1. If x=5, then the value of 2x+3is:
a) 8
b) 10
c) 13
d) 15
Answer: c) 13
Explanation: Substitute x=5: 2(5)+3=13.
2. Simplify: (a+b)2
a) a2+b2
b) a2+2ab+b2
c) a2-2ab+b2
d) None
Answer: b) a2+2ab+b2
Explanation: Square of binomial formula.
3. If x=2, value of x3+2×2+x:
a) 12
b) 18
c) 20
d) 22
Answer: b) 18
Explanation: 23+2(22)+2=8+8+2=18.
4. The roots of x2-9=0are:
a) 9, −9
b) 3, −3
c) √9, −√9
d) 0, 9
Answer: b) 3, −3
Explanation: x2=9→x=±3.
5. Simplify: (x+y)(x-y)
a) x2-y2
b) x2+y2
c) 2xy
d) None
Answer: a) x2-y2
Explanation: Difference of squares.
6. If x2=49, then x = ?
a) 7 only
b) −7 only
c) ±7
d) 0
Answer: c) ±7
Explanation: Square root has two values.
7. Simplify: (2x+3)2
a) 4x2+12x+9
b) 2x2+9
c) 2x2+6x+9
d) None
Answer: a) 4x2+12x+9
Explanation: Expand binomial.
8. The roots of quadratic x^2+5x+6=0are:
a) (2,3)
b) (−2,−3)
c) (−1,−6)
d) (3,−2)
Answer: b) (−2,−3)
Explanation: Factorize: (x+2)(x+3)=0.
9. If a+b=10and a-b=4, then a=?
a) 5
b) 7
c) 8
d) 9
Answer: c) 7
Explanation: Adding equations: 2a=14 → a=7.
10. Simplify: (x+1)(x+2)(x+3)
a) x3+6x+6
b) x3+6x2+11x+6
c) x3+11x+6
d) None
Answer: b) x3+6x2+11x+6
Explanation: Multiply step by step.
11. If p=2,q=3, then value of pq+p+q:
a) 11
b) 12
c) 13
d) 14
Answer: a) 11
Explanation: 2×3+2+3=11.
12. Solve: 2x+3=11.
a) 2
b) 3
c) 4
d) 5
Answer: c) 4
Explanation: 2x=8 → x=4.
13. Simplify: (a-b)2
a) a2-b2
b) a2-2ab+b2
c) a2+2ab+b2
d) None
Answer: b) a2-2ab+b2
Explanation: Formula.
14. If x=3, find 2x2+5x:
a) 18
b) 19
c) 21
d) 24
Answer: d) 24
Explanation: 2×9+15=24.
15. Solve: x2=64.
a) 8
b) −8
c) ±8
d) 64
Answer: c) ±8
Explanation: Square root.
16. If a+b=12, ab=20, then quadratic equation is:
a) x2-12x+20=0
b) x2+12x+20=0
c) x2-20x+12=0
d) None
Answer: a) x2-12x+20=0
Explanation: Equation with roots a and b → x²−(sum)x+(product)=0.
17. Simplify: x3-y3.
a) (x−y)(x2+xy+y2)
b) (x−y)(x2−xy+y2)
c) (x+y)(x2−y2)
d) None
Answer: b) (x−y)(x2+xy+y2)
Explanation: Standard cube formula.
18. Solve: 5x−7=18.
a) 2
b) 3
c) 4
d) 5
Answer: d) 5
Explanation: 5x=25 → x=5.
19. If x2-5x+6=0, then roots are:
a) (2,3)
b) (−2,−3)
c) (1,6)
d) None
Answer: a) (2,3)
Explanation: Factorize: (x−2)(x−3)=0.
20. Simplify: (x+2)2-(x-2)2.
a) 4x
b) 8x
c) 2x
d) 0
Answer: b) 8x
Explanation: Use a²−b²=(a−b)(a+b).
21. If x+y=6,xy=5, quadratic equation is:
a) x2+6x+5=0
b) x2-6x+5=0
c) x2-6x-5=0
d) None
Answer: b) x2-6x+5=0
Explanation: Roots α,β satisfy sum=6, product=5.
