JEE Questions for Maths Limits Continuity And Differentiability Quiz 17 - MCQExams.com


Maths-Limits Continuity and Differentiability-36954.png
  • f is discontinuous at x = 1
  • f is differentiable at x = 1
  • f is continuous but not differentiable at x = 1
  • None of the above
Which one of the following is not true always ?
  • If f(x) is not continuous at x = a, then it is not differentiable at x = a
  • If f(x) is continuous at x = a, then it is differentiable at x = a
  • If f(x) and g(x) are differentiable at x = a, then f(x) + g(x) is also differentiable at x = a

  • Maths-Limits Continuity and Differentiability-36956.png
If f(x) = ae|x| + b|x|2, a,b ∈ R and f(x) is differentiable at x = 0. Then a and b, are
  • a = 0, b ∈ R
  • a = 1, b = 3
  • a = 1, b = 2
  • a = 2, b = 3

Maths-Limits Continuity and Differentiability-36958.png
  • f is differentiable at x = 0 and at x = 1
  • f is differentiable at x = 0 but not at x = 1
  • f is differentiable at x = 1 but not at x = 0
  • f is neither differentiable at x = 0 nor at x = 1

Maths-Limits Continuity and Differentiability-36960.png
  • f(x) is continuous but non-differentiable at x = 0
  • f(x) is differentiable at x = 0
  • f(x) is not differentiable at x = 0
  • None of the above
The differentiable function f,g,h are such that f\' (x) = g(x), g\'(x) = h(x), h\'(x) = f(x), f(= 1,g(= 0 and h(= 0.Then the value of f3 (x) + g3 (x) + h3 (x) – 3f(x)g(x)h(x) at x = 5 is
  • 0
  • 1
  • 2
  • 3
A differentiable function f(x) is defined for all x > 0 and satisfies f(x3) = 4x4 for all x > 0.The value of f\' (is

  • Maths-Limits Continuity and Differentiability-36962.png
  • 2)
    Maths-Limits Continuity and Differentiability-36963.png

  • Maths-Limits Continuity and Differentiability-36964.png

  • Maths-Limits Continuity and Differentiability-36965.png
The period of the function f(x) = |sin x| + |cos x| is
  • 2π
  • 3π

  • Maths-Limits Continuity and Differentiability-36967.png

  • Maths-Limits Continuity and Differentiability-36968.png

Maths-Limits Continuity and Differentiability-36969.png
  • f(x) is continuous but not differentiable at x = 0
  • f(x) is not differentiable at x = 0
  • f(x) is differentiable at x = 0
  • None of the above

Maths-Limits Continuity and Differentiability-36971.png

  • Maths-Limits Continuity and Differentiability-36972.png
  • 2)
    Maths-Limits Continuity and Differentiability-36973.png

  • Maths-Limits Continuity and Differentiability-36974.png

  • Maths-Limits Continuity and Differentiability-36975.png
The graph of f(x) is given in the figure. f|x| is non differentiable at x = (in the interval (–1,3))
Maths-Limits Continuity and Differentiability-36977.png
  • 3 and 2
  • 1 and 2
  • 0 and 2
  • None of these

Maths-Limits Continuity and Differentiability-36979.png
  • 3a
  • 2a
  • 5a
  • 4a

Maths-Limits Continuity and Differentiability-36981.png
  • n = 1, m = 1
  • n = 1, m = –1
  • n = 2, m = 2
  • n > 2, m = n

Maths-Limits Continuity and Differentiability-36983.png
  • Continuous but not differentiable at x = 0
  • Discontinuous at x = 0
  • Continuous and differentiable at x = 0
  • Not defined at x = 0

Maths-Limits Continuity and Differentiability-36985.png

  • Maths-Limits Continuity and Differentiability-36986.png
  • 2)
    Maths-Limits Continuity and Differentiability-36987.png

  • Maths-Limits Continuity and Differentiability-36988.png

  • Maths-Limits Continuity and Differentiability-36989.png
If the derivative of the function f(x) is every where continuous and is given by
Maths-Limits Continuity and Differentiability-36991.png
  • a = 2, b = 3
  • a = 3, b = 2
  • a = –2, b = –3
  • a = –3, b = –2

Maths-Limits Continuity and Differentiability-36993.png
  • a – b
  • a + b
  • log a + log b
  • log a – log b

Maths-Limits Continuity and Differentiability-36995.png
  • 7
  • –7
  • ±7
  • None of these

Maths-Limits Continuity and Differentiability-36997.png

  • Maths-Limits Continuity and Differentiability-36998.png
  • 2)
    Maths-Limits Continuity and Differentiability-36999.png
  • f(x) is continuous at x = 1/2
  • f(x) is discontinuous at x = 1/2

Maths-Limits Continuity and Differentiability-37001.png

  • Maths-Limits Continuity and Differentiability-37002.png
  • f(x) is continuous at x = a
  • f(x) is discontinuous at x = 0
  • None of the above

Maths-Limits Continuity and Differentiability-37004.png

  • Maths-Limits Continuity and Differentiability-37005.png
  • 2)
    Maths-Limits Continuity and Differentiability-37006.png
  • f(x) is discontinuous at x = 0
  • None of the above

Maths-Limits Continuity and Differentiability-37008.png

  • Maths-Limits Continuity and Differentiability-37009.png
  • 2)
    Maths-Limits Continuity and Differentiability-37010.png

  • Maths-Limits Continuity and Differentiability-37011.png

  • Maths-Limits Continuity and Differentiability-37012.png

Maths-Limits Continuity and Differentiability-37014.png
  • 1
  • – 1
  • 0
  • None of these

