Gujarat University 2008-1st Year B.C.A Computer Application Advanced Mathematics - Question Paper
* Seat No,:
April-2008 Advanced Mathematics
lime: 3 Hours) (Max. Marks : 70
Instruction : There arc five questions. Each question carries 14 marks.
1. (a) Attempt any three of the following: 9
(1) There are 400 students in a mathematics class and 600 students in a Biology. Find the number of students which are either in mathematics class or biology class in the following cases :
(i) the two classes meet at the same hour.
(ii) the two classes meet at different hours and 200 students arc enrolled in both the subjects. i/*
{1
(2) Let A-|xeN}, B* {* |x = 2n, neft)
C- {x|x = 2n AnN},D = {jr|xisaprirrtnumbcr}
* Find v
(i) AnB (ii) Cr>D
(iii) D-A (iv) B-C
(v) BnC (vi) AnC
Q) Shade the following sets in the Venn diagrams :
L/ (i) An(C-B) (ii) B-(AnC)
(4) Define:
(i) Disjoint sets
(ii) Symmetric difference set
(iii) Cartesian product of sets
(b) Answer any five of the following : 5
[2 3 4 1001 H
' Write the set jy, J............99'f n the sc* builder form. 1
List all elements of the set A - {.t | at is a month of a year having 31 days)
T- I
-
(1 f v\2008 _ 1
lim -*----.
X->0 x
J[S) Find the points of discontinuities of the function j _ .
(6) Define left hand limit.
FBCA-04 1 P.T.O.
2. (a) Attempt any three of the following : V__- 9
(l)_ State distance formula in R2 and use this to show that the paints ( I, 2). (5, 0) and (2. I) arc collincar.
Prove that the sum of squares of the diagonals of a rectangle whose vertices arc A (0, 0), B(a, 0), C(a. b) and D(0, b) is equal to the sum of the squares of its sides.
the equations of the following lines :
(i) X-axis (it) Y-axis
(iii) A line parallel to X-axis at a distance 3 units below the X-axis
(4) Find the equation to the straight line
(i) Cutting off intercepts 2 and 5 from the axes
(ii) Having slope 4 and passes through (2, 1)
(b) Answcrany five of the following ; 5
vllf in AABC, A< 1, 2), B(k. 2) and C(2. 3) and mAli = 90, then k __.
Find the area of triangle having vertices at (4,4), (3, -2). (3,-16).
\J3__-Examinc the continuity of = x2 + 2 at x - 0. n2W + 4.n20W
. (A\ lim n-:
-v*l
i
lim (1 *-x)x *->0 v
>*, 7.n2008 + 5.n2009 log/ i eT-
3. Attempt any seven of the following : 14
vJ4*)Lct A {-2. -1,0. 1,2} and f: A - / be a function defined by liv) = .r2 - 2x. Find pre-images ofO.-I: identity function.
(3) If the function F : R -> R be given by f(x) + I and g : R -> R be given by
x
g(x) - . Find fog and gof.
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(4) If2 log** 3 logy-2 = 0; thenx2y3 =_. | ||||||||||||
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Construct a 4 x 4 matrix whose elements are given by a = j Define :
(i) Lower triangular matrix
(ii) Identity matrix
(iii) Row matrix
>. (6)
'411 f 4 0 I Jtr Given A- 7 2 :B--7 _3j.
Find (i) A i 2B
(ii) A-B
(iii) A-*-AT C
(iv) B-B1 *
4. (a) Attempt any three of the following : 9
(l_J'Differemialc each of the following functions with respect to x: <2__
(i) yfcos~x*
(ii) x4 + y4 = 4'1
(iii) e4x+1log.v
F'ndj [sin (6 cos (6 sin (cos 6x))J]
(3) If y = A c?-*-* Be*1-*; then show that y2 - (p + q)yj + pqy = 0
(4) Profit function of a company is P(.t) = 4H 24.v - 18.x;2. Find maximum profit of the company.
(b) Answer any five of the following: 5
(1) (tan2* - see2*)_.
fe) =-
OFTnd degree of 1 + =yj 1+
(4) Order of the differential equation 1 * j K .
MSf Solve
FBCA-04 3 l\T.O.
(2) Evaluate:
(i) jV'dx
00 J x log* dv
(3) Evaluate:
i
0
n/2 f
(ii) I sinnx.dx o
(4) Find ihc area enclosed by line x + 2y = 8, x-axis and line x * 1 and x - 4.
(b) Answer any five of the following : 5
y %
(1> J c*dx*____.
102
J Kx) dv = V + c; then f{x) =
.(3) J" cl (sin t + cos t) dt _
(4) Cheek whether difTercntial equation (x + y + 1) dx + (2x + 2y + 1) dy " 0 is exact or not.
(5) Solve : y dx + x dy = 0.
(6) Degree of + cos (] - 0.
KBCA-04
4
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Attachment: |
| Earning: Approval pending. |
