × 1026 kg ms1. The minimum uncertainty in the measurement of the momentum of the helium atom is

(a)   50 kg ms1

(b)   80 kg ms1

(c)   8.0 × 1026 kg ms1

(d)   5.0 × 1026 kg ms1

48. The value of log10K for a reaction A ⇌ B is

(Given : ∆r298 K = −54.07 kJ mol1,

r298K = 10 JK1 mol1 and R = 8.314 JK1 mol1; 2.303 × 8.314 × 298 = 5705)

(a)   5

(b)   10

(c)   95

(d)   100

49. If C(s) + O2(g) → CO2(g); ∆H = R and

then heat of formation of CO is:

(a)   R + S

(b)   R – S

(c)   R × S

(d)   S – R

50. Which of the following compounds does not follow Markownikoff’s law?

(a)   CH3CH = CH2

(b)   CH2CHCl

(c)   CH3CH = CHCH3

(d)   None

PART – III (MATHEMATICS)

51. The value of c in Rolle’s Theorem for the function f(x) = ex sin x, x ∈ [0, π] is

(a)   π/6

(b)   π/4

(c)   π/2

(d)   3π/4

52. The equations 2x + 3y + 4 = 0; 3x + 4y + 6 = 0 and 4x + 5y + 8 = 0 are

(a)   consistent with unique solution

(b)   inconsistent

(c)   consistent with infinitely many solutions

(d)   None of the above

53. The shortest distance between the lines x = y + 2 = 6z – 6 and x + 1 = 2y = −12z is

(a)   1/2

(b)   2

(c)   1

(d)   3/2

54. If the tangent at P(1, 1) on y2 = x(2 – x)2 meets the curve again at Q, then Q is

(a)   (2, 2)

(b)   (−1, −2)

(c)   (9/4, 3/8)

(d)   None of these

55. If  then at x = 0, f(x)

(a)   has no limit

(b)   is discontinuous

(c)   is continuous but not differentiable

(d)   is differentiable

56. Radius of the circle (x + 5)2 + (y – 3)2 = 36 is

(a)   2

(b)   3

(c)   6

(d)   5

57. If  and  is equal to :

58. If (−4, 5) is one vertex and 7x – y + 8 = 0 is one diagonal of a square, then the equation of second diagonal is

(a)   x + 3y = 21

(b)   2x – 3y = 7

(c)   x + 7y = 31

(d)   2x + 3y = 21

59. p ⇒ q can also be written as

(a)   p ⇒ ~ q

(b)   ~p ⋁ q

(c)   ~ q ⇒ ~ p

(d)   None of these

60. Let  then

(a)   f(x) = √x

(b)   f(x) = x3/2 and g(x) = sin1x

(c)   f(x) = x2/3

(d)   None of these

61. Which one of the following is an infinite set?

(a)   The set of human beings on the earth

(b)   The set of water drops in a glass of water

(c)   The set of trees in a forest

(d)   The set of all primes

62. The domain of the function

is

(a)   [2, 3]

(b)   [−2, 4]

(c)   [−2, 2] ⋃ [3, 4]

(d)   [−2, 1] ⋃ [2, 4]

63. Area bounded by the curve y = log x and the coordinate axes is

(a)   2

(b)   1

(c)   5

(d)   2√2

64. The angle of intersection to the curve y = x2, 6y = 7 – x3 at(1, 1) is :

(a)   π/2

(b)   π/4

(c)   π/3

(d)   π

65. Angle formed by the positive Y-axis and the tangent to y = x2 + 4x – 17 at (5/2, −3/4) is

(a)   tan1 9

(b)

(c)

(d)   π/2

66. The value of  is

(a)   12

(b)   2

(c)   8

(d)   16

67. The relation R defined on the set A = {1, 2, 3, 4, 5} by R = {(x, y) : |x2 – y2| < 16} is given by

(a)   {(1, 1), (2, 1), (3, 1), (4, 1), (2, 3)}

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

(c)   {(3, 3), (4, 3), (5, 4), (3, 4)}

(d)   None of these

68.

