{"id":12535,"date":"2025-09-18T07:06:16","date_gmt":"2025-09-18T06:06:16","guid":{"rendered":"https:\/\/mcqsadda.com\/?p=12535"},"modified":"2025-10-21T07:30:12","modified_gmt":"2025-10-21T06:30:12","slug":"algebra-top-100-mcqs-with-answer-and-explanation","status":"publish","type":"post","link":"https:\/\/mcqsadda.com\/index.php\/2025\/09\/18\/algebra-top-100-mcqs-with-answer-and-explanation\/","title":{"rendered":"Algebra Top 100 MCQs With Answer and Explanation"},"content":{"rendered":"\n

1. If x=5, then the value of 2x+3is:<\/mark><\/strong>
a) 8
b) 10
c) 13
d) 15
Answer: <\/strong>c) 13
Explanation:<\/strong> Substitute x=5: 2(5)+3=13.<\/p>\n\n\n\n

2. Simplify: (a+b)2<\/sup><\/mark><\/strong>
a) a2<\/sup>+b2<\/sup>
b) a2<\/sup>+2ab+b2<\/sup>
c) a2<\/sup>-2ab+b2<\/sup>
d) None
Answer:<\/strong> b) a2<\/sup>+2ab+b2<\/sup>
Explanation<\/strong>: Square of binomial formula.<\/p>\n\n\n\n

3. If x=2, value of x3<\/sup>+2×2+x:<\/mark><\/strong>
a) 12
b) 18
c) 20
d) 22
Answer: <\/strong>b) 18
Explanation: <\/strong>23<\/sup>+2(22<\/sup>)+2=8+8+2=18.<\/p>\n\n\n\n

4. The roots of x2<\/sup>-9=0are:<\/mark><\/strong>
a) 9, \u22129
b) 3, \u22123
c) \u221a9, \u2212\u221a9
d) 0, 9
Answer: <\/strong>b) 3, \u22123
Explanation: x2<\/sup>=9\u2192x=\u00b13.<\/p>\n\n\n\n

5. Simplify: (x+y)(x-y)<\/mark><\/strong>
a) x2-<\/sup>y2<\/sup>
b) x2<\/sup>+y2<\/sup>
c) 2xy
d) None
Answer: <\/strong>a) x2-<\/sup>y2<\/sup>
Explanation:<\/strong> Difference of squares.<\/p>\n\n\n\n

6. If x2<\/sup>=49, then x = ?<\/mark><\/strong>
a) 7 only
b) \u22127 only
c) \u00b17
d) 0
Answer: <\/strong>c) \u00b17
Explanation:<\/strong> Square root has two values.<\/p>\n\n\n\n

7. Simplify: (2x+3)2<\/sup><\/mark><\/strong>
a) 4x2<\/sup>+12x+9
b) 2x2<\/sup>+9
c) 2x2<\/sup>+6x+9
d) None
Answer: <\/strong>a) 4x2<\/sup>+12x+9
Explanation: <\/strong>Expand binomial.<\/p>\n\n\n\n

8. The roots of quadratic x^2+5x+6=0are:<\/mark><\/strong>
a) (2,3)
b) (\u22122,\u22123)
c) (\u22121,\u22126)
d) (3,\u22122)
Answer: <\/strong>b) (\u22122,\u22123)
Explanation: <\/strong>Factorize: (x+2)(x+3)=0.<\/p>\n\n\n\n

9. If a+b=10and a-b=4, then a=?<\/mark><\/strong>
a) 5
b) 7
c) 8
d) 9
Answer:<\/strong> c) 7
Explanation<\/strong>: Adding equations: 2a=14 \u2192 a=7.<\/p>\n\n\n\n

10. Simplify: (x+1)(x+2)(x+3)<\/mark><\/strong>
a) x3<\/sup>+6x+6
b) x3<\/sup>+6x2<\/sup>+11x+6
c) x3<\/sup>+11x+6
d) None
Answer: <\/strong>b) x3<\/sup>+6x2<\/sup>+11x+6
Explanation:<\/strong> Multiply step by step.<\/p>\n\n\n\n

11. If p=2,q=3, then value of pq+p+q:<\/mark><\/strong>
a) 11
b) 12
c) 13
d) 14
Answer:<\/strong> a) 11
Explanation: <\/strong>2\u00d73+2+3=11.<\/p>\n\n\n\n

12. Solve: 2x+3=11.<\/mark><\/strong>
a) 2
b) 3
c) 4
d) 5
Answer: <\/strong>c) 4
Explanation:<\/strong> 2x=8 \u2192 x=4.<\/p>\n\n\n\n

13. Simplify: (a-b)2<\/sup><\/mark><\/strong>
a) a2<\/sup>-b2<\/sup>
b) a2<\/sup>-2ab+b2<\/sup>
c) a2<\/sup>+2ab+b2<\/sup>
d) None
Answer:<\/strong> b) a2<\/sup>-2ab+b2<\/sup>
Explanation: <\/strong>Formula.<\/p>\n\n\n\n

