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GATE 2023 Engg. Mathematics Quiz 4

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Question 1

is________.

Question 2

The real part of an analytic function is x3 – 3xy2 + 3x2 – 3y2, then the imaginary part of the function will be

Question 3

A bag contains 5 white balls and 7 black balls. Two balls are chosen at random from the bag (without replacement). What is the probability that one is white and the other is black?

Question 4

The value of β such that the given vector field is solenoidal will be:

Question 5

Find the work done in moving a particle in the force field  along a straight line from (0, 0, 0) to (1, 2, 3)

Question 6

The function satisfies the Lagrange’s Mean Value theorem in the interval (1,4) at a value of x=_________(rounded to two decimal places)

Question 7

If f(t)=, then the Laplace transform of f(t)

Question 8

The Newton-Raphson method is used to find the roots of the equation
f(x) = x – cos πx 0 ≤ x ≤ 1
If the initial guess for the root is 0.5, then the value of x after the first iteration is ______.
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