GATE MA format:nat PYQs & Answers — Page 8 — Exam Papers

Questions 71–80 of 222. Imported answers require independent review unless marked reviewed.

Topic practice 222 questionsPage 8 of 23

For every

, let

be a polynomial of degree

with

. Further, let

satisfy the Legendre equation

If

for some positive integer

, then the value of

is ____________.

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Consider the ordinary differential equation (ODE)

If

and

are the roots of the indicial equation of the above ODE at the regular singular point

, then

is equal to ________ (rounded off to 2 decimal places).

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Let

be the solution of the non-homogeneous wave equation

Then the value of

is ____________ (rounded off to 2 decimal places).

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Consider the Linear Programming Problem P:

subject to

The optimal value of the problem P is equal to __________.

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The number of non-isomorphic abelian groups of order

is ________.

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The number of subgroups of a cyclic group of order

is ________.

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The radius of convergence of the series

is ________ (round off to TWO decimal places).

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The number of zeros of the polynomial

in the unit disc

is ________.

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If

is a polynomial of degree 5 and

where

are distinct points in the interval

, then the value of

is ________.

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The maximum value of

on the line

is _____.

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