GATE MA 2018 Paper 1 — page 14

Questions 40–42 of 65. Imported answers require review unless explicitly marked reviewed.

Which one of the following statements is true?

Your answerChoose one option.

Every group of order 12 has a non-trivial proper normal subgroup

Some group of order 12 does not have a non-trivial proper normal subgroup

Every group of order 12 has a subgroup of order 6

Every group of order 12 has an element of order 12

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For an odd prime

, consider the ring

. Then the element 2 in

Your answerChoose one option.

a unit

a square

a prime

irreducible

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Consider the following two statements:

P: The matrix

has infinitely many LU factorizations, where

is lower triangular with each diagonal entry 1 and

is upper triangular.

Q: The matrix

has no LU factorization, where

is lower triangular with each diagonal entry 1 and

is upper triangular.

Then which one of the following options is correct?

Your answerChoose one option.

P is TRUE and Q is FALSE

Both P and Q are TRUE

P is FALSE and Q is TRUE

Both P and Q are FALSE

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2018 · Paper 1