Download Assignment_Ch4 01. The name of Indian mathematician who have

Assignment_Ch4
01. The name of Indian mathematician who have given the formula of finding the roots of
quadratic equation ax2 +bx + c = 0 by perfect square method is………
(A) Pythagoras
(B) Shridhar Acharya
(C) Arya Bhatta
(D) Bhaskaracharya
02. The value of discriminate D of quadratic equation 25x2 - 10x + 1 = 0 is……
(A) 5
(B) 10
(C) 0
(D) 20
03. If one of the roots of quadratic equation x2 + 6x + k = 0 is 4, then k = ……
(A) -40
(B) 46
(C) 20
(D) -10
04. The roots of quadratic equation x2 + 18x + 81 = 0 are……
(A) fraction
(B) mutually reciprocal
(C) opposite
(D) equal
05. The value of discriminate D of quadratic equation x2 + 5x + 1 = 0 is………
(A) 5
(B) 21
(C) 14
(D) 6
06. x = ………..is a solution of a quadratic equation x2 + 7x + 12 = 0.
(A) 3
(B) 4
(C) -3
(D) 7
07. If the value of discriminate of a quadratic equation 2x2 + 5x - k = 0 is 81, then k =……
(A) 7
(B) 5
(C) 2
(D) 9
08. If one solution of quadratic equation kx2 + 3x - 4 = 0 is x = 2 then k =……
1
(A) 2
(B) 2
 1
 
(D)  2 
(C) (-2)
09. If the value of discriminate of a quadratic equation is D = 0, then the value of each root
is……
2 b
(A) a
2b
(B) a
b
(C) 2a
b
(D) 2a
10. In quadratic equation ax2 + bx + c = 0, a  0, b = 0 and D > 0, then both the roots of
equation are……
(A) equal
(B) zero
(C) opposite
(D) mutually reciprocal
11. If both the roots of 25x2 - x (m - 2) - 1 = 0 are opposite, then m =………
(A) -2
(B) 0
(C) 2
(D) 10
12. If discriminant D = 0, then the root of quadratic equation ax2 + bx + cx is……
2a
(A) b
(B)

b
2a
(C)

2a
b
b
2
(D) a
1
0
4
13. The root of
are………
1 1
1
1
1 1
 ,
 ,
 ,
(A) 2 2
(B) 2 2
(C) 4 4
4x2 + 2x +
1 1
,
(D) 4 4
14. The price of corn oil is Rs. x per kg. If the price of corn oil is decreased by Rs. 10 per
kg, then………… kg corn oil can be obtained in Rs. 500 at new rate.
500
x
(A)  10
500
x
(C)  10
x
(B) 500
500
(D) x
15. The speed of a motor-boat in still water is x km/hr and the speed of the current of the
river be 5 km/hr. Where x> 5, then time taken to cover the distance of y km in upstream
is……
x5
(A) y
y
x
(B)  5
x5
(C) y
y
x
(D)  5
16. x = …………. is a solution of quadratic equations x2 + 7x + 12 = 0.
(A) -3
(B) 7
(C) 4
(D) 3
17. If x = 2 is one of the solution of the quadratic equation kx2 + 3x - 4 = 0, then………… is
value of k.
(A) 2
1
(B) 2
(C) -2
(D)

1
2
18. The quadratic equation ………… has a root x = 3.
(A) x2 + 8x - 15 = 0
(B) x2 - 8x + 15 = 0.
(C) x2 + 8x + 15 = 0
0
(D) x2 - 8x - 15 =
19. …………. is the value of the k, if one of the roots of the quadratic equation x2 + 6x + k
= 0 is 4.
(A) 20
(B) 40
(C) -40
(D) 8
20. …………. can be taken as the value of the k, if one of the roots of the quadratic equation
3
.
kx - 7x + 6 = 0 is 2
3
(A) 2
(B) -2
(C) 2
2
(D)

3
2
21. If 81 is the discriminant of 2x2 + 5x - k = 0, then the value of k is ………… .
(A) 2
(B) 7
(C) 5
(D) -7
22. If 64 is the discriminant of kx2 - 4x - 4 = 0, then the value of k is ………… .
(A) -4
(B) 3
(C) 4
(D) -3
23. The value of discriminant D for the equation (3x - 14)2 = 0 is …………….. .
(A) 4
(B)

