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VITEEE 2009 Sample Question Papers - Mathematics

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VITEEE 2009 Sample Question Papers - Chemistry -  PART – 3 [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 =

a2b2 = 1

ab = 1

Choice (D)

 

83.  If D = diag (d1, d2, …….., dn) 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

           x4 = 16

Choice (B)

 

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

 

        Ans:   a 2- aa + b = 0

                   A n+1 - aAn + bAn- 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     =         q 2 =

                   cos q 1 = 0           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 tan a = x

                   Then from the figure sin a =

                   sin (tan- 1 x)  

                   = sin

                   Choice (B)

 

94.  If -

 

        Ans:  

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

                   x1,2 = 41, 20

                   A = tan- 1

                             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

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 g(x) = x2 + 1

Verifying (1)

(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 x2 dx =

                   \ I =

                   =

                   =

                   =

                   Choice (D)

 

107.           Area enclosed by the curve -

 

        Ans :

                    = 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

               

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

               

                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 = vx

                   \

                   \ (1)

                   \ 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

                   (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)

 

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VITEEE Information
VIT consists of four parts:

VITEEE Past Trends, Cut-offs & Marks Distribution
This is an  objective type test and consists of  four parts- Part I -Physics - 40 marks Part II - Chemistry - 40 marks Part III - Mathematics –40 marks Part IV...

Detailed Information - Vellore Institute Of Technology (VIT) This article is for all those people who have agood rank in aieee and also a good stream in vit. After seeing a no of aspirants in this forum looking for advice i try to spread a

 

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