West Bengal Institute of Technology (WBIT) 2009-2nd Sem B.Tech Electronics and Communications Engineering Electronics & Comm ( - ) Mathematics - Question Paper
CS/B. i ccL/ jliM-2/M-201/09 3
ENGINEERING ; MANAGEMENT EXAMINATIONS, JUNE - 2C09
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[ Full Marks : 70
Time : 3 Hours ]
GROUP - A ( Multiple Choice Type Questions )
1. Choose the correct alternatives for any ten of the following ;
1 0
, then A 100 is
10 x 1 --7 10
If A =
L - 1 i .
' 1 0
. - 150 1 J
' 1 0
. - 100 1
1 0
I
- 50 1
b)
a)
d) None of these.
cj
ii]
X.
5'
czi
Ths set of vciiisrs [ [ 2. 1. 1 ), ( 1, 2, 2 ), ( 1, 1, 1 ) } in R 3 Is
aj linearly dependent b) linearly independent
c) basis of K3 d) none of these.
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"vi |
fl | |
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1 |
1 |
is |
I |
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ill) The matrix A -
iO an orthogonal matrix c) an tdempotent matrix
b) a symmetric matrix d) a null matrix,
4 16 2 2 4 1 6
iv) 1113 value of the determinant
is
i
0
b) 1
J 0
d) 22.
c) 4
The solution of a system of n linear equations with n unknowns is unique i ;ic
. ..
only if I
V)
b) clet A > 0
i) det A ~ 0
d) det A * 0,
c) det A < 0
whre A is the matrix of the coefficients of the unknowns in the linear lions
1 4
vi) The eigenvalues of the matrix
are
I 4 1
b) - 5. 3
a) -5,-3
d) 5, 3.
c) 3,-5
vii) Thtf general solution of p = log ( px - y } where P ls
b) y cx ec
a) y = cx - c
c) y * c 2,v - e
i i
- c
d) none of ihese,
viii) Which of the following is not true (the notations have their usual rneaiji... ) V
b) A.V = A - 7
a) A m E- 1 A
C)
ix) A 2 e * is equal to ( h = 1 }
a) ( e - 1 } 2 a x
2x
d) e
c) e 2 v ( - 1 )
dt is equal to
x) The value of
TC
6
TC 2 '
b)
d)
a)
c)
3
Tt
11
xl) If S and T are two subspaces of a vector space Vr, then which one of u e follow!,; \g is a subspace of V also ?
b) SflT d) T-S.
a) S U T c) S.....Y
xii) If X 3 - SX 3 '! 9X - 4 ii: the characteristic equation of a square matrix A, then A " 1 is equal to
a) A 2 - 6A + 91
C
d) A 2 - 6A + 9.
ci
-2 - 3 4 1 0 1 0 - 1 4
is
xiii) Co-factor of - 3 in the determinant
b) - 4
a
c) G
d) none of these.
GROUP - B I Short Answer Type Q-tatias )
Answer any three of the following.
2. If A be a skew symmetric and ( I + A ) be a non-singular matrix, then show die B - {I - A ) (I + A ) ~ 1 is orthogonal.
1
i
Evaluate L~ 1
I { s - 1 ) 2 ( s - 2 ) 3 }
Solve uie differential equation
di; < , . 7: h! - y ( cos x - sin x )
vL\
( x + x 3 ) dx by using Trapezoidal rule, taking fi r
5. Evaluate the definite Integral
i
, then show that
ordinates and calculate the error.
cos 6 - sin 0 sin 0 cos 0
If l V ) -
i \ ( G ) A ( 9 ) = ,4 ( $ ) . A ( 0 ) = A ( 0 + <j) ) .
GROUP -C ( Long Answer Type Questions ) Answer any three of the loilowing.
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7. a) if A |
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, show that AB =. 6/ |
U tilise this result to solve the following system of equations : :f x + y + z = 5 ,x - y = 0 2x + y - z = 1
b) Solve U- :-x) [p- \ ) = p and obtain the singular soluaon. Here p = ,
C sC
*
p
i
Construct the interpolation polynomial for the function y ~ aln tw. taking the poirUi Xq - Oi x - g i aj s g * .
c)
i
*
\
Henc- fliid/j 4 where y =f[x) ,
8, a) Solv ; the difiVrentlal equation
cT dx
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Apply suitable Interpolation formula to calculate / ( 9 ) correct up o two significant figures froii, the following data : % | ||||||||||||||
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$
%
b)
c) Detejiiii-.i the conditions under which the system of equations
*
. . y + z 1 x + 2y - z * b + 7y imbD2
f:
*
I'
adms .s oi
ij only cnt aolution 11) no soiutu n Hi) , iiiuny roljtions.
\
i
9, a) Pi-o. 2 that PrA. P is a symmetric or a skew-symmetric matrix according a , A symmetric or s;a;A-symmetrlc.
fcj Fines tiie eigenvalues and the eigenvectors of the matrix
4 6 2 S
c) Solve by Cramers rule the following system of equations ;
3x + y + :r = 4
* x - y + 2z = 6 x + 2y z - 3.
10. a) What id meant by linear Independence of a set of n-vectors ?
" oke by the method of variation of parameters the equation
b)
d*y
Sy - sec 3x .
.2
dx
a 2
a
( c + a) 2
- 2abc ( a -t b +
c)
Prove that & |
c
( b + c) 2
b 2
r. 2
END
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| Earning: Approval pending. |
