GATE Mathematics Pdf

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Q. 1 The distinct eigenvalues of the matrix
are [a i 3 (A) 0 and 1 (B) 1 and - 1 (C) 1 and 2 (D) 0 and 2
Q.2 The minimal polynomial of the matrix
is
(A) X(X -l)(x -6) (B) X(X-3)
Q.3 Which of the following is the imaginary part of a possible value of in(&) ?
Q.4 Let f : c -+ c be analytic except for a simple pole at z = 0 and let g :C -+C be analytic.
Res {f ( z ) d z ) )
Then, the value of '=O
Res f ( z ) z=o
is
Q.5 Let I = f (2 x' + $) dx + ey dy, where C is the boundary (oriented anticlockwise) of the region in
C
the first quadrant bounded by y = 0, x' + y' = 1 and x = 0. The value of I is
-
4.6 The series xl""', x > 0, is convergent on the interval
m=l
Q.7 While solving the equation x2 - 3x + 1 = 0 using the Newton-Raphson method with the initial
guess of a root as 1, the value of the root after one iteration is
(A) 1.5 (B) 1 (C) 0.5 (Dl 0

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