Download PTU B.Tech 2020 March Civil 3rd Sem M 54002 Applied Mathematics Ii Question Paper

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech Civil Engineering (CE) 2020 March 3rd Sem M 54002 Applied Mathematics Ii Previous Question Paper

1 | M-54002 (S1)-2835

Roll No. Total No. of Pages : 02
Total No. of Questions : 18
B.Tech. (ECE/IT/EEE/CSE/BT/Civil/ME/EE/EIE) (Sem.?2,3)
ENGG. MATHEMATICS-I/ENGG. MATHEMATICS-
II/MATHEMATICS-II/APPLIED MATHEMATICS-II/APPLIED
MATHEMATICS-III
Subject Code : AM-102/201
M.Code : 54002
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION - B & C. have FOUR questions each.
3. Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
4. Select atleast TWO questions from SECTION - B & C.

SECTION-A
Answer the following :
1) Are the vectors (1, 1, ?1), (2, 3, ?5), (2, ?1, 4) linearly dependent.
2) Find the eigen values of the matrix
3 2
2 3
? ?
? ?
? ?
.
3) Is the differential equation (2 xy cos x
2
? 2xy + 1) dx + (sin x
2
? x
2
)dy = 0 exact ?
4) Solve (2D
2
? 2D ?1) y = 0.
5) Write any two applications of differential equations.
6) Find velocity of a particle which moves along the curve 2sin 3 2cos3 8 r t i t j t k
? ? ? ?
? ? ? .
7) State Green?s theorem.
8) If
2 3 2 2
A 2 x z i y z j xy z k
? ? ? ?
? ? ? , then find (A) Div
?
at the point (1, ?1, 1).
9) Write formulae of mean and variance of binomial distribution.
10) Define null hypothesis.

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1 | M-54002 (S1)-2835

Roll No. Total No. of Pages : 02
Total No. of Questions : 18
B.Tech. (ECE/IT/EEE/CSE/BT/Civil/ME/EE/EIE) (Sem.?2,3)
ENGG. MATHEMATICS-I/ENGG. MATHEMATICS-
II/MATHEMATICS-II/APPLIED MATHEMATICS-II/APPLIED
MATHEMATICS-III
Subject Code : AM-102/201
M.Code : 54002
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION - B & C. have FOUR questions each.
3. Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
4. Select atleast TWO questions from SECTION - B & C.

SECTION-A
Answer the following :
1) Are the vectors (1, 1, ?1), (2, 3, ?5), (2, ?1, 4) linearly dependent.
2) Find the eigen values of the matrix
3 2
2 3
? ?
? ?
? ?
.
3) Is the differential equation (2 xy cos x
2
? 2xy + 1) dx + (sin x
2
? x
2
)dy = 0 exact ?
4) Solve (2D
2
? 2D ?1) y = 0.
5) Write any two applications of differential equations.
6) Find velocity of a particle which moves along the curve 2sin 3 2cos3 8 r t i t j t k
? ? ? ?
? ? ? .
7) State Green?s theorem.
8) If
2 3 2 2
A 2 x z i y z j xy z k
? ? ? ?
? ? ? , then find (A) Div
?
at the point (1, ?1, 1).
9) Write formulae of mean and variance of binomial distribution.
10) Define null hypothesis.

2 | M-54002 (S1)-2835

SECTION-B
11) Find the rank of the matrix
2 3 4
4 3 1
1 2 4
? ?
? ?
? ?
? ?
? ?
after converting into normal form.
12) Solve the differential equation
3
3 sin dy y x
dx x
x
? ? .
13) Solve the differential equation (D
2
+ 2D + 1) y = x.
14) Solve the differential equation (D
2
+ 4) y = tan 2x using method of variation of
parameters.

SECTION-C
15) Find the unit normal vector to the surface x
2
y + 2xz
2
= 8 at the point (1, 0, 2).
16) Verify Gauss divergence theorem for
2
F 4xz i y j yz k
? ? ? ?
? ? ? over the cube x = 0, x = 1,
y = 0, y = 1, z = 0, z = 1.
17) A box A contains 2 white and 4 black balls. Another box B contains 5 white and 7 black
balls. A ball is transferred from the box A to the box B. Then a ball is drawn from the box
B. find the probability that it is white.
18) A certain stimulus administered to each of 12 patients resulted in the following increases
of blood pressure : 5, 2, 8, ?1, 3, 0, ?2, 1, 5, 0, 4, 6. Can it be concluded that the stimulus
will in general be accompanied by an increase in blood pressure. (Given that for v = 11,
t
0.05
= 2.2)

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.
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