Punjab Technical University 2007 B.C.A Computer Application s - Question Paper

Time: three Hours Max Marks:75

Note: 1. part A is compulsory and every carry 2 marks.
2.Attempt any nine ques. from part B and every ques. carry 5 marks.
Section-A
1.
(i) define the subsequent set in roster form
{x: (x>0) and (x2<10),x ? Z}
(ii) State the Principle of Mathematical Induction.
(iii) describe Relation and list different kinds of relations.
(iv) Prove that sin2 A +1 = 1
1+tan2 A
(v) If cot A= 7/24 and ?<3?/2, obtain the value of sin A
(vi) By using Principle of Mathematical Induction show that 2n> for every n? N
(vii) describe with examples Symmetric & Skew-symmetric Matrix.
(viii) State 2 Merits & Demerits of Mode.
(ix) If A={1,{2}}, Then obtain P(A), here P(A) means Power set of A.
(x) obtain the Domain of function described by rule
g(x) = one .
1-x2
(xi) Prove that (cosec A-cot A)2 =

(xii) obtain the median of the values 15,7,16,21,13,18,29,3,11.
(xiii) State Binomial theorem for positive index.
(xiv) discuss SARUS rule for expansion of Determinants with suitable Example.
(xv) Expand (1+x+x2)3 using Binomial theorem.

part – B
2. Let R be a Relation in A ={2,3,4,5} described by open sentence “|x-y| is divisable by 3”. Write R as a set of ordered pair.
3. Show that the function F:R--> R described by f(x)=3x3+5 for all x?R is objective.
4. Expand (2x-3y)4 using Bionomial Theorem.
5. Solve three tan?+cot?=5 cosec? where ? is acute angle.
6. obtain the fourth term from End in the Expansion of 2x - one .
x2
7. The mean of 200 items was 50. Later on it was discovered that 2 items were Misread as 92 and eight instead of 192 and 88. obtain out the accurate mean.
8. Prove that tan 15o + cot 15o =4.
9. Use the Principle of Mathematical Induction to prove that n(n+1) (2n+1) is divisble by six for all n ?N
10.
a a2 a2- 1
b b2 b2-1 = 0, where a?b?c,
c c2 c2-1 then show that abc=1

11. Prove by Principle of Mathematical Induction that or all n?N:
1+2+3+…………………+n=n(n+1)/2.
12. provided an example of 2 square matrices of order 2x2 every so that
(A+B)2 = A2 +2AB +B2.
13. obtain the mode from provided distribution of heights of a group of 60 college students:

Heights(IN cms) No. of students
145.0-149.9 2
150.0-154.9 5
155.0-159.9 9
160.0-164.9 15
165.0-169.0 16
170.0-174.9 7
175.0-179.9 5
180.0-184.9 1
(9 x five =45

Earning:   Approval pending.