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11th Standard Maths Differential Calculus - Limits and Continuity 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

    Answer all the questions

    10 x 1 = 10
  1. \(lim_{x\rightarrow {\pi/2}}{2x-\pi\over cosx} \)

    (a)

    2

    (b)

    1

    (c)

    -2

    (d)

    0

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

    (a)

    1

    (b)

    0

    (c)

    -1

    (d)

    \(1\over 2\)

  3. \(lim_{x \rightarrow 3}\left\lfloor x \right\rfloor =\)

    (a)

    2

    (b)

    3

    (c)

    does not exist

    (d)

    0

  4. If f : \(R \rightarrow R\) is defined by f(x)=\(\left\lfloor x-3 \right\rfloor +|x-4|\) for \(x \in R\), then\(lim_{x\rightarrow 3^-}f(x)\) is equal to

    (a)

    -2

    (b)

    -1

    (c)

    0

    (d)

    1

  5. \(lim_{n \rightarrow \infty}({1\over n^2}+{2\over n^2}+{3\over n^2}+..+{n\over n^2})\) is

    (a)

    \(1\over 2\)

    (b)

    0

    (c)

    1

    (d)

    \(\infty\)

  6. Let f :\(R \rightarrow R\) be defined by            then f is

    (a)

    discontinuous at x = \({1\over 2}\)

    (b)

    continuous at  x = \({1\over 2}\)

    (c)

    continuous everywhere

    (d)

    discontinuous everywhere

  7. \(\lim _{ x\rightarrow 1 }{ \frac { { x }^{ m }-1 }{ { x }^{ n }-1 } } is\)

    (a)

    mn

    (b)

    m+n

    (c)

    m-n

    (d)

    \(\frac { m }{ n } \)

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

    (a)

    2

    (b)

    6

    (c)

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

    (d)

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

  9. The points of discontinuity of the function \(\frac { { x }^{ 2 }+6x+8\quad }{ { x }^{ 2 }-5x+6\quad } is\)

    (a)

    3,2

    (b)

    3,-2

    (c)

    -3,2

    (d)

    -3,-2

  10. Find the odd one of the following

    (a)

    x2

    (b)

    x4

    (c)

    cos x

    (d)

    sin x

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