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#### Quarterly Exam Model Two Marks Questions

12th Standard EM

Reg.No. :
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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 ${ \overset { \rightarrow }{ r } }=\left( \overset { \wedge }{ i } +\overset { \wedge }{ j } \right) +t\left( 2\overset { \wedge }{ i } +\overset { \wedge }{ j } -2\overset { \wedge }{ k } \right)$

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p=-1