Jawaharlal Nehru Technological University Hyderabad 2010-1st Year B.Tech -\\Computer Science & Engineering\ regular\MATHEMATICAL METHODS set 4 - Question Paper
R09
SET-4
Code.No: 09A1BS04
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
I B.TECH – REGULAR EXAMINATIONS, JUNE - 2010
MATHEMATICAL METHODS
(COMMON TO EEE, ECE, CSE, EIE, BME, IT, ETE, E.COMP.E, ICE)
Time: 3hours Max.Marks:80
Code.No: 09A1BS04 R09 SET-4
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD I B.TECH - REGULAR EXAMINATIONS, JUNE - 2010 MATHEMATICAL METHODS (COMMON TO EEE, ECE, CSE, EIE, BME, IT, ETE, E.COMP.E, ICE) Time: 3hours Max.Marks:80
Answer any FIVE questions All questions carry equal marks
13 4 5 12 6 7
1.a) Find the Rank of the Matrix, by reducing it to the normal form
1 5 0 10
b) Find whether the following system of equations are consistent. If so solve them.
[7+8]
1 0 -1 1 2 1 2 2 3
[15]
2.
x + 2y + 2z = 2, 3x - 2y - z = 5, 2x - 5y + 3z = - 4, x + 4y + 6z = 0. Find the eigen values and the corresponding eigen vectors of
3. Reduce the quadratic form to the canonical form 3x2 + 2y2 + 3z2 - 2xy - 2yz
[15]
[8+7]
4.a) Prove that the newtons method has quadratic convergence.
b) Find y(5) given that y(0)=1, y(1)=3, y(3)=13, and y(8) = 123 using Lagranges formula.
[8+7]
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5.a) Find at x=7.5 from the following table. dx | |||||||||||||||||||||||||||||||||||||||||||||||||||||
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Using Eulers method, solve for y at x=2 from = 3 x2 +1, y (1) = 2 taking step size:
6.
dx
h = 0.5 h = 0.25.
a)
b)
[8+7]
[7+8]
7.a) Expand f(x)= cosx for 0 < x < n in half range sine series. b) Find cosine and sine series for f(x) = n - x in [0, n ].
8.a) Solve (mz - ny) p + (nx - lz)q = (ly - mx).
b) Solve (x2 - y2 - yz) p + (x2 - y2-zx) q = z(x - y).
[7+8]
-oOo-
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Attachment: |
| Earning: Approval pending. |
