The value of maxima of 1xx is from Mathematics JEE Year 201

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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1.

The value of maxima of 1xx is

  • 1ee

  • ee

  • e

  • e1/e


D.

e1/e

Let     y = 1xxOn taking log both sides, we get  logy = xlog1x = - xlogxOn differentiating both sides w.r.t. x, we get  1ydydx = - x . 1x + logx dydx = - 1xx1 + logx = 0     ...iNow, 1 + logx = 0            logx = - 1                   x = e- 1

Again, differentiating Eq. (i) both sides w.r.t. x, we getd2ydx2 = - 1xxddx1 + logx + 1 + logxddx1xx        = - 1xx1x + 1 + logx . 1 + logx - 1xx               From Eq. (i)        =  - 1xx1x + 1xx1 + logx . 1 + logx d2ydx2 = 1xx1 + logx . 1 + logx - 1xx1xNow, d2ydx2x = e- 1 = - ee- 1 . e < 0Thus, the function is maximum when x = e- 1Now, maximum value of function = 1e- 1e- 1 = e1e


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2.

The value of tan12cos-123 is

  • 15

  • 310

  • 52

  • 1 - 52


3.

If r2 = x2 + y2 + z2 and tan-1yzxr + tan-1xzyr = π2 - tan-1ϕ, then

  • ϕ = zrxy

  • ϕ = xyzr

  • ϕ = x + yzr

  • ϕ = yzxr + xzyr


4.

The value of determinant 1abca31bcab31cabc3

  • a2b2c2(a - b)(b - c)(c - a)

  • 0

  • (a - b)(b - c)(c - a)

  • None of the above


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5.

If 3- 1063x1 + - 2x3 = 89, then the value of x is

  • - 38

  • 7

  • - 29

  • None of these


6.

Consider A and B two square matrices of same order. Select the correct alternative.

  • AB must be greater than A

  • 1111 is not unit matrix

  • A + B must be greater than A

  • If AB = 0, either A or B must be zero matrix


7.

Function f : N  N, f(x) = 2x + 3 is

  • many-one onto function

  • many-one into function

  • one-one onto function

  • one-one into function


8.

If domain of the function f(x) = x2 - 6x + 7 is (- , ), then its range is

  • [ - 2, 3]

  • - , 2

  • - , 

  • [ - 2, )


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9.

A point particle moves along a straight line such that x = t, where t is time. Then, ratio of acceleration to cube of the velocity is

  • - 1

  • - 0.5

  • - 3

  • - 2


10.

If function f(x) = xsin1x; x  0a;           x = 0 is continuous at x = 0, then the value of a is

  • 0

  • 1

  • - 1

  • None of these


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