3
14
(C) 0
14
(D) 3
24. The value of discriminant D for the equation (x + 2)(x - 5) = 0 is …………. .
(A) 49
(B) -10
(C) 3
(D) -31
25. Among the following equations …………. has repeated (identical) roots.
(A) x2 = 4
(B) x2 - 6x + 9 = 0
(C) x2 - 9 = 0
(D) x2 - 6x - 8 = 0
26. If the roots of the equation 6x2 - 13x + m = 0 are reciprocal of each other, then m =
……. .
(A) 6
(B) -13
(C) -6
1
(D) 6
27. Every quadratic polynomial has at the most ………..zero/s.
(A) 2
(B) 3
(C) 4
(D) 1
28. ………….. are the roots of 3x2 - 4x + 1 = 0.
(A) 0, 1
(B) -1, 1
1
1
 , 
3
(D) 3
1
(C) 1, 3
29. If one of the roots of x2 - 2x - c = 0 is 5, the other root is…………… .
(A) -3
(B) 3
(C) -15
(D) 15
30. If one of the roots of x2 + bx - 12 = 0 is 2, the other root is…………… .
(A) -12
(B) -6
(C) -2
(D) 6
31. The discrimimant of the equation 3x2 - 6x + 4 = 0 is ………… .
(A) 0
(B) -12
(C) 84
(D) 12
32. The roots of x2 + 12x + 36 + 0 are …………… .
(A) reciprocal of each other
(B) equal
(C) opposite of each other
(D) fractional
33. The equation 9x2 + 30x + 25 = 0 has ………… in R.
(A) no root
(B) equal roots
(C) irrational roots
(D) unequal roots
34. If the discriminant of x2 - 10x + (2k - 1) = 0 is 40, then k = …………..
(A) 13
(B) 8
(C) 79
(D) 15
7
,
35. If one of the roots 2x - 5x + k = 0 is 2 then k = …………. .
2
(A) 4
(B) 7
(C) -7
(D) 2
36. If one of the roots of 2x2 + 5x + 3 = 0 is -1, the other root is …………..
(A)

3
2
3
(B) 2
3
(C) 5
5
(D) 2
37. The standard form of quadratic polynomial of one variable is……
(A) ax2 + by + c
(B) ax + by + c
(C) ax2 + bx + c = 0; where a  0; a, b, c  R
(D) ax2 + bx + c; where a  0; a, b, c  R
38. The necessary condition for ax2 + bx + c = 0; where a, b, c  R be a quadratic equation
is…..
(A) a  1
(B) a = 1
(C) a = 0
(D) a  0
39. …… is true for the coefficients and constant term of a quadratic equation ax2 + bx + c =
0
(A) a = 0, b = 0, c  0
(B) a  0, a, b, c  R
(C) a = 0, b  0, c = 0
(D) a = 0, b 
0, c  0
40. The quadratic equation of one variable is………
(A) 4x - y = 5
(B) 3x2 +
2x  7  0
(C) 3x2 + 2y - 6 = 0
41. ………is not a quadratic equation.
(A) x2 - 2x + 1 = 0
(B) 2x(3x - 5) + 1 = 3x(2x + 5) + 3
x(3x + 7) = (x + 1)(x - 1)
42. (x + 6)(x + 5) = 0 is a……
(A) linear polynomial
(B) linear equation
quadratic equation
(D) 5x3 - 1 = 2
(C) 4 - 3x - 2x2 = 0
(C) quadratic polynomial
(D)
(D)
43. ………is a quadratic equation.
(A)
x
1
x
2
3
(B)
x
1
2
x
(C) x(x + 1) = 2
2
1
x2   2
x
(D)
44. The solution set of x2 + 5x + 6 = 0 is…………
(A) {-2, -3}
(B) {-2, 3}
(C) {2, -3}
(D) {2, 3}
45. The root of quadratic equation x2 - 2x + 15 = 0 are……
(A) -5 and -3
(B) -5 and 3
(C) 5 and -3
(D) 5 and 3
46. The solution set of a quadratic equation x2 + 5x - 14 =0 is………
(A) {-7,-2}
(B) {7, -2}
(C) {7, 2}
(D) {-7, 2}
47. x = 2 is a solution of equation……
(A) 2x2 + 2x + 1 = 0
(B) x2 - 2x + 2 = 0
(C) x2 - 3x + 2 = 0
(D) x2 + x - 2 = 0
48. If 3 is a roots of a quadratic equation x2 - kx + 6 = 0, then k =……
(A) 5
(B) 4
(C) -5
(D) -3
49. If 3 is a roots of a quadratic equation x2 + 3(k + 2) x - 9 = 0, then k =………
(A) 3
(B) -3
(C) -2
(D) 2
50. The roots of a quadratic equation (x - 7)2 - 16 = 0 are……
(A) 3 and 4
(B) -3 and -6
(C) -3 and -11
(D) 3 and 11
51. The roots of a quadratic equation x(x + 1) - 6 = 0 are………
(A) 3 and 2
(B) -3 and -2
(C) 3 and -2
(D) -3 and 2
52. If 1 is the solution of a quadratic equation 3x2 - kx + 2 = 0, then k = ……
(A) -5
(B) 5
(C) -4
(D) 2
53. If x = -2 is the solution of a quadratic equation kx2 + 5x + 2 = 0, then k = ……
(A) 2
(B) 3
(C) 1
(D) -2
54. If -3 is a solution of 2x2 + 5x + k = 0, then k = ……
(A) 2
(B) -2
(C) 3
(D) -3
55. The roots of a quadratic equation 6x2 - 13x + 6 = 0 are……
3
3
and 
2
2
(A)
(B)

