29/07/2025
āĻāĻŖāĻŋāϤā§āϰ āĻĻā§āύāĻŋā§āĻžāϰ āϏā§āϤā§āϰ āĻāĻāϏāĻžāĻĨā§ đ āĻāϰ āĻŦāĻžāĻāϰ⧠āϤā§āĻŽāύ āĻāĻŋāĻā§ āύā§āĻ đ
1.đˇ (a+b)²= a²+2ab+b²
2.đˇ (a+b)²= (a-b)²+4ab
3.đˇ (a-b)²= a²-2ab+b²
4.đˇ (a-b)²= (a+b)²-4ab
5.đˇ a² + b²= (a+b)²-2ab.
6.đˇ a² + b²= (a-b)²+2ab.
7.đˇ a²-b²= (a +b)(a -b)
8.đˇ 2(a²+b²)= (a+b)²+(a-b)²
9.đˇ 4ab = (a+b)²-(a-b)²
10.đˇ ab = {(a+b)/2}²-{(a-b)/2}²
11.đˇ (a+b+c)² = a²+b²+c²+2(ab+bc+ca)
12.đˇ (a+b)Âŗ = aÂŗ+3a²b+3ab²+bÂŗ
13.đˇ (a+b)Âŗ = aÂŗ+bÂŗ+3ab(a+b)
14.đˇ a-b)Âŗ= aÂŗ-3a²b+3ab²-bÂŗ
15.đˇ (a-b)Âŗ= aÂŗ-bÂŗ-3ab(a-b)
16.đˇ aÂŗ+bÂŗ= (a+b) (a²-ab+b²)
17.đˇ aÂŗ+bÂŗ= (a+b)Âŗ-3ab(a+b)
18.đˇ aÂŗ-bÂŗ = (a-b) (a²+ab+b²)
19.đˇ aÂŗ-bÂŗ = (a-b)Âŗ+3ab(a-b)
20. (a² + b² + c²) = (a + b + c)² â 2(ab + bc + ca)
21.đˇ 2 (ab + bc + ca) = (a + b + c)² â (a² + b² + c²)
22.đˇ (a + b + c)Âŗ = aÂŗ + bÂŗ + cÂŗ + 3 (a + b) (b + c) (c + a)
23.đˇ aÂŗ + bÂŗ + cÂŗ â 3abc =(a+b+c)(a² + b²+ c²âabâbcâ ca)
24.đˇ a3 + b3 + c3 â 3abc =ÂŊ (a+b+c) { (aâb)²+(bâc)²+(câa)²}
25.đˇ(x + a) (x + b) = x² + (a + b) x + ab
26.đˇ (x + a) (x â b) = x² + (a â b) x â ab
27.đˇ (x â a) (x + b) = x² + (b â a) x â ab
28.đˇ (x â a) (x â b) = x² â (a + b) x + ab
29.đˇ (x+p) (x+q) (x+r) = xÂŗ + (p+q+r) x² + (pq+qr+rp) x +pqr
30.đˇ bc (b-c) + ca (c- a) + ab (a - b) = - (b - c) (c- a) (a - b)
31.đˇ a² (b- c) + b² (c- a) + c² (a - b) = -(b-c) (c-a) (a - b)
32.đˇ a (b² - c²) + b (c² - a²) + c (a² - b²) = (b - c) (c- a) (a - b)
33.aÂŗ (b - c) + bÂŗ (c-a) +cÂŗ (a -b) =- (b-c) (c-a) (a - b)(a + b + c)
34.đˇ b²-c² (b²-c²) + c²a²(c²-a²)+a²b²(a²-b²)=-(b-c) (c-a) (a-b) (b+c) (c+a) (a+b)
35.(ab + bc+ca) (a+b+c) - abc = (a + b)(b + c) (c+a)
36.(b + c)(c + a)(a + b) + abc = (a + b +c) (ab + bc + ca)
