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12th Standard Business Maths Integral Calculus – I English Medium Free Online Test One Mark Questions 2020 - 2021

12th Standard

    Reg.No. :
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Business Maths

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

    Answer all the questions

    10 x 1 = 10
  1. \(\frac { 1 }{ { x }^{ 3 } } \)dx is _______.

    (a)

    \(\frac { -3 }{ { x }^{ 2 } } +c\)

    (b)

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

    (c)

    \(\frac { -1 }{ { 3x }^{ 2 } } +c\)

    (d)

    \(\frac { -2 }{ { x }^{ 2 } } +c\)

  2. \(\frac{logx}{x}\) dx , x > 0 is _______.

    (a)

    \(\frac12\)(log x)2 + c

    (b)

    -\(\frac12\)(log x)2

    (c)

    \(\frac { 2 }{ { x }^{ 2 } } +c\)

    (d)

    \(\frac { 2 }{ { x }^{ 2 } } +c\)

  3. \(\sqrt { { e }^{ x } } \) dx is _______.

    (a)

    \(\sqrt { { e }^{ x } } +c\)

    (b)

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

    (c)

    \(\frac12\sqrt { { e }^{ x } } +c\)

    (d)

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

  4. \(\frac { { e }^{ x } }{ { e }^{ x }+1 } \) dx is _______.

    (a)

    log\(\left| \frac { { e }^{ x } }{ { e }^{ x }+1 } \right| +c\)

    (b)

    log\(\left| \frac { { e }^{ x }+1 }{ { e }^{ x } } \right| +c\)

    (c)

    log\(\left| { e }^{ x } \right| +c\)

    (d)

    log\(\left| { e }^{ x }+1 \right| +c\)

  5. \(\frac { { 2x }^{ 3 } }{ 4+{ x }^{ 4 } } \)dx is _______.

    (a)

    \(log\left| 4+{ x }^{ 4 } \right| +c\)

    (b)

    \(\frac { 1 }{ 2 } log\left| 4+{ x }^{ 4 } \right| +c\)

    (c)

    \(\frac { 1 }{4 } log\left| 4+{ x }^{ 4 } \right| +c\)

    (d)

    \(log\left| \frac { { 2x }^{ 3 } }{ { 4+x }^{ 4 } } \right| +c\)

  6. \(\frac { 2x+3 }{ \sqrt { x^{ 2 }+3x+2 } } \) dx is _______.

    (a)

    \(\sqrt { x^{ 2 }+3x+2 } \) + c

    (b)

    \(2​​\sqrt { x^{ 2 }+3x+2 } +c\)

    (c)

    log(x2 + 3x + 2)+ c

    (d)

    \(\frac{2}{3}\left(x^{2}+3 x+2\right)^{\frac{3}{2}}+c\)

  7. \(\int _{ -1 }^{ 1 }{ { x }^{ 3 }{ e }^{ { x }^{ 4 } } } \) dx is _______.

    (a)

    1

    (b)

    2\(\int _{ -1 }^{ 1 }{ { x }^{ 3 }{ e }^{ { x }^{ 4 } } } \)dx

    (c)

    0

    (d)

    \({ e }^{ { x }^{ 4 } }\)

  8. \(\int { \left( x-1 \right) } { e }^{ -x }\) dx = __________ +c

    (a)

    -xex

    (b)

    xex

    (c)

    -xe-x

    (d)

    xe-x

  9. \(\int { { \left| x \right| }^{ 3 } } \)dx = ________________ +c

    (a)

    \(\frac { { -x }^{ 4 } }{ 4 } \)

    (b)

    \(\frac { { \left| x \right| }^{ 4 } }{ 4 } \)

    (c)

    \(\frac { { x }^{ 4 } }{ 4 } \)

    (d)

    none of these

  10. If ∫ x sin x dx = - x cos x + α then α = __________ +c

    (a)

    sin x

    (b)

    cos x

    (c)

    C

    (d)

    none of these

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