14. If x=3, find 2x2<\/sup>+5x:<\/strong><\/mark>
a) 18
b) 19
c) 21
d) 24
Answer: <\/strong>d) 24
Explanation<\/strong>: 2\u00d79+15=24.<\/p>\n\n\n\n

15. Solve: x2<\/sup>=64.<\/mark><\/strong>
a) 8
b) \u22128
c) \u00b18
d) 64
Answer<\/strong>: c) \u00b18
Explanation: <\/strong>Square root.<\/p>\n\n\n\n

16. If a+b=12, ab=20, then quadratic equation is:<\/mark><\/strong>
a) x2<\/sup>-12x+20=0
b) x2<\/sup>+12x+20=0
c) x2<\/sup>-20x+12=0
d) None
Answer: <\/strong>a) x2<\/sup>-12x+20=0
Explanation<\/strong>: Equation with roots a and b \u2192 x\u00b2\u2212(sum)x+(product)=0.<\/p>\n\n\n\n

17. Simplify: x3<\/sup>-y3<\/sup><\/mark><\/strong>.
a) (x\u2212y)(x2<\/sup>+xy+y2<\/sup>)
b) (x\u2212y)(x2<\/sup>\u2212xy+y2<\/sup>)
c) (x+y)(x2<\/sup>\u2212y2<\/sup>)
d) None
Answer: <\/strong>b) (x\u2212y)(x2<\/sup>+xy+y2<\/sup>)
Explanation:<\/strong> Standard cube formula.<\/p>\n\n\n\n

18. Solve: 5x\u22127=18.<\/mark><\/strong>
a) 2
b) 3
c) 4
d) 5
Answer:<\/strong> d) 5
Explanation: <\/strong>5x=25 \u2192 x=5.<\/p>\n\n\n\n

19. If x2<\/sup>-5x+6=0, then roots are:<\/mark><\/strong>
a) (2,3)
b) (\u22122,\u22123)
c) (1,6)
d) None
Answer<\/strong>: a) (2,3)
Explanation<\/strong>: Factorize: (x\u22122)(x\u22123)=0.<\/p>\n\n\n\n

20. Simplify: (x+2)2<\/sup>-(x-2)2<\/sup>.<\/strong><\/mark>
a) 4x
b) 8x
c) 2x
d) 0
Answer: <\/strong>b) 8x
Explanation:<\/strong> Use a\u00b2\u2212b\u00b2=(a\u2212b)(a+b).<\/p>\n\n\n\n

21. If x+y=6,xy=5, quadratic equation is:<\/mark><\/strong>
a) x2<\/sup>+6x+5=0
b) x2<\/sup>-6x+5=0
c) x2<\/sup>-6x-5=0
d) None
Answer:<\/strong> b) x2<\/sup>-6x+5=0
Explanation: <\/strong>Roots \u03b1,\u03b2 satisfy sum=6, product=5.<\/p>\n\n\n\n

22. Simplify: (a+b+c)2<\/sup>.<\/mark><\/strong>
a) a2<\/sup>+b2<\/sup>+c2<\/sup>+2ab+2bc+2ca
b) a2<\/sup>+b2<\/sup>+c2<\/sup>+ab+bc+ca
c) a2<\/sup>+b2<\/sup>+c2<\/sup>
d) None
Answer: <\/strong>a) a2<\/sup>+b2<\/sup>+c2<\/sup>+2ab+2bc+2ca
Explanation:<\/strong> Expansion formula.<\/p>\n\n\n\n

23. If x=-2, value of x2<\/sup>+4x+3:<\/mark><\/strong>
a) 1
b) 2
c) 3
d) 4
Answer:<\/strong> a) 1
Explanation:<\/strong> 4\u22128+3=\u22121? \u2192 check: (\u22122)\u00b2+4(\u22122)+3=4\u22128+3=\u22121.
Correct answer: \u22121 (None of options fits; correct option should be “\u22121”).<\/p>\n\n\n\n

24. Simplify: (x+y)3<\/sup>.<\/mark><\/strong>
a) x3<\/sup>+y3<\/sup>+3x2 <\/sup>y+3xy2<\/sup>
b) x3<\/sup>+y3<\/sup>+2xy
c) x3<\/sup>-y3<\/sup>
d) None
Answer: <\/strong>a) x3<\/sup>+y3<\/sup>+3x2<\/sup> y+3xy2<\/sup>
Explanation:<\/strong> Binomial cube expansion.<\/p>\n\n\n\n

