Janardan Rai Nagar Rajasthan Vidyapeeth 2006 B.Tech Electrical and Electronics Engineering MATHEMATICS - III - Question Paper
JRN Rajasthan Vidyapeeth University
ELECTRICAL ENGINEERING
SEMESTER 3
MATHEMATICS - III
Model Question Paper
BSAE1-BSBT1-BSCH1- BSC1-BSCO1-BSE1-BSET1-BSMR1-BSM1- MATHEMATICS - III
Time : 3 hrs Maximum marks : 75
Instruction:
1. Question paper is divided into Group A, Group B and Group C
2. Each Group is 25 Marks
3. Figure to the right in bracket indicates marks.
4. Good Handwriting is expected
5. Assume suitable data if necessary.
Group A (25 Marks)
Answer any three questions (Question 1 is compulsory)
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Q.1 Solve x(y2 + z2) p + y (z2 + x2) q = 2 (y2 x2) ?
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Q.2 A sinusoidal voltage E sinwt is passed through a half-wave rectifier which clips the
negative portion of the wave. Expand the resulting periodic function UCT as farier
series defined below uct = where T =
(10)
Q.3 The temperature u is maintained at 00 c along the three edges of a square plate of
Length 100 cm and fourth edge is maintained at a constant temperature u0 until
Steady state conditions prevails. Find an expression for the temperature u at any
Point (x,y) . Calculate the temperature at the centre of the plate.
(10)
Q.4
(a) Define
Dirac-delta function (b)
(10)
Q.5 State and prove final value theorem and convolution theorem ?
Group B (25 Marks)
Answer any three questions (Questions 6 is compulsory)
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Q.6 Calculate the Laplace transform of the following
a) Unit step function b) Impulse Function
(10)
Q.7 Solve dy/dx =y-x2 with Y(0) =1, by picards method. Hence find the value of
Y(0.1), y (0.2) , y(0.3)
(10)
Q.8
Solve
the equation with
conditions u(x,0) = 3 sin nx,
U(o, t) = 0 = uc(t) 0<x<1 , t>0?
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Q.9 Solve the partial differential equation 2u =-10 ( x2 +y2 +10)
over the square with sides x=0 =y, x= 3=y with u =0 on the boundary and
mesh length =1.
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Q.10. If s= u(1-v), y=uv. Compute the Jacobains J= (x, y)/ (u,v) and
J= (u, v)/ ( x,y). Verify the result JJ =1
Group C (25 Marks)
All Questions are Compulsory.
Q.11 Fill in the blanks ( each question carry 2 marks)
1) If u = x 3 + x 3 + 3xy then u / x =________
2) L 1 (e at) =___________
3) For the fourier expansion of f(x), if f(x) is an even function then bn =______
4) If Z = x3 +y 3 /x2+y2 , then Z is a homogenous function of degree
5) 4 /4 is called ________ error.
________
Q.11 Multiple choice question. (Each question carry 2 marks)
1. One dimensional wave equation be _____________
a) b) c) d) None
2. The number of boundary conditions required to solve one dimensional heat equation.
a) 4 b) 3 c) 2 d) 7
3. = __________
a) b) c) d)
4.If u = sin 1 (x-y) then , y /x is ____
a)cos 1(x-y)
b)sin 1y
c)sin-1 x
d)none
5. L( 7 +75) is ________
a)7+5s /52
b)7/s + 5/ s2
c)7s +5 /s2
d)none
Q.11 True or false (each question carry 1 marks).
1.Two dimensions heat equation is also known as Laplace equation.
2.If f(x) = represents a triangular were with period 2a.
3. Convolution of two function are commutative.
4. If JJ=0 where J, J are Jocobian derivatives.
5. Singular solution is a solution which doesnt contain any arbitrary constants.
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Earning: Approval pending. |