#### Model paper-Basic Algebra

11th Standard

Reg.No. :
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Maths

Use blue pen Only

Time : 01:00:00 Hrs
Total Marks : 70

Part A

10 x 1 = 10
1. The solution 5x-1<24 and 5x+1 > -24 is

(a)

(4,5)

(b)

(-5,-4)

(c)

(-5,5)

(d)

(-5,4)

2. The solution set of the following inequality |x-1| $\ge$ |x-3| is

(a)

[0, 2]

(b)

$[2,\infty)$

(c)

(0, 2)

(d)

$(-\infty,2)$

3. The value of ${ log }_{ \sqrt { 2 } }512$ is

(a)

16

(b)

18

(c)

9

(d)

12

4. The value of ${ log }_{ 3 }\frac { 1 }{ 81 }$ is

(a)

-2

(b)

-8

(c)

-4

(d)

-9

5. If ${ log }_{ \sqrt { x } }$ 0.25 =4 ,then the value of x is

(a)

0.5

(b)

2.5

(c)

1.5

(d)

1.25

6. The equation whose roots are numerically equal but opposite in sign to the roots 3x2-5x-7 =0 is

(a)

3x2-5x-7 =0

(b)

3x2+5x-7 =0

(c)

3x2-5x+7 =0

(d)

3x2+x-7

7. If 8 and 2 are the roots of x2+ax+c=0 and 3,3 are the roots of x2+dx+b=0;then the roots of the equation x2+ax+b = 0 are

(a)

1,2

(b)

-1,1

(c)

9,1

(d)

-1,2

8. The value of log3 11.log11 13.log13 15log15 27.log27 81 is

(a)

1

(b)

2

(c)

3

(d)

4

9. Given $|\frac{3}{x-4}|<1$ then:

(a)

x∈(∞,3)

(b)

x∈(4,∞)

(c)

x∈(1,7)

(d)

x∈(1,4)U(4,7)

10. The condition that the equation ax2 + bx + c = 0 may have one root is the double the other is:

(a)

2b2 = 9ac

(b)

b2= ac

(c)

b2 = 4ac

(d)

9b2 = 2ac

11. Part B

10 x 2 = 20
12. Classify each element of $\left\{ \sqrt { 7 } ,\frac { -1 }{ 4 } ,0,3.14,4,\frac { 22 }{ 7 } \right\}$ as a member of N, Q, R, -Q or Z.

13. Construct a quadratic equation with roots 7 and -3

14. If the difference of the roots of the equation $2{ x }^{ 2 }-\left( a+1 \right) x+a-1=0$ is equal to their product, then prove that a=2.

15. Determine the region in the Plane determined by the inequalities $y\ge 2x,\ -2x+3y\le 6$

16. if x2+x+1 is a factor of the polynomial 3x3+8x2+8x+a, then find the value of a.

17. Determine the region in the plane determined by the inequalities.
$2x+3y\le 6,\quad x+4y\le 4,\quad x\ge 0,\quad y\ge 0.$

18. Determine the region in the plane determined by the inequalities.
$2x+y\ge 8,\quad x+2y\ge 8,\quad x+y\le 6$

19. Solve 3|x- 2| + 7 = 19 for x.

20. Our monthly electricity bill contains a basic charge, which does not change with number of units used, and a charge that depends only on how many units we use. Let us say Electricity board charges Rs.110 as basic charge and charges Rs.4 for each unit we use. If a person wants to keep his electricity bill below Rs.250, then what should be his electricity usage?

21. If $\alpha$ and $\beta$ are the roots of the equation x2 - 2x + 3 = 0 from the equation where roots are
(a) $\frac{1}{\alpha}$ and $\frac{1}{\beta}$
(b) $\alpha^2$ and $\beta^2$
(c)  $\frac{1}{\alpha^2}$ and $\frac{1}{\beta^2}$

22. Part C

5 x 3 = 15
23. Simplify $\left( 125 \right) ^{ \frac { 2 }{ 3 } }$

24. Simplify $\left( 3^{ 6 } \right) ^{ \frac { 1 }{ 3 } }$

25. Simplify and hence the value of n: $\frac { { 3 }^{ 2n }{ 9 }^{ 2 }{ 3 }^{ -n } }{ { 3 }^{ 3n } } =27$

26. Solve for x  $\left| 3-x \right| <7$

27. Prove that ap + q = 0 if f(x) = x3 - 3px + 2q is divisible by g(x) = x2 + 2ax + a2.

28. Part D

5 x 5 = 25
29. Represent the following inequalities in the interval notation:
$x\ge -1$ and $x<4$

30. Let b>0 and b≠1. Express y = bx in logarithmic form.Also state the domain and range of the logarithmic function.

31. Resolve the following rational expressions into partial fractions.
${{1}\over{x^2-a^2}}$

32. Resolve the following rational expressions into partial fractions.
${{{(x-1)}^{2}}\over{x^3+x}}$