VITEEE 2008 SOLUTIONS, DETAILED ANSWERS, CUTOFF & MARKS DISTRIBUTION

1.     In nature, the electric charge of any system is always–

 

        Ans:    Quantisation of charge

                    Choice (D)

 

2.     The energy stored in the capacitor as shown in   Fig. (a) is 4.5 ´ 10^{- 6} J. If the battery is replaced     by –

 

        Ans:   

                    = 4.5 ´ 10^{- 6} J

                   

                   Choice (B)

 

3.     Equal amounts of a metal are converted into        cylindrical wires of different lengths (L) and cross-sectional –

 

        Ans:    R =

                   Choice (C)

 

4.     If the force exerted by an electric dipole on a         charge q at a distance of 1 m is F, the force–

 

        Ans:   

                   

                    Choice (D)

 

5.     A solid sphere of radius R ₁ and volume charge   density r = is enclosed by a hollow sphere of        radius R₂ with negative surface charge density–

 

        Ans:    Q _in =

                    =

                    = 4p R₂²s

                    Choice (C)

 

6.     A solid spherical conductor of radius R has a      spherical cavity of radius a9a < R) at its centre. A        charge +Q is kept at the center.–

 

        Ans:

       

 

 

                Choice (B)

7.     A cylindrical capacitor has charge Q and length L. If both –

 

        Ans:    U ₁ =

                    U ₂ =

        Choice (B)

 

8.     Three resistances of 4 W each are connected as shown in figure. If the point D divides the resistance –

 

        Ans:   

 

 

 

 

 

 

        Choice (C)

 

9.     The resistance of a metal increases with increasing –

 

        Ans:    Vibration of lattice ions increases with                                  

                    temperature

        Choice (B)

 

10.  In the absence of applied potential, the electric current flowing through-

 

        Ans:    Thermal velocity of electrons is in random                           

                    directions

        Choice (C)

 

11.  A meter bridge is used to determine the resistance of an unknown wire by measuring the balance point length l. If the wire is replaced by –

 

        Ans:   

 

12.  Identify the INCORRECT statement regarding –

 

        Ans:    Supercurrent always flows on the surface                            

                    of the superconductor

        Choice (B)

 

13.  A sample of HCl gas is placed in an electric field of 3 ´ 10⁴ NC^{- 1}. The dipole moment of each HCl molecule is –

 

        Ans:    t = pE

        Choice (C)

 

 

 

 

14.  When a metallic plate swings between the  –

 

        Ans:    Lenz’s law

        Choice (C)

 

15.  When an electrical appliance is switched on, it responds almost-

 

        Ans:    Electromagnetic waves travel with the                                   

                    speed of light

                    Choice (B)

 

16.  Two identical incandescent light bulbs are connected as shown in the figure. When the circuit is an AC voltage source–

 

        Ans:    At resonance X_L = X_C

                    Choice (B)

 

17.  A transformer rated at 10 kW is used to connect a 5 kV transmission line to a 240 V circuit. The ratio –

 

        Ans:    n =

                    Choice (B)

 

18.  Three solenoid coils of same dimension, same number of turns and same number of layers of winding are taken. Coil 1 with inductance L₁ was wound using a Mn wire of resistance 11 W / m; –

 

        Ans:    Alternate winding in opposite direction                                  

                    total flux = 0

                    Choice (C)

 

19.  Light travels with a speed of 2 ´ 10⁸ m/s in crown glass of refractive index 1.5. What is the speed of light –

 

        Ans:    n ₁v₁ = n₂v₂

                    Choice (B)

 

20.  A parallel beam of fast moving electrons is incident normally on a narrow slit. A screen is placed at a large distance from the slit.–

 

        Ans:    sinq =

                    Choice (C)

 

21.  Two beams of light will not give rise to an –

 

        Ans:    Since the polarization vectors are                                           

                    perpendicular their vector sum ¹ 0

                    Choice (C)

 

22.  A slit of width `a’ is illuminated with a monochromatic light of wavelength l from a distant source and the diffraction pattern –

 

        Ans:    sinq =

                    Choice (B)

 

23.  A thin film of soap solution (n = 1.4) lies on the top of a glass plate (n = 1.5). When visible light is incident almost normal to the plate, two adjacent reflection –

 

        Ans:    n ₁l ₁ = n₂l ₂

                    2n ₁ = 3n₂

                    Þ n₁ = 3

                    d = = 450

                    Choice (B)

 

24.  If the speed of a wave doubles as it passes from shallow water into deeper water, –

 

        Ans:    c = fl

                    Choice (C)

 

25.  A light whose frequency is equal to 6 ´ 10¹⁴ Hz is incident on a metal whose work function is
2 eV –

 

        Ans:    hu = f + K.E

                    Choice (C)

 

26.  An electron microscope is used to probe the atomic arrangements to a resolution of . What should be the electric potential –

 

        Ans:   

                    Choice (D)

 

27.  Which phenomenon best supports the theory that matter –

 

        Ans:    Electrons behave also as waves of l =

                    Choice (B)

 

28.  The radioactivity of a certain material drops to of the initial value in 2 hours. The half –

 

        Ans:    Activity changes from A₀ to A₀/16 implies 4                             half-lives.

