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Posted By: Reena Malik Member Level: Diamond Posted Date: 22 May 2008
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2005 Indira Gandhi National Open University (IGNOU) B.C.A CS60 : FOUNDATION COURSE lN MATHEMATICS IN COMPUTING Question paper
BACHELOR IN COMPUTER APPLICATIONS
Term-End Examination
December, 2005
CS60 : FOUNDATION COURSE lN MATHEMATICS IN COMPUTING
Time: 3 hours
Maximum Marks: 75
Note : Question number 1 is compulsory. Solve any three questions from Q.no. 2 to 5.
1. (a) Find f(2), f(1/2), f(-3.5), if f(x) = [x] Further for which values of x is f(x) = 3 ? (3)
(b) Find the complex conjugate of 3+5i/1+2i. (3)
(c) Differentiate (sin x)xw.r.t. x. (2)
(d) The distance s moved by a particle in time t is given by
s = 4t3-6t2-24t
Show that the direction of motion is reversed after 2 seconds. (4)
(e) Reduce the equation
x2-4xy+4y2+5vy-10 = 0
to standard form. Hence identify the conic represented by it. (7)
(f) lf A. B and C are sets such that A ? B = A U C and A n B = F = A n C, then prove that B = C. (3)
(g) Obtain the maximum possible domain and range of the function defined by f(x) = v2-x/x. (3)
Obtain d/dt (?sint-t dx/x2(x-1)2). (3)
(i) Give an example, with justification, of a conicoid whose planar sections are either circles or parabolas. (2)
2. (a) Find the points of continuity and discontinuity, if any, for
2x3-54
------------------- , x ? ±3
f(x) = x2-9
9 , x = ±3
(b) If a, ß, ? are the roots of the equation
x3+6x2+6x+8 = 0, find the equation whose roots are (a + ß), (ß + ?), (? + a). (6)
(c) Prove that y = mx + c is a tangent to x2 = 4ay if c=-am2. (4)
3. (a) Find the length of the major and minor axes, the eccentricity, co-ordinates of the vertices and foci of 2x2 + 3y2 = 12. (4)
(b) Show that ?p/20 vsinx/vsinx + vcosx dx = &pi/4. (5)
(c) Find all z ? C such that z4 = -8(1+iv3). (4)
(d) Which of the following conicoids has a centre at the origin ? Give reasons for your answer. (2)
(i) x2+y2-z2+3xy-3yz+2zx+18x = 0
(ii) 2x2+y2+2z2+8x-4y+5 = 0
4. (a) Evaluate ? (x-1)dx/(x+1) vx+2. (4)
(b) Solve the following system of equtions using Cramer's rule : (4)
2x + y - z = 1 x - 2y + 3z = 6 x - y + 2z = 9
(c) Check whether ayz + bzx + cxy = 0 and vax+vby+vcz = 0 are reciprocal cones.
(d) If y = emtan-1x, show that
(1+x2)yn+1 + (2nx-m)yn + n(n-1)yn-2 = 0. (3)
5. (a) Sketch the surface defined by
x2/16 - y2/9 - z2/9 = 1.
Name the curves formed by intersecting this surface with (4)
(i) y = 3
(ii) x = 4.
(b) Compute the area bounded by y2 = 9x and x2 = 9y. (3)
(c) Use the Cauchy - Schwarz inequality to solve x3-25x2-4x+100 = 0, given that all its roots are rational. (6)
(d) If f and g are functions over R, such that f + g is continuous, then must f be continuous. Give reasons for your answer. (2)
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