25. Solve: x2<\/sup>-16=0.<\/mark><\/strong>
a) 4 only
b) \u22124 only
c) \u00b14
d) 8
Answer:<\/strong> c) \u00b14
Explanation:<\/strong> x\u00b2=16 \u2192 x=\u00b14.
26. If x=1, the value of x3<\/sup>+3x2<\/sup>+3x+1is:<\/mark><\/strong>
a) 4
b) 6
c) 8
d) 10
Answer:<\/strong> c) 8
Explanation:<\/strong> 13<\/sup>+3(12<\/sup>)+3(1)+1=1+3+3+1=8. (Also matches (x+1)3<\/sup>).<\/p>\n\n\n\n

27. Solve: 7x+5=40.<\/mark><\/strong>
a) 4
b) 5
c) 6
d) 7
Answer:<\/strong> b) 5
Explanation:<\/strong> 7x=35 \u2192 x=5.<\/p>\n\n\n\n

28. The value of (a+b)(a-b)is:<\/mark><\/strong>
a) a2<\/sup>+b2<\/sup>
b) a2<\/sup>-b2<\/sup>
c) a2<\/sup>+2ab+b2<\/sup>
d) None
Answer:<\/strong> b) a2<\/sup>-b2<\/sup>
Explanation: <\/strong>Difference of squares.<\/p>\n\n\n\n

29. If x2<\/sup>+4x+3=0, then roots are:<\/mark><\/strong>
a) \u22121, \u22123
b) 1, 3
c) \u22122, \u22122
d) None
Answer:<\/strong> a) \u22121, \u22123
Explanation: <\/strong>Factorize: (x+1)(x+3)=0.<\/p>\n\n\n\n

30. Simplify: (2x-3)(2x+3).<\/mark><\/strong>
a) 4x2<\/sup>-9
b) 4x2<\/sup>+9
c) 2x2<\/sup>-9
d) None
Answer:<\/strong> a) 4x2<\/sup>-9
Explanation:<\/strong> Use (a\u2212b)(a+b)=a\u00b2\u2212b\u00b2.<\/p>\n\n\n\n

31. If x=2, find value of x3<\/sup>-3x+1.<\/mark><\/strong>
a) 3
b) 5
c) 7
d) 9
Answer:<\/strong> c) 7
Explanation:<\/strong> 8-6+1=3? Wait \u2192 Check: 2^3-3(2)+1=8-6+1=3. Correct: a) 3.<\/p>\n\n\n\n

32. The roots of x2<\/sup>-25=0are:<\/mark><\/strong>
a) \u00b125
b) \u00b15
c) 0, 25
d) None
Answer:<\/strong> b) \u00b15
Explanation: <\/strong>x\u00b2=25 \u2192 x=\u00b15.<\/p>\n\n\n\n

33. If a2<\/sup>+b2<\/sup>=25and ab=12, then (a+b)2<\/sup>=?<\/mark><\/strong>
a) 37
b) 49
c) 25
d) 12
Answer:<\/strong> b) 49
Explanation: <\/strong>(a+b)\u00b2=a\u00b2+b\u00b2+2ab=25+24=49.<\/p>\n\n\n\n

34. Simplify: (x-1)(x2<\/sup>+x+1).<\/mark><\/strong>
a) x3<\/sup>-1
b) x3<\/sup>+1
c) x3<\/sup>-x+1
d) None
Answer: <\/strong>a) x3<\/sup>-1
Explanation: <\/strong>Formula for difference of cubes.<\/p>\n\n\n\n

35. If one root of quadratic x2<\/sup>+7x+12=0is \u22123, the other is:<\/mark><\/strong>
a) \u22124
b) 3
c) 4
d) 12
Answer: <\/strong>a) \u22124
Explanation: <\/strong>Factorize: (x+3)(x+4)=0. Roots are \u22123 and \u22124.<\/p>\n\n\n\n

36. Solve: 2x-7=9.<\/mark><\/strong>
a) 6
b) 7
c) 8
d) 9
Answer:<\/strong> c) 8
Explanation: <\/strong>2x=16 \u2192 x=8.<\/p>\n\n\n\n

37. If x+y=4,xy=3, then quadratic equation is:<\/mark><\/strong>
a) x2<\/sup>-4x+3=0
b) x2<\/sup>+4x+3=0
c) x2<\/sup>-3x+4=0
d) None
Answer: <\/strong>a) x2<\/sup>-4x+3=0
Explanation: <\/strong>Equation: x\u00b2\u2212(sum)x+(product)=0.<\/p>\n\n\n\n

38. Simplify: (x+y)2<\/sup>-(x-y)2<\/sup>.<\/strong><\/mark>
a) 2xy
b) 4xy
c) 4x
d) 4y
Answer: <\/strong>d) 4y
Explanation: <\/strong>Expand \u2192 (x\u00b2+2xy+y\u00b2)\u2212(x\u00b2\u22122xy+y\u00b2)=4xy. Wait carefully \u2192 Correct is b) 4xy.<\/p>\n\n\n\n

39. Solve: x2<\/sup>-6x+9=0.<\/mark><\/strong>
a) 3, 3
b) \u22123, \u22123
c) 6, 9
d) None
Answer: <\/strong>a) 3, 3
Explanation:<\/strong> (x\u22123)\u00b2=0 \u2192 double root at 3.<\/p>\n\n\n\n

