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11th Standard Maths Integral Calculus English Medium Free Online Test One Mark Questions with Answer Key 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. If\(\int f(x)dx=g(x)+c\) ,then\(\int f(x)g'(x)dx\)

    (a)

    \(\int (f(x))^2dx\)

    (b)

    \(\int f(x)g(x)dx\)

    (c)

    \(\int f'(x)g(x)dx\)

    (d)

    \(\int (g(x))^2dx\)

  2. \(\int {e^x(1+x)\over cos^2(xe^x)}dx\) is

    (a)

    cot(xex)+c

    (b)

    sec(xex)+c

    (c)

    tan(xex)+c

    (d)

    cos(xex)+c

  3. \(\int sin^3 \ xdx \) is

    (a)

    \({-3\over 4}cos \ x-{cos \ 3x\over 12}+c\)

    (b)

    \({3\over 4}cos \ x+{cos \ 3x\over 12}+c\)

    (c)

    \({-3\over 4}cos \ x+{cos \ 3x\over 12}+c\)

    (d)

    \({-3\over 4}sin \ x-{sin \ 3x\over 12}+c\)

  4. \(\int{ {e^x}(x^2 \ tan^{-1}x+tan^{-1}x+1)\over x^2+1}dx\) is

    (a)

    ex tan-1(x+1)+c

    (b)

    tan-1(ex)+c

    (c)

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

    (d)

    ex tan-1 x+c

  5. \(\int {sec^2x\over tan^2 \ x-1}\) dx

    (a)

    \(2log|{1-tan x\over 1+tan \ x}|+c\)

    (b)

    \(log|{1+tan x\over 1-tan \ x}|+c\)

    (c)

    \({1\over2}log|{tan x+1\over tan \ x-1}|+c\)

    (d)

    \({1\over2}log|{tan x-1\over tan \ x+1}|+c\)

  6. \(\int e^{\sqrt{x}}dx\) is

    (a)

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

    (b)

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

    (c)

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

    (d)

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

  7. \(\int { sin } \)ex . d (ex) = ________+c.

    (a)

    cos (ex)

    (b)

    sin(ex)

    (c)

    - cos (ex)

    (d)

    -sin(ex)

  8. \(\int { \frac { 4\left( sin^{ -1 }x \right) ^{ 3 } }{ \sqrt { 1-{ x }^{ 2 } } } } \) dx = ________+c.

    (a)

    log (sin -1x)

    (b)

    (sin -1 x)4

    (c)

    4 (sin-1 x)4

    (d)

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

  9. \(\int { \frac { { e }^{ x } }{ \left( 1+{ e }^{ x } \right) ^{ 2 } } } \) dx =_______+c

    (a)

    \(\frac { 1 }{ 1+{ e }^{ x } } \)

    (b)

    -\(\frac { 1 }{ 1+{ e }^{ x } } \)

    (c)

    1 + ex

    (d)

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

  10. \(\int { { tan }^{ 3 } } 2sec2x\) dx = __________________+c.

    (a)

    \(\frac { 1 }{ 6 } \) sec3 2x

    (b)

    \(\frac { 1 }{ 6 } \) sec32x - \(\frac { 1 }{ 2 } \) sec 2x

    (c)

    \(\frac { 1 }{ 2 } \) sec 2x

    (d)

    \(\frac { 1 }{ 6 } \) sec3 2x + \(\frac { 1 }{ 2 } \) sec 2x

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