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GATE 2023 Engg. Mathematics Quiz 2

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Question 1

If u = z logy + y logz + xyz, where x = sint, y=t²+ 1, z = cos^–1(t), then

at t = 0 is

Question 2

For real values of x, the minimum value of the function f(x) = e^x + e^-x is

Question 3

If c is the lower half of the circle centered at the origin of radius 3 with clockwise rotation so the value of

is ______.

Question 4

If f(x, y) = e^xy – x² + y³ and c is the curve shown below, Then

Question 5

The Newton-Raphson iteration

can be used to solve the equation

Question 6

A and B throw alternatively a pair of dice . A wins if he throws 6 before B throws 7 and B wins if he throws 7 before A throws 6 . If ‘A’ starts the game, then the probability that B wins the game is

Question 7

Let C be the triangular path connecting the points (0, 0), (2, 2) and (0, 2) in the counter clock wise direction then

is equal to______.

Question 8

The value of

is ______.

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