40. Simplify: (a+b)3<\/sup>-(a-b)3<\/sup>.<\/mark><\/strong>
a) 2a\u00b3+6ab\u00b2
b) 2b\u00b3+6a\u00b2b
c) 2a\u00b3\u22126a\u00b2b
d) None
Answer: <\/strong>b) 2b\u00b3+6a\u00b2b
Explanation: <\/strong>Expansion \u2192 difference of cubes.<\/p>\n\n\n\n

41. If x=2, value of x2<\/sup>+2x+1:<\/mark><\/strong>
a) 7
b) 9
c) 11
d) 13
Answer:<\/strong> b) 9
Explanation:<\/strong> 4+4+1=9.<\/p>\n\n\n\n

42. Roots of x2<\/sup>-2x-8=0are:<\/mark><\/strong>
a) 2, \u22124
b) \u22122, 4
c) 4, \u22122
d) Both b and c
Answer:<\/strong> d) Both b and c
Explanation:<\/strong> Roots are 4 and \u22122.<\/p>\n\n\n\n

43. Simplify: (p+q)(p2<\/sup>-pq+q2<\/sup>).<\/mark><\/strong>
a) p3<\/sup>+q3<\/sup>
b) p3<\/sup>-q3<\/sup>
c) p2<\/sup>+q2<\/sup>
d) None
Answer:<\/strong> a) p3<\/sup>+q3<\/sup>
Explanation:<\/strong> Standard cube identity.<\/p>\n\n\n\n

44.Solve: 3x-4=8.<\/mark><\/strong>
a) 3
b) 4
c) 5
d) 6
Answer: <\/strong>c) 4? \u2192 Check: 3x\u22124=8 \u2192 3x=12 \u2192 x=4. Correct: b) 4.<\/p>\n\n\n\n

45.If (a+b)=7,(a-b)=3, find a.<\/mark><\/strong>
a) 2
b) 4
c) 5
d) None
Answer:<\/strong> c) 5
Explanation:<\/strong> Adding \u2192 2a=10 \u2192 a=5.<\/p>\n\n\n\n

46. Simplify: (x+1)(x2<\/sup>-x+1).<\/mark><\/strong>
a) x3<\/sup>+1
b) x3<\/sup>-1
c) x3<\/sup>-x+1
d) None
Answer:<\/strong> a) x3<\/sup>+1
Explanation: <\/strong>Sum of cubes identity.<\/p>\n\n\n\n

47. Solve: x2<\/sup>+10x+25=0.<\/strong><\/mark>
<\/mark><\/strong>a) 5, \u22125
b) \u22125, \u22125
c) 10, \u221225
d) None
Answer:<\/strong> b) \u22125, \u22125
Explanation:<\/strong> (x+5)\u00b2=0 \u2192 double root at \u22125.<\/p>\n\n\n\n

48. If x+y=8,xy=15, quadratic equation is:<\/strong><\/mark>
a) x2<\/sup>-8x+15=0
b) x2<\/sup>+8x+15=0
c) x2<\/sup>-15x+8=0
d) None
Answer:<\/strong> a) x2<\/sup>-8x+15=0
Explanation:<\/strong> Standard relation.<\/p>\n\n\n\n

49. Simplify: (a+b)3<\/sup>+(a-b)3<\/sup>.<\/mark><\/strong>
a) 2a\u00b3+6ab\u00b2
b) 2a\u00b3+6a\u00b2b
c) 2a\u00b3+6ab\u00b2? \u2192 check properly.
Answer: <\/strong>a) 2a\u00b3+6ab\u00b2
Explanation: <\/strong>Expansions: (a+b)\u00b3+(a\u2212b)\u00b3=2a\u00b3+6ab\u00b2.<\/p>\n\n\n\n

50. If x=3, value of x3<\/sup>-3x2<\/sup>+3x-1:<\/mark><\/strong>
a) 8
b) 10
c) 12
d) 14
Answer: <\/strong>a) 8
Explanation: <\/strong>Expression is (x\u22121)\u00b3. For x=3 \u2192 (2)\u00b3=8.
51. If a+b=12and ab=27, then the value of a2<\/sup>+b2<\/sup>is:
<\/mark><\/strong>A) 72
B) 90
C) 120
D) 144
Answer:<\/strong> B) 90
Explanation:<\/strong>a^2+b^2=(a+b)^2-2ab=12^2-2(27)=144-54=90.<\/p>\n\n\n\n

52. Solve: If x-1\/x=4, find x2<\/sup>+1\/x2<\/sup> .<\/mark><\/strong>
A) 12
B) 14
C) 18
D) 20
Answer:<\/strong> B) 14
Explanation:<\/strong>
(x-1\/x )2<\/sup>=x2<\/sup>+1\/x2<\/sup> -2.
So, 16=x2<\/sup>+1\/x2<\/sup> -2\u21d2x2<\/sup>+1\/x2 <\/sup>=18.
Correction: Actually, 16=\u2026-2, so =18. Answer is C) 18.<\/p>\n\n\n\n

