The derivative of tan-1sinx1 + cosx with resp

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

11.

If , then x is

  • 12

  • 14

  • 16


12.

If r = aeθcotα where a and α, are real numbers, then d2r2 - 4rcot2α is

  • r

  • 1r

  • r

  • 0


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13.

The derivative of tan-1sinx1 + cosx with respect to tan-1cosx1 + sinx is

  • 2

  • - 1

  • 0

  • - 2


B.

- 1

Let u = tan-1sinx1 + cosx, v = tan-1cosx1 + sinxu = tan-12sinx2cosx21 + 2cos2x2 - 1   = tan-1tanx2v = tan-1cosxcos2x2 + sin2x2 + 2sinx2cosx2  = tan-1cos2x/2 - sin2x2cosx2 + sinx22  = tan-1cosx/2 - sinx2cosx2 + sinx2  = tan-11 - tanx21 + tanx2  = tan-1tanπ4 - π2  = π4 - x2

Now, dudx = 12 and dvdx = - 12    dudv = dudx × dxdv              = 12 × - 2 = - 1


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14.

ddxcoscot-12 +x2 - x is

  • 14

  • 12

  • - 12

  • - 34


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15.

If cos-1yb = nlogxn, then

  • xy1 = nb2 - y2

  • xy1 + nb2 - y2 = 0

  • y1 = xb2 - y2

  • xy1 - b2 - y2 = 0


16.

A sphere increases its volume at the rate of π cc/s. The rate at which its surface area increases when the radius is 1 cm is

  • 2π sq cm/s

  • π sq cm/s

  • 3π2 sq cm/s

  • π2 sq cm/s


17.

sinαcosαsinα + δsinβcosβsinβ + δsinγcosγsinγ + δ is equal to

  • 0

  • 1

  • 1 + sinαsinβsinγ

  • 1 - sinα - sinβsinβ - sinγsinγ - sinα


18.

If a, b and c are unit vectors such that a + b + c = 0, then angle between a and b is

  • π2

  • π3

  • 2π3

  • π


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19.

If a, b and c are non-coplanar, then the value of a . b × c3b . c × a - b . c × a2c . a × b is

  • - 12

  • - 13

  • - 16

  • 16


20.

If 2i + 3j, i + j + k and λi + 4j + 2k taken in an order are coterminous edges of a parallelopiped of volume 2 cu units, then value of λ is

  • - 4

  • 2

  • 3

  • 4


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