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12th Standard Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Eight

12th 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 A = \(\left[ \begin{matrix} 3 & 5 \\ 1 & 2 \end{matrix} \right] \), B = adj A and C = 3A, then \(\frac { \left| adjB \right| }{ \left| C \right| } \)

    (a)

    \(\frac { 1 }{ 3 } \)

    (b)

    \(\frac { 1 }{ 9 } \)

    (c)

    \(\frac { 1 }{ 4 } \)

    (d)

    1

  2. Let A = \(\left[ \begin{matrix} 2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 2 \end{matrix} \right] \) and 4B = \(\left[ \begin{matrix} 3 & 1 & -1 \\ 1 & 3 & x \\ -1 & 1 & 3 \end{matrix} \right] \). If B is the inverse of A, then the value of x is

    (a)

    2

    (b)

    4

    (c)

    3

    (d)

    1

  3. If |z - 2 + i | ≤ 2, then the greatest value of |z| is

    (a)

    \(\sqrt { 3 } -2\)

    (b)

    \(\sqrt { 3 } +2\)

    (c)

    \(\sqrt { 5 } -2\)

    (d)

    \(\sqrt { 5 } +2\)

  4. If \(\omega =cis\cfrac { 2\pi }{ 3 } \), then the number of distinct roots of \(\left| \begin{matrix} z+1 & \omega & { \omega }^{ 2 } \\ \omega & z+{ \omega }^{ 2 } & 1 \\ { \omega }^{ 2 } & 1 & z+\omega \end{matrix} \right| \)=0

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  5. If \(\sin ^{-1} x+\sin ^{-1} y=\frac{2 \pi}{3}\)then cos-1 x + cos-1 y is equal to

    (a)

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

    (b)

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

    (c)

    \(\frac{\pi}{6}\)

    (d)

    \(\pi\)

  6. The domain of cos-1(x2 - 4) is______

    (a)

    [3, 5]

    (b)

    [-1, 1]

    (c)

    \(\left[ -\sqrt { 5 } ,-\sqrt { 3 } \right] \cup \left[ \sqrt { 3 } ,\sqrt { 5 } \right] \)

    (d)

    [0, 1]

  7. The equation 7x2- 6\(\sqrt { 3 } \) xy + 13y2 - 4\(\sqrt { 3 } \) x - 4y - 12 = 0 represents ____________

    (a)

    parabola

    (b)

    ellipse

    (c)

    hyperbola

    (d)

    rectangular hyperbola

  8. If t1 and t2 are the extremities of any focal chord of y2 = 4ax then t1tis ______________

    (a)

    -1

    (b)

    0

    (c)

    ±1

    (d)

    \(\frac12\)

  9. The angle between the vector \(3\overset { \wedge }{ i } +4\overset { \wedge }{ j } +\overset { \wedge }{ 5k } \) and the z-axis is ___________

    (a)

    30o

    (b)

    60o

    (c)

    45o

    (d)

    90o

  10. The distance from the origin to the plane \(\overset { \rightarrow }{ r } .\left( \overset { \wedge }{ 2i } -\overset { \wedge }{ j } +5\overset { \wedge }{ k } \right) =7\) is ______________ 

    (a)

    \(\frac { 7 }{ \sqrt { 30 } } \)

    (b)

    \(\frac { \sqrt { 30 } }{ 7 } \)

    (c)

    \(\frac { 30 }{ 7 } \)

    (d)

    \(\frac { 7 }{ 30 } \)

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