53. If x2<\/sup>-7x+12=0, then the roots are:<\/mark><\/strong>
A) (3, 4)
B) (2, 6)
C) (1, 12)
D) (7, 12)
Answer:<\/strong> A) (3, 4)
Explanation:<\/strong>
Equation factors: (x-3)(x-4)=0\u21d2x=3,4.<\/p>\n\n\n\n

54. If 2x+3y=12and x+2y=6, find the value of x.<\/mark><\/strong>
A) 0
B) 2
C) 3
D) 6
Answer: <\/strong>B) 2
Explanation:<\/strong>
Multiply second eqn by 2: 2x+4y=12. Subtract from first: (2x+3y)-(2x+4y)=0\u21d2-y=0\u21d2y=0.
Then x+0=6. Wait correction: if y=0, then x=6. Correct answer: D) 6.<\/p>\n\n\n\n

55. Solve: x2<\/sup>-5x+6=0.<\/mark><\/strong>
A) 2, 3
B) 1, 6
C) 3, 4
D) 2, 6
Answer:<\/strong> A) 2, 3
Explanation:<\/strong>
Factorize: (x-2)(x-3)=0\u21d2x=2,3.<\/p>\n\n\n\n

56. If x+y=8and xy=15, then find x<\/mark><\/strong>2<\/sup>+y2<\/sup>.<\/strong><\/mark>
A) 34
B) 49
C) 64
D) 94
Answer:<\/strong> B) 49
Explanation:<\/strong>
x2<\/sup>+y2<\/sup>=(x+y)2<\/sup>-2xy=64-30=34. Correction: Answer is A) 34.<\/p>\n\n\n\n

57. The value of (x+a)(x+b)-x2<\/sup>is:<\/mark><\/strong>
A) ab
B) a+b
C) ax + bx + ab
D) (a+b)x + ab
Answer: <\/strong>D) (a+b)x + ab
Explanation:<\/strong>
Expand: x^2+ax+bx+ab-x^2=(a+b)x+ab.<\/p>\n\n\n\n

58. Solve: 3x-7=2x+8.<\/mark><\/strong>
A) 15
B) -15
C) 7.5
D) 0
Answer: <\/strong>A) 15
Explanation:<\/strong>
3x-2x=8+7\u21d2x=15.<\/p>\n\n\n\n

59. If x=1\/2, find value of (1-x)\/(1+x).<\/mark><\/strong>
A) 1\/3
B) 2\/3
C) 1\/2
D) 3\/2
Answer: <\/strong>B) 1\/3
Explanation:<\/strong>
(1-1\/2)\/(1+1\/2)=(1\/2)\/(3\/2)=1\/3.<\/p>\n\n\n\n

60. Solve: 2x+5=19.<\/mark><\/strong>
A) 5
B) 7
C) 6
D) 8
Answer:<\/strong> B) 7
Explanation:<\/strong>
2x=14\u21d2x=7.<\/p>\n\n\n\n

61. If a+b=7and ab=10, find a2<\/sup>+b2<\/sup>.<\/mark><\/strong>
A) 29
B) 39
C) 49
D) 59
Answer:<\/strong> A) 29
Explanation:<\/strong>
a2<\/sup>+b2<\/sup>=(a+b)2<\/sup>-2ab=49-20=29.<\/p>\n\n\n\n

62. If x-3=7, find x.<\/mark><\/strong>
A) 4
B) 5
C) 7
D) 10
Answer:<\/strong> D) 10
Explanation:<\/strong>
x=7+3=10.<\/p>\n\n\n\n

63. If x^2-4=0, then x is:<\/mark><\/strong>
A) \u00b12
B) \u00b14
C) \u00b11
D) 0
Answer: <\/strong>A) \u00b12
Explanation:<\/strong>
x2<\/sup>=4\u21d2x=\u00b12.<\/p>\n\n\n\n

64. If 2x=3y, then ratio x:yis:<\/mark><\/strong>
A) 2:3
B) 3:2
C) 1:1
D) 3:4
Answer: <\/strong>B) 3:2
Explanation:<\/strong>
2x=3y\u21d2x\/y=3\/2\u21d23:2.<\/p>\n\n\n\n

65. If x=2, value of x3<\/sup>-2x2<\/sup>+1.<\/mark><\/strong>
A) 1
B) 3
C) 5
D) 7
Answer:<\/strong> A) 1
Explanation:<\/strong>
=8-8+1=1.<\/p>\n\n\n\n

66. If a2<\/sup>-b2<\/sup>=(a-b)(a+b), then identity is known as:<\/mark><\/strong>
A) Difference of squares
B) Square of sum
C) Square of difference
D) Perfect cube
Answer: <\/strong>A) Difference of squares<\/p>\n\n\n\n

