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Code No: A109100203
Set No. 1
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
I B.Tech. I Mid Examinations, December – 2010
MATHEMATICAL METHODS
Objective Exam
Name: ______________________________ Hall Ticket No.
A
Answer All Questions. All Questions Carry Equal Marks. Time: 20 Min. Marks: 10.
I.
1.
Choose the correct alternative:
The rank of the matrix
⎡ 1 − 1 2⎤
⎢2
2 2⎥
⎢
⎥
⎢ 3 − 3 6⎥
⎣
⎦
(a)
2.
3.
4.
(b)
0
7.
(c)
2
(d)
3
R
O
⎡ 1 −2 ⎤
LU decomposition of ⎢
⎥ is
⎣ −1 4 ⎦
⎡ 1 0 ⎤ ⎡ 1 −2 ⎤
⎡ 1 0 ⎤ ⎡ 1 −2 ⎤
(a) ⎢
b) ⎢
⎥ ⎢0 1 ⎥
⎥⎢
⎥
⎣ −1 0 ⎦ ⎣
⎦
⎣ −1 1 ⎦ ⎣ 0 2 ⎦
⎡ 1 0 ⎤ ⎡1 −2 ⎤
⎡1 0 ⎤ ⎡1 −2 ⎤
(c) ⎢
(d) ⎢
⎥ ⎢0 3 ⎥
⎥⎢
⎥
⎣2 1⎦ ⎣
⎣3 1 ⎦ ⎣ 0 1 ⎦
⎦
⎡ 2 −1 3⎤
If the rank of the matrix ⎢ x 2 1 ⎥ is 2 then x =
⎢
⎥
⎢ 1 −4 5⎥
⎣
⎦
W
U
[
If A =
J
1
(b)
⎡1 0 −1⎤
⎢0 2 3 ⎥ ,
⎢
⎥
⎢0 0 4 ⎥
⎣
⎦
2
(c)
3
(c) 1, 4, 8
If A is a matrix of order m × n and m < n then the rank of A is
(a)
m
(b)
n
(c)
≤ m (d)
>m
⎡1 2 3 ⎤
If the rank of the matrix ⎢ 4 5 x ⎥ is 2 then x =
⎢
⎥
⎢
⎥
⎣3 3 4⎦
(a) 2
(b) 3
(c) 7
]
[
]
[
]
4
then the eigen values of A−1 are
(b) - 1, - 2, - 4
]
[
(d)
]
[
T
N
(a) 1, 2, 4
6.
D
L
is
1
]
If there are 4 equations in two unknowns and the rank of the coefficient matrix is 2. then the system
will have
[
]
(a) Uniquie solution
(b)
Infinite number of solutions
(c)
Two solutions
(d)
No Solution
(a)
5.
[
(d) 1,
1 1
,
2 4
(d) 5
Cont…..2
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Code No: A109100203
8.
9.
10.
:2:
Set No. 1
If A is a matrix of order 3 × 3 and X is 3 × 1 then the system of equations AX = 0 will have only
trivial solution if the rank of A is
[
]
(a) > 3
(b) < 3
(c)
1
(d)
3
⎡5 2 ⎤
The characteristic equation of ⎢
⎥ is
⎣3 1 ⎦
2
2
2
(a) λ + 6λ + 1 = 0 (b) λ − 6λ − 1 = 0
(c) λ + 6λ − 1 = 0
[
[
⎡ −1⎤ ⎡ 2 ⎤
⎡ −1⎤ ⎡ 2⎤
⎡ −1⎤ ⎡ 3 ⎤
⎡1⎤ ⎡ 2 ⎤
(b) ⎢ ⎥ ⎢ ⎥
⎣ 1 ⎦ ⎣0⎦
]
(d) λ 2 − 6λ + 1 = 0
⎡8 −4 ⎤
The eigen vectpors of ⎢
⎥ are
⎣2 2 ⎦
(a) ⎢ ⎥ ⎢ ⎥
⎣ 1 ⎦ ⎣ −1⎦
]
(c) ⎢ ⎥ ⎢ ⎥
1 1
(d) ⎢ ⎥ ⎢ ⎥
⎣ 1 ⎦ ⎣ −1⎦
⎣ ⎦⎣ ⎦
D
L
II
Fill in the Blanks
11.
