Basic Algebra Book Back Questions

11th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
    5 x 1 = 5
  1.  Give that x;y and b are real numbers x<y;b>0, then

    (a)

    xb < yb

    (b)

    xb > yb

    (c)

    xb ≤ yb

    (d)

    \(\frac { x }{ b } \ge \frac { y }{ b } \)

  2. 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

  3. If a and b are the roots of the equation x2-kx+16=0 and a2+b2=32 then the value of k is

    (a)

    10

    (b)

    -8

    (c)

    -8,8

    (d)

    6

  4. If a and b are the roots of the equation x2-kx+c = 0 then the distance between the points (a, 0) and (b, 0)

    (a)

    \(\sqrt { { 4k }^{ 2 }-c } \)

    (b)

    \(\sqrt { { k }^{ 2 }-4c } \)

    (c)

    \(\sqrt { 4c-{ k }^{ 2 } } \)

    (d)

    \(\sqrt { k-8c } \)

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

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  6. 3 x 2 = 6
  7. Evaluate \(\left( \left[ (256)^{ \frac { -1 }{ 4 } } \right] ^{ \frac { -1 }{ 4 } } \right) ^{ 3 }\)

  8. Solve for x  \(\left| 3-\frac { 3 }{ 4 } x \right| \le \frac { 1 }{ 4 } \)

  9. Factorize: x4+1

  10. 3 x 3 = 9
  11. If x=\(\sqrt { 2 } +\sqrt { 3 } \)  find \(\frac { { x }^{ 2 }+1 }{ { x }^{ 2 }-1 } \)

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

  13. Solve the linear inequalities and exhibit the solution set graphically: x+y ≥ 3, 2x-y ≤ 5, -x+2y ≤ 3.

  14. 2 x 5 = 10
  15. Evaluate \(\sqrt [ 3 ]{ {{{(45.4)}^{2}}\over{{(3.2)}^{2}}\times{(6.5)}^{2}} } \)

  16. Resolve into partial fractions \(\frac { 9 }{ (x-1)(x+2)^{ 2 } } \)

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