Guru Gobind Singh Indraprastha Vishwavidyalaya 2008-2nd Year B.C.A Computer Application Mathematics-II, Second Semester, End Term , Year , , - Question Paper
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Q1 (prfSrve all partitions of S*{2,3.4}. (2)
Let f(x)=xJ-2. g<K)=3x and h(x)=(x*1)* be functions on R. Find goh. f*og. g3 (3) Let A*{2.3.7.8). B{1.3.5}. C*{3.5.9.11) find (i) BOC (ii) (A-6M&-C) (iil) (AxB)rv(0xB). - - .... (3)
to) Grve an example of a relation which is (i) neither symmetric nor ant)-symmetric (ii) not rreflexive (3)
(e) Grve a topological sorting of the poset (On. I). where Dn denotes the set of all . positive divisors of and I denote divides. ' (3)
iff Ge an example of an infinite lattice with finite length (2)
) Find Uie angle between the line and the ptane x-y+2z3 (3)
*(h)What <s the shortest distance between two given lines? Also, give the equations of shortest distance (3)
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'Change (he order of integration in / * . (3)
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SECTION-A
02 (a) Using set theory, prove the identity (AxBMP*Q>*(A-'P)x(Br>Q) (6.5)
(b> F*>d whether the function f.N-N defined by f(n)nJ+n*1 is invertible or not (6)
04 (a) Given A={1.2,3,4,5.6). Let R be a relation on A defined as R{{x.y); x*y is a divisor of 24} (6.S)
(0 Determine the matrix of relation R jri) Find the composition RoR J[iH) Find the domain and range of R Compute transitive closure of R.
JpyPtnd the domain and range of the functions t})yf{x) ()
(a) Consider the poset (1). {2}. {4). {1.2}. {1,4}. {2.4}. {3.4}. {1,3.4}. {2.3.4}}. cXe.S) W Find all max*nai and minanal elements yi) Find the first and last elements
Find all the upper bounds of {{2}, (4)} and its supremum. if it exists (rv)Find al the lower bounds of {1,3,4} and us Irvfimum. if it exists (pf\n a distnbutjve lattice, rf an element has a complement then this complement is unique (6)
05 (a) Consider relation R on the set 2 of aM integers as follows aRbe=>a*b s even for aN a, beZ Is R a partial order relation? Prove or give a counter example (4)
P.T.O.
(b)Glve an example of a fetation, on the set {1,2.3} which is both partial ordering and an equivalence relation (2.8)
(i) Find all join-irreducWe elements
(ii) Find the atoms.
(iii) Is I complemented?
(tv) Is L distrtouOve?
r . I
06 (a) If m -,-a- I then show that
... du du -1
(b) Find (he equationa of the spheres through the circle xJ*y2*z25, x+2y*3za3 and touching the plane 4x*3y15. (0)
Q7 Hind the ..tfxima and minima at tftefunctton f(x,y)xs*ys-63(x*y>*12xy. (6.5)
(b)Snow that the lines and 4x.3y+l0*5x-3z+2 are
_>/ 2 3 4
copianar Also And their point of Intersection. (6)
SECnON-O
Qti By changing to polar co-ordinates evaluate j J(xz y )ixdy where R is the region
A
m xy-plane bounded by x2*/ and (12.5)
Q9 Find the volume of the sphere (12.8)
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