The value of x in the interval [ 4, 9] at which the function f(x)

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The total revenue in rupees received from the sale of x units of a product is given by R(x) = 13x2 + 26x + 15. Then, the marginal revenue in rupees, when x = 15 is

  • 116

  • 126

  • 136

  • 416


2.

If a tangent of the curve y = 2 + 4x + 1 has slope 25 at a point, then the point is

  • (0, 2)

  • 34, 4

  • (2, 5)

  • (6, 7)


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3.

The value of x in the interval [ 4, 9] at which the function f(x) = x satisfies the mean value theorem is

  • 134

  • 174

  • 214

  • 254


D.

254

Function f(x) = x and [4, 9]Here, a = 4 and b = 9fa = f4 = 2 and fb = f9 = 3By Lagrange's mean value theorem, fb - fab - a = f'x 3 - 29 - 4 = 12x 12x = 15       x = 254

Which lies in the given interval [4, 9].


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4.

If the function f : [1, )  [1, ) is defined by f(x) = 2x(x - 1), then f-1(x) is

  • 12xx - 1

  • 121 - 1 + 4log2x

  • 121 + 4log2x

  • 121 + 1 + 4log2x


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5.

If n(A) = 8 and nA  B = 2, then nA  B'  A is equal to

  • 2

  • 4

  • 6

  • 8


6.

If f(x) = sinx + cosxx  - ,  and g(x) = x2x  - , , then (fog)(x) is equal to

  • 1

  • 0

  • sin2x + cosx2

  • sinx2 + cosx2


7.

If A = 12221- 2a2b is a matrix satisfying AAT = 9I3, then the values of a and b are respectively.

  • 1, 2

  • - 1, 2

  • - 1, - 2

  • - 2, - 1


8.

If A = 210x and A- 1121601x, then the value of x is equal to

  • - 3

  • 3

  • - 2

  • 6


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9.

If A = cosαsinαsinαcosα, then A10 is equal to

  • cos10αsin10α- sin10αcos10α

  • cos10α- sin10αsin10αcos10α

  • cos10αsin10α- sin10α- cos10α

  • cos10αsin10α- sin10αcos10α


10.

If A = 100010ab- 1 and I is the unit matrix of order 3, then A2 + 2A4 + 4A6 is equal to

  • 7 A8

  • 7 A7

  • 8 I

  • 6 I


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