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

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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


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112.

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

  • a minimum

  • a discontinuity

  • a point of inflexion

  • a maximum


D.

a maximum

Given, ft = sintt

At t = 0, first we will check continuity of the function

Now, LHL = f(0 - h)

              = limh0sin0 - h0 - h= limh0- sinh- h= 1

RHL= f0 + h= limh0sin0 + h0 + h= limh0sinhh= 1

and f(0) = 1

Since, LHL = RHL = f(0)

So, the function is continuous att = 0.

Now, we check the function is maximum or minimum

        f't = 1tcost - 1t2sintand f''(t) = - 1tsint - 1t2cost - 1t2cost + 2t3sint              = - sintt - 2costt2 + 2sintt3

For maximum or minimum value of f(x), put

                         f'(x) = 0 costt - sintt2 = 0                 tantt = 1

Now, limt0f''(t)= - limt0sintt - 2limt0tcost - sintt3           00 form= - 1 - 2limt0cost - tsint - cost3t2                 using L' Hospital rule= - 1 + 23limt0sintt= - 1 + 23 × 1 = - 13 < 0

So, function f(t) is maximum at t = 0.


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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


120.

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

  • - π2, π2 - 1

  • - π2, π2 - 1

  • - π2, π2

  • None of these


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