If fx = x - x4, x ∈ 

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The total number matrices A = 02y12xy- 12x- y1x, y  R, x  y for which ATA = 3I3 is

  • 2

  • 6

  • 4

  • 3


2.

If the function f(x) = a|π - x| + 1,     x  5bx - π + 3,     x > 5 is continuous at x = 5, then the value of a - b is

  • - 2π + 5

  • 2π + 5

  • 2π - 5

  • 25 - π


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3.

If fx = x - x4, x  R , where [x] denotes the greatest integer function, then:

  • Both limx4-fx and limx4+fx exist but noot equal

  • f is continuous at x = 4

  • limx4-fx exist but limx4+fx does not exist

  • limx4+fx exist but limx4-fx does not exist


B.

f is continuous at x = 4

fx = x - x4, x  R, x = GUIFlimx4x - x44 - 1 = 3So, limx4x - x4 = 3at x = 4, f(x) = 4 - 44 = 3


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4.

If the system of equation 2x + 3y - z = 0, x + ky - 2z = 0 and 2x - y + z = 0 has a non – trivial solution (x, y, z) , then xy +yz + zx + k is equal to

  • 34

  • 12

  • - 4

  • 14


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5.

A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is tan-112. Water is poured into it at a constant rate of 5 cubic meter per minute. Then the rate (in m/min), at which the level of water is rising at the instant when the depth of water in the tank is 10m; is :

  • 110π

  • 115π

  • 15π

  • 2π


6.

The vertices B and C of a ABC lie on line, x + 23 = y - 10 = z4 such that BC = 5 units. Then the area (in sq.units) of this triangle, given that the point A(1, - 1, 2)

  • 34

  • 517

  • 234

  • 6


7.

The area (in sq.units) of the region A = x, y : y22  x  y +4 is

  • 18

  • 16

  • 533

  • 30


8.

If f : R  R is a differentiable function and f(2) = 6, then limx26f(x)2t dtx - 2 is

  • 0

  • 24f'(2)

  • 12f'(2)

  • 2f'(2)


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9.

If unit vector a makes angles π3 with i^, π4, with j^ and θ  0, π with k^, then a value of θ is

  • 2π3

  • 5π6

  • 5π12

  • π4


10.

The value of the integral 01xcot-11 - x2 +x4dx is

  • π2 - 12loge2

  • π4 - loge2

  • π4 - 12loge2

  • π2 - loge2


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