If xy = ex - y, then dydx is equal to from Mathematics

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Let * be a binary operation defined on R by a * b = a + b4,  a, b  R, then the operation * is

  • commutative and associative

  • commutative but not associative

  • associative but not commutative

  • neither associative nor commutative


2.

The value of sin-1cos53π5 is

  • 3π5

  • - 3π5

  • π10

  • - π10


3.

If 3tan-1x + cot-1x = π, then x is equal to

  • 0

  • 1

  • - 1

  • 1/2


4.

The simplified form of tan-1xy - tan-1x - yx + y is equal to

  • 0

  • π4

  • π2

  • π


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5.

If x, y,z are all different and not equal to zero and 1+ x1111 + y1111 + z = 0, then the value of x-1 + y-1 + z-1 is equal to

  • xyz

  • x-1y-1z-1

  • - x - y - z

  • - 1


6.

If A is any square matrix of order 3 x 3, then 3A is equal to

  • 3A

  • 13A

  • 27A

  • 9A


7.

If y = esin-1t2 - 1 and x = esec-11t2 - 1, then dydx is equal to

  • xy

  • - yx

  • yx

  • - xy


8.

If A = 1πsin-1πxtan-1xπsin-1xπcot-1πx, B = 1π- cos-1πxtan-1xπsin-1xπ- tan-1πx, then A - B is equal to

  • I

  • 0

  • 2I

  • 12I


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9.

If xy = ex - y, then dydx is equal to

  • logxlogx - y

  • exxx - y

  • logx1 + logx2

  • 1y - 1x - y


C.

logx1 + logx2

We have, xy = ex - yTakinglog on both sides, we get             ylogx = x - y    loge = 1 ylogx + y = x                 y = x1 + logxOn differentiating both sides w.r.t. x, we getdydx = 1 + logx1 - x1x1 + logx2      = 1 + logx - 11 + logx2      = logx1 + logx2


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10.

If A is a matrix of order m x n and B is  a matrix, such that AB' and B'A are both defined, then the order of the matrix B is

  • m x m

  • n x n

  • n x m

  • m x n


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