                    Choice (C)

 

29.  An observer `A’ sees an asteroid with a radioactive element moving by at a speed = 0.3 c and measures the radioactivity decay time to be T<sub>A</sub>. Another observer `B’ –

 

        Ans:    Moving clocks are slower T_B < T_A

                    Choice (A)

 

30.  ²³⁴U has 92 protons and 234 nucleons total in its nucleus. It decays by emitting an alpha –

 

        Ans:    ²³⁴U₉₂ à ²³⁰Th₉₀ + a

                    Choice (C)

 

31.  K_a and K_b x-rays are emitted when there is a transition of electron –

 

        Ans:    K series end in n = 1

                    Choice (A)

 

32.  A certain radioactive material _ZX^A starts emitting a and b particles successively such that the end product –

 

        Ans:    _ZX^A à _{Z- 3}Y^{A- 8} + 2a + 1b

                    Choice (B)

 

33.  In the circuit shown above, an input of 1 V is fed into the inverting input of an ideal Op-amp A. The output signal –

 

        Ans:    = - 10 (negative feedback)

                    Choice (B)

 

34.  When a solid with a band gap has a donor level just below its empty energy band, -

 

        Ans:    Knowledge based

                    Choice (D)

 

35.  A p – n junction has acceptor impurity concentration of 10¹⁷ cm^{- 3} in the P side and donor impurity concentration of 10¹⁶ cm^{- 3} in the N side. What is the contact potential at the –

 

        Ans:    V _contact =

                    Choice (A)

 

36.  A zener diode has a contact potential of 1 V in the absence of biasing. It undergoes zener breakdown for an electric field of 10⁶ V/m at the depletion region of p-n junction. If the width –

 

        Ans:    V = Ed

                    Choice (B)

 

 

37.  In Colpitt oscillator the feedback network –

 

        Ans:    a-c equivalent circuit.

                    Choice (B)

 

38.  The reverse saturation of p-n diode

 

        Ans:    Knowledge based

                    Choice (D)

 

39.  A radio station has two channels. One is AM at 1020 kHz and the other FM at 89.5 MHz. –

 

        Ans:    Knowledge based

                    Choice (A)

 

40.  The communication using optical fibers is –

 

        Ans:    Optic fibre uses T.I.R.

                    Choice (A)

 

PART – II [CHEMISTRY]

 

41.  The oxidation number of oxygen ¾

 

        Ans:   KO ₃: + 1 + 3x = 0,              x =

                   Na ₂O₂: + 2 + 2x = 0,          x = - 1

                   Choice (D)

 

42.  Reaction of I Cl₃ and PhMgBr ¾

 

        Ans:   Triphenyl phosphene

                   3C ₆H₅MgBr + PCl₃ ® (C₆H₅)₃P + 3MgClBr

                   Choice (C)

 

43.  ……. not a characteristic of transition elements?

 

        Ans:   Choice (D)

 

44.  Cl - P - Cl bond ¾

 

        Ans:   Arial bonds are 90° and Equatorial bonds are 120°.

                   Choice (A)

 

45.  --- magnetic moment ¾

        Ans:   No unpaired electron.

                   Choice (A)

 

46.  The number of Formula units of calcium fluoride CaF₂ ¾

 

        Ans:   Number of moles =

                   Number of formula units =  ´ 6.023

                                                                                  ´ 10²³

                                                                = 1.129 ´ 10²⁴

                   Choice (A)

 

47.  The IUPAC name of the given ¾

 

        Ans:   Choice (C)

 

48.  When SCN^‑ is added to an aqueous ¾

 

        Ans:   Fe ³⁺ + SCN^‑ + H₂O ® [Fe(H₂O)₅SCN]²⁺

                   Choice(B)

 

 

49.  Hair dyes contain

 

        Ans:   Choice (C)

 

50.  Schottky defects occurs ¾

 

        Ans:   Schottky defect occurs when the ions have almost the same size

                   Choice (B)

 

51.  The number of unpaired electron ¾

 

