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12th Standard Maths English Medium Free Online Test Volume 1 One Mark Questions 2020

12th Standard

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Maths

Time : 00:25:00 Hrs
Total Marks : 25

    Answer all the questions

    25 x 1 = 25
  1. If A is a non-singular matrix such that A-1 = \(\left[ \begin{matrix} 5 & 3 \\ -2 & -1 \end{matrix} \right] \), then (AT)−1 =

    (a)

    \(\left[ \begin{matrix} -5 & 3 \\ 2 & 1 \end{matrix} \right] \)

    (b)

    \(\left[ \begin{matrix} 5 & 3 \\ -2 & -1 \end{matrix} \right] \)

    (c)

    \(\left[ \begin{matrix} -1 & -3 \\ 2 & 5 \end{matrix} \right] \)

    (d)

    \(\left[ \begin{matrix} 5 & -2 \\ 3 & -1 \end{matrix} \right] \)

  2. If A =\(\left( \begin{matrix} cosx & sinx \\ -sinx & cosx \end{matrix} \right) \) and A(adj A) =\(\lambda \) \(\left( \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right) \) then \(\lambda \) is

    (a)

    sinx cosx

    (b)

    1

    (c)

    2

    (d)

    none

  3. In the non - homogeneous system of equations with 3 unknowns if \(\rho\)(A) = \(\rho\)([AIB]) = 2, then the system has _______

    (a)

    unique solution

    (b)

    one parameter family of solution

    (c)

    two parameter family of solutions

    (d)

    in consistent

  4. If A = [2 0 1] then the rank of AAT is ______

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    0

  5. The conjugate of a complex number is \(\cfrac { 1 }{ i-2 } \)/Then the complex number is

    (a)

    \(\cfrac { 1 }{ i+2 } \)

    (b)

    \(\cfrac { -1 }{ i+2 } \)

    (c)

    \(\cfrac { -1 }{ i-2 } \)

    (d)

    \(\cfrac { 1 }{ i-2 } \)

  6. If z=cos\(\frac { \pi }{ 4 } \)+i sin\(\frac { \pi }{ 6 } \), then

    (a)

    |z| =1, arg(z) =\(\frac { \pi }{ 4 } \)

    (b)

    |z| =1, arg(z) =\(\frac { \pi }{ 6 } \)

    (c)

    |z|=\(\frac { \sqrt { 3 } }{ 2 } \), arg(z)=\(\frac { 5\pi }{ 24 } \)

    (d)

    |z| =\(\frac { \sqrt { 3 } }{ 2 } \), arg (z) =tan-1\(\left( \frac { 1 }{ \sqrt { 2 } } \right) \)

  7. If z = \(\frac { 1 }{ (2+3i)^{ 2 } } \) then |z| =

    (a)

    \(\frac { 1 }{ 13 } \)

    (b)

    \(\frac { 1 }{ 5} \)

    (c)

    \(\frac { 1 }{ 12 } \)

    (d)

    none of these

  8. If a =cosα + i sinα, b= -cosβ + i sinβ then \(\left( ab-\frac { 1 }{ ab } \right) \) is _________

    (a)

    -2i sin(α - β)

    (b)

    2i sin(α - β)

    (c)

    2 cos(α - β)

    (d)

    -2 cos(α - β)

  9. If x3+12x2+10ax+1999 definitely has a positive zero, if and only if

    (a)

    a≥0

    (b)

    a>0

    (c)

    a<0

    (d)

    a≤0

  10. For real x, the equation \(\left| \frac { x }{ x-1 } \right| +|x|=\frac { { x }^{ 2 } }{ |x-1| } \) has

    (a)

    one solution

    (b)

    two solution

    (c)

    at least two solution

    (d)

    no solution

  11. If x2 - hx - 21 = 0 and x2 - 3hx + 35 = 0 (h > 0) have a common root, then h = ___________

    (a)

    0

    (b)

    1

    (c)

    4

    (d)

    3

  12. The number of real solutions of the equation \(\sqrt { 1+cos2x } ={ 2sin }^{ -1 }\left( sinx \right) ,-\pi <x<\pi \) is

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    infinte

  13. If tan-1(3)+tan-1(x)=tan-1(8)then x= 

    (a)

    5

    (b)

    \(\cfrac { 1 }{ 5 } \)

    (c)

    \(\cfrac { 5 }{ 14 } \)

    (d)

    \(\cfrac { 14 }{ 5 } \)

  14. 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)

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

  15. The equation of the normal to the circle x2+y2−2x−2y+1=0 which is parallel to the line
    2x+4y=3 is

    (a)

    x+2y=3

    (b)

    x+2y+3= 0

    (c)

