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#### Algebra Book Back Questions

10th Standard EM

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
6 x 1 = 6
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. The solution of the system x + y − 3x = −6, −7y + 7z = 7 , 3z = 9 is

(a)

x = 1, y = 2, z = 3

(b)

x = −1, y = 2, z = 3

(c)

x = −1, y = −2, z = 3

(d)

x = 1, y = 2, z = 3

3. If (x - 6) is the HCF of x2 - 2x - 24 and x2 - kx - 6 then the value of k is

(a)

3

(b)

5

(c)

6

(d)

8

4. $\frac { x }{ { x }^{ 2 }-25 } -\frac { 8 }{ { x }^{ 2 }+6x+5 }$ gives

(a)

$\frac { { x }^{ 2 }-7x+40 }{ \left( x-5 \right) \left( x+5 \right) }$

(b)

$\frac { { x }^{ 2 }+7x+40 }{ \left( x-5 \right) \left( x+5 \right) \left( x+1 \right) }$

(c)

$\frac { { x }^{ 2 }-7x+40 }{ \left( { x }^{ 2 }-25 \right) \left( x+1 \right) }$

(d)

$\frac { { x }^{ 2 }+10 }{ \left( { x }^{ 2 }-25 \right) \left( x+1 \right) }$

5. The solution of (2x - 1)2 = 9 is equal to

(a)

-1

(b)

2

(c)

-1, 2

(d)

None of these

6. Graph of a linear polynomial is a

(a)

straight line

(b)

circle

(c)

parabola

(d)

hyperbola

7. 3 x 2 = 6
8. 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.

9. Solve: $\frac { 1 }{ 2x } +\frac { 1 }{ 4y } -\frac { 1 }{ 3z } =\frac { 1 }{ 4 }$;  $\frac { 1 }{ x } =\frac { 1 }{ 3y }$$\frac { 1 }{ x } -\frac { 1 }{ 5y } +\frac { 4 }{ z } =2\frac { 2 }{ 15 }$

10. Solve $2{ x }^{ 2 }-2\sqrt { 6 } x+3$ = 0

11. 2 x 5 = 10
12. Find the GCD of the polynomials x3 + x2 - x + 2 and 2x3 - 5x2 + 5x - 3.

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

14. 1 x 8 = 8
15. Simplify $\frac { \frac { 1 }{ p } +\frac { 1 }{ q+r } }{ \frac { 1 }{ p } -\frac { 1 }{ q+r } } \times \left( 1+\frac { { q }^{ 2 }+{ r }^{ 2 }-{ p }^{ 2 } }{ 2qr } \right)$