GATE MA kind:question PYQs & Answers — Page 23

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Questions 221–230 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 23 of 65

Let

be the solution of

for some positive real number

. Let the domain of dependence of the solution

at the point

be the line segment on the

-axis with end points

and

. If the area of the triangle

is 8 square units, then the value of

is __________.

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Let

for all

in some neighbourhood of

. Then the value of

is equal to __________.

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Let

. If

is the interpolating polynomial of degree less than or equal to 4 for the data

then the value of

is ____________.

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For a fixed

, let

. If the value of

obtained by using the Trapezoidal rule is equal to

, then the value of

is __________ (rounded off to 2 decimal places).

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If for some

then the value of

equals ______.

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Let

be the portion of the plane

which lies inside the cylinder

. If the surface area of

, then the value of

is equal to __________.

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Let

and the norm

for

. Let

be defined by

denotes the norm of the linear functional

, then

is equal to _________.

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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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