    2x+4y+3=0

    (d)

    x−2y+3= 0

  16. Equation of tangent at (-4, -4) on x2 = -4y is

    (a)

    2x - y + 4 = 0

    (b)

    2x + y - 4 = 0

    (c)

    2x - y - 12 = 0

    (d)

    2x + y + 4 = 0

  17. The area of the circle (x - 2)2 + (y - k)2 = 25 is

    (a)

    25ㅠ

    (b)

    5ㅠ

    (c)

    10ㅠ

    (d)

    25

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

    (a)

    -1

    (b)

    0

    (c)

    ±1

    (d)

    \(\frac12\)

  19. If \(\vec { a } \) and \(\vec { b } \) are unit vectors such that \([\vec { a } ,\vec { b },\vec { a } \times \vec { b } ]=\frac { \pi }{ 4 } \), then the angle between \(\vec { a } \) and \(\vec { b } \) is

    (a)

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

    (b)

    \(\frac { \pi }{ 4 } \)

    (c)

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

    (d)

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

  20. 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

  21. If \(\overset { \rightarrow }{ a } =\overset { \wedge }{ i } +\overset { \wedge }{ 2j } +\overset { \wedge }{ 3k } \)\(\overset { \rightarrow }{ b } =-\overset { \wedge }{ i } +\overset { \wedge }{ 2j } +\overset { \wedge }{ k } \)\(\overset { \rightarrow }{ c } =3\overset { \wedge }{ i } +\overset { \wedge }{ j } \) then \(\overset { \rightarrow }{ a } +\left( -\overset { \rightarrow }{ b } \right) \)will be perpendiculur to \(\overset { \rightarrow }{ c } \) only when t =

    (a)

    5

    (b)

    4

    (c)

    3

    (d)

    \(\frac { 7 }{ 3 } \)

  22. The value of \({ \left| \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right| }^{ 2 }+{ \left| \overset { \rightarrow }{ a } -\overset { \rightarrow }{ b } \right| }^{ 2 }\) is

    (a)

    \(2\left( { \left| \overset { \rightarrow }{ a } \right| }^{ 2 }+{ \left| \overset { \rightarrow }{ b } \right| }^{ 2 } \right) \)

    (b)

    \(\overset { \rightarrow }{ a } .\overset { \rightarrow }{ b } \)

    (c)

    \(2\left( { \left| \overset { \rightarrow }{ a } \right| }^{ 2 }-{ \left| \overset { \rightarrow }{ b } \right| }^{ 2 } \right) \)

    (d)

    \({ \left| \overset { \rightarrow }{ a } \right| }^{ 2 }{ \left| \overset { \rightarrow }{ b } \right| }^{ 2 }\)

  23. If \(\lambda \overset { \wedge }{ i } +2\lambda \overset { \wedge }{ j } +2\lambda \overset { \wedge }{ k } \) is a unit vector, then the value of λ is 

    (a)

    土 \(\frac { 1 }{ 3 } \)

    (b)

    土 \(\frac { 1 }{ 4 } \)

    (c)

    土 \(\frac { 1 }{ 9 } \)

    (d)

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

  24. The unit normal vectors to the plane 2x - y + 2z = 5 are ________________

    (a)

    \(\overset { \wedge }{ 2i } -\overset { \wedge }{ j } +2\overset { \wedge }{ k } \)

    (b)

    \(\frac { 1 }{ 3 } \left( \overset { \wedge }{ 2i } -\overset { \wedge }{ j } +2\overset { \wedge }{ k } \right) \)

    (c)

    \(-\frac { 1 }{ 3 } \left( \overset { \wedge }{ 2i } -\overset { \wedge }{ j } +2\overset { \wedge }{ k } \right) \)

    (d)

    \(\pm \frac { 1 }{ 3 } \left( \overset { \wedge }{ 2i } -\overset { \wedge }{ j } +2\overset { \wedge }{ k } \right) \)

  25. The area of the parallelogram having diagonals \(\overset { \rightarrow }{ a } =\overset { \wedge }{ 3i } +\overset { \wedge }{ j } -2\overset { \wedge }{ k } \) and \(\overset { \rightarrow }{ b } =\overset { \wedge }{ i } -3\overset { \wedge }{ j } +4\overset { \wedge }{ k } \) is _______________

    (a)

    4

    (b)

    \(2\sqrt { 3 } \)

    (c)

    \(4\sqrt { 3 } \)

    (d)

    \(5\sqrt { 3 } \)

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