The maximum value of function x3 - 12x2 + 36x + 17 in the interva

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The inverse matrix of 012123311, is

  • 12- 1212- 43- 152- 3212

  • 12- 4521- 6312- 1

  • 12123321423

  • 121- 1- 1- 86- 25- 31


2.

If fx = xsin1x, x  0k,           x  = 0 is continuous at x = 0, then the value of k is

  • 1

  • - 1

  • 0

  • 2


3.

If x = 1 - t21 + t2 and y = 2at1 +t2, then dydx is equal to

  • a1 - t22t

  • at2 - 12t

  • at2 + 12t

  • at2 - 1t


4.

The velocity of a particle at time t is given by the relation v = 6t - t26. The distance traveled in 3 s is, if s = 0 at t = 0

  • 392

  • 572

  • 512

  • 332


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5.

The maximum value of function x3 - 12x2 + 36x + 17 in the interval [1, 10] is

  • 17

  • 177

  • 77

  • None of these


B.

177

Let fx = x3 - 12x2 + 36x + 17 f'x = 3x2 - 24x + 36 = 0For maxima, put f'x = 0  3x2 - 24x + 36 = 0    x - 2x - 6 = 0                         x = 2, 6

Again, f''(x) = 6x - 24 is negative at x = 2 So that, f(6) = 17, f(2) = 49

At the end points, f(1) = 42, f(10) = 177

So that, f(x) has its maximum value 177.


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6.

The value of logfx + 23x is

  • log1 + fxfx + 4 . 3x

  • log1 + fxfx + 3x

  • logfx1 + fx + 4 . 3x

  • logfx1 + fx + 3x


7.

The solution of the equation

101- 1100- 11xyz = 112 is (x, y, z) = 

  • (1, 1, 1)

  • (0, - 1, 2)

  • (- 1, 2, 2)

  • (- 1, 0, 2)


8.

The abscissae of the points, where the tangent is to curve y = x3 - 3x2 - 9x + 5 is parallel to x-axis, are

  • x = 0 and 0

  • x = 1 and - 1

  • x = 1 and - 3

  • x = - 1 and 3


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9.

If a . i^ = 4, then a × j^ . 2j^ - 3k^ is equal to

  • 12

  • 2

  • 0

  • - 12


10.

The line joining the points 6a - 4b + 4c, - 4c and the line joining the points - a - 2b - 3c, a + 2b - 5c intersect at

  • - 4a

  • 4a - b - c

  • 4c

  • None of the above


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