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11th Standard Maths Integral Calculus English Medium Free Online Test One Mark Questions 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. If \(\int {3^{1\over x}\over x^2}dx=k(3^{1\over x})+c\) ,then the value of k is

    (a)

    log 3

    (b)

    -log 3

    (c)

    \(-{1\over log3}\)

    (d)

    \({1\over log3}\)

  2. \(\int {e^{6logx}-e^{5logx}\over e^{4logx}-e^{3logx}}dx\) is

    (a)

    x+c

    (b)

    \({x^3\over 3}+c\)

    (c)

    \({3\over x^3}+c\)

    (d)

    \({1\over x^2}+c\)

  3. \(\int {sin^8x-cos^8x\over 1-2sin^2 \ x \ cos^2 \ x}dx\) is

    (a)

    \({1\over2}sin 2x+c\)

    (b)

    \(-{1\over2}sin 2x+c\)

    (c)

    \({1\over2}cos 2x+c\)

    (d)

    \(-{1\over2}cos 2x+c\)

  4. \(\int{x^2+cos^2x\over x^2+1}cosec^2xdx\) is

    (a)

    cot x+sin -1x+c

    (b)

    -cot x+tan-1x+c

    (c)

    -tan x+cot-1x+c

    (d)

    -cot x-tan-1x+c

  5. \(\int e^{-4x}cos \ x \ d x\) is

    (a)

    \({e^{-4x}\over 17}[4cos \ x-sin \ x]+c\)

    (b)

    \({e^{-4x}\over 17}[-4cos \ x+sin \ x]+c\)

    (c)

    \({e^{-4x}\over 17}[4cos \ x+sin \ x]+c\)

    (d)

    \({e^{-4x}\over 17}[-4cos \ x-sin \ x]+c\)

  6. \(\int {x+2\over \sqrt{x^2+1}}dx\)is

    (a)

    \(\sqrt{x^2-1}-2 log|x+\sqrt{x^2-1}|+c\)

    (b)

    \(sin^{-1}x-2 log|x+\sqrt{x^2-1}|+c\)

    (c)

    \(2 log|x+\sqrt{x^2-1}|-sin^{-1}x+c\)

    (d)

    \(\sqrt{x^2-1}+2log|x+\sqrt{x^2-1}|+c\)

  7. \(\int sin \sqrt{x}\) dx is

    (a)

    \(2(-\sqrt{x}cos\sqrt{x}+sin\sqrt{x})+c\)

    (b)

    \(2(-\sqrt{x}cos\sqrt{x}-sin\sqrt{x})+c\)

    (c)

    \(2(-\sqrt{x}sin\sqrt{x}-cos\sqrt{x})+c\)

    (d)

    \(2(-\sqrt{x}sin\sqrt{x}+cos\sqrt{x})+c\)

  8. \(\int { \frac { \left( 1+logx \right) ^{ 2 } }{ x } } \) dx = _______+C.

    (a)

    \(\frac { \left( 1+logx \right) ^{ 3 } }{ 3 } \)

    (b)

    3 log ( 1 + log x)

    (c)

    2(1 + log x)

    (d)

    none of these

  9. \(\int { \frac { 1 }{ 9x^{ 2 }-4 } } \) dx = ____________+c.

    (a)

    log\(\left| \frac { 3x-2 }{ 3x+2 } \right| \)

    (b)

    \(\frac { 1 }{ 12 } \)log\(\left| \frac { 3x-2 }{ 3x+2 } \right| \)

    (c)

    12log\(\left| \frac { 3x-2 }{ 3x+2 } \right| \)

    (d)

    \(\frac { 1 }{ 12 } log\left| \frac { 3x+2 }{ 3x-2 } \right| \)

  10. \(\int { \frac { x }{ 4+{ x }^{ 4 } } } \) dx is equal to________+c.

    (a)

    \(\frac { 1 }{ 4 } \) tan-1 (x2)

    (b)

    \(\frac { 1 }{ 4 } \) tan-1 \(\left( \frac { { x }^{ 2 } }{ 2 } \right) \)

    (c)

    \(\frac { 1 }{ 2 } \) tan-1 \(\left( \frac { { x }^{ 2 } }{ 2 } \right) \)

    (d)

    none of these

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