22. Simplify: (a+b+c)2.
a) a2+b2+c2+2ab+2bc+2ca
b) a2+b2+c2+ab+bc+ca
c) a2+b2+c2
d) None
Answer: a) a2+b2+c2+2ab+2bc+2ca
Explanation: Expansion formula.
23. If x=-2, value of x2+4x+3:
a) 1
b) 2
c) 3
d) 4
Answer: a) 1
Explanation: 4−8+3=−1? → check: (−2)²+4(−2)+3=4−8+3=−1.
Correct answer: −1 (None of options fits; correct option should be “−1”).
24. Simplify: (x+y)3.
a) x3+y3+3x2 y+3xy2
b) x3+y3+2xy
c) x3-y3
d) None
Answer: a) x3+y3+3x2 y+3xy2
Explanation: Binomial cube expansion.
25. Solve: x2-16=0.
a) 4 only
b) −4 only
c) ±4
d) 8
Answer: c) ±4
Explanation: x²=16 → x=±4.
26. If x=1, the value of x3+3x2+3x+1is:
a) 4
b) 6
c) 8
d) 10
Answer: c) 8
Explanation: 13+3(12)+3(1)+1=1+3+3+1=8. (Also matches (x+1)3).
27. Solve: 7x+5=40.
a) 4
b) 5
c) 6
d) 7
Answer: b) 5
Explanation: 7x=35 → x=5.
28. The value of (a+b)(a-b)is:
a) a2+b2
b) a2-b2
c) a2+2ab+b2
d) None
Answer: b) a2-b2
Explanation: Difference of squares.
29. If x2+4x+3=0, then roots are:
a) −1, −3
b) 1, 3
c) −2, −2
d) None
Answer: a) −1, −3
Explanation: Factorize: (x+1)(x+3)=0.
30. Simplify: (2x-3)(2x+3).
a) 4x2-9
b) 4x2+9
c) 2x2-9
d) None
Answer: a) 4x2-9
Explanation: Use (a−b)(a+b)=a²−b².
31. If x=2, find value of x3-3x+1.
a) 3
b) 5
c) 7
d) 9
Answer: c) 7
Explanation: 8-6+1=3? Wait → Check: 2^3-3(2)+1=8-6+1=3. Correct: a) 3.
32. The roots of x2-25=0are:
a) ±25
b) ±5
c) 0, 25
d) None
Answer: b) ±5
Explanation: x²=25 → x=±5.
33. If a2+b2=25and ab=12, then (a+b)2=?
a) 37
b) 49
c) 25
d) 12
Answer: b) 49
Explanation: (a+b)²=a²+b²+2ab=25+24=49.
34. Simplify: (x-1)(x2+x+1).
a) x3-1
b) x3+1
c) x3-x+1
d) None
Answer: a) x3-1
Explanation: Formula for difference of cubes.
35. If one root of quadratic x2+7x+12=0is −3, the other is:
a) −4
b) 3
c) 4
d) 12
Answer: a) −4
Explanation: Factorize: (x+3)(x+4)=0. Roots are −3 and −4.
36. Solve: 2x-7=9.
a) 6
b) 7
c) 8
d) 9
Answer: c) 8
Explanation: 2x=16 → x=8.
37. If x+y=4,xy=3, then quadratic equation is:
a) x2-4x+3=0
b) x2+4x+3=0
c) x2-3x+4=0
d) None
Answer: a) x2-4x+3=0
Explanation: Equation: x²−(sum)x+(product)=0.
38. Simplify: (x+y)2-(x-y)2.
a) 2xy
b) 4xy
c) 4x
d) 4y
Answer: d) 4y
Explanation: Expand → (x²+2xy+y²)−(x²−2xy+y²)=4xy. Wait carefully → Correct is b) 4xy.
39. Solve: x2-6x+9=0.
a) 3, 3
b) −3, −3
c) 6, 9
d) None
Answer: a) 3, 3
Explanation: (x−3)²=0 → double root at 3.
40. Simplify: (a+b)3-(a-b)3.
a) 2a³+6ab²
b) 2b³+6a²b
c) 2a³−6a²b
d) None
Answer: b) 2b³+6a²b
Explanation: Expansion → difference of cubes.
41. If x=2, value of x2+2x+1:
a) 7
b) 9
c) 11
d) 13
Answer: b) 9
Explanation: 4+4+1=9.
