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# GATE ME 2021 || Subject Revision Quiz 10 (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

If

then is

then is

Question 3

If 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 ___.

The value of is ___.

Question 8

The integral is evaluated along the circle traversed in counter clockwise direction. The integral is equal to

Question 9

Using Gauss- Seidel method , starting form [0,0,0]

x

x

3x

Find (2x

x

_{1}+ x_{2}– x_{3}= 1,x

_{1}+ 4x_{2}+ x_{3}=15,3x

_{1}+ 2x_{2}+ 3x_{3}= 20.Find (2x

_{3}+ x_{2}– x_{1}) after two iterations approximately.Question 10

The area of the plane region bounded by the curves and x+3y^{2}=1 is equal to ____ sq. units.

Question 11

is a Partial differential equation whose solution is given by

The value of K is

The value of K is

Question 12

Evaluate By Residue method

Question 13

The surface integral of + 3by + 4cz ) .N ds over the sphere given by x

^{2}+ y^{2}+ z^{2}= 4Question 14

The principle value of argument of complex number Z = 64i + (1 + i)

^{12}isQuestion 15

The work done in moving a particle in the force field along the curve defined by from y = 0 to y = 1 is ---------------------.

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Nov 19ESE & GATE ME

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