67. Value of (a+b)2<\/sup>-(a-b)2<\/sup>:<\/mark><\/strong>
A) 2ab
B) 4ab
C) 2(a+b)
D) 4ab + 2a
Answer:<\/strong> C) 4ab? Let\u2019s check.
(a+b)2<\/sup>-(a-b)2<\/sup>=(a2<\/sup>+2ab+b2<\/sup>)-(a2<\/sup>-2ab+b2<\/sup>)=4ab. Correct Answer: B) 4ab.<\/p>\n\n\n\n

68. Solve: x2<\/sup>=64.<\/mark><\/strong>
A) 8
B) -8
C) \u00b18
D) 0
Answer:<\/strong> C) \u00b18<\/p>\n\n\n\n

69. If x=3, value of (x2<\/sup>+2x+1)\/(x+1).<\/mark><\/strong>
A) 3
B) 4
C) 5
D) 6
Answer: <\/strong>B) 4
Explanation:<\/strong>
Numerator: 9+6+1=16. Denominator: 4. Value=4.<\/p>\n\n\n\n

70. Roots of x2<\/sup>+7x+10=0.<\/mark><\/strong>
A) -2, -5
B) 2, 5
C) -7, -10
D) -1, -10
Answer:<\/strong> A) -2, -5
Explanation:<\/strong>
Factorize: (x+2)(x+5)=0.<\/p>\n\n\n\n

71. If p+q=0, then p3<\/sup>+q3<\/sup>=?<\/mark><\/strong>
A) 0
B) 2pq
C) 3pq
D) -3pq
Answer: <\/strong>A) 0
Explanation:<\/strong>
Since q=-p, p3<\/sup>+(-p)3<\/sup>=0.<\/p>\n\n\n\n

72. Solve: x2<\/sup>-2x-3=0.<\/mark><\/strong>
A) 3, -1
B) 2, -3
C) -3, -1
D) 1, 3
Answer:<\/strong> A) 3, -1
Explanation:<\/strong>
Factorize: (x-3)(x+1)=0.<\/p>\n\n\n\n

73. Simplify: (x+y)2<\/sup>-(x-y)2<\/sup>.<\/mark><\/strong>
A) 4xy
B) 2xy
C) 2x+2y
D) 4x
Answer:<\/strong> A) 4xy
Explanation:<\/strong>
Expand both: (x2<\/sup>+2xy+y2<\/sup>)-(x2<\/sup>-2xy+y2<\/sup>)=4xy.<\/p>\n\n\n\n

74. Solve: 5x=2x+12.<\/mark><\/strong>
A) 2
B) 3
C) 4
D) 5
Answer:<\/strong> C) 4
Explanation:<\/strong>
5x-2x=12 \u21d2 x=4.<\/p>\n\n\n\n

75. If x=1, find (x2<\/sup>+3x+2)\/(x+2).<\/mark><\/strong>
A) 2
B) 3
C) 4
D) 5
Answer: <\/strong>B) 3
Explanation:<\/strong>
Numerator=1+3+2=6. Denominator=3. Value=2. Correction: A) 2.
76. If x2<\/sup>+9=0, then x is:<\/mark><\/strong>
A) 3
B) -3
C) \u00b13i
D) 0
Answer: <\/strong>C) \u00b13i
Explanation:<\/strong>
x2<\/sup>=-9\u21d2x=\u00b1\u221a(-9)=\u00b13i(imaginary roots).<\/p>\n\n\n\n

77. If a+b=0, then a3<\/sup>+b3<\/sup>=?<\/mark><\/strong>
A) 0
B) 2ab
C) -3ab
D) ab
Answer: <\/strong>A) 0
Explanation:
<\/strong>If b=-a, then a3<\/sup>+(-a)3<\/sup>=0.<\/p>\n\n\n\n

78. If x+y=10, xy=21, then x2<\/sup>+y2<\/sup>=?<\/mark><\/strong>
A) 37
B) 58
C) 79
D) 100
Answer: <\/strong>B) 58
Explanation:<\/strong>
(x+y)2<\/sup>-2xy=100-42=58.<\/p>\n\n\n\n

79. Solve: x2<\/sup>+2x+1=0.<\/mark><\/strong>
A) 0, -2
B) -1, -1
C) 1, -1
D) 0, 1
Answer: <\/strong>B) -1, -1
Explanation:<\/strong>
Equation = (x+1)^2=0. Double root -1.<\/p>\n\n\n\n

80. If (x-1)(x-2)=0, roots are:<\/mark><\/strong>
A) 1, 2
B) -1, -2
C) 0, 2
D) -1, 2
Answer: <\/strong>A) 1, 2<\/p>\n\n\n\n

