Janardan Rai Nagar Rajasthan Vidyapeeth 2006 B.Tech Chemical Engineering MATHEMATICS - III - Question Paper

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)

	(5)

 

Q.1 Solve x(y² + z²) p + y (z² + x²) q = 2 (y² x²) ?

	(10)

 

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)

	(5)

 

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?

	(10)

 

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.

	(10)

 

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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