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11th Standard Maths Differential Calculus - Limits and Continuity English Medium Free Online Test One Mark Questions 2020 - 2021

11th Standard

    Reg.No. :
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Maths

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

    Answer all the questions

    10 x 1 = 10
  1. \(lim_{x\rightarrow\infty}{sin \ x \over x} \)

    (a)

    1

    (b)

    0

    (c)

    \(\infty\)

    (d)

    -\(\infty\)

  2. \(lim_{x\rightarrow0}{\sqrt{1-cos 2x}\over x} \)

    (a)

    0

    (b)

    1

    (c)

    \(\sqrt{2}\)

    (d)

    does not exist

  3. If f(x)=x(-1)\(\left\lfloor 1\over x \right\rfloor \),\(x\le0\),then the value of \(lim_{x\rightarrow 0}f(x)\) is equal to

    (a)

    -1

    (b)

    0

    (c)

    2

    (d)

    4

  4. Let the function f be defined by  ,then

    (a)

    \(lim_{x \rightarrow1}f(x)=1\)

    (b)

    \(lim_{x \rightarrow1}f(x)=3\)

    (c)

    \(lim_{x \rightarrow1}f(x)=2\)

    (d)

    \(lim_{x \rightarrow1}f(x)\) does not exist

  5. The value of \(lim_{x \rightarrow 0}{sin x\over \sqrt{x^2}}\) is

    (a)

    1

    (b)

    -1

    (c)

    0

    (d)

    \(\infty\)

  6. The function is not defined for x = −1. The value of f(−1) so that the function extended by this value is continuous is

    (a)

    \({2\over3}\)

    (b)

    -\({2\over3}\)

    (c)

    1

    (d)

    0

  7. \(\lim _{ x\rightarrow 2 }{ \frac { 2{ x }^{ 2 }+x+1 }{ x+2 } } \) is equal to

    (a)

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

    (b)

    2

    (c)

    \(\frac { 11 }{ 4 } \)

    (d)

    0

  8. \(\lim _{ x\rightarrow \infty }{ \left( \frac { 1 }{ x } +2 \right) } \)is equal to

    (a)

    \(\infty \)

    (b)

    0

    (c)

    1

    (d)

    2

  9. \(\lim _{ x\rightarrow \frac { \pi }{ 2 } }{ \frac { \sin { x } }{ x } } =\)

    (a)

    \(\pi \)

    (b)

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

    (c)

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

    (d)

    1

  10. The slop of the curve \(y={ x }^{ 3 }-7{ x }^{ 2 }+5x+10\quad \) at x=1 is

    (a)

    6

    (b)

    -6

    (c)

    5

    (d)

    15

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