Question 73-79 of 216: Algebra (Section A: Common) | CUET (Common University Entrance Test) UG Mathematics Common (319) | Includes PYQs | Get Solutions with Detailed Explanations

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Question 73

Section A: CommonAlgebraAlgebra of Matrices

MCQ

Read the question, then carefully choose the correct answer(s).

Let a and b be two real numbers such that a > 1 , b > 1 , If A = ( a 0 0 b ) , then lim n ⇾ ∞ A − n is

Choices

Choice (4)Response

a.

I + 2 A + 2 A 2

b.

Unit matrix

c.

I − A − A 2

d.

Question does not provide sufficient information or is vague.

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Question 74

Section A: CommonAlgebraInverse of A Matrix

MCQ

Read the question, then carefully choose the correct answer(s).

Let A = [ a i j ] 4 × 4 such that a i j = { 2 w h e n i = j 0 w h e n i ≠ j , then

{ det ( adj ( adj A ) ) 7 } is (where { ∙ } represents fractional part function)

Choices

Choice (4)Response

a.

2 7

b.

3 7

c.

1 7

d.

None of the above.

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Question 75

Section A: CommonAlgebraAlgebra of Matrices

MCQ

Read the question, then carefully choose the correct answer(s).

Let A = [ 0 α 0 0 ] and ( A + I ) 50 − 50 A = [ a b c d ] . Then the value of a + b + c + d is

Choices

Choice (4)Response

a.

1

b.

4

c.

2

d.

None of the above.

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Question 76

Section A: CommonAlgebraAlgebra of Matrices

MCQ

Read the question, then carefully choose the correct answer(s).

If A and B are two non-zero square matrices of the same order such that the product A B = 0 , then

Choices

Choice (4)Response

a.

A and B must be singular

b.

A and B of them are nonsingular

c.

Exactly one of then must be singular

d.

All of the above.

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Question 77

Section A: CommonAlgebraDeterminants

MCQ

Read the question, then carefully choose the correct answer(s).

If the system of equations x + k y + 3 z = 0 , 3 x + k y − 2 z = 0 , 2 x + 3 y − 4 z = 0 has non-trivial solution, then ( x y z 2 ) = …

Choices

Choice (4)Response

a.

( 6 5 )

b.

− ( 5 6 )

c.

− ( 6 5 )

d.

( 5 6 )

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Question 78

Section A: CommonAlgebraMatrices

MCQ

Read the question, then carefully choose the correct answer(s).

| n n P n n C n n + 1 n + 1 P n + 1 n + 1 C n + 1 n + 2 n + 2 P n + 2 n + 2 C n + 2 | = …

Choices

Choice (4)Response

a.

( n + 2 ) n !

b.

( n 2 + n + 1 ) n !

c.

n ( n + 1 ) !

d.

( n + 1 ) n !

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Question 79

Section A: CommonAlgebraDeterminants

MCQ

Read the question, then carefully choose the correct answer(s).

Let a , b , c be such that b ( a + c ) ≠ 0 . If | a a + 1 a − 1 − b b + 1 b − 1 c c − 1 c + 1 | + | a + 1 b + 1 c − 1 a − 1 b − 1 c + 1 ( − 1 ) n + 2 a ( − 1 ) n + 1 b ( − 1 ) n c | = 0 then n is

Choices

Choice (4)Response

a.

Any odd integer

b.

Any even integer

c.

Any integer

d.

Zero

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