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

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 is a 3 × 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT = 

    (a)

    A

    (b)

    B

    (c)

    I

    (d)

    BT

  2. If A, B and C are invertible matrices of some order, then which one of the following is not true?

    (a)

    adj A = |A|A-1

    (b)

    adj(AB) = (adj A)(adj B)

    (c)

    det A-1 = (det A)-1

    (d)

    (ABC)-1 = C-1B-1A-1

  3. If A = \(\left[ \begin{matrix} \frac { 3 }{ 5 } & \frac { 4 }{ 5 } \\ x & \frac { 3 }{ 5 } \end{matrix} \right] \) and AT = A−1 , then the value of x is

    (a)

    \(\frac { -4 }{ 5 } \)

    (b)

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

    (c)

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

    (d)

    \(\frac { 4 }{ 5 } \)

  4. If A = \(\left[ \begin{matrix} 2 & 3 \\ 5 & -2 \end{matrix} \right] \) be such that λA−1 =A, then λ is

    (a)

    17

    (b)

    14

    (c)

    19

    (d)

    21

  5. The area of the triangle formed by the complex numbers z,iz, and z+iz in the Argand’s diagram is

    (a)

    \(\cfrac { 1 }{ 2 } \left| z \right| ^{ 2 }\)

    (b)

    |z|2

    (c)

    \(\cfrac { 3 }{ 2 } \left| z \right| ^{ 2 }\)

    (d)

    2|z|2

  6. If z is a non zero complex number, such that 2iz2=\(\bar { z } \) then |z| is

    (a)

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

    (b)

    1

    (c)

    2

    (d)

    3

  7. If |z1|=1,|z2|=2|z3|=3 and |9z1z2+4z1z3+z2z3|=12, then the value of |z1+z2+z3| is 

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  8. The principal argument of \(\cfrac { 3 }{ -1+i } \)

    (a)

    \(\cfrac { -5\pi }{ 6 } \)

    (b)

    \(\cfrac { -2\pi }{ 3 } \)

    (c)

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

    (d)

    \(\cfrac { -\pi }{ 2 } \)

  9. If the coordinates at one end of a diameter of the circle x2+y2−8x−4y+c = 0 are (11,2) ,
    the coordinates of the other end are

    (a)

    (-5,2)

    (b)

    (2,-5)

    (c)

    (5,-2)

    (d)

    (-2,5)

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

    (a)

    4

    (b)

    2\(\sqrt { 3 } \)

    (c)

    4\(\sqrt { 3 } \)

    (d)

    5\(\sqrt { 3 } \)

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