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11th Standard English Medium Maths Subject Differential Calculus - Limits and Continuity Book Back 1 Mark Questions with Solution Part - I

11th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 10

    1 Marks

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

    (a)

    2

    (b)

    1

    (c)

    -2

    (d)

    0

  2. \(lim_{\theta\rightarrow0}{Sin\sqrt{\theta}\over \sqrt{sin \theta}} \)

    (a)

    1

    (b)

    -1

    (c)

    0

    (d)

    2

  3. \(\underset { x\rightarrow \infty }{ lim } \left( \cfrac { { x }^{ 2 }+5x+3 }{ { x }^{ 2 }+x+3 } \right) ^{ x }\)is

    (a)

    e4

    (b)

    e2

    (c)

    e3

    (d)

    1

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

    (a)

    1

    (b)

    0

    (c)

    -1

    (d)

    \(1\over 2\)

  5. \(lim_{x \rightarrow 0}{a^x-b^x\over x}=\)

    (a)

    log ab

    (b)

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

    (c)

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

    (d)

    \({a\over b}\)

  6. \(lim_{x\rightarrow o}{8^x-4^x-2^x+1^x\over x^2}=\)

    (a)

    2 log 2

    (b)

    2( log2)2

    (c)

    log 2

    (d)

    3 log 2

  7. 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

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

    (a)

    2

    (b)

    3

    (c)

    does not exist

    (d)

    0

  9. Let the function f be defined by \(f(x)=\left\{\begin{array}{ll} 3 x & 0 \leq x \leq 1 \\ -3 x+5 & 1<x \leq 2 \end{array},\right. \text { then }\)

    (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

  10. The value of \(lim_{x\rightarrow k^-}x-\left\lfloor x \right\rfloor \)where k is an integer is

    (a)

    -1

    (b)

    1

    (c)

    0

    (d)

    2

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