GATE MA format:nat PYQs & Answers — Page 3

Questions 21–30 of 222. Imported answers require independent review unless marked reviewed.

Topic practice 222 questionsPage 3 of 23

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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Consider the inner product space of all real-valued continuous functions defined on

with the inner product

. If

is orthogonal to all the polynomials having degree less than or equal to

, with respect to this inner product, then

is equal to _____ (in integer)

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For

, consider the quadratic form:

Let

be the symmetric matrix associated with the quadratic form

with respect to the standard basis of

. Let

be a non-zero vector, and let

where

is the

identity matrix. Then, the value of

is _____ (in integer)

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GATE MA format:nat PYQs

Question 28

Question 29

Question 30

Question 31

Question 32

Question 33

Question 34

Question 35

Question 61

Question 62