42. Roots of x2-2x-8=0are:
a) 2, −4
b) −2, 4
c) 4, −2
d) Both b and c
Answer: d) Both b and c
Explanation: Roots are 4 and −2.
43. Simplify: (p+q)(p2-pq+q2).
a) p3+q3
b) p3-q3
c) p2+q2
d) None
Answer: a) p3+q3
Explanation: Standard cube identity.
44.Solve: 3x-4=8.
a) 3
b) 4
c) 5
d) 6
Answer: c) 4? → Check: 3x−4=8 → 3x=12 → x=4. Correct: b) 4.
45.If (a+b)=7,(a-b)=3, find a.
a) 2
b) 4
c) 5
d) None
Answer: c) 5
Explanation: Adding → 2a=10 → a=5.
46. Simplify: (x+1)(x2-x+1).
a) x3+1
b) x3-1
c) x3-x+1
d) None
Answer: a) x3+1
Explanation: Sum of cubes identity.
47. Solve: x2+10x+25=0.
a) 5, −5
b) −5, −5
c) 10, −25
d) None
Answer: b) −5, −5
Explanation: (x+5)²=0 → double root at −5.
48. If x+y=8,xy=15, quadratic equation is:
a) x2-8x+15=0
b) x2+8x+15=0
c) x2-15x+8=0
d) None
Answer: a) x2-8x+15=0
Explanation: Standard relation.
49. Simplify: (a+b)3+(a-b)3.
a) 2a³+6ab²
b) 2a³+6a²b
c) 2a³+6ab²? → check properly.
Answer: a) 2a³+6ab²
Explanation: Expansions: (a+b)³+(a−b)³=2a³+6ab².
50. If x=3, value of x3-3x2+3x-1:
a) 8
b) 10
c) 12
d) 14
Answer: a) 8
Explanation: Expression is (x−1)³. For x=3 → (2)³=8.
51. If a+b=12and ab=27, then the value of a2+b2is:
A) 72
B) 90
C) 120
D) 144
Answer: B) 90
Explanation:a^2+b^2=(a+b)^2-2ab=12^2-2(27)=144-54=90.
52. Solve: If x-1/x=4, find x2+1/x2 .
A) 12
B) 14
C) 18
D) 20
Answer: B) 14
Explanation:
(x-1/x )2=x2+1/x2 -2.
So, 16=x2+1/x2 -2⇒x2+1/x2 =18.
Correction: Actually, 16=…-2, so =18. Answer is C) 18.
53. If x2-7x+12=0, then the roots are:
A) (3, 4)
B) (2, 6)
C) (1, 12)
D) (7, 12)
Answer: A) (3, 4)
Explanation:
Equation factors: (x-3)(x-4)=0⇒x=3,4.
54. If 2x+3y=12and x+2y=6, find the value of x.
A) 0
B) 2
C) 3
D) 6
Answer: B) 2
Explanation:
Multiply second eqn by 2: 2x+4y=12. Subtract from first: (2x+3y)-(2x+4y)=0⇒-y=0⇒y=0.
Then x+0=6. Wait correction: if y=0, then x=6. Correct answer: D) 6.
55. Solve: x2-5x+6=0.
A) 2, 3
B) 1, 6
C) 3, 4
D) 2, 6
Answer: A) 2, 3
Explanation:
Factorize: (x-2)(x-3)=0⇒x=2,3.
56. If x+y=8and xy=15, then find x2+y2.
A) 34
B) 49
C) 64
D) 94
Answer: B) 49
Explanation:
x2+y2=(x+y)2-2xy=64-30=34. Correction: Answer is A) 34.
57. The value of (x+a)(x+b)-x2is:
A) ab
B) a+b
C) ax + bx + ab
D) (a+b)x + ab
Answer: D) (a+b)x + ab
Explanation:
Expand: x^2+ax+bx+ab-x^2=(a+b)x+ab.
58. Solve: 3x-7=2x+8.
A) 15
B) -15
C) 7.5
D) 0
Answer: A) 15
Explanation:
3x-2x=8+7⇒x=15.
59. If x=1/2, find value of (1-x)/(1+x).
A) 1/3
B) 2/3
C) 1/2
D) 3/2
Answer: B) 1/3
Explanation:
(1-1/2)/(1+1/2)=(1/2)/(3/2)=1/3.
