Basic Algebra - Important Question Paper

11th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 50

Part A

10 x 1 = 10
1. If $\frac { |x-2| }{ x-2 } \ge 0$, then x belongs to

(a)

$[2,\infty]$

(b)

$(2,\infty )$

(c)

$(-\infty,2)$

(d)

$(-2,\infty )$

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

(a)

(4,5)

(b)

(-5,-4)

(c)

(-5,5)

(d)

(-5,4)

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

(a)

[0, 2]

(b)

$[2,\infty)$

(c)

(0, 2)

(d)

$(-\infty,2)$

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

(a)

16

(b)

18

(c)

9

(d)

12

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

(a)

-2

(b)

-8

(c)

-4

(d)

-9

6. If x < 7,then

(a)

-x < -7

(b)

- x ≤ -7

(c)

-x > -7

(d)

-x ≥ -7

7. If -3x+17 < -13 then

(a)

x ∈ (10,∞)

(b)

x ∈ [10,∞)

(c)

x ∈ (-∞,10]

(d)

x ∈ [10,10)

8. If |x+3| ≥10 then

(a)

x ∊ (-13,7]

(b)

x ∊ [-13,7)

(c)

x ∊ (-∞,-13] ᴗ [7,∞)

(d)

x ∊ (-∞,-13] ᴗ [7,∞)

9. $\sqrt [ 4 ]{ 11 }$ is equal to

(a)

$\sqrt [ 8 ]{ 11^{ 2 } }$

(b)

$\sqrt [ 8 ]{ 11^{ 4 } }$

(c)

$\sqrt [ 8 ]{ 11^{ 8 } }$

(d)

$\sqrt [ 8 ]{ 11^{ 6 } }$

10. The number of real solution of |2x-x2-3|=1 is

(a)

0

(b)

2

(c)

3

(d)

4

11. Part B

9 x 2 = 18
12. Are there two distinct irrational numbers such that their difference is a rational number? Justify.

13. Find two irrational numbers such that their sum is a rational number. Can you find two irrational numbers whose product is a rational number?

14. A quadratic polynomial has one of its zeros as $1+\sqrt { 5 }$ and it satisfies p(1) = 2. Find the quadratic polynomial.

15. Find the condition that one of the roots of ax2+bx+c may be negative of the other. thrice the other

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

17. Given log216 =4.Find log162

18. If a3+b3=ab(8-3a-3b),show that log $\left( \frac { a+b }{ 2 } \right) =\frac { 1 }{ 3 }$  (log a +log b)

19. If a and b are both rational numbers,find the values of a and b if $\frac { 3+\sqrt { 7 } }{ 3-\sqrt { 7 } } =a+b\sqrt { 7 }$

20. Simplify the rational expression : $\frac { { y }^{ 2 }-15y-34 }{ { 3y }^{ 2 }-12 }$

21. Part C

4 x 3 = 12
22. Simplify $(-1000)^{ \frac { -2 }{ 3 } }$

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

24. Simplify $\frac { 1 }{ 3-\sqrt { 8 } } -\frac { 1 }{ \sqrt { 8 } -\sqrt { 7 } } +\frac { 1 }{ \sqrt { 7 } -\sqrt { 6 } } -\frac { 1 }{ \sqrt { 6 } -\sqrt { 5 } } +\frac { 1 }{ \sqrt { 5 } -2 }$

25. If x=$\sqrt { 2 } +\sqrt { 3 }$  find $\frac { { x }^{ 2 }+1 }{ { x }^{ 2 }-1 }$

26. Part D

2 x 5 = 10
27. Solve: ${{2x+5}\over{x-1}}>5$

28. The largest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is atleast 61 cm, find the minimum length of the shortest side?