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12th Standard Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Four

12th Standard

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Maths

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

    Answer all the questions

    10 x 1 = 10
  1. If A = \(\left[ \begin{matrix} 1 & \tan { \frac { \theta }{ 2 } } \\ -\tan { \frac { \theta }{ 2 } } & 1 \end{matrix} \right] \) and AB = I , then B = 

    (a)

    \(\left( \cos ^{ 2 }{ \frac { \theta }{ 2 } } \right) A\)

    (b)

    \(\left( \cos ^{ 2 }{ \frac { \theta }{ 2 } } \right) { A }^{ T }\)

    (c)

    \(\left( \cos ^{ 2 }{ \theta } \right) I\)

    (d)

    (Sin2\(\frac { \theta }{ 2 } \))A

  2. If \(\sqrt { a+ib } \) =x+iy, then possible value of \(\sqrt { a-ib }\) is

    (a)

    x2+y2

    (b)

    \(\sqrt { { x }^{ 2 }+{ y }^{ 2 } } \)

    (c)

    x+iy

    (d)

    x-iy

  3. The complex number z which satisfies the condition \(\left| \frac { 1+z }{ 1-z } \right| \) =1 lies on

    (a)

    circle x2+y2 =1

    (b)

    x-axis

    (c)

    y-axis

    (d)

    the lines x+y=1

  4. Let a > 0, b > 0, c >0. h n both th root of th quatlon ax2+b+C= 0 are

    (a)

    real and negative

    (b)

    real and positive

    (c)

    rational numb rs

    (d)

    none

  5. The value of tan \(\left( { cos }^{ -1 }\cfrac { 3 }{ 5 } +{ tan }^{ -1 }\cfrac { 1 }{ 4 } \right) \) is ______

    (a)

    \(\cfrac { 19 }{ 8 } \)

    (b)

    \(\cfrac { 8 }{ 19 } \)

    (c)

    \(\cfrac { 19 }{ 12 } \)

    (d)

    \(\cfrac { 3 }{ 4 } \)

  6. The equation of the director circle of the hyperbola \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } \) = 1 is ___________

    (a)

    x2 + y2 = a2+ b2

    (b)

    x2 +y2 = a2

    (c)

    x2+ y2 = b2

    (d)

    x2+y2 = a2- b2

  7. If  \(\left| \overset { \rightarrow }{ a } \right| =\left| \overset { \rightarrow }{ b } \right| =1\)such that \(\overset { \rightarrow }{ a } +2\overset { \rightarrow }{ b } \) and \(5\overset { \rightarrow }{ a } -\overset { \rightarrow }{ b } \) are perpendicular to each other, then the angle between \(\overset { \rightarrow }{ a } \) and \(\overset { \rightarrow }{ b } \) is

    (a)

    45o

    (b)

    60o

    (c)

    cos-1 \(\left( \frac { 1 }{ 3 } \right) \)

    (d)

    cos-1 \(\left( \frac { 2 }{ 7 } \right) \)

  8. The length of the 丄r from the origin to plane \(\overset { \rightarrow }{ r } .\left( \overset { \wedge }{ 3i } +4\overset { \wedge }{ j } +12\overset { \wedge }{ k } \right) \)26 is _____________

    (a)

    2

    (b)

    \(\frac { 1 }{ 2 } \)

    (c)

    26

    (d)

    \(\frac { 26 }{ 169 } \)

  9. The order and degree of the differential equation \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +{ \left( \frac { dy }{ dx } \right) }^{ 1/3 }+{ x }^{ 1/4 }=0\)are respectively

    (a)

    2, 3

    (b)

    3, 3

    (c)

    2, 6

    (d)

    2, 4

  10. The integrating factor of the differential equation \(\frac { dy }{ dx } +y=\frac { 1+y }{ \lambda } \) is

    (a)

    \(\frac { x }{ { e }^{ \lambda } } \)

    (b)

    \(\frac { { e }^{ \lambda } }{ x } \)

    (c)

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

    (d)

    ex

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