GATE MA 2023 Paper 1 — page 19

Questions 55–57 of 65. Imported answers require review unless explicitly marked reviewed.

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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2023 · Paper 1

Question 55

Question 56

Question 57