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12th Standard Maths English Medium Free Online Test Book Back One Mark Questions - Part Two

12th Standard EM

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Maths

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

    Answer all the questions

    10 x 1 = 10
  1. If A = \(\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right] \) then |adj (AB)| = 

    (a)

    -40

    (b)

    -80

    (c)

    -60

    (d)

    -20

  2. If \(z=\cfrac { \left( \sqrt { 3 } +i \right) ^{ 3 }\left( 3i+4 \right) ^{ 2 } }{ \left( 8+6i \right) ^{ 2 } } \) , then |z| is equal to 
     

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    3

  3. The polynomial x3+2x+3 has

    (a)

    one negative and two real roots

    (b)

    one positive and two imaginary roots

    (c)

    three real roots

    (d)

    no solution

  4. The domain of the function defined by f(x)=sin−1\(\sqrt{x-1} \) is

    (a)

    [1,2]

    (b)

    [-1,1]

    (c)

    [0,1]

    (d)

    [-1,0]

  5. The length of the diameter of the circle which touches the x -axis at the point (1,0) and passes through the point (2,3) .

    (a)

    \(\frac { 6 }{ 5 } \)

    (b)

    \(\frac { 5 }{ 3 } \)

    (c)

    \(\frac { 10 }{ 5 } \)

    (d)

    \(\frac { 3 }{ 5 } \)

  6. Tangents are drawn to the hyperbola  \(\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1\) 1parallel to the straight line2x−y=1. One of the points of contact of tangents on the hyperbola is

    (a)

    \(\frac { 9 }{ 2\sqrt { 2 } } ,\frac { -1 }{ \sqrt { 2 } } \)

    (b)

    \(\frac { -9 }{ 2\sqrt { 2 } } ,\frac { 1 }{ \sqrt { 2 } } \)

    (c)

    \(\frac { 9 }{ 2\sqrt { 2 } } ,\frac { 1 }{ \sqrt { 2 } } \)

    (d)

    \(\left( 3\sqrt { 3 } ,-2\sqrt { 2 } \right) \)

  7. If the volume of the parallelepiped with \(\vec { a } \times \vec { b } ,\vec { b } \times \vec { c } ,\vec { c } \times \vec { a } \)  as coterminous edges is 8 cubic units, then the volume of the parallelepiped with \((\vec { a } \times \vec { b } )\times (\vec { b } \times \vec { c } ),(\vec { b } \times \vec { c } )\times (\vec { c } \times \vec { a } )\) and \((\vec { c } \times \vec { a } )\times (\vec { a } \times \vec { b } )\)as coterminous edges is, 

    (a)

    8 cubic units

    (b)

    512 cubic units

    (c)

    64 cubic units

    (d)

    24 cubic units

  8. The abscissa of the point on the curve \(f\left( x \right) =\sqrt { 8-2x } \) at which the slope of the tangent is -0.25 ?

    (a)

    -8

    (b)

    -4

    (c)

    -2

    (d)

    0

  9. If v (x, y) = log (ex + ev), then \(\frac { { \partial }v }{ \partial x } +\frac { \partial v }{ \partial y } \) is equal to

    (a)

    ex + ey

    (b)

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

    (c)

    2

    (d)

    1

  10. The value of \(\int _{ 0 }^{ \pi }{ \frac { dx }{ 1+{ 5 }^{ cos\ x } } } \) is

    (a)

    \(\frac{\pi}{2}\)

    (b)

    \(\pi\)

    (c)

    \(\frac{3\pi}{2}\)

    (d)

    \(2\pi\)

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