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 © 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 © 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 © 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 © 95. Argument of the complex number - Ans: = - (1 + i) </span> Arg Choice © 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 = </span> By Cosine formula, a 2 = b2 + c2 - 2bc cos A a 2 = 412 + 202 - 2(41)(20) = 2081 - 984 = 1097 Choice © 97. The shortest distance between the straight lines through - Ans: </span> Shortest distance = = = Choice (D) 98. The center and radius of the sphere - Ans: Centre is at Choice © 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) </span> 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 </span> = 2 r = 5 </span> V = p r3 = 4p (5)2 ´ (2) = 200 p Choice © 105. The length of the parabola - Ans : Length = = = = = = = = = 2 - = = = = = Choice (A) 106. If I = - Ans : I = Put 1 + x3 = t Þ x2 dx = </span> I = = = = Choice (D) 107. Area enclosed by the curve - Ans : Þ = 1 </span> 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 © 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 Ans: , |y| > 0 , 3 > 0 Three positive quantities cannot add to give zero. </span> No solution. Choice (B) 112. Solution of the differential equation xdy - Ans : ¾ (1) which is homogeneous put y = vx </span> </span> (1) Þ </span> x </span> Integrating log log </span> y + Choice (B) 113. Let P, Q, R and S be statements and suppose- Ans: p ® G ® R R ® p and ~ S ® R Þ © and (D) are not true also ~ S ® R . </span> (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. 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.
</span> 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) = </span> 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) Source:-http://www.time4education.com
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VITEEE 2009 Sample Question Papers - Chemistry
VITEEE 2009 Sample Question Papers - Mathematics
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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