GATE MA format:nat PYQs & Answers — Page 7

Questions 61–70 of 222. Imported answers require independent review unless marked reviewed.

Topic practice 222 questionsPage 7 of 23

Let

be the solution of the initial value problem

, then the value of

is ______ (rounded off to 2 decimal places).

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Consider

with the inner product

, for

and

. Let

and

denote the orthogonal complement of

. The dimension of

is equal to ______.

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Let

and

. If

for some

, then the value of

is equal to __________.

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Let

be the curve of intersection of the cylinder

and the plane

. Suppose

is oriented in the counterclockwise direction and the

-axis, when viewed from above. If

then the value of

equals __________.

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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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GATE MA format:nat PYQs

Question 33

Question 34

Question 35

Question 55

Question 56

Question 57

Question 58

Question 59

Question 60

Question 61