For the function 3x4 - 8x3 + 12x2 - 48x + 25 in the interval [1,

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Domain of y = cot-1x is

  • - , 0

  • 0, 

  • - , 

  • None of these


2.

If limx0log3 + x - log3 - xx = k, then the value of k will be

  • 0

  • - 13

  • 23

  • - 23


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3.

For the function 3x4 - 8x3 + 12x2 - 48x + 25 in the interval [1, 3]. The value of maxima and minima are

  • 16, - 39

  • - 16, 39

  • 6, - 9

  • None of these


A.

16, - 39

Let    fx = 3x4 - 8x3 + 12x2 - 48x + 25        f'x = 12x3 - 24x2 + 24x - 48and f''x = 36x2 - 48x + 24For maxima or minima, put f'(x) = 0 12x3 - 24x2 + 24x - 48 = 0          x3 - 2x2 + 2x - 4 = 0                 x - 2x2 + 2 = 0                                        x = 2 f''2 = 36 × 4 - 48 × 2 + 24 = 72 > 0 f(x) is minimum at x = 2f2 = 324 - 823 + 1222 - 482 + 25      = 48 - 64 + 48 - 96 + 25 = - 39At the end pointsf3 = 334 - 833 + 1232 - 483 + 25      = 243 - 216 + 108 - 144 + 25      = 376 - 360 = 16and f1 = 3 - 8 + 12 - 48             = 40 - 56 = - 16

So, the maximum and mmimum value of f(x) are 16 and - 39 respectively.


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4.

f(x) = x3 - 27x + 5 is an increasing function when

  • x < - 3

  • x >3

  • x  - 3

  • x <3


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5.

In the interval 0, π2 function log(sin(x)) is

  • increasing

  • decreasing

  • neither increasing nor decreasing

  • None of the above


6.

A cone of maximum volume is being cut from sphere, then ratio between height of cone and diameter of sphere is

  • 23

  • 13

  • 34

  • 14


7.

The nth derivative of e2x + 5 is

  • 22nn! e2x + 5

  • 2n e2x + 5

  • 22n e2x + 5

  • 2nn e2x + 5


8.

If 1 - x2 + 1 - y2 = ax - y, then dydx is equal to

  • 1 - x21 - y2

  • 1 - y21 - x2

  • x2 - 11 - y2

  • y2 - 11 - x2


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9.

Function f(x) = x - 1,   x < 22x - 3, x  2 is continuous function for

  • all real values of x

  • only x = 2

  • only real values of x, when x  2

  • the integer values of x


10.

If g(x) = x2 + x - 2 and gof(x) = 2x2 - 5x+ 2, then f(x) is equal to

  • 2x - 3

  • 2x + 3

  • 2x2 + 3x + 1

  • 2x2 - 3x - 1


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