GATE MA topic:statistics PYQs & Answers — Page 26

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Questions 251–260 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 26 of 65

Let

. For a sequence

, define

Consider the subspace

. Let

denote the orthogonal complement of

in the Hilbert space

. Consider

If the orthogonal projection of

onto

is given by

for some

, then

equals __________.

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Consider the transportation problem between five sources and four destinations as given in the cost table below. The supply and demand at each of the source and destination are also provided:

Sources	P	Q	R	S	Supply
1	13	8	12	9	20
2	10	7	5	20	10
3	3	19	5	12	50
4	4	9	7	15	30
5	14	0	1	7	40
Demand	60	10	20	60

Let

and

be the total cost of the initial basic feasible solution obtained from the North-West corner method and the Least-Cost method, respectively. Then

equals __________.

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Let

, where

is the permutation group on 8 elements. Suppose

is the product of

and

, where

is a 4-cycle and

is a 3-cycle in

. If

and

are disjoint cycles, then the number of elements in

which are conjugate to

is __________.

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Let

be a

real matrix with

, where

and

is the

identity matrix. If

, then the trace of

is __________.

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Let

be a

real matrix such that

is the degree of the minimal polynomial of

, then

equals __________.

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Let

be the disk

with boundary

. If

is the solution of the Dirichlet problem

then the value of

is ____________.

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For every

, let

be a polynomial of degree

with

. Further, let

satisfy the Legendre equation

for some positive integer

, then the value of

is ____________.

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Consider the ordinary differential equation (ODE)

and

are the roots of the indicial equation of the above ODE at the regular singular point

, then

is equal to ________ (rounded off to 2 decimal places).

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Let

be the solution of the non-homogeneous wave equation

Then the value of

is ____________ (rounded off to 2 decimal places).

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Consider the Linear Programming Problem P:

subject to

The optimal value of the problem P is equal to __________.

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GATE MA topic:statistics PYQs

Question 56

Question 57

Question 58

Question 59

Question 60

Question 61

Question 62

Question 63

Question 64

Question 65