Punjab Technical University 2010-1st Sem B.C.A Computer Application Bridge in Mathematics ( ) - Question Paper
Roll No...........................
Total No. of Questions : 13]
[Total No. of Pages : 03
(Please fill this Paper ID in OMR Sheet)
BCA (102) (S05) (O) (Sem. - 1st)
BRIDGE COURSE IN MATHEMATICS Time : 03 Hours Maximum Marks : 75
Instruction to Candidates:
1) Section - A is Compulsory.
2) Attempt any Nine questions from Section - B.
Section - A
Q1) (15 x 2 = 30)
a) Prove that A n AC = f by example.
b) Draw Venn diagram of B - A and A B.
c) If A = {- 3, 0, 1, 2} & B = {1, 2, 3, 4} then write B - A and A D B.
d) Find A B & A B if : A = {2, 3, 4, 8}, B = {1, 6}
e) If A = {1, 2, 3}, B = {2, 5, 6, 1}eC = {Jv3, 5, 9} then find (A B) x C.
f) Expand (1 - 2x)3 by Binomial.
g) Define cofactor of matrix with example.
h) Write the difference between matrix and determined.
i) Write 4th term of
j) If A =
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5 |
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- 3" |
3 |
6 |
7 | |
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6 |
7 |
1 _ |
, B = | |||
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1 |
0 |
-17 |
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1 |
6 |
1" | |
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, C = | |||
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5 |
3 |
7 |
find A + B - C. k) Define Raw Data and discrete frequency distribution.
l) Define mode and write formula to find mode. m) Find range and its coefficient from data :
Size : 5 7 9 10 11
12
3
Freq. : 1 3 5 7 4
n) Define pure and applied statistics.
o) Find mean of the following marks obtained by 10 students in mathematics. 52, 40, 70, 75, 43, 40, 35, 65, 48, 62
Section - B
(9 x 5 = 45)
Q2) Prove that A - B = A n BC
Q3) Let A = {1, 2} and B = {3, 4}, find the number of relations from A into B and B into A.
Q4) Find the range of function .
Q5) Prove A x (B u C) = (A x B) (A x C). Q6) Prove by mathematical induction
V neN.
Q7) Using the Binomial theorem, prove that
C + 2.C2 x + 3. C3x2 +..........+ n.C xn-1 =
12 3 n
n 2 (4n 3
7+ x-e-R---(2n -1) (2n + 1)
1 x yz-1 y zx 1 z xy
4x2' -1
Q8) Evaluate the determinant
Q9) Prove that A3 - 4A2 - 3A + 11 I = 0 where A
13 2 2 0 -1 1 2 3
Q10) Find mean for the data :
Marks : 0-10 10-20 20-30 30-40 40-50 No. of girls : 6 8 14 16 4
50-60
2
Q11) Write a note on the following :
(a) Graphical representation of distribution.
(b) Histogram.
Q12) Find the mode for the following data :
Marks : 0-10 10-20 20-30 30-40 40-50
No. of Students : 4 5 6 9 2
Q13) Calculate the medean of distribution of the marks obtained by the students. Marks : 0-10 10-20 20-30 30-40 40-50 50-60 Frequency : 3 9 15 30 18 5
A-59 3
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| Earning: Approval pending. |
