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#### Term 1 Five Mark Model Questions

12th Standard EM

Reg.No. :
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Maths

Time : 02:00:00 Hrs
Total Marks : 50
10 x 5 = 50
1. If A = $\left[ \begin{matrix} 5 & 3 \\ -1 & -2 \end{matrix} \right]$, show that A2 - 3A - 7I2 = O2. Hence find A−1.

2. If ax2 + bx + c is divided by x + 3, x − 5, and x − 1, the remainders are 21,61 and 9 respectively. Find a,b and c. (Use Gaussian elimination method.)

3. Solve the system: x + y − 2z = 0, 2x − 3y + z = 0, 3x − 7y + 10z = 0, 6x − 9y + 10z = 0.

4. Solve the following systems of linear equations by Cramer’s rule:
3x + 3y − z = 11, 2x − y + 2z = 9, 4x + 3y + 2z = 25.

5. Solve the equation z3+27=0 .

6. Solve the following equation: x4-10x3+26x2-10x+1=0

7. Find the principal value of
cosec−1(−1)

8. Find the equation of the ellipse whose eccentricity is $\frac { 1 }{ 2 }$, one of the foci is(2,3) and a directrix is x = 7 . Also find the length of the major and minor axes of the ellipse.

9. At a water fountain, water attains a maximum height of 4m at horizontal distance of 0 5 . m from its origin. If the path of water is a parabola, find the height of water at a horizontal distance of 0.75m from the point of origin.

10. Find the point of intersection of the lines $\frac { x-1 }{ 2 } =\frac { y-2 }{ 3 } =\frac { z-3 }{ 4 }$ and $\frac { x-4 }{ 5 } =\frac { y-1 }{ 2 } =z$