The system of equations x + 2y = 5, –2x + ay = 4 are consistent if _________
12.
13.
The eigen vector corresponding to λ = 2 of
R
O
⎡ 1 2 − 1⎤
⎢0 2
2⎥
⎢
⎥
⎢0 0 − 2 ⎥
⎣
⎦
is ______________
W
U
The eigen values of the matrix
⎛ 1 1⎞
⎜
⎜ 1 1⎟
⎟
⎝
⎠
are ___________
T
N
⎡6 2 ⎤
⎢ 1 −1⎥
⎣
⎦,
2
then 2 A − 8 A − 16I = _______________
14.
If A =
15.
If the eigen values of A are 1, -1 and 2, then the eigen values of adj A are___________
J
⎡1
⎢0
⎢
⎢0
⎢
⎣0
1 1 0⎤
0 1 0⎥
⎥
1 1 1⎥
⎥
1 0 1⎦
16.
The rank of the matrix
17.
The system of equations 3x + y + 2z = 3, 2x – 3y – z = –3, x + 2y + z = 4 will have________
18.
If A is of order 3X4, and the rank of A is 2, then the number of independent solutions of AX = o
are __________
19.
20.
The eigen values of
⎛1 0 ⎞
⎜
⎜ 2 −1⎟
⎟
⎝
⎠
is___________
are ____________
The eigen vector corresponding to λ = 1 of
⎡ 1 0 − 1⎤
⎢1 2
1⎥
⎢
⎥
⎢2 2
3⎥
⎣
⎦
-oOo-
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is _____________

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Code No: A109100203
Set No. 2
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
I B.Tech. I Mid Examinations, December – 2010
MATHEMATICAL METHODS
Objective Exam
Name: ______________________________ Hall Ticket No.
A
Answer All Questions. All Questions Carry Equal Marks. Time: 20 Min. Marks: 10.
I.
1.
2.
Choose the correct alternative:
⎡ 2 −1 3⎤
If the rank of the matrix ⎢ x 2 1 ⎥ is 2 then x =
⎢
⎥
⎢ 1 −4 5⎥
⎣
⎦
(a)
1
(b)
2
(c)
3
(d)
If A =
⎡1 0 −1⎤
⎢0 2 3 ⎥ ,
⎢
⎥
⎢0 0 4 ⎥
⎣
⎦
4.
4
R
O
(b) - 1, - 2, - 4
(c) 1, 4, 8
(d) 1,
[
T
N
(a) 2
(b) 3
(c) 7
]
[
]
1 1
,
2 4
If A is a matrix of order m × n and m < n then the rank of A is
(a)
m
(b)
n
(c)
≤ m (d)
>m
⎡1 2 3 ⎤
If the rank of the matrix ⎢ 4 5 x ⎥ is 2 then x =
⎢
⎥
⎢3 3 4⎥
⎣
⎦
W
U
]
D
L
then the eigen values of A−1 are
(a) 1, 2, 4
3.
[
(d) 5
5. If A is a matrix of order 3 × 3 and X is 3 × 1 then the system of equations AX = 0 will have only
trivial solution if the rank of A is
[
]
(a) > 3
(b) < 3
(c)
1
(d)
3
6.
7.
