Thapar University 2007 B.E ENGINEERING MATHEMATICS - Question Paper

THAPAR UNIVERSITY,PATIALA
B.TECH(DISTANCE EDUCATION),SEPTEMBER 2007
ENGINEERING MATHEMATICS

Thapar University , I'utiala B. Tech (Distance Education) Examination, September, 2007 Engineering Mathematics) MA 001D)

Time Allowed = 3 Hours    Maximum Marks : 10

Note : All the question¹. all compulsory.

Ql. (a) Graph the following function. Discuss ill [lie salient features also. x^J 4 '^V~ x⁷~2'

(b) Identify the symmetry and sketch the following polar curve:

. e

;=sin.

2

. . . <⁸⁺⁸> Q2. (a) For the following function, find the direction in which the function increase and decrease most rapidly at the given point P. Also find the derivative in these direction.

/(I. In,2,, ).

(b) For the function j{x,y)= + xv + y²-G.r, find the absolute maxima and minima on the rectangular plate 0 < _r i-5, - 3 v <, 3.

. . . . (⁴⁺¹²> Q3. (a) Find (the Particular solution for following differential equation using operator method.

y - y' + y = x^s -3.v^! + I.

(b) Find the complete solution of the following differential equation:

(x⁷ -1)V^,-2at+2.v' = {x¹ -1)³

(6+10)

Q4. (a) Define row reduced echelon form and tise it to examine whether the following system of equations is consistent or not, if yes find its solution 2*. 4- jc, + 2.v, = I *,+*,=0 jc, - 2.r₂ + 6,i, = 3

x,~2x_t -\    ¹

jt, - x, + 4jc, = 2

Q5. (a) Slate and prove convolution theorem and lienee fimi L

+ I)

(b) Find the Fourier Series of the function /'(v) = .v + x¹, ~n <x< K

06. (i) (a) Examine the function f(.\) = .v - 3.r + 3, x e 'Ji anil

(b) j\x) = sin* jc, 0 < x < it for maximum and minimum values.

.v (J < j: < I 0 ,r = l

differentiable on (01), but its derivative on (0, I) is never zero, llow can this be? Doesnt Rollcs theorem say the derivative.h;is to be zero somewhere in (0,1)? Give reasons for your answer.

(iii)    rind the values uf and ut thepoim (4, *5) if /(*, y) =jc^a + 3*)' + y - I.

dr ay

d\v . Ow .    ,

(iv)    Express and in terms of r and s if w = x + y ; x = r - 2s v = r + 2s

dr as

(v)    Solve the following first order differential equation: dx + (3x- e~^ls )dv = 0.

(vi)    Solve the following liuler-Cauchy equation : 2.* V'+IO.vy'+Sj,' = ().

(vii)    Find Lel

(viii)    f-'ind L\e'~^Au(t - 4)J

(ix)    Determine the eigen values of 4 =

(x) Write the matrix A -symmetric matrix.

(2 x 10)

Attachment: thapar-university-2007-b-e-25943-1.pdf

Earning:   Approval pending.