Janardan Rai Nagar Rajasthan Vidyapeeth 2007 B.Tech Electrical Engineering B-tech - Question Paper
Tuesday, 14 May 2013 10:50Web
BIT - III TOTAL PAGES: 03
BACHELOR IN TECHNOLOGY
SEMESTER –III)(COMMON)
BSAE1/BSBT1/BSCH1/BSC1/BSCO1/BSE1/BSET1/BSMR1/BSM1/BSMI1/BSMT1- MATHEMATICS - III
TIME: 03 HOURS MAX. MARKS: 75
GENERAL INSTRUCTIONS:
1. Question paper is divided into 3 groups
2. Each group is of 25 marks every
3. Figure to the right in bracket shows mark
4. Assume suitable data if necessary
GROUP A: ans any 3 ques.. ques. No. one is compulsory.
Q.1 Solve x(y2 + z2) p + y (z2 + x2) q = two (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 described beneath uct = where T = (10)
Q.3 The temperature ‘u’ is maintained at 00 c along the 3 edges of a square plate of Length 100 cm and 4th edge is maintained at a constant temperature ‘u0’ until Steady state conditions prevails. obtain an expression for the temperature ‘u’ at any Point (x,y) . compute the temperature at the centre of the plate. (10)
Q.4 (a) describe Dirac-delta function (b)
Q.5 State and prove final value theorem and convolution theorem ? (10)
GROUP B: ans any 3 ques.. ques. No. six 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 obtain the
value of Y(0.1), y (0.2) , y(0.3) (10)
Q.8 Solve the formula with conditions u(x,0) = three sin n x,
U(o, t) = 0 = uc(t) 0
Q.9 Solve the partial differential formula ? 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. calculate the Jacobains J= ?’ (x, y)/ ?(u,v) and
J= ?’ (u, v)/ ?( x,y). Verify the outcome JJ’ =1 (10)
GROUP C: All ques. are Compulsory.
Q.11 Fill in the blanks (each ques. carries two 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 ------------ fault.
(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 option ques.. (Each ques. carries two marks)
(i) The partial differential formula 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 formula of heat flow in 1 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 formula
(c) Hyperbolic (d)Quadratic formula
| Earning: Approval pending. |