J
⎡5 2 ⎤
The characteristic equation of ⎢
⎥ is
⎣3 1 ⎦
2
2
2
(a) λ + 6λ + 1 = 0 (b) λ − 6λ − 1 = 0
(c) λ + 6λ − 1 = 0
⎡ −1⎤ ⎡ 2 ⎤
[
(a)
1
]
⎡ −1⎤ ⎡ 3 ⎤
⎡1⎤ ⎡ 2 ⎤
(c) ⎢ ⎥ ⎢ ⎥
1 1
(d) ⎢ ⎥ ⎢ ⎥
⎣ 1 ⎦ ⎣ −1⎦
⎣ ⎦⎣ ⎦
The rank of the matrix
⎡ 1 − 1 2⎤
⎢2
2 2⎥
⎥
⎢
⎢ 3 − 3 6⎥
⎣
⎦
]
[
⎡ −1⎤ ⎡ 2⎤
(b) ⎢ ⎥ ⎢ ⎥
⎣ 1 ⎦ ⎣0⎦
]
(d) λ 2 − 6λ + 1 = 0
⎡8 −4 ⎤
The eigen vectpors of ⎢
⎥ are
⎣2 2 ⎦
(a) ⎢ ⎥ ⎢ ⎥
⎣ 1 ⎦ ⎣ −1⎦
8.
[
is
(b)
0
(c)
2
(d)
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3
Cont…..2

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Code No: A109100203
9.
10.
II
:2:
Set No. 2
If there are 4 equations in two unknowns and the rank of the coefficient matrix is 2. then the system
will have
[
]
(a) Uniquie solution
(b)
Infinite number of solutions
(c)
Two solutions
(d)
No Solution
⎡ 1 −2 ⎤
LU decomposition of ⎢
⎥ is
⎣ −1 4 ⎦
⎡ 1 0 ⎤ ⎡ 1 −2 ⎤
⎡ 1 0 ⎤ ⎡ 1 −2 ⎤
(a) ⎢
b) ⎢
⎥ ⎢0 1 ⎥
⎥⎢
⎥
⎦
⎣ −1 1 ⎦ ⎣ 0 2 ⎦
⎣ −1 0 ⎦ ⎣
⎡1 0 ⎤ ⎡1 −2 ⎤
⎡ 1 0 ⎤ ⎡1 −2 ⎤
(c) ⎢
(d) ⎢
⎥ ⎢0 3 ⎥
⎥⎢
⎥
⎦
⎣3 1 ⎦ ⎣ 0 1 ⎦
⎣2 1⎦ ⎣
[
D
L
Fill in the Blanks
⎡6 2 ⎤
⎢ 1 −1⎥
⎣
⎦,
]
R
O
2
then 2 A − 8 A − 16I = _______________
11.
If A =
12.
If the eigen values of A are 1, -1 and 2, then the eigen values of adj A are___________
⎡1
⎢0
⎢
⎢0
⎢
⎣0
W
U
1 1 0⎤
0 1 0⎥
⎥
1 1 1⎥
⎥
1 0 1⎦
13.
The rank of the matrix
14.
The system of equations 3x + y + 2z = 3, 2x – 3y – z = –3, x + 2y + z = 4 will have________
15.
If A is of order 3X4, and the rank of A is 2, then the number of independent solutions of AX = o
are __________
16.
17.
18.
19
20.
T
N
J
The eigen values of
⎛1 0 ⎞
⎜
⎜ 2 −1⎟
⎟
⎝
⎠
is___________
are ____________
The eigen vector corresponding to λ = 1 of
⎡ 1 0 − 1⎤
⎢1 2
1⎥
⎢
⎥
⎢2 2
3⎥
⎣
⎦
is _____________
The system of equations x + 2y = 5, –2x + ay = 4 are consistent if _________
The eigen vector corresponding to λ = 2 of
The eigen values of the matrix
⎛ 1 1⎞
⎜
⎜ 1 1⎟
⎟
⎝
⎠
⎡ 1 2 − 1⎤
⎢0 2
2⎥
⎢
⎥
⎢0 0 − 2 ⎥
⎣
⎦
are ___________
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is ______________

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Code No: A109100203
Set No. 3
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
I B.Tech. I Mid Examinations, December – 2010
MATHEMATICAL METHODS
Objective Exam
Name: ______________________________ Hall Ticket No.
