Model paper-Basic Algebra

11th Standard

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Maths

Use blue pen Only

Time : 01:00:00 Hrs
Total Marks : 70

    Part A

    Answer all the questions

    10 x 1 = 10
  1. The solution 5x-1<24 and 5x+1 > -24 is

    (a)

    (4,5)

    (b)

    (-5,-4)

    (c)

    (-5,5)

    (d)

    (-5,4)

  2. The solution set of the following inequality |x-1| \(\ge\) |x-3| is

    (a)

    [0, 2]

    (b)

    \([2,\infty)\)

    (c)

    (0, 2)

    (d)

    \((-\infty,2)\)

  3. The value of \({ log }_{ \sqrt { 2 } }512\) is

    (a)

    16

    (b)

    18

    (c)

    9

    (d)

    12

  4. The value of \({ log }_{ 3 }\frac { 1 }{ 81 } \) is

    (a)

    -2

    (b)

    -8

    (c)

    -4

    (d)

    -9

  5. 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

  6. The equation whose roots are numerically equal but opposite in sign to the roots 3x2-5x-7 =0 is

    (a)

    3x2-5x-7 =0

    (b)

    3x2+5x-7 =0

    (c)

    3x2-5x+7 =0

    (d)

    3x2+x-7

  7. 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

  8. The value of log3 11.log11 13.log13 15log15 27.log27 81 is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  9. Given \(|\frac{3}{x-4}|<1\) then:

    (a)

    x∈(∞,3)

    (b)

    x∈(4,∞)

    (c)

    x∈(1,7)

    (d)

    x∈(1,4)U(4,7)

  10. The condition that the equation ax2 + bx + c = 0 may have one root is the double the other is:

    (a)

    2b2 = 9ac

    (b)

    b2= ac

    (c)

    b2 = 4ac

    (d)

    9b2 = 2ac

  11. Part B

    Answer all the questions

    10 x 2 = 20
  12. Classify each element of \(\left\{ \sqrt { 7 } ,\frac { -1 }{ 4 } ,0,3.14,4,\frac { 22 }{ 7 } \right\} \) as a member of N, Q, R, -Q or Z.

  13. Construct a quadratic equation with roots 7 and -3

  14. If the difference of the roots of the equation \(2{ x }^{ 2 }-\left( a+1 \right) x+a-1=0\) is equal to their product, then prove that a=2.

  15. Determine the region in the Plane determined by the inequalities \(y\ge 2x,\ -2x+3y\le 6\)

  16. if x2+x+1 is a factor of the polynomial 3x3+8x2+8x+a, then find the value of a.

  17. Determine the region in the plane determined by the inequalities.
    \(2x+3y\le 6,\quad x+4y\le 4,\quad x\ge 0,\quad y\ge 0.\)

  18. Determine the region in the plane determined by the inequalities.
    \(2x+y\ge 8,\quad x+2y\ge 8,\quad x+y\le 6\)

  19. Solve 3|x- 2| + 7 = 19 for x.

  20. Our monthly electricity bill contains a basic charge, which does not change with number of units used, and a charge that depends only on how many units we use. Let us say Electricity board charges Rs.110 as basic charge and charges Rs.4 for each unit we use. If a person wants to keep his electricity bill below Rs.250, then what should be his electricity usage?

  21. If \(\alpha\) and \(\beta\) are the roots of the equation x2 - 2x + 3 = 0 from the equation where roots are
    (a) \(\frac{1}{\alpha}\) and \(\frac{1}{\beta}\)
    (b) \(\alpha^2\) and \(\beta^2\)
    (c)  \(\frac{1}{\alpha^2}\) and \(\frac{1}{\beta^2}\)

  22. Part C

    Answer all the questions

    5 x 3 = 15
  23. Simplify \(\left( 125 \right) ^{ \frac { 2 }{ 3 } }\)

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

  25. Simplify and hence the value of n: \(\frac { { 3 }^{ 2n }{ 9 }^{ 2 }{ 3 }^{ -n } }{ { 3 }^{ 3n } } =27\)

  26. Solve for x  \(\left| 3-x \right| <7\)

  27. Prove that ap + q = 0 if f(x) = x3 - 3px + 2q is divisible by g(x) = x2 + 2ax + a2.

  28. Part D

    Answer all the questions

    5 x 5 = 25
  29. Represent the following inequalities in the interval notation:
    \(x\ge -1\) and \(x<4\)

  30. Let b>0 and b≠1. Express y = bx in logarithmic form.Also state the domain and range of the logarithmic function.

  31. Resolve the following rational expressions into partial fractions.
    \({{1}\over{x^2-a^2}}\)

  32. Resolve the following rational expressions into partial fractions.
    \({{{(x-1)}^{2}}\over{x^3+x}}\)

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