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11th Standard Maths Differentiability & Methods of Differentiation English Medium Free Online Test 1 Mark Questions with Answer key 2020-2021

11th Standard

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Maths

Time : 00:10:00 Hrs
Total Marks : 10
    10 x 1 = 10
  1. If g(x)=(x2+2x+3) f(x) and f(0)=5 and \(lim_{x \rightarrow 0}{f(x)-5\over x}=4\),then g'(0) is 

    (a)

    20

    (b)

    14

    (c)

    18

    (d)

    12

  2. The derivative of f(x)=x|x| at x =−3 is

    (a)

    6

    (b)

    -6

    (c)

    does not exist

    (d)

    0

  3.  Choose the correct or the most suitable answer from the given four alternatives.
     \(If\quad y=\sin ^{ -1 }{ x } +\cos ^{ -1 }{ x } \) then\(\frac { dy }{ dx } \) is

    (a)

    1

    (b)

    \(\pi \)

    (c)

    \(\frac { \pi }{ 2 } \)

    (d)

    0

  4. Choose the correct or the most suitable answer from the given four alternatives.
    If \(f\left( x \right) =x+1\), then \(\frac { d }{ dx } ({ f }_{ 0 }f\left( x \right) )\) is

    (a)

    1

    (b)

    0

    (c)

    2

    (d)

    x

  5. Choose the correct or the most suitable answer from the given four alternatives.
    For the curve \(\sqrt { x } +\sqrt { y } =1,\quad \frac { dy }{ dx } at\left( \frac { 1 }{ 4 } ,\frac { 1 }{ 4 } \right) is\)

    (a)

    \(\frac { 1 }{ 2 } \)

    (b)

    1

    (c)

    -1

    (d)

    2

  6. 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)

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

  7. Choose the correct or the most suitable answer from the given four alternatives.
    \(If\quad x=a(\theta +\sin { \theta ),y=a(1+\cos { \theta } ) } then\quad \frac { dy }{ dx }\) is

    (a)

    \(\tan { \frac { \theta }{ 2 } } \)

    (b)

    \(-\tan { \frac { \theta }{ 2 } } \)

    (c)

    \(\cot { \frac { \theta }{ 2 } } \)

    (d)

    \(-\cot { \frac { \theta }{ 2 } } \)

  8. Choose the correct statement

    (a)

    Derivative of odd functionis odd

    (b)

    Derivative of even function is even

    (c)

    Inverse of odd function is even

    (d)

    Inverse function of sin x is sin-1 x

  9. Assertion (A):f (x) =\(\begin{cases} \begin{matrix} x+1, & x<2 \end{matrix} \\ \begin{matrix} 2x-1, & x\ge 2 \end{matrix} \end{cases}\) then f'(2) does not exist.
    Reason (R) :f(x) is not continuous at 2.

    (a)

    Both A and it are true and R is the correct explanation of A

    (b)

    Both A and R are true but R is not the correct explantion of A

    (c)

    A is true R is false

    (d)

    A is false R is true

  10. Choose the incorrect pair

    (a)

    330o\(\frac{11\pi}{6}\)radians

    (b)

    \(\frac{7\pi^c}{3}\) - 200o

    (c)

    0o - 0c

    (d)

    2\(\pi\)c - 360o

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