A
Answer All Questions. All Questions Carry Equal Marks. Time: 20 Min. Marks: 10.
I.
Choose the correct alternative:
1.
If A is a matrix of order m × n and m < n then the rank of A is
(a)
m
(b)
n
(c)
≤ m (d)
>m
⎡1 2 3 ⎤
If the rank of the matrix ⎢ 4 5 x ⎥ is 2 then x =
⎢
⎥
⎢3 3 4⎥
⎣
⎦
2.
(a) 2
3.
4.
5.
(b) 3
R
O
⎡5 2 ⎤
The characteristic equation of ⎢
⎥ is
⎣3 1 ⎦
2
2
2
(a) λ + 6λ + 1 = 0 (b) λ − 6λ − 1 = 0
(c) λ + 6λ − 1 = 0
W
U
[
]
⎡ −1⎤ ⎡ 2⎤
J
(b) ⎢ ⎥ ⎢ ⎥
⎣ 1 ⎦ ⎣0⎦
[
1
]
]
⎡ −1⎤ ⎡ 3 ⎤
⎡1⎤ ⎡ 2 ⎤
(d) ⎢ ⎥ ⎢ ⎥
⎣ 1 ⎦ ⎣ −1⎦
(c) ⎢ ⎥ ⎢ ⎥
1 1
⎣ ⎦⎣ ⎦
The rank of the matrix
(a)
]
[
T
N
[
(d) λ 2 − 6λ + 1 = 0
⎡8 −4 ⎤
The eigen vectpors of ⎢
⎥ are
⎣2 2 ⎦
⎡ 1 − 1 2⎤
⎢2
2 2⎥
⎥
⎢
⎢ 3 − 3 6⎥
⎣
⎦
7.
D
L
(d) 5
]
If A is a matrix of order 3 × 3 and X is 3 × 1 then the system of equations AX = 0 will have only
trivial solution if the rank of A is
[
]
(a) > 3
(b) < 3
(c)
1
(d)
3
⎡ −1⎤ ⎡ 2 ⎤
(a) ⎢ ⎥ ⎢ ⎥
⎣ 1 ⎦ ⎣ −1⎦
6.
(c) 7
[
is
(b)
0
(c)
2
(d)
3
If there are 4 equations in two unknowns and the rank of the coefficient matrix is 2. then the system
will have
[
]
(a) Uniquie solution
(b)
Infinite number of solutions
(c)
Two solutions
(d)
No Solution
Cont….2
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Code No: A109100203
8.
9.
1
(b)
If A =
⎡1 0 −1⎤
⎢0 2 3 ⎥ ,
⎢
⎥
⎢0 0 4 ⎥
⎣
⎦
2
(c)
3
(d)
[
(b) - 1, - 2, - 4
1 1 0⎤
0 1 0⎥
⎥
1 1 1⎥
⎥
1 0 1⎦
]
[
]
4
D
L
(c) 1, 4, 8
(d) 1,
1 1
,
2 4
R
O
Fill in the Blanks
⎡1
⎢0
⎢
⎢0
⎢
⎣0
]
[
then the eigen values of A−1 are
(a) 1, 2, 4
II
Set No. 3
⎡ 1 −2 ⎤
LU decomposition of ⎢
⎥ is
⎣ −1 4 ⎦
⎡ 1 0 ⎤ ⎡ 1 −2 ⎤
⎡ 1 0 ⎤ ⎡ 1 −2 ⎤
(a) ⎢
b) ⎢
⎥ ⎢0 1 ⎥
⎥⎢
⎥
⎣ −1 1 ⎦ ⎣ 0 2 ⎦
⎣ −1 0 ⎦ ⎣
⎦
⎡ 1 0 ⎤ ⎡1 −2 ⎤
⎡1 0 ⎤ ⎡1 −2 ⎤
(c) ⎢
(d) ⎢
⎥ ⎢0 3 ⎥
⎥⎢
⎥
⎣2 1⎦ ⎣
⎦
⎣3 1 ⎦ ⎣ 0 1 ⎦
⎡ 2 −1 3⎤
If the rank of the matrix ⎢ x 2 1 ⎥ is 2 then x =
⎢
⎥
⎢ 1 −4 5⎥
⎣
⎦
(a)
10.
