If f(x) = 803x4 + 8x3 - 18x2 + 60,

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The number of solutions of the system of equations 2x + y - z = 7, x - 3y + 2z = 1 and x + 4y - 3z = 5 is

  • 0

  • 1

  • 2

  • 3


2.

If x2828x8x2 = 3x7x7373x = 55x5x5x55 = 0, then x is equal to

  • 0

  • - 10

  • 3

  • None of these


3.

Let R = {(1, 1), (1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is

  • a function

  • transitive

  • not symmetric

  • reflexive


4.

If α = sin-1cossin-1x and β = cos-1sincos-1x, then tanα . tanβ is equal to

  • 1

  • - 1

  • 2

  • 12


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5.

At which point the function f(x) = x2x, where [.] is greatest integer function, is discontinuous ?

  • Only positve integers

  • All postive and negative integers and (0,1)

  • all rational numbers

  • None of these


6.

The function y = 2sinx is continuous for any x but it is not differentiable at

  • only x = 0

  • only x = π

  • only x = π2

  • x =  k is integer


7.

If y = elog1 + x +x2 + x3 + , where x < 1, then dydx is equal to

  • - 11 - x2

  • 11 - x2

  • 11 + x2

  • None of these


8.

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


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9.

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


B.

- 3, 1

We have,      fx = 803x4 + 8x3 - 18x2 + 60 f'x = - 8012x3 + 24x2 - 36x3x4 + 8x3 - 18x2 + 60             = - 8012xx2 + 2x - 33x4 + 8x3 - 18x2 + 60            = - 8012xx - 1x + 33x4 + 8x3 - 18x2 + 60Put f'x = 0      x = 0, x = 1 and x = - 3Clearly, the sign scheme of f'x is

Hence, x = - 3 and x = 1 are the points of maxima.


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10.

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


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