If A = α22α and detA3 =

Subject

Mathematics

Class

NDA Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

21.

The sum of all the two-digit odd numbers is

  • 2475

  • 2530

  • 4905

  • 5049


22.

The sum of the first n terms of the series 12 + 34 + 78 + 1516 + ... = ?

  • 2n - n - 1

  • 1 - 2 - n

  • 2 - n + n - 1

  • 2n - 1


23.

The expansion of (x -  y)n, n  > 5 is done in  the descending powers of r.  If the sum of the fifth and sixth term is zero, then xy = ?

  • n - 56

  • n - 45

  • 5n - 4

  • 6n - 5


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24.

If A = α22α and detA3 = 125, Then α = ?

  • ± 1

  • ± 2

  • ± 3

  • ± 5


C.

± 3

Given, A = α22α    A = α2 - 4Also, given A3 = 125      A3 = 125       A = 5 α2 - 4 = 5        α2 = 9         α = ± 3


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25.

If B is a non-singular matrix and A is a square matrix, then the value of det (B - 1 AB) is equal to

  • det(B)

  • det(A)

  • detB - 1

  • detA - 1


26.

If a  b  c, then one value of x which satisfies the equation0x - ax - bx + a0x - cx +bx + c0 = 0 is given by

  • a

  • b

  • c

  • 0


27.

If A = cosαsinα - sinαcosα then what is AAT = ?Where AT is the transpose of A ?

  • Null matrix 

  • Identity Matrix

  • A

  • - A


28.

The equations

x + 2y + 3z = 12

x + y + 3z  = 25

x + 5y + 9z = 4

  • have the unique solution

  • Have infinitely many solutions

  • are inconsistent

  • None of the above


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29.

What is the value of the determinant

11111 + xyz1111 +xyz 

  • 1 + x + y + z

  • 2xyz

  • x2y2z2

  • 2x2y2z2


30.

If xy00xyy0x = 0, then which one of the following is correct ?

  • xy is one of the cube roots of unity

  • x is one of the cube roots of unity

  • y is one of the cube roots of unity

  • xy is one of the cube roots - 1


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