Punjab Technical University 2008 B.C.A Computer Application Math-ii(computer oriented methods) - Question Paper
[Total No. of Pages : 03
Roll No.......................
Total No. of Questions : 13]
(Please fill this Paper ID in OMR Sheet)
BCA (301)/B.Sc.(IT - 404) (S05) (O/N) (Sem. - 3rd) MATHS - II (COMPUTER ORIENTED METHODS)
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
a) If
b) Evaluate
, find the value of x, y, z and w.
3 - 2 -1 1
1 3 5
2 4 6
+
|
"3 |
2" |
x |
l x 3 | |
|
4 |
7_ |
2 x + z |
l 3 |
1 3 -1 - 4
c) Find rank of the following matrix
3 -1 2 - 6 2 4 3 1 2
, show that A2 - 5A + 7I = 0, where I is a unit matrix.
' 3 1" -1 2
d) If A =
e) Using matrix, find the area of a triangle with vertices (3,8), (-4,2) and
(5,1).
f) Find the mean of the data 65, 58, 68, 44, 48, 45, 60, 62, 60 and 50.
g) Write a short note on kurtosis of data.
h) Find the geometric mean of 50, 100, 1920, 143740.
i) Find -X if ax2 + 2hxy + by2 + 2fx + 2gy + c = 0.
x
j) If (x)y= @y)x , find -X
D-491 k) Evaluate j-,J 1+cos 2xdx.
_ 1 , cos0
l) Evaluate J
_JQ
(2+sin0)(3+4sin0)
2n
m) Evaluate j cos5 xdx.
x
n) Evaluate using properties of definite integral j +4
dx
x
o) Give Simpsons 1/3 rule of numerical integration.
|
, verify that (AB)T = BT AT. |
Q3) Solve following system of equations by Gauss Jordan method
Q2) If A =
2x -y + 3z = 5; 3x + 2y - z = 5 and 4x + 5y - 5z = 9
, as sum of a symmetric and skew symmetric
3 -10 2 0 3 1 -1 2
Q4) ixpress matrix a matrixF
Q5) Find the inverse of the matrix
2 -1 1 1 2 -1 1 -1 2
Q6) Differentiate with respect to x, tan"
x
Q7) Find if x = a( 1 -cos 0 ) and y = a(6 + sin0).
dx
Q8) Show that the semi vertical angle of a cone of maximum volume and of given slant height is tan1 J2 .
Q9) The first of two samples has 100 items with mean 15 and standard deviation
3. If the whole group has 250 items with mean 15.6 and standard deviation of
n/1344 , find mean and the standard deviation of the second group.
2 x-1
QIO) Evaluate f-dx.
(x -1)( x+ 2)( x- 3)
k /2 n
Qll)Vrove that J log(cos x) dx=--(log 2).
o 2
f 2
Ql2)Evaluate J x dx as the limit of sum
6 1
Ql3)Evaluate J dx using Trapezoidal rule. Jj 1+x2
D-491 3
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Attachment: |
| Earning: Approval pending. |
