#### Basic Algebra Important Questions

11th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
9 x 1 = 9
1. If |x+2| $\le$ 9, then x belongs to

(a)

$(-\infty ,-7)$

(b)

[-11, 7]

(c)

$(-\infty ,-7)\cup (11,\infty)$

(d)

(-11, 7)

2.  Give that x;y and b are real numbers x<y;b>0, then

(a)

xb < yb

(b)

xb > yb

(c)

xb ≤ yb

(d)

$\frac { x }{ b } \ge \frac { y }{ b }$

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

(a)

$[2,\infty]$

(b)

$(2,\infty )$

(c)

$(-\infty,2)$

(d)

$(-2,\infty )$

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

(a)

(4,5)

(b)

(-5,-4)

(c)

(-5,5)

(d)

(-5,4)

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

(a)

[0, 2]

(b)

$[2,\infty)$

(c)

(0, 2)

(d)

$(-\infty,2)$

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. 8 x 2 = 16
11. Simplify $\left( 125 \right) ^{ \frac { 2 }{ 3 } }$

12. Simplify ${ 16 }^{ -\frac { 3 }{ 4 } }$

13. Simplify $(-1000)^{ \frac { -2 }{ 3 } }$

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

15. Simplify $\frac { { (27) }^{ \frac { -2 }{ 3 } } }{ { (27) }^{ \frac { -1 }{ 3 } } }$

16. Solve the inequation 5x-1 < 15 when x is a natural number

17. If k > 0,then solve the inequation |x| ≤ K

18. A solution is to be kept between 68oF and 77oF. What is the range in temperature in degree Celsius (c) or Fahrenheit (F),conversion formula is given by  $F=\frac { 9 }{ 5 }$C + 32?

19. 5 x 3 = 15
20. Solve the linear in equation 4-x$\le$3x+12.

21. Solve the quadratic equation 52x-5x+3+125=5x.

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

23. Solve $\frac { 1 }{ \left| 2x-1 \right| } <6$ and express the solution using the interval notation.

24. Solve $\sqrt [ 8 ]{{{x}\over{x+3}} } -\sqrt{{{x+3}\over{x}}}=2.$

25. 2 x 5 = 10
26. Prove that $\sqrt { 3 }$ is an irrational number. (Hint: Follow the method that we have used to prove $\sqrt { 2 } \notin Q$)

27. Solve: ${{2x+5}\over{x-1}}>5$