2007 Janardan Rai Nagar Rajasthan Vidyapeeth B.Tech Electrical Engineering B-tech Examination University Question paper
BIT - III TOTAL PAGES: 03
BACHELOR IN TECHNOLOGY
BSAE1/BSBT1/BSCH1/BSC1/BSCO1/BSE1/BSET1/BSMR1/BSM1/BSMI1/BSMT1- MATHEMATICS - III
TIME: 03 HOURS MAX. MARKS: 75
1. Question paper is divided into three groups
2. Each group is of 25 marks each
3. Figure to the right in bracket indicates mark
4. Assume suitable data if necessary
GROUP A: Answer any three questions. Question No. 1 is compulsory.
Q.1 Solve x(y2 + z2) p + y (z2 + x2) q = 2 (y2 – x2)? (05)
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)
Q.5 State and prove final value theorem and convolution theorem ? (10)
GROUP B: Answer any three questions. Question No. 6 is compulsory.
Q.6 Calculate the Laplace transform of the following (05)
a) Unit step function b) Impulse Function
Q.7 Solve dy/dx =y-x2 with Y(0) =1, by picard's 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 n x,
U(o, t) = 0 = uc(t) 00? (10)
Q.9 Solve the partial differential equation ? 2u =-10 ( x2 +y2 +10) (10)
over the square with sides x=0 =y, x= 3=y with u =0 on the boundary and mesh length =1.
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 (10)
GROUP C: All Questions are Compulsory.
Q.11 Fill in the blanks (each question carries 2 marks)
(i) If f(x,y,z)= 0 then ?x/?y . ?y/?z . ?z/?x = --------------.
(ii) If z = f ( x , y) then ?x is known as ------------ error.
(iii) If u & v are the functions of x & y , then ?( u , v) / ? ( x , y) X ? ( x , y) / ? ( u , v) = --------.
(iv) ? (x , y)/ ? ( r, ?) X ? ( r, ?) / ? ( x, y) = ---------.
(v) L[ eat tn] = ---------.
Q.12 Multiple choice question. (Each question carries 2 marks)
(i) The partial differential equation of all spheres whose centre lies on z- axis is
(a) py =qx (b) p =qx (c) py =q (d)py -qx
(ii) If f(x) = x sin x in (-? , ?) ,then value of bn =
(a) 1 (b) 0 (c) 2 (d)-1
(iii) The equation of heat flow in one dimension is
(a) ?u/?t =c2 ?2u/?x (b) ?u/?t =c2 ?u/?x2
(c) ?u/?t =c2 ?2u/?x2 (d) ?u/?t =c ?2u/?x2
(iv) Laplace transform of (t sin t) is
(a) 2s/(1+ s) (b) s/(1+ s2)
(c) 2s/(1+ s2) (d) 2s/(1+ s2)2
(v) ?2u/?x2 + ?2u/?y2 = f(x,y) is known as
(a) Linear equation (b) Poisson equation
(c) Hyperbolic (d)Quadratic equation
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