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: \({{2x+5}\over{x-1}}>5\)

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