#### Basic Algebra Important Questions

11th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
1. 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

2. The value of loga b logb c logc a is

(a)

2

(b)

1

(c)

3

(d)

4

3. If 8 and 2 are the roots of x2+ ax + c = 0 and 3, 3 are the roots of x+ 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

4. If |x + 3| ≥ 10 then ___________

(a)

x ∊ (-13, 7]

(b)

x ∊ [-13, 7)

(c)

x ∊ (-∞, -13] $\cup$ [7, ∞)

(d)

x ∊ (-∞, -13] $\cup$ [7, ∞)

5. The logarithmic form of 5= 25 is ___________

(a)

${ log }_{ 5 }^{ 2 }=25$

(b)

${ log }_{ 2 }^{ 5 }=25$

(c)

${ log }_{ 2 }^{ 25 }=2$

(d)

${ log }_{ 25 }^{ 5 }=2$

6. 5 x 2 = 10
7. Find the radius of the spherical tank whose volume is  $\frac { 32\pi }{ 3 }$ units

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

9. Without sketching the graphs, find whether the graphs of the following functions will intersect the x-axis and if so in how many points. y = x2 + 6x + 9

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

11. Solve |x - 9| < 2 for x.

12. 5 x 3 = 15
13. Solve for x  $\left| 4x-5 \right| \ge -2$

14. Solve for x  $\left| 3-\frac { 3 }{ 4 } x \right| \le \frac { 1 }{ 4 }$

15. A factory kept increasing its out-put by the same percentage every year. Find the percentage, if it is known that the output has doubled in the last two years.

16. Find the value of log2 $\left({{\sqrt [ 3 ]{4 } }\over{4^2\sqrt{8}}} \right).$

17. Solve |2x- 3| = |x - 5|.

18. 4 x 5 = 20
19. Solve : ${ log }_{ 2 }x-3{ log }_{ \frac { 1 }{ 2 } }x=6$

20. Solve  log5-x (x2-6x+65)=2

21. Show that ${{1}\over{3-\sqrt{8}}}-{{1}\over{\sqrt{8}-\sqrt{7}}}+{{1}\over{\sqrt{7}-\sqrt{6}}}-{{1}\over{\sqrt{6}-\sqrt{5}}}+{{1}\over{\sqrt{5}-2}}=5$

22. Solve $(x+1)^{ \frac { 1 }{ 3 } }=\sqrt { x-3 }$