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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_________.
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
,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
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 _____________.
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?
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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