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GATE 2019: Engineering Mathematics Champion Test 2
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Question 1
Let S be the set of points in the complex plane corresponding to the unit circle. (That is, S = {z : |z| = l}). Consider the function f(z)=zz* where z* denotes the complex conjugate of z. The f(z) maps S to which one of the following in the complex plane
Question 2
The differential equation whose solution is Ax2 + By2 = 1 where A and B are arbitrary constants, is of
Question 3
At t = 0, the function f (t) = 
has
has Question 4
If the Laplace transform of f(t) is w/(
then the value of
is
then the value of is Question 5
The ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students doubled in 2009, by what percent did the number of male students increase in 2009?
Question 6
Consider the following equations
3x – y – z + 2w = 0
3x + y – z – 2w = 0
12x + 3y – 4z – 6w = 0
The system of equations will be
3x – y – z + 2w = 0
3x + y – z – 2w = 0
12x + 3y – 4z – 6w = 0
The system of equations will be
Question 7
The value of 
where C is the contour 
is
where C is the contour is Question 8
For the function f(x) = x2e-x, the maximum occurs when x is equal to:
Question 9
A United Airlines flight has 10 seats (a very small aircraft). The probability that any passenger will not show up is 0.6. This causes United Airlines to overbook and sell more tickets than the numbers of seats to increase profit/minimize loss. So if United Airlines sells 12 tickets for the flight, what is the probability that at least one passenger will have to be asked to leave (since you can’t stand onboard a plane)?
Question 10
Find the inverse fourier transform of x (ω) = 3πδ (ω-π) + δ (ω-2π) -2πδ (ω -3π)|?
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Sep 10ESE & GATE EE