:2:
W
U
11.
The rank of the matrix
12.
The system of equations 3x + y + 2z = 3, 2x – 3y – z = –3, x + 2y + z = 4 will have________
13.
If A is of order 3X4, and the rank of A is 2, then the number of independent solutions of AX = o
are __________
14.
15.
16.
17.
18.
is___________
T
N
J
The eigen values of
⎛1 0 ⎞
⎜
⎜ 2 −1⎟
⎟
⎝
⎠
are ____________
The eigen vector corresponding to λ = 1 of
⎡ 1 0 − 1⎤
⎢1 2
1⎥
⎢
⎥
⎢2 2
3⎥
⎣
⎦
is _____________
The system of equations x + 2y = 5, –2x + ay = 4 are consistent if _________
The eigen vector corresponding to λ = 2 of
The eigen values of the matrix
⎡6 2 ⎤
⎢ 1 −1⎥
⎣
⎦,
⎛ 1 1⎞
⎜
⎜ 1 1⎟
⎟
⎝
⎠
⎡ 1 2 − 1⎤
⎢0 2
2⎥
⎢
⎥
⎢0 0 − 2 ⎥
⎣
⎦
is ______________
are ___________
2
then 2 A − 8 A − 16I = _______________
19.
If A =
20.
If the eigen values of A are 1, -1 and 2, then the eigen values of adj A are___________
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Code No: A109100203
Set No. 4
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
I B.Tech. I Mid Examinations, December – 2010
MATHEMATICAL METHODS
Objective Exam
Name: ______________________________ Hall Ticket No.
A
Answer All Questions. All Questions Carry Equal Marks. Time: 20 Min. Marks: 10.
I.
1.
2.
3.
Choose the correct alternative:
If A is a matrix of order 3 × 3 and X is 3 × 1 then the system of equations AX = 0 will have only
trivial solution if the rank of A is
[
]
(a) > 3
(b) < 3
(c)
1
(d)
3
⎡8 −4 ⎤
The eigen vectpors of ⎢
⎥ are
⎣2 2 ⎦
⎡ −1⎤ ⎡ 2 ⎤
(a)
5.
6.
(b) ⎢ ⎥ ⎢ ⎥
⎣ 1 ⎦ ⎣0⎦
T
N
The rank of the matrix
⎡ 1 − 1 2⎤
⎢2
2 2⎥
⎥
⎢
⎢ 3 − 3 6⎥
⎣
⎦
J
1
⎡1⎤ ⎡ 2 ⎤
(c) ⎢ ⎥ ⎢ ⎥
1 1
⎣ ⎦⎣ ⎦
]
[
]
[
R
O
[
]
(d) λ 2 − 6λ + 1 = 0
W
U
⎡ −1⎤ ⎡ 2⎤
(a) ⎢ ⎥ ⎢ ⎥
⎣ 1 ⎦ ⎣ −1⎦
4.