81. Solve: 3x+4=19.<\/mark><\/strong>
A) 3
B) 4
C) 5
D) 7
Answer: C) 5
Explanation:
3x=15 \u21d2 x=5.<\/p>\n\n\n\n

82. If x2<\/sup>-6x+9=0, root is:<\/mark><\/strong>
A) 3,3
B) 2,4
C) 0,9
D) 1,9
Answer: <\/strong>A) 3,3
Explanation:<\/strong>
Equation = (x-3)2<\/sup>=0.<\/p>\n\n\n\n

83. If a+b=20,ab=96, find a2<\/sup>+b2<\/sup>.<\/mark><\/strong>
A) 112
B) 118
C) 120
D) 128
Answer: <\/strong>B) 118
Explanation:<\/strong>
(a+b)2<\/sup>-2ab=400-192=208. Correction: Actually 208 not in options. Typo check: maybe ab=141?
But with ab=96 \u2192 400-192=208. Correct answer should be 208 (option misprint).<\/p>\n\n\n\n

84. Solve: x2<\/sup>-25=0.<\/strong><\/mark>
A) \u00b15
B) \u00b125
C) \u00b110
D) 0
Answer: <\/strong>A) \u00b15<\/p>\n\n\n\n

85. If p2<\/sup>+q2<\/sup>=20, p+q=6, find pq.<\/mark><\/strong>
A) 8
B) 10
C) 12
D) 16
Answer:<\/strong> B) 8
Explanation:<\/strong>
(p+q)2<\/sup>=p2<\/sup>+q2<\/sup>+2pq\u21d236=20+2pq\u21d22pq=16\u21d2pq=8.<\/p>\n\n\n\n

86. Solve: 7x-3=11.<\/mark><\/strong>
A) 1
B) 2
C) 3
D) 4
Answer: <\/strong>B) 2
Explanation:<\/strong>
7x=14 \u21d2 x=2.<\/p>\n\n\n\n

87. If a2<\/sup>+b2<\/sup>=50, ab=24, find (a+b)2<\/sup>.<\/mark><\/strong>
A) 74
B) 98
C) 100
D) 110
Answer: <\/strong>A) 74
Explanation:<\/strong>
(a+b)2<\/sup>=a2<\/sup>+b2<\/sup>+2ab=50+48=98. Correct Answer: B) 98.<\/p>\n\n\n\n

88. If a-b=5,ab=14, find a2<\/sup>+b2<\/sup>.<\/mark><\/strong>
A) 53
B) 67
C) 75
D) 81
Answer:<\/strong> C) 75
Explanation:<\/strong>
(a-b)2<\/sup>=a2<\/sup>+b2<\/sup>-2ab=25\u21d2a2<\/sup>+b2<\/sup>=25+28=53. Correction: A) 53.<\/p>\n\n\n\n

89. Solve: x2<\/sup>+4x+4=0.<\/mark><\/strong>
A) -2, -2
B) -4, 0
C) 2, 2
D) 0, 4
Answer: A) -2, -2
Explanation:
(x+2)2<\/sup>=0\u21d2x=-2.<\/p>\n\n\n\n

90. If a+b=15,ab=56, find a2<\/sup>+b2<\/sup>.<\/mark><\/strong>
A) 113
B) 121
C) 133
D) 145
Answer: <\/strong>A) 113
Explanation:<\/strong>
(a+b)^2-2ab=225-112=113.<\/p>\n\n\n\n

91. If x+1\/x=3, find x2<\/sup>+1\/x2<\/sup> .<\/mark><\/strong>
A) 5
B) 7
C) 9
D) 11
Answer: <\/strong>B) 7
Explanation:<\/strong>
(x+1\/x)2<\/sup>=x2<\/sup>+1\/x2<\/sup>+2\u21d29=x2<\/sup>+1\/x2<\/sup>+2\u21d2=7.<\/p>\n\n\n\n

92. If x2<\/sup>-10x+21=0, roots are:<\/mark><\/strong>
A) 3, 7
B) 7, 21
C) 1, 21
D) 2, 10
Answer:<\/strong> A) 3, 7
Explanation:<\/strong>
(x-3)(x-7)=0.<\/p>\n\n\n\n

93. Solve: 5x+2=17.<\/mark><\/strong>
A) 2
B) 3
C) 4
D) 5
Answer:<\/strong> C) 3
Explanation:<\/strong>
5x=15 \u21d2 x=3.<\/p>\n\n\n\n

94. If x2<\/sup>+y2<\/sup>=13,xy=6, find (x+y)2<\/sup>.<\/mark><\/strong>
A) 19
B) 25
C) 31
D) 37
Answer: <\/strong>B) 25
Explanation:<\/strong>
(x+y)^2=x2<\/sup>+y^2+2xy=13+12=25.<\/p>\n\n\n\n

95. If x+y=9,xy=20, find x2<\/sup>+y2<\/sup>.<\/strong><\/mark>
A) 41
B) 49
C) 61
D) 81
Answer:<\/strong> A) 41
Explanation:<\/strong>
(x+y)2<\/sup>-2xy=81-40=41.<\/p>\n\n\n\n

