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#### Algebra Model Question Paper

10th Standard EM

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Maths

Time : 01:30:00 Hrs
Total Marks : 50
5 x 1 = 5
1. A system of three linear equations in three variables is inconsistent if their planes

(a)

intersect only at a point

(b)

intersect in a line

(c)

coincides with each other

(d)

do not intersect

2. $\frac {3y - 3}{y} \div \frac {7y - 7}{3y^{2}}$ is

(a)

$\frac {9y}{7}$

(b)

$\frac {9y^{2}}{(21y - 21)}$

(c)

$\frac {21y^2 - 42y + 21}{3y^{2}}$

(d)

$\frac {7(y^{2} - 2y + 1)}{y^{2}}$

3. Which of the following should be added to make x4 + 64 a perfect square

(a)

4x2

(b)

16x2

(c)

8x2

(d)

-8x2

4. Graph of a linear polynomial is a

(a)

straight line

(b)

circle

(c)

parabola

(d)

hyperbola

5. Transpose of a column matrix is

(a)

unit matrix

(b)

diagonal matrix

(c)

column matrix

(d)

row matrix

6. 7 x 2 = 14
7. 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.

8. Solve x + 2y - z = 5; x - y + z = -2; -5x - 4y + z = -11

9. Reduce the rational expressions to its lowest form
$\frac { x-3 }{ { x }^{ 2 }-9 }$

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

11. The product of Kumaran’s age (in years) two years ago and his age four years from now is one more than twice his present age. What is his present age?

12. A passenger train takes 1 hr more than an express train to travel a distance of 240 km from Chennai to Virudhachalam. The speed of passenger train is less than that of an express train by 20 km per hour. Find the average speed of both the trains.

13. If a matrix has 16 elements, what are the possible orders it can have?

14. 3 x 5 = 15
15. Find the GCD of the polynomials x3 + x2 - x + 2 and 2x3 - 5x2 + 5x - 3.

16. Find the square root of the following expressions
16x2 + 9y2 - 24xy + 24x - 18y + 9

17. If A = $\left[ \begin{matrix} 5 & 4 & -2 \\ \frac { 1 }{ 2 } & \frac { 3 }{ 4 } & \sqrt { 2 } \\ 1 & 9 & 4 \end{matrix} \right]$, B = $\left[ \begin{matrix} -7 & 4 & -3 \\ \frac { 1 }{ 4 } & \frac { 7 }{ 2 } & 3 \\ 5 & -6 & 9 \end{matrix} \right]$, find 4A - 3B.

18. 2 x 8 = 16
19. In a three-digit number, when the tens and the hundreds digit are interchanged the new number is 54 more than three times the original number. If 198 is added to the number, the digits are reversed. The tens digit exceeds the hundreds digit by twice as that of the tens digit exceeds the unit digit. Find the original number.

20. If α and β are the roots of the polynomial f(x) = x2 - 2x + 3, find the polynomial whose roots are
α + 2, β + 2