APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY Previous Years Question Paper & Answer

Course : B.Tech

Semester : SEMESTER 3

Year : 2019

Term : MAY

Scheme : 2015 Full Time

Course Code : MA 201

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C1100 Pages: 2

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‎f@) = 7൭ = tanz‏ رم

‎E 27 4.
valuate So 5-36

‎Evaluate ‏ع‎ 1092707 where C is the circle |z| = 1

‎00 x?

‎Evaluate |

‎-ഠ (x24+1)(x24+4)
PART C

‎Answer any two full questions, each carries 20 marks

‎1 2 3 4
Fi ಸ 12 1 4 5
ind the rank of the matrix 15 5 7

‎8 1 14 17

‎Find the values of a and b for which the system of linear equations
x+2y+3z = 6,x+3y+5z = 9,2x+5y + az =b has (i) no solution
(ii) a unique solution (iii) infinitely many solutions

‎Show that the vectors[3 4 0 1], [2 -1 3 5] and [1 6 -8 -2]
are linearly independent in ೧5,

‎Solve the system of equations by Gauss Elimination Method:
3x + 3} + 22 = 1, > + 2) = 4, 109 + 32 = -2, 22८ - 3) - 2 = 5
Find the nature, index, rank and signature of the quadratic form

‎ऋ + 22 + 3x2 + 22122 - 22123 + 22223

‎4 2 -2
Find the Eigen values and Eigen vectors of | 2 5 0 |
-2 0 3

‎2 -1 1
Diagonalize the matrix ಗೆ = | -1 2 -1
1 -1 2

‎Define symmetric and skew symmetric matrices. Show that any real square
matrix can be written as the sum of a symmetric and a skew symmetric matrix.

‎What type of conic section is represented by the quadratic form

‎3x?+22xy+3y” = 0 by reducing it into canonical form.

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