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# GATE 2023 Engg. Mathematics Quiz 5

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Question 1

If A3×3 is any real matrix such that lAl = 24, trace of ‘A’ = 9 and one of the eigen values is ‘2’ then trace of Adj A = _____?

Question 2

The value of integral where C is the circle |z| = 1, will be_________.

Question 3

If u = sin (x2 + y2) where a2x2 + b2y2 = 1 & x and y both are variable then value of (du/dx) will be?

Question 4

If f(x)= ,then the points of local maxima for the function f(x) are

Question 5

Find the value of limit Question 6

The coefficient of in the Taylor series expansion of about the point x = 1 is

Question 7

The value of the contour integral evaluated over the unit circle |z| = 1 is _____________.

Question 8

Consider the system of equations given below:
4x – ay – z = 0
ax + 8y – az = 0
3x + 2y – z = 0

If the system of equation has only trivial solution, then which of the following is true?
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