The value of costan-1sincot-1x is from Mathematics JEE

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

If α, β, γ are the cube roots of unity, then the value of the determinant eαe2αe3α - 1eβe2βe3β - 1eγe2γe3γ - 1 is equal to

  • - 2

  • - 1

  • 0

  • 1


2.

If B is a non-singular matrix and A is a square matrix such that B-1AB exists, then det (B-1AB) is equal to

  • det(A-1)

  • det (B-1)

  • det(B)

  • det(A)


3.

If 1, w, w2 are the cube roots of unity and if

, a2 + b2 is equal to

  • 1 + w2

  • w2 - 1

  • 1 + w

  • (1 + w)2


4.

If the three linear equations

x + 4ay + az = 0

x + 3by + bz = 0

x + 2cy + cz = 0

have a non-trivial solution, where aa  0, b  0, c  0, then ab + bc is equal to

  • 2ac

  • - ac

  • ac

  • - 2ac


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5.

If A = 100x10xx1 and I = 100010001, then A3 - 4A2 + 3A + I is equal to

  • 3I

  • I

  • - I

  • - 2I


6.

If A = 1235, then the value of the determinant A2009 - 5A2008 is

  • - 6

  • - 5

  • - 4

  • 4


7.

The boolean expression corresponding to the combinational circuit is

  • (x1 + x2 · x'3)x2

  • (x1 . (x2 + x3)) + x2

  • (x1 . (x2 + x'3)) + x2

  • (x1 + (x2 + x'3)) + x3


8.

In a boolean algebra B with respect to '+' and '.', x' denotes the negation of x B. Then

  • x - x' = 1 and x · x' = 1

  • x + x' = 1 and x . x' = 0

  • x + x' = 0 and x . x' = 0

  • x + x' = 0 and x . x' = 0


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9.

If cos-1513 - sin-11213 = cos-1x,  then x is equal to

  • 1

  • 12

  • 0

  • 32


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10.

The value of costan-1sincot-1x is

  • x2 + 1x2 - 1

  • 1 - x2x2 + 2

  • 1 - x21 + x2

  • x2 + 1x2 + 2


D.

x2 + 1x2 + 2

costan-1sincot-1x= costan-1sinsin-111 + x2= costan-111 + x2= coscos-11 + x22 + x2= 1 + x22 + x2


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