Maths-Limits Continuity and Differentiability-37016.png

  • Maths-Limits Continuity and Differentiability-37017.png
  • 2)
    Maths-Limits Continuity and Differentiability-37018.png
  • f(x) is discontinuous at x = 0
  • None of these

Maths-Limits Continuity and Differentiability-37020.png

  • Maths-Limits Continuity and Differentiability-37021.png
  • 2)
    Maths-Limits Continuity and Differentiability-37022.png
  • f(x) is discontinuous at x = 0
  • None of the above
Which of the following statements is true for graph f (x) = log x
  • Graph shows that function is continuous
  • Graph shows that function is discontinuous
  • Graph finds for negative and positive values of x
  • Graph is symmetric along x-axis

Maths-Limits Continuity and Differentiability-37024.png
  • a2
  • 2a2
  • 3a2
  • 4a2

Maths-Limits Continuity and Differentiability-37026.png

  • Maths-Limits Continuity and Differentiability-37027.png
  • 2)
    Maths-Limits Continuity and Differentiability-37028.png
  • f(x) is discontinuous at x = 0
  • None of these

Maths-Limits Continuity and Differentiability-37030.png

  • Maths-Limits Continuity and Differentiability-37031.png
  • 2)
    Maths-Limits Continuity and Differentiability-37032.png

  • Maths-Limits Continuity and Differentiability-37033.png
  • None of the above

Maths-Limits Continuity and Differentiability-37034.png
  • Only positive integers
  • All positive and negative integers and (0,1)
  • All rotational numbers
  • None of the above

Maths-Limits Continuity and Differentiability-37036.png
  • f(x) is continuous at x = 0
  • f(x) is discontinuous at x = 0, when a ≠ ± 1
  • f(x) is continuous at x = a
  • None of the above

Maths-Limits Continuity and Differentiability-37038.png
  • f(x) is continuous at x = 0
  • f(x) is continuous x = 2
  • f(x) is discontinuous at x = 1
  • None of the above

Maths-Limits Continuity and Differentiability-37040.png

  • Maths-Limits Continuity and Differentiability-37041.png
  • 2)
    Maths-Limits Continuity and Differentiability-37042.png
  • f(x) is continuous at x = 0
  • None of the above

Maths-Limits Continuity and Differentiability-37044.png
  • 1
  • 2/5
  • –2/5
  • None of these

Maths-Limits Continuity and Differentiability-37046.png

  • Maths-Limits Continuity and Differentiability-37047.png
  • 2)
    Maths-Limits Continuity and Differentiability-37048.png
  • f(x) is discontinuous at x = 1
  • None of these

Maths-Limits Continuity and Differentiability-37050.png

  • Maths-Limits Continuity and Differentiability-37051.png
  • 2)
    Maths-Limits Continuity and Differentiability-37052.png
  • f(x) is continuous at x = –1
  • All the above are correct

Maths-Limits Continuity and Differentiability-37054.png
  • f(x) is continuous at x = a
  • f(x) is discontinuous at x = a

  • Maths-Limits Continuity and Differentiability-37055.png
  • None of the above

Maths-Limits Continuity and Differentiability-37057.png

  • Maths-Limits Continuity and Differentiability-37058.png
  • 2)
    Maths-Limits Continuity and Differentiability-37059.png

  • Maths-Limits Continuity and Differentiability-37060.png
  • f and g can not be determined

Maths-Limits Continuity and Differentiability-37062.png
  • f(x) is continuous at x = 0
  • f(x) is continuous at x = π
  • f(x) is continuous at x = 3π/4
  • f(x) is discontinuous at x = 3π/4

Maths-Limits Continuity and Differentiability-37064.png
  • f(x) is discontinuous at x = π/2
  • f(x) is continuous at x = π/2
  • f(x) is continuous at x = 0
  • None of the above

Maths-Limits Continuity and Differentiability-37066.png
  • 8
  • –8
  • 4
  • None of these

Maths-Limits Continuity and Differentiability-37068.png
  • a = 2, b = 0
  • a = 1, b = –1
  • a = 4, b = 2
  • All of these

Maths-Limits Continuity and Differentiability-37070.png
  • f(x) is continuous at x = 1
  • f(x) is discontinuous at x = 1

  • Maths-Limits Continuity and Differentiability-37071.png
  • None of the above

Maths-Limits Continuity and Differentiability-37073.png

  • Maths-Limits Continuity and Differentiability-37074.png
  • 2)
    Maths-Limits Continuity and Differentiability-37075.png

  • Maths-Limits Continuity and Differentiability-37076.png

  • Maths-Limits Continuity and Differentiability-37077.png

Maths-Limits Continuity and Differentiability-37079.png
  • 4
  • 3
  • 2
  • 1

Maths-Limits Continuity and Differentiability-37081.png
  • 8
  • 1
  • –1
  • None of these

Maths-Limits Continuity and Differentiability-37083.png
  • x = 1 only
  • x = 1 and x = –1 only
  • x = 1,x = –1, x = –3 only
  • x = 1, x = –1, x = –3 and other values of x

Maths-Limits Continuity and Differentiability-37085.png
  • a = 0, b = 0
  • a = 1, b = 1
  • a = –1, b = 1
  • a = 1, b = –1

Maths-Limits Continuity and Differentiability-37087.png
  • R
  • R – {1}
  • R – {2}
  • R – {1,2}

Maths-Limits Continuity and Differentiability-37089.png
  • 2/3
  • 6
  • 2
  • 4
0:0:1


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