69. The value of tan1 (1) + tan1(0) + tan1(2) + tan1(3) is equal to

(a)   π

(b)   5π/4

(c)   π/2

(d)   None of these

70. In a culture the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000 if the rate of growth of bacteria is proportional to the number present.

71. What is the angle between the two straight lines y = (2 – √3)x + 5 and y = (2 + √3) x – 7?

(a)   60°

(b)   45°

(c)   30°

(d)   15°

72. If the angle θ between the line  and the plane 2x – y + √λz + 4 = 0 is such that sin θ = 1/3 then the value of λ is

(a)   5/3

(b)   −3/5

(c)   3/4

(d)   −4/3

73. The distance of the point (−5, −5, −10) from the point of intersection of the line  and the plane  is

(a)   13

(b)   12

(c)   4√15

(d)   10√2

74. is equal to :

(a)   √3

(b)   1/√3

(c)   3√3/2

(d)   1/2√3

75. If  then x ∈

(a)   (−5, −2)

(b)   (−1, ∞)

(c)   (−5, −2) ∪ (−1, ∞)

(d)   None of these

PART-IV (ENGLISH & LOGICAL REASONING)

Directions (76-78): Study the paragraph and answer the questions that follow.

A training calendar and schedule for Fire Agency Specialties Team (F.A.S.T) membership is available in this office to all applicants for F.A.S.T. membership. Training will take place the third week of each month. Classes will be taught on Monday afternoons, Wednesday evenings, and Saturday afternoons.

So that the F.A.S.T. can maintain a high level of efficiency and preparedness for emergency response situations, its members must meet certain requirements.

First, in order for you to be considered for membership on F.A.S.T., your department must be a member of the F.A.S.T. organization, and you must have written permission from your fire chief or your department’s highest ranking administrator.

Once active, you must meet further requirements to maintain active status. These include completion of technician-level training and certification in hazardous material (hazmat) operations. In addition, after becoming a member, you must also attend a minimum of 50% of all drills conducted by F.A.S.T. and go to at least one F.A.S.T. conference. You may qualify for alternative credit for drills by proving previous experience in actual hazmat emergency response.

If you fail to meet minimum requirements, you will be considered inactive, and the director of your team will be notified. You will be placed back on active status only after you complete the training necessary to meet the minimum requirements.

76. Potential F.A.S.T. members can attend less than half of F.A.S.T. drills if they

(a)   complete technician-level training requirements.

(b)   indicate prior real emergency experience.

(c)   receive permission from their fire chief.

(d)   enroll in three weekly training sessions.

77. Which of the following is the main subject of the passage?

(a)   preparing for hazmat certification

(b)   the main goal of F.A.S.T.

(c)   completing F.A.S.T. membership requirements

78. Applicants must be available for training

(a)   three days each months.

(b)   three days each week.

(c)   every third month.

(d)   for 50% of classes.

79. Jatin starting from a fixed point, goes 15 m towards North and then after turning to his right, he goes 15 m. Then, he goes 10 m, 15 m and 15 m after turning to his left each time. How far is he from this starting point?

(a)   15 m

(b)   5 m

(c)   10 m

(d)   20 m

80. Examine the following statements:

(1) All members of Mohan’s family are honest.

(2) Some members of Mohan’s family are not employed.

(3) Some employed persons are not honest.

(4) Some hones persons are not employed.

Which one of the following inferences can be drawn from the above statements?

(a)   All members of Mohan’s family are employed

(b)   The employed members of Mohan’s family are honest

(c)   The honest members of Mohan’s family are not employed

(d)   The employed member of Mohan’s family are not honest

## VITEEE 2017 Biology Syllabus

PART – IV- BIOLOGY

1. Taxonomy

Need for classification; three domains of life. Linnaean, Whittaker, Bentham and Hooker systems of classification. Salient features of non-chordates up to phyla levels and chordates up to class levels.

