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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 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

  4. If |x+3| ≥10 then

    (a)

    x ∊ (-13,7]

    (b)

    x ∊ [-13,7)

    (c)

    x ∊ (-∞,-13] ᴗ [7,∞)

    (d)

    x ∊ (-∞,-13] ᴗ [7,∞)

  5. The logarithmic form of 52=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 Ix - 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|= Ix - 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 \((x+1)^{ \frac { 1 }{ 3 } }=\sqrt { x-3 } \)

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