#### Basic Algebra - Important One Mark Question Paper

11th Standard

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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