2. Cell and Molecular Biology

Cell theory. Prokaryotic cell and it’s ultrastructure. Eukaryotic cell- cell wall, cell membrane, cytoskeleton, nucleus, chloroplast, mitochondria, endoplasmic reticulum, Golgi bodies, ribosomes, lysosomes, vacuoles and centrosomes. Cell cycle and division – amitosis, mitosis and meiosis. Search for genetic material; structure of DNA and RNA; replication, transcription, genetic code, translation, splicing, gene expression and regulation (lac operon) and DNA repair.

3. Reproduction

Asexual reproduction – binary fission, sporulation, budding, gemmule formation and fragmentation. Vegetative propagation in plants, sexual reproduction in flowering plants and structure of flowers. Pollination, fertilization, development of seeds and fruits, seed dispersal, apomixis, parthenocarpy and polyembryony. Human reproductive system. Gametogenesis, menstrual cycle, ferti lization, implantation, embryo development upto blastocyst formation, pregnancy, parturition and lactation. Assisted reproductive technologies.

4. Genetics and evolution

Chromosomes – structure and types, linkage and crossing over, recombination of chromosomes, mutation and chromosomal aberrations. Mendelian inheritance, chromosomal theory of inheritance, deviation from Mendelian ratio (incomplete dominance, co-dominance, multiple allelism, pleiotrophy), sex linked inheritance and sex determination in humans. Darwinism, neo Darwinism, Hardy and Weinberg’s principle and factors affecting the equilibrium: selection, mutation, migration and random genetic drift.

5. Human health and diseases

Pathogens, parasites causing human diseases (malaria, dengue, chickengunia, filariasis, ascariasis, typhoid, pneumonia, common cold, amoebiasis, ring worm) and their control. Basic concepts of immunology, vaccines, antibiotics, cancer, HIV and AIDS. Adolescence, drug and alcohol abuse.

6. Biochemistry

Structure and function of carbohydrates, lipids and proteins. Enzymes – types, properties and enzyme action. Metabolism – glycolysis, Kreb’s cycle and pentose phosphate pathway.

7. Plant physiology

Movement of water, food, nutrients, gases and minerals. Passive diffusion, facilitated diffusion, and active transport. Imbibition, osmosis, apoplast and symplast transport and guttation. Transpiration, photosynthesis (light and dark reactions) and electron transport chain. Hormones and growth regulators, photo-periodism and vernalization. Nitrogen cycle and biological nitrogen fixation.

8. Human physiology

Digestion and absorption, breathing and respiration, body fluids and circulation, excretory system, endocrine system, nervous system, skeletal and muscular systems. Locomotion and movement, growth, aging and death. Hormones – types of hormones, functions and disorders.

9. Biotechnology and its applications

Recombinant DNA technology, applications in health, agriculture and industries; genetically modified organisms; Human insulin, vaccine and antibiotic production. Stem cell technology and gene therapy. Apiculture and animal husbandry. Plant breeding, tissue culture, single cell protein, fortification, Bt crops and transgenic animals. Microbes in food processing, sewage treatment, waste management and energy generation. Biocontrol agents and biofertilizers. Bio-safety issues, biopiracy and patents.

10. Biodiversity, ecology and environment

Ecosystems: components, types, pyramids, nutrient cycles (carbon and phosphorous), ecological succession and energy flow in an ecosystem; Biodiversity – concepts, patterns, importance, conservation, hot spots, endangered organisms, extinction, Red data book, botanical gardens, national parks, sanctuaries, museums, biosphere reserves and Ramsar sites. Environmental issues: pollution and its control. Population attributes – growth, birth and death rate and age distribution.

## VITEEE 2017 Mathematics Syllabus

PART – III – MATHEMATICS

1. Matrices and their Applications

Adjoint, inverse – properties, computation of inverses, solution of system of linear equations by matrix inversion method.

Rank of a matrix – elementary transformation on a matrix, consistency of a system of linear equations, Cramer’s rule, nonhomogeneous equations, homogeneous linear system and rank method.

Solution of linear programming problems (LPP) in two variables.

2. Trigonometry and Complex Numbers

Definition, range, domain, principal value branch, graphs of inverse trigonometric functions and their elementary properties.

