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11th Standard English Medium Maths Subject Differentiability and Methods of Differentiation Creative 1 Mark Questions with Solution Part - II

11th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 5

    1 Marks

    5 x 1 = 5
  1.  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)

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

  2. 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)

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

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

    (a)

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

    (b)

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

    (c)

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

    (d)

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

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

    (a)

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

    (b)

    \(\frac { 2 }{ 1+{ x }^{ 2 } } \)

    (c)

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

    (d)

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

  5. Choose the correct or the most suitable answer from the given four alternatives.
    If, \(y=a+b{ x }^{ 2 }\) where a, b are arbitrary constants, then ____

    (a)

    \(\frac { d^{ 2 }y }{ d{ x }^{ 2 } } =2xy\)

    (b)

    \(x\frac { d^{ 2 }y }{ d{ x }^{ 2 } } ={ y }_{ 1 }\)

    (c)

    \(x\frac { d^{ 2 }y }{ d{ x }^{ 2 } } -\frac { dy }{ dx } +y=0\)

    (d)

    \(x\frac { d^{ 2 }y }{ d{ x }^{ 2 } } =2xy\)

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