Jaypee Institute of Information Technology (JIIT) 2008 B.E test 3: mathematics 1 - Question Paper

JAYPEE UNIVERSITY OF INFORMATION TECHNOLOGY

WAKNAGHAT

TEST-3 1 SEMESTER 2008

COL'RSECODE : 07BUMA10I MAXM.T1MF: :I1IRS30MIN

COURSE NAME MATHEMATICS-I

COURSE CREDIT 4    MAXM. MARKS: 30

Note: All questions are compulsory.

]. Reducc the quadratic form 3*^! + 5y* +32^r -2>-z + 2-2xy to the canonical form and specify the matrix of transformation.

(5)

2. Solve the following system of equations by Gauss elimination method : x + y + r 6, x - y ^- 2z 5, 3x + y + z 8 .

(5)

d{r.O)

>yY O)

4. (i) Show that

(ii) If uF Vv. where u and v are scalar fields and 7 is a vector field, show that

Avr* 0.

(5)

5. Find the eiyen value and eigen vectors of the matrix.

6 -2 2 -2 3 -1 2-1 3

(4)

6. Find ()

[s² * A

7. Using Laplace transformation, solve

f-3 ₊ 2y-4e\ y(0) = -3. ,v'(0)=5.

(4)

Attachment: jaypee-institute-of-information-technology--jiit--2008-b-e-21264-1.jpg

Earning:   Approval pending.