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

  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?

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