Basic Algebra - Important One Mark Question Paper

11th Standard

    Reg.No. :
  •  
  •  
  •  
  •  
  •  
  •  

Maths

Time : 01:00:00 Hrs
Total Marks : 60

    Part A

    Multiple Choice Question

    60 x 1 = 60
  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. The value of \({ log }_{ 3 }\frac { 1 }{ 81 } \) is

    (a)

    -2

    (b)

    -8

    (c)

    -4

    (d)

    -9

  4. 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

  5. If 3 is the logarithm of 343 then the base is

    (a)

    5

    (b)

    7

    (c)

    6

    (d)

    9

  6. Find a so that the sum and product of the roots of the equation 2x2+(a-3)x+3a-5 = 0 are equal is

    (a)

    1

    (b)

    2

    (c)

    0

    (d)

    4

  7. 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

  8. The number of solution of x2+|x-1|=1 is

    (a)

    1

    (b)

    0

    (c)

    2

    (d)

    3

  9. 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

  10. 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

  11. 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)

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

  12. If  \(\frac { kx }{ (x+2)(x-1) } =\frac { 2 }{ x+2 } +\frac { 1 }{ x-2 } \) ,then the value of k is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  13. If  \(\frac { 1-2x }{ 3+2x-{ x }^{ 2 } } =\frac { A }{ 3-x } +\frac { B }{ x+1 } \) ,then the value of A+B is

    (a)

    \(\frac { -1 }{ 2 } \)

    (b)

    \(\frac { -2 }{ 3 } \)

    (c)

    \(\frac { 1 }{ 2 }\)

    (d)

    \(\frac { 2 }{ 3 } \)

  14. The number of roots of (x+3)4+(x+5)4=16 is

    (a)

    4

    (b)

    2

    (c)

    3

    (d)

    0

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

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  16. If x < 7,then

    (a)

    -x < -7

    (b)

    - x ≤ -7

    (c)

    -x > -7

    (d)

    -x ≥ -7

  17. If -3x+17 < -13 then

    (a)

    x ∈ (10,∞)

    (b)

    x ∈ [10,∞)

    (c)

    x ∈ (-∞,10]

    (d)

    x ∈ [10,10)

  18. If x is a real number and |x| < 5 then

    (a)

    x ≥ 5

    (b)

    -5 < x < 5

    (c)

    x ≤ -5

    (d)

    -5 ≤ x ≤ 5

  19. If |x+3| ≥10 then

    (a)

    x ∊ (-13,7]

    (b)

    x ∊ [-13,7)

    (c)

    x ∊ (-∞,-13] ᴗ [7,∞)

    (d)

    x ∊ (-∞,-13] ᴗ [7,∞)

  20. \(\sqrt [ 4 ]{ 11 } \) is equal to

    (a)

    \(\sqrt [ 8 ]{ 11^{ 2 } } \)

    (b)

    \(\sqrt [ 8 ]{ 11^{ 4 } } \)

    (c)

    \(\sqrt [ 8 ]{ 11^{ 8 } } \)

    (d)

    \(\sqrt [ 8 ]{ 11^{ 6 } } \)

  21. The rationalising factor of \(\frac { 5 }{ \sqrt [ 3 ]{ 3 } } \) is

    (a)

    \(\sqrt [ 3 ]{ 6 } \)

    (b)

    \(\sqrt [ 3 ]{ 3 } \)

    (c)

    \(\sqrt [ 3 ]{ 9 } \)

    (d)

    \(\sqrt [ 3 ]{ 27 } \)

  22. \((\sqrt { 5 } -2)(\sqrt { 5 } +2)\) is equal to

    (a)

    1

    (b)

    3

    (c)

    23

    (d)

    21

  23. The number of real solution of |2x-x2-3|=1 is

    (a)

    0

    (b)

    2

    (c)

    3

    (d)

    4

  24. If x is real and k = \(\frac { { x }^{ 2 }-x+1 }{ { x }^{ 2 }+x+1 } \) then

    (a)

    \(k\epsilon \left[ \frac { 1 }{ 3 } ,3 \right] \)

    (b)

    k ≥ 3

    (c)

    \(k\le \frac { 1 }{ 3 } \)

