If xy = ex - y, then dydx is from Mathematics JEE Year

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The value of y +zxxyz + xyzzx +y is

  • xyz

  • x2y2z2

  • 4xyz

  • 4x2y2z2


2.

If A and B are square matrices of order 3 such that A = - 1, B = 3, then 3AB is equal to

  • - 9

  • - 81

  • - 27

  • 81


3.

Let A = 00- 10- 10- 100, the only correct statement about the matrix A, is

  • A is a zero matrix

  • A = (- 1)I, where I is a unit matrix

  • A- 1 does not exist

  • A2 = I


4.

If A = 200020002, then A2 is equal to

  • 5A

  • 10A

  • 16A

  • 32A


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5.

The trigonometric equation sin-1x = 2sin-1a, has a solution for

  • 12 < a  12

  • all real values of a

  • a  12

  • a  12


6.

tan-112 + tan-113 is equal to

  • 0

  • π4

  • π2

  • π


7.

The equation of normal to the circle 2x2 + 2y2 - 2 - 5y + 3 = 0 at (1, 1) is

  • 2x + y = 3

  • x - 2y = 3

  • x + 2y = 3

  • None of these


8.

A function f from the set of natural numbers to integers defined by f(n) = n - 12, when n is odd- n2,  when n is even, is

  • one - one but not onto

  • onto but not one - one

  • one - one and onto both

  • neither one - one nor onto


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9.

If xy = ex - y, then dydx is

  • 1 + x1 + logx

  • 1 - logx1 + logx

  • not defined

  • logx1 + logx2


D.

logx1 + logx2

Given, xy = ex - yTaking log on both sides, we get     ylogx = x - yloge ylogx = x - yOn differentiating w.r.t. x, we gety . 1x + logx . dydx = 1 - dydx  1 + logxdydx = 1 - yx                   dydx = x - yx1 + logx                             = x - x1 + logxx1 + logx                             = 1 + logx - 11 + logx2                  dydx = logx1 + logx2


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10.

If f(x) = xn, then the value of f1 - f'11! + f''12! - f'''13! + ... + - 1nf'n1n! is

  • 2n

  • 2n - 1

  • 0

  • 1


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