Differential Calculus - Limits and Continuity One Mark Question

11th Standard

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Maths

Time : 00:30:00 Hrs
Total Marks : 10
    10 x 1 = 10
  1. \(lim_{x\rightarrow\infty}{sin \ x \over x} \)

    (a)

    1

    (b)

    0

    (c)

    \(\infty\)

    (d)

    -\(\infty\)

  2. \(lim_{x\rightarrow {\pi/2}}{2x-\pi\over cosx} \)

    (a)

    2

    (b)

    1

    (c)

    -2

    (d)

    0

  3. \(lim_{x \rightarrow \infty}{\sqrt{x^2-1}\over 2x+1}=\)

    (a)

    1

    (b)

    0

    (c)

    -1

    (d)

    \(1\over 2\)

  4. \(lim_{x \rightarrow \infty}{a^x-b^x\over x}=\)

    (a)

    log ab

    (b)

    log\(({a\over b})\)

    (c)

    log\(({b\over a})\)

    (d)

    \({a\over b}\)

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

    (a)

    \(\infty \)

    (b)

    0

    (c)

    1

    (d)

    2

  6. \(\lim _{ x\rightarrow \infty }{ \frac { 1+2+3+....+n }{ { 2n }^{ 2 }+6 } } \)

    (a)

    2

    (b)

    6

    (c)

    \(\frac { 1 }{ 4 } \)

    (d)

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

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

    (a)

    \(\pi \)

    (b)

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

    (c)

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

    (d)

    1

  8. The point of discontinuity for the function \(\frac { { 2x }^{ 2 }-8 }{ x-2 } \) is

    (a)

    0

    (b)

    8

    (c)

    2

    (d)

    4

  9. The function y =\(\frac { \left| 3x-4 \right| }{ 3x-4 } \) is discontinuous at x =

    (a)

    0

    (b)

    \(\frac { 3 }{ 4 } \)

    (c)

    \(\frac { 4 }{ 3 } \)

    (d)

    1

  10. The function \(f\left( x \right) =\tan { x } \) is discontinuous on the set

    (a)

    \(\left\{ n\pi :\quad n\in z \right\} \)

    (b)

    \(\left\{ 2n\pi :\quad n\in z \right\} \)

    (c)

    \(\left\{ (2n+1)\frac { \pi }{ 2 } ,\quad n\in z \right\} \)

    (d)

    \(\left\{ n\frac { \pi }{ 2 } ,\quad n\in z \right\} \)

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