Complex number system – conjugate, properties, ordered pair representation.

Modulus – properties, geometrical representation, polar form, principal value, conjugate, sum, difference, product, quotient, vector interpretation, solutions of polynomial equations, De Moivre’s theorem and its applications.

Roots of a complex number – nth roots, cube roots, fourth roots.

3. Analytical Geometry of two dimensions

Definition of a conic – general equation of a conic, classification with respect to the general equation of a conic, classification of conics with respect to eccentricity.

Equations of conic sections (parabola, ellipse and hyperbola) in standard forms and general forms- Directrix, Focus and Latusrectum – parametric form of conics and chords. – Tangents and normals – Cartesian form and parametric form- equation of chord of contact of tangents from a point (x1 ,y1) to all the above said curves.

Asymptotes, Rectangular hyperbola – Standard equation of a rectangular hyperbola.

4. Vector Algebra

Scalar Product – angle between two vectors, properties of scalar product, and applications of dot product. Vector product, right handed and left handed systems, properties of vector product, applications of cross product.

Product of three vectors – Scalar triple product, properties of scalar triple product, vector triple product, vector product of four vectors, scalar product of four vectors.

5. Analytical Geometry of Three Dimensions

Direction cosines – direction ratios – equation of a straight line passing through a given point and parallel to a given line, passing through two given points, angle between two lines.

Planes – equation of a plane, passing through a given point and perpendicular to a line, given the distance from the origin and unit normal, passing through a given point and parallel to two given lines, passing through two given points and parallel to a  given line, passing through three given non-collinear points, passing through the line of intersection of two given planes, the distance between a point and a plane, the plane which contains two given lines (co-planar lines), angle between a line and a plane.

Skew lines – shortest distance between two lines, condition for two lines to intersect, point of intersection, collinearity of three points.

Sphere – equation of the sphere whose centre and radius are given, equation of a sphere when the extremities of the diameter are given.

6. Differential Calculus

Limits, continuity and differentiability of functions – Derivative as a rate of change, velocity, acceleration, related rates, derivative as a measure of slope, tangent, normal and angle between curves.

Mean value theorem – Rolle’s Theorem, Lagrange Mean Value Theorem, Taylor’s and Maclaurin’s series, L’ Hospital’s Rule, stationary points, increasing, decreasing, maxima, minima, concavity, convexity and points of inflexion.

Errors and approximations – absolute, relative, percentage errors – curve tracing, partial derivatives, Euler’s theorem.

7. Integral Calculus and its Applications

Simple definite integrals – fundamental theorems of calculus, properties of definite integrals.

Reduction formulae – reduction formulae for ∫ sinn x dx and ∫ cosnn x dx, Bernoulli’s formula.

Area of bounded regions, length of the curve.

8. Differential Equations

Differential equations – formation of differential equations, order and degree, solving differential equations (1st order), variables separable, homogeneous and linear equations.

Second order linear differential equations – second order linear differential equations with constant co-efficients, finding the particular integral if f(x) = emx, sin mx, cos mx, x, x2.

9. Probability Distributions

Probability – Axioms – Addition law – Conditional probability – Multiplicative law – Baye’s Theorem – Random variable – probability density function, distribution function, mathematical expectation, variance

Theoretical distributions – discrete distributions, Binomial, Poisson distributions- Continuous distri butions, Normal distribution.

10. Discrete Mathematics

Functions – Relations – Basics of counting.

Mathematical logic – logical statements, connectives, truth tables, logical equivalence, tautology, contradiction.

Groups-binary operations, semi groups, monoids, groups, order of a group, order of an element, properties of groups.

## VITEEE 2017 Chemistry Syllabus

PART – II – CHEMISTRY

1. Atomic Structure

Bohr ’s atomic model-Sommerfeld’s extension of atomic structure; Electronic configuration and Quantum numbers; Shapes of s,p,d,f orbitals – Pauli’s exclusion principle – Hund’s Rule of maximum multiplicity- Aufbau principle. Emission spectrum, absorption spectrum, line spectra and band spectra; Hydrogen spectrum – Lyman, Balmer, Paschen, Brakett and Pfund series; deBroglie’s theory; Heisenberg’s uncertainty principle – wave nature of electron – Schrodinger wave equation (No derivation). Eigen values and eigen functions. Hybridization of atomic orbitals involving s,p,d orbitals.

