Veer Narmad South Gujarat University 2011-1st Year B.C.A Computer Application SB-1402 Mathematics - 1 ( Sem - 1 ) - Question Paper
SB-1402
First Year B. C. A. (Sem. - I) Examination March / April - 2011 Mathematics - I
[Total Marks : 70
Time : 3 Hours]
Instructions :
(1)
6silq<3i Puunkiufl [qaim SuwiA u* qsq d-onql. Fillup strictly the details of signs on your answer book.
Name of the Examination :
F. Y. B. C. A. (SEM. -1)
Name of the Subject:
MATHEMATICS -1
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Student's Signature
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(2) All questions are compulsory.
(3) Figures to the right indicates full marks.
1 Answer the following questions : 10
(1) Prove that (A')' = A
(2) Define equivalent set will illustration.
(3) Every function is a relation or Every relations is a function. Which is true ? Justify your answer.
(4) If f(x) = 3x2+mx + 5 and /(2) = 27 then find the value of m.
(5) Explain idempotent law in Boolean Algebra.
(6) Every skew symmetric matrix is a Diagonal matrix true or false ? Justify your answer.
then find the values of a and b.
(8) Find the equation of line with slope and passing through (5, 4).
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a + b 2 |
'6 2 | ||
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(7) If |
5 ab |
5 8 |
(9) Give the truth table of (/?=>#) and (/?<=>g).
(10) Define orthogonal matrix.
2 (a) If A = {x\x is a positive integer between 1 and 4}
12
B = {x\x is a natural no. between 1 and 5}
C = {x|x is an odd natural no. less than 6}
D = {x\x is an even natural no. less than 5} then verify
(AxB)c\(CxD) = (Ac\C)x(B C\D).
(b) If A = jx|x2-2x-3 = 0; xei?j B = jx|x3 = x; x e Zj C = jx|x3 = x; x e ivj
then verify Ax(B-C) = (AxB)-(AxC)
(c) If A = {l,2,3,4j, B = { 1,2,3}, C = {2,4} find all possible sets X which satisfy the following conditions :
(i)
(ii) X c B, X 4: C, X B
(iii) X <z A, X <z B, X C.
2 (a) In usual notation prove that A-(A-B) = AnB . 12
(b) If / = {x|xeiV; x<10] y4 = jx|xeiV, x2<loj
B = {2,4,6}
C = jx|x3 3x2 -4x = 0} then verify that
(c) In a housing society, 50 residents have scooters, 20 home cars and 15 have both types of vehicles. If there are 60 residents in the society, how many of them have neither scooter nor car ?
3 (a) The supply function of a commodity is S = ap2 +bp + c 12
the respective value of price and supply are given by the ordered pairs (2, 12), (3, 38), (4, 74) then determine the supply function and find the price when supply is 120 units.
(b) / = {(1,1), (2, 3), (3, 5), (4, 7)}, A = { 1,2, 3, 4}, B = 2- If
/ : A > B is a function such that / (x) = ax + b then find a and b.
(c) If / (x) = x2 + x -1 then find the value of /(x + l)-3/(x-l) + 2/(x).
3 (a) If f{x) = 1--; jc e i? {0,3} then find /(l), /(2), 12
JC JC j
AlA)and /(-3)
(b) A function is defined as, /(x) = 2x + 3; xe[-2, 0]
= 4-3x; xe(0,<)
_ /(-2)-/(-l) then find the value of +
(c) The cost function of an item is C(x) = 4x + 770 and the
selling price per item is Rs. 15. Find the break even point. If the profit is Rs. 1100, find the number of units produced.
4 (a) Show that Dl0 (Divisor of 10) is a Boolean Algebra 12
where, \/a,beDl0
a + b = 1cm of a, b a b = gcd of a, b and
a = a
(b) Is the argument in following example valid ?
Hypothesis : Sx :pq, S2'.q>r, conclusion S: p>r (use truth table)
(c) Construct the input/output table for
(i) f(xi,x2) = xrx2
(ii) /(x1,x2,x3) = (x1-x)-x3
4 (a) Show that D1X is a boolean algebra where V a,b e D1X 12
a + b = 1cm of a, b a b = ged of a,b and
, 21 a = a
(b) Is the argument given below is logically valid ? Hypothesis : Sx.p, S2'.pq=>rvs,S3:q,S4:~s and conclusion : S : r.
(c) Construct the input/output table for
(i) f{xxi) = x\-x2
(ii) /(x1,x2) = (xrx2)'+x2
ab -b2 be
-ar
ba
ac
ac
be
= 4a2b2c2
(a) Prove that
12
and B = 3A, C = -B then find
7 3-5
0 4 2
1 5 4
(b) If
2 A-B+C-
1 3 2 1 -4 4 1 3 -3
(c) Find the inverse of the matrix
x y z
x2 y2 z2 x3 y3 z3
5 (a) Show that
12
= xyz(x-y)(y-z)(z-x)
(b) Solve using Crammer's rule
and (4 + B)2 = A2 + B2 then
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'1 |
-1' |
1 a | |
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, B = | |||
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2 |
-1 |
4 b_ |
(c) If A
find a, b.
6 (a) If the distance between (a,-5) and (2,a) is 13 units 12 then find the value of a.
(b) Find the equation of a line passing through (-2, 3) and parallel to the line joining (l, 7) and (-2,-5).
(c) Show that the points (-3,2),(l, 2) and (-3,5) form a right angled triangle.
6 (a) Find the equation of a line joining the point (l, 3) 12 and the point of intersection of the line x + y +1 = 0 and
3x + _y + 5 = 0.
(b) Prove that the line 4x + 3y + 2 = 0 and 6x-8 + 11 = 0 are perpendicular to each other.
(c) Find the equation of the parallel to the line joining (3, 2) and (4, 0) and passing through the point (5, l).
SB-1402] 7 [ 3000 ]
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| Earning: Approval pending. |
