GATE MA kind:question PYQs & Answers — Page 10

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Questions 91–100 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 10 of 65

Let

be a function defined by

Consider the following three statements:

S1:

exists.

S2:

exists.

S3:

exists.

Then, which of the following is/are correct?

Your answerSelect all correct options. You can choose more than one.

S2 and S3 are TRUE and S1 is FALSE

S1 and S2 are TRUE and S3 is FALSE

S1 and S3 are TRUE and S2 is FALSE

S1, S2 and S3 all are TRUE

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Let

be a

matrix with entries in

and having the characteristic polynomial

Let

, where

is the

identity matrix. If

is the minimal polynomial of

, then

is equal to _____ (in integer)

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Let

be the unique polynomial of degree

satisfying the Legendre differential equation

Then, the value of

is equal to _____ (in integer)

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Let

be a unit vector parallel to the tangent at the point

to the curve of intersection of the surfaces

and

. Then, the absolute value of the directional derivative of

in the direction of

is _____ (in integer)

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The volume of the region bounded by the cylinders

and

is _____ (rounded off to TWO decimal places)

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Let

be the vector space (over

) consisting of all bounded real-valued solutions of the differential equation

Then, the dimension of

is _____ (in integer)

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Let

be a vector field, and let

be the surface

. If

denotes the unit outward normal vector to

, then the value of

is equal to _____ (in integer)

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Consider

where

is oriented positively as a simple closed curve. Then, the value of

is equal to _____ (in integer)

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Let

be such that the quadrature formula

is exact for all polynomials of degree less than or equal to 3. Then,

is equal to _____ (in integer)

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Let

be the solution of the initial value problem

. Using Euler’s method, with the step-size

, the approximate value of

is equal to _____ (in integer)

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