2. p,d and f – Block Elements

p-block elements – Phosphorous compounds; PCl3, PCl5 – Oxides. Hydrogen halides, Inter halogen compounds. Xenon fluoride compounds. General Characteristics of d – block elements – Electronic Configuration – Oxidation states of first row transition elements and their colours. Occurrence and principles of extraction: Copper, Silver, Gold and Zinc. Preparation, properties of CuSO4, AgNO3 and K2Cr2O7.

Lanthanides – Introduction, electronic configuration, general characteristics, oxidation state – lanthanide contraction, uses, brief comparison of Lanthanides and Actinides.

3. Coordination Chemistry and Solid State Chemistry

Introduction – Terminology in coordination chemistry – IUPAC nomenclature of mononuclear coordination compounds. Isomerism, Geometrical isomerism in 4-coordinate, 6-coordinate complexes. Theories on coordination compounds – Werner’s theory (brief), Valence Bond theory. Uses of coordination compounds. Bioinorganic compounds (Haemoglobin and chlorophyll).

Lattice – unit cell, systems, types of crystals, packing in solids; Ionic crystals – Imperfections in solids – point defects. X-Ray diffraction – Electrical Property, Amorphous solids (elementary ideas only).

4. Thermodynamics, Chemical Equilibrium and Chemical Kinetics

I and II law of thermodynamics – spontaneous and non spontaneous processes, entropy, Gibb’s free energy – Free energy change and chemical equilibrium – significance of entropy.

Law of mass action – Le Chatlier’s principle, applications of chemical equilibrium. Rate expression, order and molecularity of reactions, zero order, first order and pseudo first order reaction – half life period. Determination of rate constant and order of reaction . Temperature dependence of rate constant – Arrhenius equation, activation energy.

5. Electrochemistry

Theory of electrical conductance; metallic and electrolytic conductance. Faraday’s laws – theory of strong electrolytes – Specific resistance, specific conductance, equivalent and molar conductance – Variation of conductance with di lution – Kohlrausch’s Law – Ionic product of water, pH and pOH – buffer solutions – use of pH values. Cells – Electrodes and electrode potentials – construction of cell and EMF values, Fuel cells, Corrosion and its prevention.

6. Isomerism in Organic Compounds

Definition, Classification – structural isomerism, stereo isomerism – geometrical and optical isomerism. Optical activitychirality – compounds containing chiral centres – R – S notation, D – L notation.

7. Alcohols and Ethers

Nomenclature of alcohols – Classification of alcohols – distinction between 10, 20 and 30 alcohols – General methods of preparation of primary alcohols, properties. Methods of preparation of dihydric alcohols: Glycol – Properties – Uses. Methods of preparation of trihydric alcohols – Properties – Uses. Aromatic alcohols – preparation and properties of phenols and benzyl alcohol.

Ethers – Nomenclature of ethers – general methods of preparation of aliphatic ethers – Properties – Uses. Aromatic ethers – Preparation of Anisole – Uses.

8. Carbonyl Compounds

Nomenclature of carbonyl compounds – Comparison of aldehydes and ketones. General methods of preparation of aldehydes – Properties – Uses. Aromatic aldehydes – Preparation of benzaldehyde – Properties and Uses. Ketones – general methods of preparation of aliphatic ketones (acetone) – Properties – Uses. Aromatic ketones – preparation of acetophenone – Properties – Uses, preparation of benzophenone – Properties. Name reactions; Clemmenson reduction, Wolff – Kishner reduction, Cannizzaro reaction, Claisen Schmidt reaction, Benzoin Condensation, aldol Condensation. Preparation and applications of Grignard reagents.