    (d)

    none of these

  25. If the roots of x2-bx+c =0 are two consecutive integer,then b2-4c is

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    none of these

  26. The logarithmic form of 52=25 is

    (a)

    \({ log }_{ 5 }^{ 2 }=25\)

    (b)

    \({ log }_{ 2 }^{ 5 }=25\)

    (c)

    \({ log }_{ 2 }^{ 25 }=2\)

    (d)

    \({ log }_{ 25 }^{ 5 }=2\)

  27. The Value of \({ log }_{ 3/4 }^{ (4/3) }\) is 

    (a)

    -2

    (b)

    1

    (c)

    2

    (d)

    -1

  28. The value of log108+log105-log10=

    (a)

    \({ log }_{ 10 }^{ 9 }\)

    (b)

    \({ log }_{ 10 }^{ 36 }\)

    (c)

    1

    (d)

    -1

  29. (x2-2x+2)(x2+2x+2) are the factors of the polynomial

    (a)

    (x2-2x)2

    (b)

    x4-4

    (c)

    x4+4

    (d)

    (x2-2x+2)2

  30. The factors of the polynomial \(6\sqrt { { 3x }^{ 2 } } -47x+5\sqrt { 3 } \) are

    (a)

    \((2x-5\sqrt { 3 } )(3\sqrt { 3 } x-1)\)

    (b)

    \((2x-5\sqrt { 3 } )(3\sqrt { 3 } x+1)\)

    (c)

    \((2x+5\sqrt { 3 } )(3\sqrt { 3 } x+1)\)

    (d)

    \((2x+5\sqrt { 3 } )(3\sqrt { 3 } x-1)\)

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

    (a)

    x∈(∞,3)

    (b)

    x∈(4,∞)

    (c)

    x∈(1,7)

    (d)

    x∈(1,4)U(4,7)

  32. If \(\alpha\) and \(\beta\) are the roots of 2x2 - 3x - 4 = 0 find the value of \(\alpha^2+\beta^2\)

    (a)

    \(\frac{41}{4}\)

    (b)

    \(\frac{\sqrt{14}}{2}\)

    (c)

    0

    (d)

    none of these

  33. If \(\alpha\) and \(\beta\) are the roots of 2x2+4x+5=0 the equation where roots are 2\(\alpha\) and 2\(\beta\) is:

    (a)

    4x2+ 4x + 5 = 0

    (b)

    2x2 + 4x + 50 = 0

    (c)

    x2+4x+5=0

    (d)

    x2+4x+10=0

  34. The minimum point of y = x2 -4x - 5 is:

    (a)

    (2,-9)

    (b)

    (-2,-9)

    (c)

    (-2,9)

    (d)

    (4,5)

  35. 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

  36. Solve \(\sqrt{7+6x-x^2}=x+1\)

    (a)

    (1, -3)

    (b)

    (3, -1)

    (c)

    (1, -1)

    (d)

    (3, -3)

  37. Solve 3x2 + 5x - 2≤0

    (a)

    (2,\(\frac{1}{3}\))

    (b)

    [2,\(\frac{1}{3}\)]

    (c)

    (-2,\(\frac{1}{3}\))

    (d)

    (-2,\(\frac{-1}{3}\))

  38. The zero of the polynomial function f(x)=9x2-16 are:

    (a)

    (9,16)

    (b)

    (3,4)

    (c)

    \((\frac{4}{3},-\frac{4}{3})\)

    (d)

    \((\frac{3}{4},-\frac{3}{4})\)

  39. The value of a when x3-2x2+3x+a is divided by (x - 1), the remainder is 1, is:

    (a)

    -1

    (b)

    1

    (c)

    2

    (d)

    -2

  40. Find the other root of x2-4x+1=0 given that 2+\(\sqrt{3}\) is a root:

    (a)

    \(\sqrt{3}\)+2

    (b)

    -\(\sqrt{3}\)-\(\sqrt{2}\)

    (c)

    2-\(\sqrt{3}\)

    (d)

    \(\sqrt{3}\)-2

  41. If \(\frac{x}{x^2-5x+6}=\frac{A}{x-2}+\frac{B}{x-3}\) then value of A is:

    (a)

