VIT - Unsolved Mathematics -2009

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Vit – Past papers: 

Vit – Past papers MATHEMATICS - UNSOLVED PAPER - 2009

SECTION – I: 

SECTION – I Single Correct Answer Type There are five parts in this question. Four choices are given for each part and one of them is correct. Indicate you choice of the correct answer for each part in your answer-book by writing the letter (a), (b), (c) or (d) whichever is appropriate

Problem: 

01 If is defined by , then the range f(x) is contained in the interval [1, 12] [12, 34] [35, 50] [-12, 12] Problem

Problem: 

02 The number of subsets of {1, 2, 3, ..... , 9} containing at least one odd number is 324 396 496 512 Problem

Problem: 

Problem 03 A binary sequence is an array of 0's and 1's.The number of n-digit binary sequences which contain even number of 0's is a. b. c. d.

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Problem 04 If x is numerically so small so that and higher powers of x can be neglected, then is approximately equal to a. b. c. d.

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Problem 05 The roots of (x - a) (x - a-1) + (x - a -1)(x - a - 2)+ (x - a) (x - a - 2) = 0 are always equal imaginary nial and distinct rational and equal

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Problem 06 Let , where . If f(x) = 0 has all its roots imaginary, then the roots of f(x) + f' (x) + f" (x) = 0 are real and distinct imaginary equal rational and equal

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Problem 07 If is divisible by , then (a, b) is equal to (-9, -2) (6, 4) (9, 2) (2, 9)

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Problem 08 If x, y, z are all positive and are the pth , qth and , rth terms of a geometric progression respectively, then the value of the determinant , Equals log xyz (p -1)(q -1)(r -1) pqr 0

Problem: 

Problem 09 The locus of z satisfying the inequality ,where z = x + iy,is a. b. c. d.

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Problem 10 If n is an integer which leaves remainder one when divided by three, then Equals a. b. c. d.

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Problem 11 The period of is a. b. c. d.

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Problem 12 If , then the general solution of is a. b. c. d.

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Problem 13 equals: a. b. c. d.

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Problem 14 In a. b. c. d.

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Problem 15 The angle between the lines whose direction cosines satisfy' the equations 1+ m + n = 0 , is a. b. c. d.

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Problem 16 If are respectively the magnitudes of the vectors , then the correct order of is a. b. c. d.

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Problem 17 If X is a binomial variate with the range {0, 1, 2, 3, 4, 5, 6} and P(X = 2) = 4P(X = 4), then the parameter p of X is a. b. c. d.

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Problem 18 The area (in square unit) of the circle which touches the lines 4x + 3y = 15 and 4x + 3y =5 is a. b. c. d.

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Problem 19 The area (in square unit) of the triangle formed by x+ y + 1 = 0 and the pair of straight lines is

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Problem 20 The pairs of straight lines form a square but not rhombus rhombus parallelogram rectangle but not a square

Problem: 

Problem 21 The equations of the circle which pass through the origin and makes intercepts of lengths 4 and 8 on the x and y-axes respectively are a. b. c. d.

Problem: 

Problem 22 The point (3, - 4) lies on both the circles Then, the angle between the circles is a. b. c. d.

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Problem 23 The equation of the circle which passes through the origin and cuts orthogonally each of the circles is a. b. c. d.

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Problem 24 The number of normals drawn to the parabola from the point (1, 0)is 0 1 2 3

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Problem 25 If the circle , for i = 1, 2, 3 and 4, then equals 0 c a

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Problem 26 The mid point of the chord 4x - 3y = 5 of the hyperbola is: (2, 1)

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Problem 27 The perimeter of the triangle with vertices at (1, 0, 0), (0, 1, 0) and (0, 0, 1) is 3 2

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Problem 28 If a line in the space makes angle with the coordinate axes, then equals -1 0 1 2

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Problem 29 The radius of the sphere is 13/2 13 26 52

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Problem 30 equals e

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Problem 31 If is defined by then the value of a so that f is continuous at 0 is 2 1 -1 0

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Problem 32 is equal to 0 tan t 1 sin t cost

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Problem 33 is equal to 1 -1 0 2

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Problem 34 is equal to a. b. c. d.

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Problem 35 The function has one maximum value one minimum value no extreme value one maximum and one minimum value

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Problem 36 . is equal to a. b. c. d.

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Problem 37 If equals a. b. c. d.

Problem: 

Problem 38 The line divides the area of the region bounded by y = sin x, y = cos x and x-axis into two regions of areas equals 4: 1 3: 1 2: 1 1: 1

Problem: 

Problem 39 The solution of the differential equation is cosec (x + y)+ tan (x + y)= x + c x + cosec(x + y)=c x + tan (x + y)=c x + sec (x + y) = c

Problem: 

Problem 40 If is false, the truth value of p and q are respectively F, T F, F T, F T, T

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