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#### Algebra Model Questions

10th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
4 x 1 = 4
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. $\frac { x }{ { x }^{ 2 }-25 } -\frac { 8 }{ { x }^{ 2 }+6x+5 }$ 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)

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

3. The square root of $\frac { 256{ x }^{ 8 }{ y }^{ 4 }{ z }^{ 10 } }{ 25{ x }^{ 6 }{ y }^{ 6 }{ z }^{ 6 } }$ is equal to

(a)

$\frac { 16 }{ 5 } \left| \frac { { x }^{ 2 }{ z }^{ 4 } }{ { y }^{ 2 } } \right|$

(b)

$16\left| \frac { { y }^{ 2 } }{ { x }^{ 2 }{ z }^{ 2 } } \right|$

(c)

$\frac { 16 }{ 5 } \left| \frac { y }{ x{ z }^{ 2 } } \right|$

(d)

$\frac { 16 }{ 5 } \left| \frac { x{ z }^{ 2 } }{ y } \right|$

4. If the roots of the equation q2x2 + p2x + r2 = 0 are the squares of the roots of the equation qx2 + px + r = 0, then q, p, r are in __________.

(a)

A.P

(b)

G.P

(c)

Both A.P and G.P

(d)

none of these

5. 5 x 2 = 10
6. Solve $\frac { x }{ 2 } -1=\frac { y }{ 6 } +1=\frac { z }{ 7 } +2$$\frac { y }{ 3 } +\frac { z }{ 2 } =13$

7. The sum of thrice the first number, second number and twice the third number is 5. If thrice the second number is subtracted from the sum of first number and thrice the third we get 2. If the third number is subtracted from the sum of twice the first, thrice the second, we get 1. Find the numbers.

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

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

10. Prove that the equation x2(a2+b2)+2x(ac+bd)+(c2+ d2) = 0 has no real root if ad≠bc.

11. 4 x 5 = 20
12. Write down the quadratic equation in general form for which sum and product of the roots are given below.
9, 14

13. Draw the graph of y = x2 + 4x + 3 and hence find the roots of x2 + x + 1 = 0

14. The sum of two numbers is 15. If the sum of their reciprocals is $\frac{3}{10}$, find the numbers.

15. A chess board contains 64 equal squares and the area of each square is 6.25 cm2, A border round the board is 2 cm wide.

16. 2 x 8 = 16
17. Find the GCD of the following by division algorithm 2x4 + 13x3 + 27x + 7, x3 + 3x2 + 3x + 1, x2 + 2x + 1

18. If –4 is a root of the equation x2 + px - 4 = 0 and if the equation x2 + px + q has equal roots, find the values of p and q.