The value of maxima of 1xx is from Mathematics Application

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 Multiple Choice QuestionsMultiple Choice Questions

191.

The values of a and b for which the function y = aloge(x ) + bx2 + x, has extremum at the points x1 = 1 and x2 = 2 are

  • a = 23, b = - 16

  • a = - 23, b = - 16

  • a = - 23, b = 16

  • a = - 13, b = - 16


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192.

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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193.

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


194.

The tangents to curve y = x3 - 2x2 + x - 2 which are parallel to straight line y = x, are

  • x + y = 2 and x - y = 8627

  • x - y = 2 and x - y = 8627

  • x - y = 2 and x + y = 8627

  • x + y = 2 and x + y = 8627


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195.

If two sides of a triangle are given, then the area of the triangle will be maximum, if. the angle between the given sides is

  • π3

  • π4

  • π6

  • π2


196.

If f(x) = 803x4 + 8x3 - 18x2 + 60, then the points of local maxima for the function f(x) are

  • 1, 3

  • - 3, 1

  • - 1, 3

  • - 1, - 3


197.

The adjacent sides of a rectangle with given parameter as 200 cm and enclosing minimum area are

  • 20 cm and 80 cm

  •  50 cm and 50 cm40 cm and 60 cm

  • 50 cm and 50 cm

  • 30 cm and 70 cm


198.

The altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is

  • r2

  • r3

  • 3r4

  • 4r3


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199.

Let f(x) = x(x - 1)2, the point at which f(x) assumes maximum and minimum are respectively

  • 13, 1

  • 1, 13

  • 3, 1

  • None of these


200.

Rectangles are inscribed ina circle of radius r. The dimensions of the rectangle which has the maximum area, are

  • r, r

  • 2r, 2r

  • 2r, 2r

  • None of the above


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