9. Carboxylic Acids and their derivatives

Nomenclature – Preparation of aliphatic monobarboxylic acids – formic acid – Properties – Uses. Monohydroxy mono carboxylic acids; Lactic acid – Synthesis of lactic acid. Aliphatic dicarboxylic acids; Preparation of oxalic and succinic acid. Aromatic acids; Benzoic and Salicylic acid – Properties – Uses. Derivatives of carboxylic acids; acetyl chloride (CH3COCl) – Preparation – Properties – Uses. Preparation of acetamide, Properties – acetic anhydride – Preparation, Properties. Preparation of esters – methyl acetate – Properties.

10. Organic Nitrogen Compounds and Biomolecules

Aliphatic nitro compounds – Preparation of aliphatic nitroalkanes – Properties – Uses. Aromatic nitro compounds – Preparation – Properties – Uses. Distinction between aliphatic and aromatic nitro compounds. Amines; aliphatic amines – General methods of preparation – Properties – Distinction between 10, 20 and 30 amines. Aromatic amines – Synthesis of benzylamine – Properties, Aniline – Preparation – Properties – Uses. Distinction between aliphatic and aromatic amine. Aliphatic nitriles – Preparation – properties – Uses. Diazonium salts – Preparation of benzene diazoniumchloride – Properties.

Carbohydrates – distinction between sugars and non sugars, structural formulae of glucose, fructose and sucrose, with their linkages, invert sugar – definition, examples of oligo and polysaccharides,

Amino acids – classification with examples, Peptides-properties of peptide bond,

Lipids – Definition, classification with examples, difference between fats, oils and waxes.

## VITEEE 2017 Physics Syllabus

PART – I – PHYSICS

1.Laws of Motion & Work, Energy and Power

Law of conservation of linear momentum and its applications. Static and kinetic friction – laws of friction – rolling friction – lubrication.

Work done by a constant force and a variable force; kinetic energy – work-energy theorem – power.

Conservative forces: conservation of mechanical energy (kinetic and potential energies) – non-conservative forces: motion in a vertical circle – elastic and inelastic collisions in one and two dimensions.

2.Properties of Matter

Elastic behaviour – Stress-strain relationship – Hooke’s law – Young’s modulus – bulk modulus – shear modulus of rigidity – Poisson’s ratio – elastic energy. Viscosity – Stokes’ law – terminal velocity – streamline and turbulent flow – critical velocity. Bernoulli’s theorem and its applications.

Heat – temperature – thermal expansion: thermal expansion of solids – specific heat capacity: Cp, Cv – latent heat capacity. Qualitative ideas of Blackbody radiation: Wein’s displacement Law – Stefan’s law.

3.Electrostatics

Charges and their conservation; Coulomb’s law-forces between two point electric charges – Forces between multiple electric charges-superposition principle. Electric field – electric field due to a point charge, electric field lines; electric dipole, electric field intensity due to a dipole – behaviour of a dipole in a uniform electric field. Electric potential – potential difference-electric potential due to a point charge and dipole-equipotential surfaces – electrical potential energy of a system of two point charges.

Electric flux-Gauss’s theorem and its applications. Electrostatic induction-capacitor and capacitance – dielectric and electric polarisation – parallel plate capacitor with and without dielectric medium – applications of capacitor – energy stored in a capacitor – Capacitors in series and in parallel – action of points – Van de Graaff generator.

4.Current Electricity

Electric Current – flow of charges in a metallic conductor – drift velocity and mobility and their relation with electric current. Ohm’s law, electrical resistance – V-I characteristics – electrical resistivity and conductivity-classification of materials in terms of conductivity – Carbon resistors – colour code for carbon resistors – combination of resistors – series and parallel – temperature dependence of resistance – internal resistance of a cell – potential difference and emf of a cell – combinations of cells in series and in parallel.

Kirchoff ’s law – Wheatstone’s Bridge and its application for temperature coefficient of resistance measurement – Me t re br i dge – sp ec i a l cas e o f Wheats to n e br i dge – Potentiometer principle – comparing the emf of two cells.

