West Bengal Institute of Technology (WBIT) 2010-1st Year B.Tech Electronics and Communications Engineering WBUT Mathematics - Question Paper
CS/B.Tech/SEM-2/M-201/2010
Mathematics
Time Allotted : three Hours
Full Marks : 70
Name :
Roll No. : .9. 9.3015 Invigilator's Signature:.....
CS/B,Tech/SEM-2/M-201/2010 2010 MATHEMATICS
Time Allotted : 3 Hours
Full Marks : 70
The figures in the margin indicate full marlfe>
Candidates are required to give their answers in their own words
as far as practicable. (Cjft
GROUP - A (tgj)
( Multiple Choice Type 9*&ons )
1. Choose the correct alternatives ten of the following :
10 x 1 = 10
i) If A =
d) none of these.
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11) If X is a eigenvalue of A, then X 4 is an eigenvalue of
a) A 4 b) A3
c) A d) none of these.
iii) The rank of
is
b)
|
d) n |  |
these. |
iv)
v)
{f//p4p + 5
>p + 2. r + 4p + 5
d)
Which of the following sets is linjjr independent ?
a) { ( 1, 2 ), ( 2, 4 ) }
b) { ( 1, 2, 3 ), ( 2, 4, 6
c) { ( 2, 0, 0 ), ( 0, 3
d) none of thes
c)
a) 0
vi) Wmch of the following is not true ?
b) A VsA-V
a) AsE-l
d) A = 1 - E~ 1
SL \
vii) If the true and approximate value ot a quantity are x t and x respectively, then the relative error is given by
XaXt
b)
a)
a
d)
c)
Xt~Xa
|
A |
 |
vlii) The sum of the eigenvalues of 1 2 3 0 2 3 0 0 2 J
ix) The value of thfe de
is
|
1 |
1 |
1 |
|
2 |
- 3 |
1 |
|
3 |
- 2 |
X |
x) The value of X for which the matrix
is singular, is a) 3/2 c) 1
J>) 2 d) 1/3
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3
x2 + 2x + 2
a)
b)
c) 2x - x 2
d) -( 2x-x2) .
xli) The norm of the vector a = ( 1 in R 3 with
standard inner product is
b)
xiii) The degree and order &\Jhe differential equation ~H + 2 \3/2 - x respectively
dx
b) 2, 3 d) 1, 4.
a)
, 2
2
gK' 3, 2
GROUP -B ( SDnswer Type Questions )
Ajfeyr any three of the following.
3x5 = 15 .
2. Solve the ((following system of equations with the help of Gauss! nation method :
Xj + x2 + 4x3 = 6
3x j + 2x 2 - 2x 3=9
5Xj + x2 + 2x3 = 13.
3. Prove that A = e - 1.
(The notations have their usual meanings ),
4. Expand by Laplaces method to prove that
| ||||||||||||||||||||
|
n/6 | ||||||||||||||||||||
Evaluate
|
= ( af - be + cd) 2 |
 |
V 1 + sin x dx using Sinroscms one-third rule by
taking five ordinates.
GROUP
( Long AnswcrOTfj 9ue8ons )
Answer any<jra&of the following. 3 x 15 = 45
a) Show that ( 3, 1 I 2, 1, 4 ) and ( 1, - 1, 2 ) form a basis of R
b) Find the eiWues and eigenvectors of the matrix 1 - *
3 6 J
c) Solve by Cramers rule : x + y + z = 6 x + 2y + 3z = 14 x - y + z = 2.
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5
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CS/B.Tech/SEM-2/M-201/2010
8. a) Solve the differential equaion Transformation :
- 3y = tcost
by Lapla*
dfy_2dy
d t2
b) Solve by the method of variation ofjfjameters d2y
% + a2y = sec ax
dx
c) Find the particular integrf ( D2 + 4)y = x
9. a) Estimate the missing twin from the table :
|
2 <* |
6 |
8 |
10 | ||
|
>13 |
* |
53 |
85 |
b) The valua function fix) are given for cert values oCx)ks follows :
|
4 |
5 |
6 |
8 | |
|
3-11. |
296 |
2*85 |
2-7 |
tain the value of / ( 5*5 ) using Lagran interpolation formula.
sin x
dx using Simpson's one-third
c) Compute
a
\.
W
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%h
\
\
CS/B.Tech/SEM-2/M-201 /2010
10. a) Prove that for two invertible matrices A and B of the same order { AB ) ~1 = B 1 A~ 1 .
b) Reduce the following matrix to a row-re form and hence find its rank :
echelon
1 0
2 4 8 6 0 0 5 8
|
- 3 6 6 3 -1 |
 |
e 3x , D = dx
c) Solve ( D 2 - 5D + 6 ) /fp=
|
Attachment: |
| Earning: Approval pending. |
