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GATE 2023 Engg. Mathematics Quiz 4
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Question 1
A fix faced dice is so biased that when thrown, it is twice as likely to show on even number than an odd number. If it is thrown thrice, The probability that sum of the numbers appeared is odd is
Question 2
The directional derivative of 
at the point (1, –1, 1) in the direction towards the point (–2, 4, 5) is______.
at the point (1, –1, 1) in the direction towards the point (–2, 4, 5) is______.Question 3
If the real part of the analytic function f(z) is given by e–x(cosy + siny), then the function f(z) will be
Question 4
Find the inverse Laplace Transforms of L-1{
}
} Question 5
Given 
, y(0) = 1
The value of y(0.1) using Runge-kutta second order method is (Take h = 0.1)
, y(0) = 1The value of y(0.1) using Runge-kutta second order method is (Take h = 0.1)
Question 6
While expanding 
in a laurent’s series valid for the region |Z| > 3 , the coefficient of Z-3 will be
in a laurent’s series valid for the region |Z| > 3 , the coefficient of Z-3 will be
Question 7
The directional derivative of f (x, y, z) =x2 - y2 +2z2 at P (1, 2, 3) in the direction of line PQ, where Q = (5, 0, 4), is ________.
Question 8
The joint density function of two continuous random variables X and Y is given by 
. Then what will be the probability P( X + Y < 3).
. Then what will be the probability P( X + Y < 3).
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