Domain of the function f(x) = logx(cos(x)), is from Mathematics

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 Multiple Choice QuestionsMultiple Choice Questions

111.

If a = i^ - j^ + 2k^ and b = 2i^ - j^ +k^, then the angle θ between a and b is given by

  • tan-11

  • sin-112

  • sec-11

  • tan-113


112.

At t = 0, the function f(t) = sintt has

  • a minimum

  • a discontinuity

  • a point of inflexion

  • a maximum


113.

If r = 2r - 1Crm1m2 - 12mm + 1sin2m2sin2msin2m + 1, then the value of r = 0mr

  • 1

  • 0

  • 2

  • None of these


114.

If cosα + isinα, b = cosβ + isinβ, c = cosγ + isinγ and bc + ca + ab = 1, then cosβ - γ + cosγ - α + cosα - β is equal to

  • 32

  • 32

  • 0

  • 1


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115.

The maximum value of 4 sin2(x) - 12sin(x) + 7 is

  • 25

  • 4

  • does not exist

  • None of the above


116.

A line making angles 45° and 60° with the positive directions of the axes of x and y makes with the positive direction of z-axis, an angle of

  • 60°

  • 120°

  • 60° or 120°

  • None of these


117.

If I = 1001, J = 01- 10 and B = cosθsinθ- sinθcosθ, then B is equal to

  • I cosθ + Jsinθ

  • I sinθ + Jcosθ

  • I cosθ - Jsinθ

  • - I cosθ + Jsinθ


118.

Find the value of sin12°sin48°sin54°.

  • 12

  • 14

  • 16

  • 18


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119.

If 3sinθ + 5cosθ, then the value of 5sinθ - 3cosθ is equal to

  • 5

  • 3

  • 4

  • None of these


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120.

Domain of the function f(x) = logx(cos(x)), is

  • - π2, π2 - 1

  • - π2, π2 - 1

  • - π2, π2

  • None of these


D.

None of these

We have the function

f(x) = logxcosx

f(x) is defined for cos(x) > 0,

                       x > 0, x  1

                 cosx > 0                 - π2 < x < π2

Also, x > 0, x  1

 Domain of f is 0, π2 - 1.


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