5.Magnetic Effects of Electric Current
Magnetic effect of electric current – Concept of magnetic field – Oersted’s experiment – Biot – Savart law – Magnetic field due to an infinitely long current carrying straight wire and circular coil – Tangent galvanometer – construction and working – Bar magnet as an equivalent solenoid – magnetic field lines.

Ampere’s circuital law and its application. Force on a moving charge in uniform magnetic field and electric field – cyclotron – Force on current carrying conductor in a uniform magnetic field – Forces between two parallel current carrying conductors – definition of ampere.

Torque experienced by a current loop in a uniform magnetic field – moving coil galvanometer – conversion to ammeter and voltmeter – current loop as a magnetic dipole and its magnetic dipole moment – Magnetic dipole moment of a revolving electron.

6.Electromagnetic Induction and Alternating Current

Electromagnetic induction – Faraday’s law – induced emf and current – Lenz’s law. Self induction – Mutual induction – self inductance of a long solenoid – mutual inductance of two long solenoids. Methods of inducing emf – (i) by changing magnetic induction (ii) by changing area enclosed by the coil and (iii) by changing the orientation of the coil (quantitative treatment).

AC generator – commercial generator. (Single phase, three phase). Eddy current – applications – transformer – long distance transmission. Alternating current – measurement of AC – AC circuit with resistance – AC circuit with inductor – AC circuit with capacitor – LCR series circuit – Resonance and Q – factor – power in AC circuits.

7.Optics

Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal reflection and its applications, optical fibers, refraction at spherical surfaces, lenses, thin lens formula, lens maker ’s formula. Magnification, power of a lens, combination of thin lenses in contact, combination of a lens and a mirror. Refraction and dispersion of light through a prism. Scattering of light-blue colour of sky and reddish appearances of the sun at sunrise and sunset.

Wavefront and Huygens’s principle – Reflection, total internal reflection and refraction of plane wave at a plane surface using wavefronts. Interference – Young’s double slit experiment and expression for fringe width – coherent source – interference of light – Formation of colours in thin films – Newton’s rings. Diffraction – differences between interference and diffraction of light- diffraction grating. Polarisation of light waves – polarisation by reflection – Brewster’s law – double refraction – nicol prism – uses of plane polarised light and Polaroids – rotatory polarisation – polarimeter.

8.Dual Nature of Radiation and Atomic Physics

Electromagnetic waves and their characteristics – Electromagnetic spectrum – Photoelectric effect – Light waves and photons- Einstein’s photoelectric equation – laws of photoelectric emission – particle nature of light – photo cells and their applications.

Atomic structure – discovery of the electron – specific charge (Thomson’s method) and charge of the electron (Millikan’s oil drop method) – alpha scattering – Rutherford’s atom model.

9.Nuclear Physics

Nuclear properties – nuclear radii, masses, binding energy, density, charge – isotopes, isobars and isotones – nuclear mass defect – binding energy – stability of nuclei – Bainbridge mass spectrometer.

Nature of nuclear forces – Neutron – discovery – properties – artificial transmutation – particle accelerator. Radioactivity – alpha, beta and gamma radiations and their properties – Radioactive decay law – half life – mean life – artificial radioactivity – radio isotopes – effects and uses – Geiger – Muller counter. Radio carbon dating. Nuclear fission – chain reaction – atom bomb – nuclear reactor – nuclear fusion – Hydrogen bomb – cosmic rays – elementary particles.

10.Semiconductor Devices and their Applications

Semiconductor basics – energy band in solids: difference between metals, insulators and semiconductors – semiconductor doping – Intrinsic and Extrinsic semiconductors. Formation of P-N Junction – Barrier potential and depletion layer-P-N Junction diode – Forward and reverse bias characteristics – diode as a rectifier – Zener diode-Zener diode as a voltage regulator – LED. Junction transistors – characteristics – transistor as a switch – transistor as an amplifier – transistor as an oscillator.

Logic gates – NOT, OR, AND, EXOR using discrete components – NAND and NOR gates as universal gates – De Morgan’s theorem – Laws and theorems of Boolean algebra.