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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______.

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 =x2-y2, y (0) =1 The 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

Question 7

The directional derivative of f (x, y, z) =x2 - y2 +2zat 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).
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