37. đŖāĻāϝāĻŧāϤāĻā§āώā§āϤā§āϰđŖ
38. 1.āĻāϝāĻŧāϤāĻā§āώā§āϤā§āϰā§āϰ āĻā§āώā§āϤā§āϰāĻĢāϞ = (āĻĻā§āϰā§āĻā§āϝ à āĻĒā§āϰāϏā§āĻĨ) āĻŦāϰā§āĻ āĻāĻāĻ
39. 2.āĻāϝāĻŧāϤāĻā§āώā§āϤā§āϰā§āϰ āĻĒāϰāĻŋāϏā§āĻŽāĻž = 2 (āĻĻā§āϰā§āĻā§āϝ+āĻĒā§āϰāϏā§āĻĨ)āĻāĻāĻ
40. 3.āĻāϝāĻŧāϤāĻā§āώā§āϤā§āϰā§āϰ āĻāϰā§āĻŖ = â(āĻĻā§āϰā§āĻā§āĻ¯Â˛+āĻĒā§āϰāϏā§āĻĨ²)āĻāĻāĻ
41. 4.āĻāϝāĻŧāϤāĻā§āώā§āϤā§āϰā§āϰ āĻĻā§āϰā§āĻā§āϝ= āĻā§āώā§āϤā§āϰāĻĢāĻ˛ÃˇāĻĒā§āϰāϏā§āϤ āĻāĻāĻ
42. 5.āĻāϝāĻŧāϤāĻā§āώā§āϤā§āϰā§āϰ āĻĒā§āϰāϏā§āϤ= āĻā§āώā§āϤā§āϰāĻĢāĻ˛ÃˇāĻĻā§āϰā§āĻā§āϝ āĻāĻāĻ
43. đŖāĻŦāϰā§āĻāĻā§āώā§āϤā§āϰđŖ
44. 1.āĻŦāϰā§āĻāĻā§āώā§āϤā§āϰā§āϰ āĻā§āώā§āϤā§āϰāĻĢāϞ = (āϝ⧠āĻā§āύ āĻāĻāĻāĻŋ āĻŦāĻžāĻšā§āϰ āĻĻā§āϰā§āĻā§āϝ)² āĻŦāϰā§āĻ āĻāĻāĻ
45. 2.āĻŦāϰā§āĻāĻā§āώā§āϤā§āϰā§āϰ āĻĒāϰāĻŋāϏā§āĻŽāĻž = 4 à āĻāĻ āĻŦāĻžāĻšā§āϰ āĻĻā§āϰā§āĻā§āϝ āĻāĻāĻ
46. 3.āĻŦāϰā§āĻāĻā§āώā§āϤā§āϰā§āϰ āĻāϰā§āĻŖ=â2 à āĻāĻ āĻŦāĻžāĻšā§āϰ āĻĻā§āϰā§āĻā§āϝ āĻāĻāĻ
47. 4.āĻŦāϰā§āĻāĻā§āώā§āϤā§āϰā§āϰ āĻŦāĻžāĻšā§=âāĻā§āώā§āϤā§āϰāĻĢāϞ āĻŦāĻž āĻĒāϰāĻŋāϏā§āĻŽāĻžÃˇ4 āĻāĻāĻ
48. đˇđˇāϤā§āϰāĻŋāĻā§āĻđˇ
49. 1.āϏāĻŽāĻŦāĻžāĻšā§ āϤā§āϰāĻŋāĻā§āĻā§āϰ āĻā§āώā§āϤā§āϰāĻĢāϞ = âžÃ(āĻŦāĻžāĻšā§)²
50. 2.āϏāĻŽāĻŦāĻžāĻšā§ āϤā§āϰāĻŋāĻā§āĻā§āϰ āĻāĻā§āĻāϤāĻž = â3/2Ã(āĻŦāĻžāĻšā§)
51. 3.āĻŦāĻŋāώāĻŽāĻŦāĻžāĻšā§ āϤā§āϰāĻŋāĻā§āĻā§āϰ āĻā§āώā§āϤā§āϰāĻĢāϞ = âs(s-a) (s-b) (s-c)
52. āĻāĻāĻžāύ⧠a, b, c āϤā§āϰāĻŋāĻā§āĻā§āϰ āϤāĻŋāύāĻāĻŋ āĻŦāĻžāĻšā§āϰ āĻĻā§āϰā§āĻā§āϝ, s=āĻ
āϰā§āϧāĻĒāϰāĻŋāϏā§āĻŽāĻž
53. â
āĻĒāϰāĻŋāϏā§āĻŽāĻž 2s=(a+b+c)
54. 4āϏāĻžāϧāĻžāϰāĻŖ āϤā§āϰāĻŋāĻā§āĻā§āϰ āĻā§āώā§āϤā§āϰāĻĢāϞ = ÂŊ
55. (āĻā§āĻŽāĻŋÃāĻāĻā§āĻāϤāĻž) āĻŦāϰā§āĻ āĻāĻāĻ
56. 5.āϏāĻŽāĻā§āĻŖā§ āϤā§āϰāĻŋāĻā§āĻā§āϰ āĻā§āώā§āϤā§āϰāĻĢāϞ = ÂŊ(aÃb)
57. āĻāĻāĻžāύ⧠āϤā§āϰāĻŋāĻā§āĻā§āϰ āϏāĻŽāĻā§āĻŖ āϏāĻāϞāĻā§āύ āĻŦāĻžāĻšā§āĻĻā§āĻŦāϝāĻŧ a āĻāĻŦāĻ b.
