If sec-11 + x2 + csc-11 + y2

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

If l, m and n are real numbers such that l2 + m2 + n2 = 0, then

1 + l2lmlnlm1 + m2mnlnmn1 + n2 is equal to

  • 0

  • 1

  • l + m + n + 2

  • 2(l + m + n) + 3


2.

If f (x) = x2 + 4x - 5 and A = 124- 3, then f(A) is equal to

  • 0- 488

  • 2120

  • 1110

  • 8480


3.

α- β00αββ0α = 0, then

  • αβ is one of the cube roots of unity

  • α is one of the cube roots of unity

  • β is one of the cube roots of unity

  • αβ is one of the cube roots of unity 


4.

The coefficient of x in

fx = x1 + sinxcosx1log1 + x2x21 + x20, - 1 < x  1, is

  • 1

  • - 2

  • - 1

  • 0


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5.

If x3636x6x3 = 2x7x7272x = 45x5x4x45 = 0, then x is equal to

  • 9

  • - 9

  • 0

  • - 1


6.

If w be the complex cube root of unity and matrix H = w00w, then H70 is equal to

  • 0

  • - H

  • H

  • H2


7.

The output of the circuit is

  • (x2 + x3) . [(x1 · x2) . x3']

  • (x2 + x3') . [(x1 · x2) . x3']

  • (x2 + x3) + [(x1 · x2) . x3']

  • (x2 . x3) . [(x1 · x2) . x3']


8.

If tan-1mn - tan-1m - nm +n is equal to

  • tan-1nm

  • tan-1m +nm - n

  • π4

  • tan-112


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9.

If sec-11 + x2 + csc-11 +y2y + cot-11z = π, then x + y + z is equal to

  • xyz

  • 2xyz

  • xyz2

  • x2yz


A.

xyz

sec-11 + x2 + csc-11 +y2y + cot-11z = π                               tan-1x + tan-1y + tan-1z = π                                         tan-1x +y +z - xyz1 - xy - yz - zx = π                                                                    x +y +z = xyz


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10.

If x = 2at1 + t3 and y = 2at21 + t32, then dydx is

  • ax

  • a2x2

  • xa

  • x2a


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