        Ans:   [Co(NH ₃)₆]³⁺ - Inner orbital complex

                                          - No unpaired electron

                   [CoF ₆]^3‑         - Outer orbital complex

                                          - 4 unpaired electrons

                   Choice (D)

 

52.  The standard free energy change of a reaction ¾

 

        Ans:   - D G° = 2.303 RT log K_p

                    log K_p

                   0.02016 ´ 10³ = log K_p

                                             = log K _p = 20.16

                   Choice (A)

 

53.  If an endothermic reaction occurs spontaneously at ¾

 

        Ans:   For an endothermic reaction D H is positive, the reaction occurs spontaneously when D S > 0

                   Choice (C)

 

54.  If a plot of log10 C versus t fives a straight line ¾

 

        Ans:   t =

                   t ´  = logC₀ - logC

                   logC = logC₀ - t ´

                   logC is t in a stline with slope

                   Choice (B)

 

55.  A spontaneous process is one in which ¾

 

        Ans:   For a spontaneous process D G is negative.

                   Choice (B)

 

 

56.  The half life period of a first order reaction ¾

 

        Ans:   t _½ = 100 sec.

                   For a first order reaction t _½ =

                   K =  =  = 6.93 ´ 10^‑3 sec^‑1

                   Choice (B)

 

57.  The molar conductivities of KCl, NaCl and KNO₃ are ¾

 

        Ans:   =

                   = 128 + 111 - 152 = 87 S cm² mol^‑1

                   Choice (B)

 

58.  The electrochemical cell stops working ¾

 

        Ans:   When both the electrode potentials become equal cell reactions stops.

                   Choice (B)

 

59.  The amount of electricity required to produce ¾

 

        Ans:   1 mole of copper is 2 equivalents

                   Current required = 2 Faraday

                   Choice (C)

 

60.  Dipping iron article into a strongly alkaline ¾

 

        Ans:   Choice (C)

 

61.  Hydroboration oxidation of 4-methyl-octene ¾

 

        Ans:   Hydroboration – oxidation of alkenes give alcohols containing the same number of carbon atoms. Net reaction involves addition of H₂O against Markownikoff’s rule.

                   Choice (A)

 

62.  When ethyl alcohol is heated

 

        Ans:   Ethanol undergoes dehydration when heated with conc.H₂SO₄ to form ethylene.

                   Choice (D)

 

63.  Anisole is the product obtained from ¾

 

        Ans:   Anisole is phenyl methyl ether.

                   Choice (B)

 

 

 

64.  Ethylene glycol gives oxalic acid ¾

 

        Ans:   Choice (C)

 

65.  Diamond is hard ¾

 

        Ans:   Choice (A)

 

66.  A Wittig reaction with an aldehyde ¾

 

        Ans:   Carbonyl compounds react with phosphorous yields to form alkenes. This is known as Witting reaction.

                   Choice (C)

 

67.  Cannizzaro reaction is ¾

 

        Ans:   HCHO does not contain a -hydrogen atom. So it undergoes Cannizzaro reaction.

                   Choice (A)

 

68.  ¾

 

        Ans:   C ₆H₆ + CO  C₆H₅ - CHO

        This is known as Gattermann-Koch aldehyde synthesis.

                   Choice (C)

 

69.  Maleic acid and Fumaric acids ¾

 

        Ans:   Maleic acid is the cis-isomer and fumaric acid is the trans-isomer.

                   Choice (B)

 

70.  The gas evolved on heating ¾

 

        Ans:   HCOONa + NaOH

                                                        H ₂ + Na₂CO₃.

                   Choice (C)

 

 

 

 

71.  CH ₃CH₃ + HNO₃ ¾

 

        Ans:   Choice (B)

 

72.  When acetamide is hydrolysed by ¾

 

        Ans:   Choice (A)

 

73.  Which will not go for diazotization?

 

        Ans:   Choice (B)

 

74.  Secondary nitroalkanes can be ¾

 

        Ans:  

                   Choice(A)

 

75.  ………. Stephen reduction to ¾

 

        Ans:   Alkyl cyanides on reduction with SnCl₂ and HCl will give aldehyde.

                   Choice (A)

 

76.  The continuous phase contains ¾

 

        Ans:   Choice (C)

 

77.  The number of hydrogen atoms present in ¾

 

        Ans:   = 9.91 ´ 10²³

                   Choice (B)

 

78.  Milk changes after digestion ¾

 

        Ans:   Choice (C)

 

79.  ……… essential amino acids?

 

        Ans:   Choice (B)

 

80.  ….. is a Ketohexose?

