#### Algebra Two Marks Question

10th Standard EM

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Maths

Time : 00:45:00 Hrs
Total Marks : 20
15 x 2 = 30
1. The father’s age is six times his son’s age. Six years hence the age of father will be four times his son’s age. Find the present ages (in years) of the son and father.

2. Find $\frac { { x }^{ 2 }+20x+36 }{ { x }^{ 2 }-3x-28 } -\frac { { x }^{ 2 }+12x+4 }{ { x }^{ 2 }-3x-28 }$

3. Find the square root of 64x4 - 16x3 + 17x2 - 2x + 1

4. If 9x4 + 12x3 + 28x2 + ax + b is a perfect square, find the values of a and b.

5. Solve 2m2+ 19m + 30 = 0

6. A ladder 17 feet long is leaning against a wall. If the ladder, vertical wall and the floor from the bottom of the wall to the ladder form a right triangle, find the height of the wall where the top of the ladder meets if the distance between bottom of the wall to bottom of the ladder is 7 feet less than the height of the wall?

7. If the difference between the roots of the equation x2 - 13x + k = 0 is 17. find k

8. Construct a 3 x 3matrix whose elements are aij = i2j2

9. If A = $\left[ \begin{matrix} 1 & 1 \\ -1 & 3 \end{matrix} \right]$, B = $\left[ \begin{matrix} 1 & 2 \\ -4 & 2 \end{matrix} \right]$, C = $\left[ \begin{matrix} -7 & 6 \\ 3 & 2 \end{matrix} \right]$ verify that A(B + C) = AB + AC

10. Find the excluded values of the following expressions (if any).
$\frac { x }{ { x }^{ 2 }+1 }$

11. If α and β are the roots of x2 + 7x + 10 = 0 find the values of
α4 + β4

12. If α, β are the roots of the equation 3x2 + 7x - 2 = 0, find the values of
$\frac { { \alpha }^{ 2 } }{ \beta } +\frac { { \beta }^{ 2 } }{ \alpha }$

13. Solve the following system of linear equations in three variables.
x + y + Z = 6; 2x + 3y + 4z = 20;
3x + 2y + Sz = 22

14. Using quadratic formula solve the following equations.
9x2-9(a+b)x+(2a2+5ab+2b2)=0

15. Find the values of k for which the following equation has equal roots.
(k - 12)r + 2(k - 12)x + 2 = 0