3
2
and 
2
3
3
2
and 
2
3
(C)
x
(D)

3
3
and 
2
2
2
3
x
are………
56. The roots of a quadratic equation
(A) 2 and 1
(B) -2 and -2
(C) -2 and 1
(D) 2 and -1
57. The root of quadratic equation……………are recurring.
(A) x2 - 6x - 8 = 0
(B) x2 - 6x + 9 = 0
(C) x2 - 9 = 0
(D) x2 = 4
58. 16x2 + 40x + k is a perfect square polynomial, then k = ……
(A) 25
(B) 15
(C) 20
(D) 10
59. …….is a golden number.
1 3
2
(A)
1 2
3
(B)
1 5
2
(C)
1 5
3
(D)
60. The golden number is associated with………….sequence in mathematics.
(A) Fibonacci
(B) Arithmetic
(C) Harmonic
(D) Geometric
61. The roots of quadratic equation x2 = 49 are………
(A) 7 and 1/7
(B) 7 and -7
(C) 7 and 7
(D) -7 and -7
62. The roots of quadratic equation (x + 2)2 = 16 are………
(A) -6 and 2
(B) 6 and -2
(C) 3 and 4
(D) 2 and 3
63. The quadratic equation having roots -1 and 2 is………
(A) x2 - x - 2 = 0
(B) x2 + x - 2 = 0
(C) x2 + x + 2 = 0
(D) x2 - x + 2 = 0
64. The quadratic equation of variable x having roots -8 and 8 is………
(A) x2 - 8 = 0
(B) x2 = 16
(C) x2 = 64
(D) x2 - 8x + 16 = 0
65. The symbol used for the discriminate of a quadratic equation is…….
(A) 
(B) 
(C) 
(D) D
66. If………….then real roots of a quadratic equation do not exist. (No real solution.)
(A) D = 0
(B) D < 0
(C) D = 1
(D) D > 0
67. For a quadratic equation ax2+ bx + c = 0 if…………….then the roots are distinct and
rational.
(A) D = 0
(B) D > 0
(C) D is a square of a rational number and a, b, c  Q
(D) D
<0
68. For a quadratic equation, if………….,then the roots of an equation are distinct and real.
(A) D ≼ 0
(B) D = 0
(C) D < 0
(D) D > 0
69. For a quadratic equation, if………….,then both the roots are equal.
(A) D < 0
(B) D = 1
(C) D = 0
(D) D > 0
b D
,
2a
70. If one root of a quadratic equation ax + bx + c = 0 is
then other root is……
2
b  D
2a
(A)
c  D
2a
(B)
c D
2a
(C)
b D
(D) 2a
71. Comparing the quadratic equation 5x2 - 4x - 1 = 0 with standard form ax2 + bx + c = 0,
we get b =……
(A) 5
(B) -4
(C) 4
(D) -1
72. Comparing the quadratic equation x(2x - 1) - 5 = 0 with standard form ax2 + bx + c = 0,
we get b =……
(A) 5
(B) -1
(C) 2
(D) 1
73. If both the roots of a quadratic equation ax2 + bx + c = 0 (a  0)are equal, then……
(A) b2 = 4ac
(B) a = c
(C) a2 = 4bc
(D) c2 = 4ab
74. The value of discriminate of a quadratic equation 4x2 + 20x + 25 = 0 is………
(A) 10
(B) 0
(C) 5
(D) 25
75. The value of discriminate of a quadratic equation 5x2 + x + 2 = 0 is……
(A) -39
(B) 5
(C) 1
(D) 41
76. The value of discriminant of a quadratic equation x2 - 8x + 15 = 0 is………
(A) 4
(B) -4
(C) 60
(D) 64
77. The value of discriminate of a quadratic equation kx2 - 4x - 4 = 0 is……
(A) 0
(B) -3
(C) 5
(D) 3
78. If the value of discriminate of a quadratic equation 6x2 - x - k = 0 is 25, then k =………
(A) 2
(B) -1
(C) -2
(D) 1
79. If the value of discriminate of a quadratic equation kx2 - 6x + 1 = 0 is 0, then k =……
(A) 3
(B) 9
(C) 2
(D) 1
80. If both the roots of a quadratic equation kx2 + 4x + 1 = 0 are recurring, then k =………
(A) 4
(B) 1
(C) 2
(D) -4
81. If one of the roots of quadratic equation x2 - ax - 8 = 0 is -4, then a =……
(A) -2
(B) -4
(C) 4
(D) 2
82. If one of the roots of quadratic equation x2 + 4x + m = 0 is 2, then other root is……
(A) 6
(B) 4
(C) 3
(D) -6
83. If one of the roots of quadratic equation x2 + bx - 15 = 0 is 3, then other root is………
(A) -5
(B) -15
(C) 5
(D) 15
84. If the value of discriminate of quadratic equation x2 - 10x + (2k - 1) = 0 is 40, then k
=………
(A) 15
(B) 10
(C) 7
(D) 8
2
85. If the value of discriminate of quadratic equation x  2x  2  0 is .......
(A) 6
(B) -16
(C) 18
(D) -14
86. If one root of x2 - 5x + 6 = 0 is also the root of x2 + 3x + c = 0 then c =…
(A) -9 or -5
(B) 9 or 5
(C) -10 or -18
(D) 10 or 18
87. The formula for finding the value of D is……
(A) D = b2 - 4a2c2
(B) D = b2 + 4a2c2
(C) D = b2 + 4ac
(D) D = b2 - 4ac
88. The roots of quadratic equation……… are -4 and 5.
(A) x2 - x - 20 = 0
(B) x2 + x - 20 = 0
(C) x2 - x + 20 = 0
(D) x2 - x - 9 = 0
89. …….. is a solution of quadratic equation x2 - 3x + 2 = 0
(A) -2
(B) -3
(C) 1
(D) 3
90. Discriminant D = …… for the quadratic equation 5x2 - 6x + 1 = 0.
(A) 4
(B) 16
(C)
56
(D) 56
91. If x = 2 is a root of the equation x2 - 4x + a = 0, then a = …… .
(A) -2
(B) 4
(C) 2
(D) -4
92. A quadratic equation ha two equal roots, if ……. .
(A) D > 0
(B) is non-zero perfect square
(C) D = 0
(D) D < 0
93. The quadratic equation …… has 3 as one of its roots.
(A) x2 - x + 6 = 0
(B) x2 + x - 6 = 0
(C) x2 + x + 6 = 0
(D) x2 - x - 6 = 0
94. If 4 is a root of quadratic equation x2 + ax - 8 = 0, then a = …….. .
(A) -2
(B) 4
(C) 2
(D) -4
95. If one of roots of kx2 - 7x + 3 = 0 is 3, then k = ……
(A) -3
(B) -2
(C) 2
(D) 3
96. The discriminant of x2 - 3x - k = 0 is 1. A value of x is ……..
(A) 4
(B) -2
(C) 2
(D) -4
Answers:
01 : A B C D  02 : A B C D  03 : A B
C

