VITEEE 2009 Sample Question Papers - Mathematics
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 = 
Þ a2b2 = 1
Þ 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
Þ 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 = 
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 x1,2 = 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 = vx
\ 
\ (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)
VITEEE 2009 Sample Question Papers - Chemistry
VITEEE 2009 Sample Question Papers - Mathematics
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