Punjab Technical University 2009-1st Sem B.Tech <>EnggMathematics -I (AMA-101) (_ 2nd) << >> - Question Paper

Roll No.

(Total No*, of Pages : 02

Jotal No. of Questions : 091

Paper ID [A0119]

(Phrase I1H this Paper II) in OMR Shed)

B.Tcch. (Sent. - I^4,/2^nd) ENGINEERING MATHEMATICS - II (AM - 102)

Roll No.

(Total No*, of Pages : 02

Jotal No. of Questions : 091

Maximum Marks: 60

Time: 03 Hours Instruction to Candidates:

1)    Section - A is Compulsory.

2)    Attempt any Five questions from Section - B & C.

3)    Select at least Two questions from Section - B & C.

Section - A

(2 Marks Each,)

a)    Are the solutions= cos x & y = sin jc, linearly independent.

b)    Explain Hcrmitian matrix with suitable example.

c)    Is the dilTerential eg. (yV^r + 4x^ydx+[2xye'' -3y²)</v=0, exact?

d)    Find the Particular Integral of - + 4- sin 2a-.

dx dx

e)    Explain the technique of Bernoullis linear equation.

f)

g)    Evaluate div[3.v²/ +5xy^zj+xyz*k] al the point (1, 2, 3).

h)    From a pack of 52 cards, three cards arc drawn at random. Find the chance that they are a king, a queen and a jack.

i)    A variate X lias following probability distribution

X	-3	6	9
P(X)	%	Vl	'X

Evaluate E(X²). j) Explain confidence limits of sampling.

1    4

2    3

express A⁵ - 4A⁴ - 7A³ + 11 A² - A - 10 I as a linear polynomial in A.

Q3) Solve (xy³ + y)dx + 2(x²y² + x + y⁴)dy = 0.

Q4) Solve y"-2y'+y=e' logx, using method of variation.

Q5) A particle is executing simple harmonic motion with amplitude 20 cm and time 4 seconds. Find the time required by the particle in passing between points which arc at distances 15 cm and 5 cm from the centre of force and arc on the same side of it.

Section - C

(8 Marks Each)

Q6) Find the work done in moving a particle in the force field F=3.v²/ + (2xy-y)j + 3k along

(a)    the straight line from (0, 0, 0) to (2, 1, 3);

(b)    the curve x² = 4y, 3x² = 8z from x = 0 to x = 2.

Q7) Evaluate J[(a-² + xy)dx+(x² + v²V/>^!], where C is the square formed by the lines <

X = i,y = [.

Q8) A car hire firm has two cars which it hires out day to day. The number of demands for a car on each day is distributed as a Poisson distribution with mean 1.5. Calculate the proportion of days

(a)    on which there is no demand,

(b)    on which demand is refused. (e~^ls ~ 0.2231).

Q9) Two random samples from two normal populations are given as :

Sample I	16	26	27	23	24	22
Sample II	33	42	35	32	28	31

Do the estimates of population variances differ significantly?

DoF	(5,5)	(5, 6)	(6, 5)
	5.05	4.39	4.95

Attachment: punjab-technical-university-2009-b-tech-23817-1.pdf

Earning:   Approval pending.