58. 6.āϏāĻŽāĻĻā§āĻŦāĻŋāĻŦāĻžāĻšā§ āϤā§āϰāĻŋāĻā§āĻā§āϰ āĻā§āώā§āϤā§āϰāĻĢāϞ = 2â4b²-a²/4 āĻāĻāĻžāύā§, a= āĻā§āĻŽāĻŋ; b= āĻ
āĻĒāϰ āĻŦāĻžāĻšā§āĨ¤
59. 7.āϤā§āϰāĻŋāĻā§āĻā§āϰ āĻāĻā§āĻāϤāĻž = 2(āĻā§āώā§āϤā§āϰāĻĢāϞ/āĻā§āĻŽāĻŋ)
60. 8.āϏāĻŽāĻā§āĻŖā§ āϤā§āϰāĻŋāĻā§āĻā§āϰ āĻ
āϤāĻŋāĻā§āĻ =â āϞāĻŽā§āĻŦ²+āĻā§āĻŽāĻŋ²
61. 9.āϞāĻŽā§āĻŦ =âāĻ
āϤāĻŋāĻā§āϲ-āĻā§āĻŽāĻŋ²
62. 10.āĻā§āĻŽāĻŋ = âāĻ
āϤāĻŋāĻā§āϲ-āϞāĻŽā§āĻŦ²
63. 11.āϏāĻŽāĻĻā§āĻŦāĻŋāĻŦāĻžāĻšā§ āϤā§āϰāĻŋāĻā§āĻā§āϰ āĻāĻā§āĻāϤāĻž = âb² - a²/4
64. āĻāĻāĻžāύ⧠a= āĻā§āĻŽāĻŋ; b= āϏāĻŽāĻžāύ āĻĻā§āĻ āĻŦāĻžāĻšā§āϰ āĻĻā§āϰā§āĻā§āϝāĨ¤
65. 12.â
āϤā§āϰāĻŋāĻā§āĻā§āϰ āĻĒāϰāĻŋāϏā§āĻŽāĻž=āϤāĻŋāύ āĻŦāĻžāĻšā§āϰ āϏāĻŽāώā§āĻāĻŋ
66. đˇđˇāϰāĻŽā§āĻŦāϏđˇ
67. 1.āϰāĻŽā§āĻŦāϏā§āϰ āĻā§āώā§āϤā§āϰāĻĢāϞ = ÂŊà (āĻāϰā§āĻŖāĻĻā§āĻāĻāĻŋāϰ āĻā§āĻŖāĻĢāϞ)
68. 2.āϰāĻŽā§āĻŦāϏā§āϰ āĻĒāϰāĻŋāϏā§āĻŽāĻž = 4à āĻāĻ āĻŦāĻžāĻšā§āϰ āĻĻā§āϰā§āĻā§āϝ
69. đˇđˇāϏāĻžāĻŽāĻžāύā§āϤāϰāĻŋāĻđˇ
70. 1.āϏāĻžāĻŽāĻžāύā§āϤāϰāĻŋāĻā§āϰ āĻā§āώā§āϤā§āϰāĻĢāϞ = āĻā§āĻŽāĻŋ à āĻāĻā§āĻāϤāĻž =
71. 2.āϏāĻžāĻŽāĻžāύā§āϤāϰāĻŋāĻā§āϰ āĻĒāϰāĻŋāϏā§āĻŽāĻž = 2Ã(āϏāύā§āύāĻŋāĻšāĻŋāϤ āĻŦāĻžāĻšā§āĻĻā§āĻŦāϝāĻŧā§āϰ āϏāĻŽāώā§āĻāĻŋ)
72. đˇđˇāĻā§āϰāĻžāĻĒāĻŋāĻāĻŋāϝāĻŧāĻžāĻŽđˇ
73. 1. āĻā§āϰāĻžāĻĒāĻŋāĻāĻŋāϝāĻŧāĻžāĻŽā§āϰ āĻā§āώā§āϤā§āϰāĻĢāϞ =ÂŊÃ(āϏāĻŽāĻžāύā§āϤāϰāĻžāϞ āĻŦāĻžāĻšā§ āĻĻā§āĻāĻāĻŋāϰ āϝāĻžā§āĻāĻĢāϞ)ÃāĻāĻā§āĻāϤāĻž