60. Solve: 2x+5=19.
A) 5
B) 7
C) 6
D) 8
Answer: B) 7
Explanation:
2x=14⇒x=7.
61. If a+b=7and ab=10, find a2+b2.
A) 29
B) 39
C) 49
D) 59
Answer: A) 29
Explanation:
a2+b2=(a+b)2-2ab=49-20=29.
62. If x-3=7, find x.
A) 4
B) 5
C) 7
D) 10
Answer: D) 10
Explanation:
x=7+3=10.
63. If x^2-4=0, then x is:
A) ±2
B) ±4
C) ±1
D) 0
Answer: A) ±2
Explanation:
x2=4⇒x=±2.
64. If 2x=3y, then ratio x:yis:
A) 2:3
B) 3:2
C) 1:1
D) 3:4
Answer: B) 3:2
Explanation:
2x=3y⇒x/y=3/2⇒3:2.
65. If x=2, value of x3-2x2+1.
A) 1
B) 3
C) 5
D) 7
Answer: A) 1
Explanation:
=8-8+1=1.
66. If a2-b2=(a-b)(a+b), then identity is known as:
A) Difference of squares
B) Square of sum
C) Square of difference
D) Perfect cube
Answer: A) Difference of squares
67. Value of (a+b)2-(a-b)2:
A) 2ab
B) 4ab
C) 2(a+b)
D) 4ab + 2a
Answer: C) 4ab? Let’s check.
(a+b)2-(a-b)2=(a2+2ab+b2)-(a2-2ab+b2)=4ab. Correct Answer: B) 4ab.
68. Solve: x2=64.
A) 8
B) -8
C) ±8
D) 0
Answer: C) ±8
69. If x=3, value of (x2+2x+1)/(x+1).
A) 3
B) 4
C) 5
D) 6
Answer: B) 4
Explanation:
Numerator: 9+6+1=16. Denominator: 4. Value=4.
70. Roots of x2+7x+10=0.
A) -2, -5
B) 2, 5
C) -7, -10
D) -1, -10
Answer: A) -2, -5
Explanation:
Factorize: (x+2)(x+5)=0.
71. If p+q=0, then p3+q3=?
A) 0
B) 2pq
C) 3pq
D) -3pq
Answer: A) 0
Explanation:
Since q=-p, p3+(-p)3=0.
72. Solve: x2-2x-3=0.
A) 3, -1
B) 2, -3
C) -3, -1
D) 1, 3
Answer: A) 3, -1
Explanation:
Factorize: (x-3)(x+1)=0.
73. Simplify: (x+y)2-(x-y)2.
A) 4xy
B) 2xy
C) 2x+2y
D) 4x
Answer: A) 4xy
Explanation:
Expand both: (x2+2xy+y2)-(x2-2xy+y2)=4xy.
74. Solve: 5x=2x+12.
A) 2
B) 3
C) 4
D) 5
Answer: C) 4
Explanation:
5x-2x=12 ⇒ x=4.
75. If x=1, find (x2+3x+2)/(x+2).
A) 2
B) 3
C) 4
D) 5
Answer: B) 3
Explanation:
Numerator=1+3+2=6. Denominator=3. Value=2. Correction: A) 2.
76. If x2+9=0, then x is:
A) 3
B) -3
C) ±3i
D) 0
Answer: C) ±3i
Explanation:
x2=-9⇒x=±√(-9)=±3i(imaginary roots).
77. If a+b=0, then a3+b3=?
A) 0
B) 2ab
C) -3ab
D) ab
Answer: A) 0
Explanation:
If b=-a, then a3+(-a)3=0.
78. If x+y=10, xy=21, then x2+y2=?
A) 37
B) 58
C) 79
D) 100
Answer: B) 58
Explanation:
(x+y)2-2xy=100-42=58.
79. Solve: x2+2x+1=0.
A) 0, -2
B) -1, -1
C) 1, -1
D) 0, 1
Answer: B) -1, -1
Explanation:
Equation = (x+1)^2=0. Double root -1.
