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11th Standard Maths Differential Calculus - Differentiability and Methods of Differentiation English Medium Free Online Test 1 Mark Question 2020-2021

11th Standard

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Maths

Time : 00:10:00 Hrs
Total Marks : 10

    Answer all the questions

    10 x 1 = 10
  1. \({d\over dx}({2\over \pi}sin \ x^o)\)is

    (a)

    \({\pi\over 180}cos \ x^o\)

    (b)

    \({1\over 90} cos \ x^o\)

    (c)

    \({\pi\over 90}cos \ x^o\)

    (d)

    \({2\over \pi}cos \ x^o\)

  2. If y = mx + c and f(0) =\(f '(0)=1\),then f(2) is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    -3

  3. \({d\over dx}(e^{x+5log \ x})\) is

    (a)

    exx4(x+5)

    (b)

    exx(x+5)

    (c)

    ex\(+{5\over x}\)

    (d)

    ex\(-{5\over x}\)

  4. The differential coefficient of log10 x with respect to logx10 is

    (a)

    1

    (b)

    -(log10 x)2

    (c)

    (logx 10)2

    (d)

    \(x^2\over100\)

  5. If ,then the right hand derivative of f(x) at x = 2 is

    (a)

    0

    (b)

    2

    (c)

    3

    (d)

    4

  6. Choose the correct or the most suitable answer from the given four alternatives.
    \(Iff\left( x \right) =4{ x }^{ 8 },\quad then\)

    (a)

    \(f^{ ' }\left( \frac { 1 }{ 2 } \right) =f^{ ' }\left( \frac { -1 }{ 2 } \right) \)

    (b)

    \(f\left( \frac { 1 }{ 2 } \right) =-f^{ ' }\left( \frac { -1 }{ 2 } \right) \)

    (c)

    \(f\left( \frac { 1 }{ 2 } \right) =f\left( \frac { -1 }{ 2 } \right) \)

    (d)

    \(f\left( \frac { 1 }{ 2 } \right) =f^{ ' }\left( \frac { -1 }{ 2 } \right) \)

  7.  Choose the correct or the most suitable answer from the given four alternatives.
    If \(y=\log _{ a }{ x } \) then \(\frac { dy }{ dx } \) is

    (a)

    \(\frac { 1 }{ x } \)

    (b)

    \(\frac { 1 }{ x\log _{ e }{ a } } \)

    (c)

    \(\log { _{ e }^{ a } } \)

    (d)

    \(\frac { 1 }{ \log _{ a }{ x } } \)

  8. Choose the correct or the most suitable answer from the given four alternatives.
    The derivative of \(\cos ^{ -1 }{ (2{ x }^{ 2 } } -1)\) with respect to \(\cos ^{ -1 }{ x } \) is

    (a)

    2

    (b)

    \(\frac { 1 }{ 2\sqrt { 1-{ x }^{ 2 } } } \)

    (c)

    \(\frac { 2 }{ x } \)

    (d)

    \(1-{ x }^{ 2 }\)

  9. Choose the correct or the most suitable answer from the given four alternatives.
    \(If\quad y=\log { \left( \frac { 1-{ x }^{ 2 } }{ 1+{ x }^{ 2 } } \right) } then\quad \frac { dy }{ dx } \quad is\)

    (a)

    \(\frac { 4{ x }^{ 3 } }{ 1-{ x }^{ 4 } } \)

    (b)

    \(-\frac { 4x }{ 1-{ x }^{ 4 } } \)

    (c)

    \(\frac { 1 }{ 4-{ x }^{ 4 } } \)

    (d)

    \(\frac { -4{ x }^{ 3 } }{ 1-{ x }^{ 4 } } \)

  10. Choose the correct or the most suitable answer from the given four alternatives.
    If f(x) is an odd function, then  f'(x) is an ______ function

    (a)

    even

    (b)

    odd

    (c)

    even or odd

    (d)

    neither even nor odd

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