04 : A
C

07 : A
C

10 : A
C

13 : A
C

16 : A
C

19 : A
C

22 : A
C

25 : A
C

28 : A
C

31 : A
C

34 : A
C

37 : A
C

40 : A
C

43 : A
C

46 : A
C

49 : A
D 
B C D  05 : A B C D  06 : A B
D 
B C D  08 : A B C D  09 : A B
D 
B C D  11 : A B C D  12 : A B
D 
B C D  14 : A B C D  15 : A B
D 
B C D  17 : A B C D  18 : A B
D 
B C D  20 : A B C D  21 : A B
D 
B C D  23 : A B C D  24 : A B
D 
B C D  26 : A B C D  27 : A B
D 
B C D  29 : A B C D  30 : A B
D 
B C D  32 : A B C D  33 : A B
D 
B C D  35 : A B C D  36 : A B
D 
B C D  38 : A B C D  39 : A B
D 
B C D  41 : A B C D  42 : A B
D 
B C D  44 : A B C D  45 : A B
D 
B C D  47 : A B C D  48 : A B
D 
B C D  50 : A B C D  51 : A B
C

52 : A
C

55 : A
C

58 : A
C

61 : A
C

64 : A
C

67 : A
C

70 : A
C

73 : A
C

76 : A
C

79 : A
C

82 : A
C

85 : A
C

88 : A
C

91 : A
C

94 : A
C
D 
B C D  53 : A B C D  54 : A B
D 
B C D  56 : A B C D  57 : A B
D 
B C D  59 : A B C D  60 : A B
D 
B C D  62 : A B C D  63 : A B
D 
B C D  65 : A B C D  66 : A B
D 
B C D  68 : A B C D  69 : A B
D 
B C D  71 : A B C D  72 : A B
D 
B C D  74 : A B C D  75 : A B
D 
B C D  77 : A B C D  78 : A B
D 
B C D  80 : A B C D  81 : A B
D 
B C D  83 : A B C D  84 : A B
D 
B C D  86 : A B C D  87 : A B
D 
B C D  89 : A B C D  90 : A B
D 
B C D  92 : A B C D  93 : A B
D 
B C D  95 : A B C D  96 : A B
D 