 

        Ans:   Choice (C)

 

PART – III [MATHEMATICS]

 

81.  The system of equations -

 

        Ans:  

                   = 1(1 - 3) - 2(1 - 2) = - 2 + 2 = 0

                   Choice (B)

 

82.  , then -

 

        Ans:   = I

                   A ⁴ = I

A³ = I A^{- 1}

A² = I A^{- 2}

     =

A^{- 1} =

     =

A^{- 2} =  =

ab =

Þ a²b² = 1

Þ ab = 1

Choice (D)

 

83.  If D = diag (d₁, d₂, …….., d_n) where -

       

        Ans:   Choice (D)

 

84.  If x, y, z are different from zero and D = -

       

        Ans:   = 0

                    = 0

                  

                =

           Choice (D)

 

85.  Probability of getting positive integral roots of the equation, -

 

        Ans:   x = ±

                   n = 1, 4, 9, 16, 25, 36

                   Probability =

                   Choice (C)

 

86.  The number of real roots of equation -

 

Ans:   = 22 - x⁴

           x ⁴ + 20 = (22 - x⁴)²

                = 484 + x ⁸ - 44x⁴

           x ⁸ - 45x⁴ + 464 = 0

           x ⁴ =

                = =

                = 29, 16

           x ⁴ = 29 is not admissible

           Þ x⁴ = 16

Choice (B)

 

87.  Let a , b be the roots of the equation -

 

        Ans:   a ²- aa + b = 0

                   A _n+1 - aA_n + bA_{n- 1}

                             = a ⁿ⁺¹ + b ⁿ⁺¹- a(a ⁿ + b ⁿ) + b(a ^{n- 1} + b ^{n- 1})

                   = a ^{n- 1}(a ²- aa + b) + b ^{n- 1}(b ²- ab + b)

                   = 0

                   Choice (C)

88.  If the sides of a right – angle triangle -

       

        Ans:   b, c, a ® AP

       

        a =

        sin B =

        Choice (A)

 

89.  The plane through the point -

       

        Ans:   x + 3y - z = 0

y + 2z = 0

Let the plane be

A(x + 1) + B(y + 1) + C(z + 1) = 0

Plane passes through the origin

A + B + C = 0

Choice (A)

 

90.  are one of the sides -

       

        Ans:       

 

 

 

 

 

 

                       

                                    =

                   Area =

                            =

                   Choice (D)

 

91.  If be three unit vectors such that -

 

        Ans :       =

                        =

                        =

                        cos q ₂     =         Þ q ₂ =

                   cos q ₁ = 0           Þ q ₁ =

                   Choice (C)

 

 

92.  The equation  -

 

        Ans:   Equation is

                   x ² + y² + z² - 2xc₁ - 2yc₂ - 2zc₃ + h = 0

                   Choice (D)

 

93.  The simplified expression of -

 

        Ans:

 

 

 

 

 

 

                   Let tan^{- 1} x be a Þ tan a = x

                   Then from the figure sin a =

                   Þ sin (tan^{- 1} x)  

                   = sin

                   Choice (B)

 

94.  If -

 

        Ans:  

Þ z lies on the line perpendicular to the real axis and divides the line segment between 1 and 25 in the ratio 1 : 5 Þ   z = (5, 0) Þ |z| = 5

                     Choice (C)

 

95.  Argument of the complex number -

 

Ans:  

                            

                                     = - (1 + i)

                   \ Arg

                   Choice (C)

 

96.  In a triangle ABC, the sides b and c are -

 

        Ans:   x ² - 61x + 820 = 0

                   x ² - 41x - 20x + 820 = 0

                   Þ x_1,2 = 41, 20

                   A = tan^{- 1}

                             Þ cosA =

                   \ By Cosine formula,

                   a ² = b² + c² - 2bc cos A

                   a ² = 41² + 20² - 2(41)(20)

                   = 2081 - 984 = 1097

                   Choice (C)

 

97.  The shortest distance between the straight lines through -

 

        Ans:           

                               

                   \ Shortest distance =

                   =

                   =

                   Choice (D)

 

98.  The center and radius of the sphere -

 

        Ans:   Centre is at

                   Choice (C)

 

99.  Let A and B are two fixed points in a plane then locus of another -

       

        Ans:   Ellipse

                   Choice (B)

 

100.        The directrix of the parabola -

 

        Ans:   y ² = - 4x - 3

                        = - 4

                   Equation of the directrix is

                   x =

 

 

 

 

 

 

 

 

                   Choice (D)

 

 

101.        If g(x) is a polynomial satisfying g(x) -

 

        Ans:   g(x) . g(y) = g(x) + g(y) + g(xy) - 2 ¾ (1)

                   g(2) . g(y) = g(x) + g(y) + g(xy) - 2

5.g(y) = 5 + g(y) + g(xy) - 2

Þ 4g(y) = 3 + g(xy)

\ g(0) = 1

g(x) is given in a polynomial, and by the relation given g(x) cannot be linear.

