Quarterly Exam Model Two Marks Questions

12th Standard EM

    Reg.No. :
  •  
  •  
  •  
  •  
  •  
  •  

Maths

Time : 01:00:00 Hrs
Total Marks : 30
    15 x 2 = 30
  1. If A = \(\left[ \begin{matrix} a & b \\ c & d \end{matrix} \right] \) is non-singular, find A−1.

  2. Reduce the matrix \(\left[ \begin{matrix} 3 & -1 & 2 \\ -6 & 2 & 4 \\ -3 & 1 & 2 \end{matrix} \right] \) to a row-echelon form.

  3. Find the rank of the following matrices by minor method:
    \(\left[ \begin{matrix} 1 & -2 & 3 \\ 2 & 4 & -6 \\ 5 & 1 & -1 \end{matrix} \right] \)

  4. Simplify \(\left( \cfrac { 1+i }{ 1-i } \right) ^{ 3 }-\left( \cfrac { 1-i }{ 1+i } \right) ^{ 3 }\)

  5. Represent the complex number −1−i

  6. Find the following \(\left| \cfrac { i(2+i)^{ 3 } }{ \left( 1+i \right) ^{ 2 } } \right| \)

  7. If (cosθ + i sinθ)2 = x + iy, then show that x2+y2 =1

  8. Find the principal value of sin-1 \(\left( -\frac { 1 }{ 2 } \right) \)(in radians and degrees).

  9. Find the value of  
    i) \({ sin }^{ -1 }\left( sin\left( \frac { 5\pi }{ 4 } \right) \right) \)
    ii) \({ sin }^{ -1 }\left( sin\left( \frac { 2\pi }{ 3 } \right) \right) \)

  10. Find the value of
    \({ cos }^{ -1 }\left( cos\frac { \pi }{ 7 } cos\frac { \pi }{ 17 } -sin\frac { \pi }{ 17 } sin\frac { \pi }{ 17 } \right) .\)

  11. Prove that \(2{ tan }^{ -1 }\left( \cfrac { 2 }{ 3 } \right) ={ tan }^{ -1 }\left( \cfrac { 12 }{ 5 } \right) \)
     

  12. y2+4x+3y+4=0

  13. If \(\vec { a } =\hat { i } -2\hat { j } +3\hat { k }, \vec { 6 } =2\hat { i } +\hat { j } -2\hat { k }, \vec { c } =3\hat { i } +2\hat { j } +\hat { k } \) find \(\vec { a } .(\vec { b } \times \vec { c } )\).

  14. Find the distance of a point (2,5, −3) from the plane \(\vec { r } .(6\hat { i } -3\hat { j } +2\hat { k } )\)=5

  15. Find the parametric form of vector equation of a line passing through a point (2, -1, 3) and parallel to line \({ \overset { \rightarrow }{ r } }=\left( \overset { \wedge }{ i } +\overset { \wedge }{ j } \right) +t\left( 2\overset { \wedge }{ i } +\overset { \wedge }{ j } -2\overset { \wedge }{ k } \right) \)

    ()

    p=-1

*****************************************

TN 12th Standard EM Maths free Online practice tests

Reviews & Comments about 12th Maths Quarterly Exam Model Two Marks Question Paper

Write your Comment