D
L
⎡5 2 ⎤
The characteristic equation of ⎢
⎥ is
⎣3 1 ⎦
2
2
2
(a) λ + 6λ + 1 = 0 (b) λ − 6λ − 1 = 0
(c) λ + 6λ − 1 = 0
⎡ −1⎤ ⎡ 3 ⎤
(d) ⎢ ⎥ ⎢ ⎥
⎣ 1 ⎦ ⎣ −1⎦
is
(b)
0
(c)
2
(d)
3
If there are 4 equations in two unknowns and the rank of the coefficient matrix is 2. then the system
will have
[
]
(a) Uniquie solution
(b)
Infinite number of solutions
(c)
Two solutions
(d)
No Solution
⎡ 1 −2 ⎤
LU decomposition of ⎢
⎥ is
⎣ −1 4 ⎦
⎡ 1 0 ⎤ ⎡ 1 −2 ⎤
⎡1
(a) ⎢
b) ⎢
⎥ ⎢0 1 ⎥
⎣ −1 0 ⎦ ⎣
⎦
⎣ −1
⎡ 1 0 ⎤ ⎡1 −2 ⎤
⎡1
(c) ⎢
(d) ⎢
⎥ ⎢0 3 ⎥
⎣2 1⎦ ⎣
⎦
⎣3
[
]
0 ⎤ ⎡ 1 −2 ⎤
1 ⎥ ⎢0 2 ⎥
⎦⎣
⎦
0 ⎤ ⎡1 −2 ⎤
1 ⎥ ⎢0 1 ⎥
⎦⎣
⎦
Cont…..2
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Code No: A109100203
7.
:2:
Set No. 4
⎡ 2 −1 3⎤
If the rank of the matrix ⎢ x 2 1 ⎥ is 2 then x =
⎢
⎥
⎢ 1 −4 5⎥
⎣
⎦
(a)
1
(b)
2
(c)
3
(d)
[
]
[
]
[
]
[
]
4
⎡1 0 −1⎤
8.
If A = ⎢0 2 3 ⎥ , then the eigen values of A−1 are
⎢
⎥
⎢0 0
⎣
4⎥
⎦
(a) 1, 2, 4
9.
10.
(b) - 1, - 2, - 4
11.
12.
13.
14.
15.
16.
(d) 1,
If A is a matrix of order m × n and m < n then the rank of A is
(a)
m
(b)
n
(c)
≤ m (d)
>m
⎡1 2 3 ⎤
If the rank of the matrix ⎢ 4 5 x ⎥ is 2 then x =
⎢
⎥
⎢3 3 4⎥
⎣
⎦
(a) 2
II
(c) 1, 4, 8
(b) 3
1 1
,
2 4
D
L
R
O
(c) 7
(d) 5
Fill in the Blanks
W
U
If A is of order 3X4, and the rank of A is 2, then the number of independent solutions of AX = o
are __________
The eigen values of
⎛1 0 ⎞
⎜
⎜ 2 −1⎟
⎟
⎝
⎠
are ____________
T
N
The eigen vector corresponding to λ = 1 of
J
⎡ 1 0 − 1⎤
⎢1 2
1⎥
⎢
⎥
⎢2 2
3⎥
⎣
⎦
is _____________
The system of equations x + 2y = 5, –2x + ay = 4 are consistent if _________
The eigen vector corresponding to λ = 2 of
The eigen values of the matrix
⎡6 2 ⎤
⎢ 1 −1⎥
⎣
⎦,
⎛ 1 1⎞
⎜
⎜ 1 1⎟
⎟
⎝
⎠
⎡ 1 2 − 1⎤
⎢0 2
2⎥
⎢
⎥
⎢0 0 − 2 ⎥
⎣
⎦
is ______________
are ___________
2
then 2 A − 8 A − 16I = _______________
17.
If A =
18.
If the eigen values of A are 1, -1 and 2, then the eigen values of adj A are___________
⎡1
⎢0
⎢
⎢0
⎢
⎣0
1 1 0⎤
0 1 0⎥
⎥
1 1 1⎥
⎥
1 0 1⎦
19.
The rank of the matrix
is___________
20.
The system of equations 3x + y + 2z = 3, 2x – 3y – z = –3, x + 2y + z = 4 will have________
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