    2

    (b)

    0

    (c)

    3

    (d)

    -2

  42. If \(\frac{1}{\sqrt{3}\times\sqrt{2}}=\sqrt{3}+a\) then a is

    (a)

    \(\sqrt{2}\)

    (b)

    -\(\sqrt{2}\)

    (c)

    \(\sqrt{\frac{3}{2}}\)

    (d)

    \(\sqrt{\frac{2}{3}}\)

  43. \(\sqrt [ 4 ]{ { \left( -2 \right) }^{ 4 } } \times { \left( -1000 \right) }^{ \frac { 1 }{ 3 } }\)is

    (a)

    20

    (b)

    -20

    (c)

    2-10

    (d)

    100

  44. Logarithm of 144 to the base 2\(\sqrt{3}\) is

    (a)

    2

    (b)

    3

    (c)

    4

    (d)

    5

  45. The value of log23 . log2732:

    (a)

    \(\frac{5}{2}\)

    (b)

    \(\frac{2}{5}\)

    (c)

    \(\frac{5}{3}\)

    (d)

    \(\frac{3}{5}\)

  46. The value of 2 log10 3 + log10 16 - 2 log10 \(6\over 5\) is

    (a)

    1

    (b)

    0

    (c)

    2

    (d)

    3

  47. The value of \({3^{-3}\times6^4\times 12^{-3}\over 9^{-4}\times 2^{-2}}\) is

    (a)

    35

    (b)

    36

    (c)

    34

    (d)

    3

  48. If (x + 1) and (x - 3) are factors of x3 - 4x2 + x + 6 then other linear factor is

    (a)

    x + 2

    (b)

    x - 2

    (c)

    x - 1

    (d)

    x + 3

  49. If P(x) = x3 + 3x2 + 2x + 1, then the remainder on dividing p(x) by (x - 1) is

    (a)

    7

    (b)

    0

    (c)

    6

    (d)

    1

  50. The value of loga+ log1/ax is

    (a)

    1

    (b)

    0

    (c)

    2 logax

    (d)

    2 logax

  51. The condition for one root of the quadratic equation ax2 + bx + c = 0 to be double the other

    (a)

    b2 = 3ac

    (b)

    b2 = 4ac

    (c)

    2b2 = 9ac

    (d)

    c2 = ac - b2

  52. If one root of the quadratic equation ax2 + bx + c = 0 is the reciprocal of the other then

    (a)

    a = b

    (b)

    a = c

    (c)

    ac = 1

    (d)

    b = c

  53. The number of real solutions of the equation |x2| - 3|x| + 2 = 0 is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  54. If a and b are roots of x2 + x + 1 = 0 then the value of a2 + b2 =

    (a)

    1

    (b)

    -1

    (c)

    cannot be determined

    (d)

    0

  55. For the below figure of ax2 + bx + c = 0

    (a)

    a < 0, D > 0

    (b)

    a > 0, D > 0

    (c)

    a < 0, D < 0

    (d)

    a > 0, D = 0

  56. Let \(\alpha\) and \(\beta\) are the roots of a quadratic equation px2 + qx + r = 0 then

    (a)

    \(\alpha +\beta=-{p\over r}\)

    (b)

    \(\alpha\beta={p\over r}\)

    (c)

    \(\alpha +\beta={-q\over p}\)

    (d)

    \(\alpha \beta =r\)

  57. Zero of the polynomial p(x) = x2 - 4x + 4

    (a)

    1

    (b)

    2

    (c)

    -2

    (d)

    -1

  58. The roots of the equation \(x+{1\over x}=3{1\over 3},x\ne 0\) are

    (a)

    1, 3

    (b)

    \({1\over 3},3\)

    (c)

    \(3,{-1\over 3}\)

    (d)

    \(1,{1\over 3}\)

  59. If \(x={1\over 2+\sqrt{3}}\) then the value of x3 - x2 - 11x + 3 is 

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    4

  60. Which whole number is not a natural number?

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    0

*****************************************

TN 11th Standard Maths free Online practice tests

Reviews & Comments about Basic Algebra Important One Mark Question Paper In 11th Maths

Write your Comment