Let g(x) = x² + k

Since g(0) = 1 Þ g(x) = x² + 1

Verifying (1) Þ

(x² + 1) (y² + 1)

             = x ² + 1 + y² + 1 + x²y² + 1 - 2

(1) is satisfied by g(x) = x² + 1

g(x) = g(3) (Q g(x) in a polynomial)

     = 10

                   Choice (B)

 

102.        The value of f(0) so that -

 

        Ans:  

                        =

                        = 2 ⁰n2 - 1 = l n2 - 1

                        = f(0)

                   Choice (D)

 

103.           Let [   ]   denote the greatest integer -

 

        Ans :

 

                   f(x) is continuous at x = 0

                   Choice (B)

 

104.           A spherical balloon is expanding -

 

        Ans : Let r be the radius and V be the volume

                   \ = 2            r = 5

                   \ V = p r³

                  

                   = 4p (5)² ´ (2)

                   = 200 p

                   Choice (C)

 

105.           The length of the parabola -

 

Ans :

 

 

 

 

 

 

 

 

 

                   Length =

                         =

                         =

                         =

                          =

                         =

                        =

        =

                   = 2

                   -

        =

                   =

                   =

                    = 

                   =

                   Choice (A)

106.           If I = -

        Ans :  I =

                   Put 1 + x³ = t Þ x² dx =

                   \ I =

                   =

                   =

                   =

                   Choice (D)

 

107.           Area enclosed by the curve -

 

        Ans :

                   Þ  = 1

                   \ Area of ellipse = p ab

                   = p ´

                   = 4

                   Choice (D)

 

108.The value of -

 

        Ans :

                   x = a sin² q

                   dx = 2a sin q cos q dq

                   x = 0 ® q = 0

                   x = a ® q =

                  

                       =

                   = 2a ´

                   Choice (C)

 

109.           Let y be the number of people -

 

        Ans : 

                  

                   l n y = - kt + c

                   y = ce^{- kt},  c > 0

                                    k ³ 0

                                Choice (B)

 

110.        The differential equation of -

 

         Ans:  x cos q + y sin q = a ¾ (1)

                differentiating cos q + y’ sin q = 0 ¾ (2)

                Eliminating sin q and cos q from (1) and (2)

                cos q =

                sin q =

                sin ² q + cos² q = 1

                Þ

                Þ a²y’ + a² = (xy’ - g)²

                Þ

                Choice (B)

 

111.           The differential equation
        admits -

 

        Ans:  

                   , |y| > 0 , 3 > 0

     Three positive quantities cannot add to give zero.

   \ No solution.

                   Choice (B)

 

112.           Solution of the differential equation xdy -

 

        Ans : ¾ (1)

                   which is homogeneous put y = v_x

                   \

                   \ (1) Þ

                   \ x

                   \

                   Integrating

                  

                   log

                   log

                  

                   \ y +

                   Choice (B)

 

113.           Let P, Q, R and S be statements and suppose-

 

        Ans:   p ® G ® R R ® p and ~ S ® R

                   Þ (C) and (D) are not true also ~ S ® R .

                   \ (A) is not true

                   Choice (B)

 

114. In how many number of ways -

 

        Ans  :   Required number of ways =

                                     = 2100

                     Choice (D)

 

115.        If R be a relation defined -

 

        Ans :       Relation is symmetric and transitive

                        Choice (D)

 

116.        Let S be a finite set containing n elements.
Then -

 

        Ans:        For commutative binary operations, there are  pairs available. For each of there pairs the result of the Binary operation should be among the n elements of S.

 

 

 

 

 

 

 

 

 

                \ Total number of required operations

                        =

                        =

                Choice (B)

 

117.           A manufacturer of cotter pins knows that-

 

Ans:   Probability of a cotter pin to be defective
 =

      Average number of defective cotter pins in a box of 100 is = 100 ´

                                   = 5

      We use Poisson distribution with parameter m = 5

      Choice (B)

       

118.           The probability that a certain kind -

 

        Ans : p = , q = , n = 4

                   P(X = x) =

                   \ p(X = 2) =

                         =

                   Choice (D)

 

119.           Mean and standard deviation -

 

        Ans : For best performance &  is less

                   Which true for  = 75, s = 5

                   Choice (B)

 

120.           A random variable X follows -

 

        Ans : For Binomial distribution

   0 < variance < mean

                   0 < b < a

                   Choice (B)