80. If (x-1)(x-2)=0, roots are:
A) 1, 2
B) -1, -2
C) 0, 2
D) -1, 2
Answer: A) 1, 2
81. Solve: 3x+4=19.
A) 3
B) 4
C) 5
D) 7
Answer: C) 5
Explanation:
3x=15 ⇒ x=5.
82. If x2-6x+9=0, root is:
A) 3,3
B) 2,4
C) 0,9
D) 1,9
Answer: A) 3,3
Explanation:
Equation = (x-3)2=0.
83. If a+b=20,ab=96, find a2+b2.
A) 112
B) 118
C) 120
D) 128
Answer: B) 118
Explanation:
(a+b)2-2ab=400-192=208. Correction: Actually 208 not in options. Typo check: maybe ab=141?
But with ab=96 → 400-192=208. Correct answer should be 208 (option misprint).
84. Solve: x2-25=0.
A) ±5
B) ±25
C) ±10
D) 0
Answer: A) ±5
85. If p2+q2=20, p+q=6, find pq.
A) 8
B) 10
C) 12
D) 16
Answer: B) 8
Explanation:
(p+q)2=p2+q2+2pq⇒36=20+2pq⇒2pq=16⇒pq=8.
86. Solve: 7x-3=11.
A) 1
B) 2
C) 3
D) 4
Answer: B) 2
Explanation:
7x=14 ⇒ x=2.
87. If a2+b2=50, ab=24, find (a+b)2.
A) 74
B) 98
C) 100
D) 110
Answer: A) 74
Explanation:
(a+b)2=a2+b2+2ab=50+48=98. Correct Answer: B) 98.
88. If a-b=5,ab=14, find a2+b2.
A) 53
B) 67
C) 75
D) 81
Answer: C) 75
Explanation:
(a-b)2=a2+b2-2ab=25⇒a2+b2=25+28=53. Correction: A) 53.
89. Solve: x2+4x+4=0.
A) -2, -2
B) -4, 0
C) 2, 2
D) 0, 4
Answer: A) -2, -2
Explanation:
(x+2)2=0⇒x=-2.
90. If a+b=15,ab=56, find a2+b2.
A) 113
B) 121
C) 133
D) 145
Answer: A) 113
Explanation:
(a+b)^2-2ab=225-112=113.
91. If x+1/x=3, find x2+1/x2 .
A) 5
B) 7
C) 9
D) 11
Answer: B) 7
Explanation:
(x+1/x)2=x2+1/x2+2⇒9=x2+1/x2+2⇒=7.
92. If x2-10x+21=0, roots are:
A) 3, 7
B) 7, 21
C) 1, 21
D) 2, 10
Answer: A) 3, 7
Explanation:
(x-3)(x-7)=0.
93. Solve: 5x+2=17.
A) 2
B) 3
C) 4
D) 5
Answer: C) 3
Explanation:
5x=15 ⇒ x=3.
94. If x2+y2=13,xy=6, find (x+y)2.
A) 19
B) 25
C) 31
D) 37
Answer: B) 25
Explanation:
(x+y)^2=x2+y^2+2xy=13+12=25.
95. If x+y=9,xy=20, find x2+y2.
A) 41
B) 49
C) 61
D) 81
Answer: A) 41
Explanation:
(x+y)2-2xy=81-40=41.
96. Solve: x2-8x+16=0.
A) 4, 4
B) 8, 0
C) -4, -4
D) 2, 8
Answer: A) 4, 4
Explanation:
(x-4)2=0.
97. If a+b=11,ab=28, find a2+b2.
A) 65
B) 81
C) 93
D) 121
Answer: C) 93
Explanation:
121-56=65. Correction: Answer A) 65.
98. If x-1/x=5, find x2+1/x2 .
A) 23
B) 25
C) 27
D) 29
Answer: A) 23
Explanation:
(x-1/x)2=x2+1/x2-2=25 ⇒ x2+1/x2=27. Correct Answer: C) 27.
99. Solve: x2-3x-10=0.
A) 2, 5
B) -2, 5
C) 10, -1
D) -5, 2
Answer: B) -2, 5
Explanation:
(x-5)(x+2)=0.
100. If a2+b2=29,ab=10, find (a+b)2.
A) 39
B) 49
C) 59
D) 69
Answer: B) 49
Explanation:
(a+b)2=a2+b2+2ab=29+20=49.