96. Solve: x2<\/sup>-8x+16=0.<\/mark><\/strong>
A) 4, 4
B) 8, 0
C) -4, -4
D) 2, 8
Answer:<\/strong> A) 4, 4
Explanation:<\/strong>
(x-4)2<\/sup>=0.<\/p>\n\n\n\n

97. If a+b=11,ab=28, find a2<\/sup>+b2<\/sup>.<\/mark><\/strong>
A) 65
B) 81
C) 93
D) 121
Answer:<\/strong> C) 93
Explanation:<\/strong>
121-56=65. Correction: Answer A) 65.<\/p>\n\n\n\n

98. If x-1\/x=5, find x2<\/sup>+1\/x2<\/sup> .<\/mark><\/strong>
A) 23
B) 25
C) 27
D) 29
Answer: <\/strong>A) 23
Explanation:<\/strong>
(x-1\/x)2<\/sup>=x2<\/sup>+1\/x2<\/sup>-2=25 \u21d2 x2<\/sup>+1\/x2<\/sup>=27. Correct Answer: C) 27.<\/p>\n\n\n\n

99. Solve: x2<\/sup>-3x-10=0.<\/mark><\/strong>
A) 2, 5
B) -2, 5
C) 10, -1
D) -5, 2
Answer:<\/strong> B) -2, 5
Explanation:<\/strong>
(x-5)(x+2)=0.<\/p>\n\n\n\n

100. If a2<\/sup>+b2<\/sup>=29,ab=10, find (a+b)2<\/sup>.<\/mark><\/strong>
A) 39
B) 49
C) 59
D) 69
Answer:<\/strong> B) 49
Explanation:<\/strong>
(a+b)2<\/sup>=a2<\/sup>+b2<\/sup>+2ab=29+20=49.<\/p>\n\n\n","protected":false},"excerpt":{"rendered":"

1. If x=5, then the value of 2x+3is:a) 8b) 10c) 13d) 15Answer: c) 13Explanation: Substitute x=5: 2(5)+3=13. 2. Simplify: (a+b)2a) a2+b2b) a2+2ab+b2c) a2-2ab+b2d) NoneAnswer: b) a2+2ab+b2Explanation: Square of binomial formula. 3. If x=2, value of x3+2×2+x:a) 12b) 18c) 20d) 22Answer: b) 18Explanation: 23+2(22)+2=8+8+2=18. 4. The roots of x2-9=0are:a) 9, \u22129b) 3, \u22123c) \u221a9, \u2212\u221a9d) 0,<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"[]"},"categories":[3],"tags":[13029,13019,13034,13014,13031,13017,13032,13016,13022,13012,13036,13020,13028,13018,13027,13024,13035,10938,13023,13033,13021,12983,12181,13013,13025,12975,12964,12978,12976,4029,5649,5623,13030,13026],"class_list":{"0":"post-12535","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-mathematics","7":"tag-algebra-examples","8":"tag-algebra-exercises","9":"tag-algebra-for-students","10":"tag-algebra-formulas","11":"tag-algebra-learning","12":"tag-algebra-mcqs","13":"tag-algebra-notes","14":"tag-algebra-practice","15":"tag-algebra-problems","16":"tag-algebra-questions","17":"tag-algebra-questions-with-answers","18":"tag-algebra-quiz","19":"tag-algebra-revision","20":"tag-algebra-solutions","21":"tag-algebra-study-material","22":"tag-algebra-test","23":"tag-algebra-tips","24":"tag-algebra-top-100-mcqs-with-answer-and-explanation","25":"tag-algebra-tricks","26":"tag-algebra-tutorials","27":"tag-algebraic-expressions","28":"tag-competitive-exams","29":"tag-exam-preparation","30":"tag-heres-a-set-of-top-keyword-tags-for-algebra-top-100-mcqs-with-explanation-mathematics","31":"tag-linear-equations","32":"tag-math-exercises","33":"tag-math-mcqs","34":"tag-math-practice","35":"tag-mathematics-questions","36":"tag-mcqs-adda","37":"tag-mcqs-for-pc-psi-sda-fda-pdo-vao-banking-kas-ias-ssc-gd-ssc-chsl-ssc-cgl-for-all-compitative-exams","38":"tag-mcqs-for-sda-fda-pdo-vao-banking-kas-ias-ssc-gd-ssc-chsl-ssc-cgl-for-all-compitative-exams","39":"tag-polynomials","40":"tag-quadratic-equations"},"_links":{"self":[{"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/posts\/12535","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/comments?post=12535"}],"version-history":[{"count":2,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/posts\/12535\/revisions"}],"predecessor-version":[{"id":12582,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/posts\/12535\/revisions\/12582"}],"wp:attachment":[{"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/media?parent=12535"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/categories?post=12535"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/tags?post=12535"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}