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Gate CE 2021: Subject Revision Quiz 11 (App update required to attempt this test)

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Question 1

Which of the following statements are correct?

a) Taylor series of a function can be expanded only when f(z) is analytic about z = a

b) Laurent series of a function can be expanded even if f(z) is not analytic about z = a

c) Taylor series of a function can be expanded irrespective of f(z) is analytic or non-analytic about z = a

d) Laurent series of a function can be expanded only when f(z) is analytic about z = a

Question 2

then

Question 3

then

will be:

Question 4

The condition for which the eigen values of the matrix

are positive, is

Question 5

A fair coin is tossed independently five times. The probability of the event "the number of times tails show up is less than the number of times heads show up” is

Question 6

There are 3 fair coins and 1 false coin with tails on both sides. A coin is chosen at random and tossed 4 times. If ‘tails’ occurs in all 4 times, then the probability that the false coin has been chosen for tossing is ___.

Question 7

The given eigen values of the following matrix are represented by

and

The value of

is ___.

Question 8

The integral $Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE-ME-2014-Set-1_files\image063.png$ is evaluated along the circle $Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE-ME-2014-Set-1_files\image064.png$ traversed in counter clockwise direction. The integral is equal to

Question 9

Using Gauss- Seidel method , starting form [0,0,0] x₁+ x₂ – x₃ = 1, x₁+ 4x₂ + x₃ =15, 3x₁+ 2x₂+ 3x₃= 20 Find (2x₃+ x₂ – x₁) after two iterations approximately.

Question 10

The area of the plane region bounded by the curves and x+3y²=1 is equal to ____ sq. units.