74. đˇđˇ āĻāύāĻđˇ
75. 1.āĻāύāĻā§āϰ āĻāύāĻĢāϞ = (āϝā§āĻā§āύ āĻŦāĻžāĻšā§)Âŗ āĻāύ āĻāĻāĻ
76. 2.āĻāύāĻā§āϰ āϏāĻŽāĻā§āϰāϤāϞā§āϰ āĻā§āώā§āϤā§āϰāĻĢāϞ = 6à āĻŦāĻžāĻšā§Â˛ āĻŦāϰā§āĻ āĻāĻāĻ
77. 3.āĻāύāĻā§āϰ āĻāϰā§āĻŖ = â3ÃāĻŦāĻžāĻšā§ āĻāĻāĻ
78. đˇđˇāĻāϝāĻŧāϤāĻāύāĻđˇ
79. 1.āĻāϝāĻŧāϤāĻāύāĻā§āϰ āĻāύāĻĢāϞ = (āĻĻā§ā§°ā§āĻāĻžÃāĻĒā§āϰāϏā§āϤÃāĻāĻā§āĻāϤāĻž) āĻāύ āĻāĻāĻ
80. 2.āĻāϝāĻŧāϤāĻāύāĻā§āϰ āϏāĻŽāĻā§āϰāϤāϞā§āϰ āĻā§āώā§āϤā§āϰāĻĢāϞ = 2(ab + bc + ca) āĻŦāϰā§āĻ āĻāĻāĻ
81. [ āϝā§āĻāĻžāύ⧠a = āĻĻā§āϰā§āĻā§āϝ b = āĻĒā§āϰāϏā§āϤ c = āĻāĻā§āĻāϤāĻž ]
82. 3.āĻāϝāĻŧāϤāĻāύāĻā§āϰ āĻāϰā§āĻŖ = âa²+b²+c² āĻāĻāĻ
83. 4. āĻāĻžāϰāĻŋ āĻĻā§āĻāϝāĻŧāĻžāϞā§āϰ āĻā§āώā§āϤā§āϰāĻĢāϞ = 2(āĻĻā§āϰā§āĻā§āϝ + āĻĒā§āϰāϏā§āĻĨ)ÃāĻāĻā§āĻāϤāĻž
84. đˇđˇāĻŦā§āϤā§āϤđˇ
85. 1.āĻŦā§āϤā§āϤā§āϰ āĻā§āώā§āϤā§āϰāĻĢāϞ = Īr²=22/7r² {āĻāĻāĻžāύ⧠Ī=āϧā§āϰā§āĻŦāĻ 22/7, āĻŦā§āϤā§āϤā§āϰ āĻŦā§āϝāĻžāϏāĻžāϰā§āϧ= r}
86. 2. āĻŦā§āϤā§āϤā§āϰ āĻĒāϰāĻŋāϧāĻŋ = 2Īr
87. 3. āĻā§āϞāĻā§āϰ āĻĒā§āώā§āĻ āϤāϞā§āϰ āĻā§āώā§āϤā§āϰāĻĢāϞ = 4Īr² āĻŦāϰā§āĻ āĻāĻāĻ
88. 4. āĻā§āϞāĻā§āϰ āĻāϝāĻŧāϤāύ = 4ĪrÂŗÃˇ3 āĻāύ āĻāĻāĻ
89. 5. h āĻāĻā§āĻāϤāĻžāϝāĻŧ āϤāϞāĻā§āĻā§āĻĻā§ āĻā§āĻĒāύā§āύ āĻŦā§āϤā§āϤā§āϰ āĻŦā§āϝāĻžāϏāĻžāϰā§āϧ = âr²-h² āĻāĻāĻ
90. 6.āĻŦā§āϤā§āϤāĻāĻžāĻĒā§āϰ āĻĻā§āϰā§āĻā§āϝ s=Īrθ/180° ,
91. āĻāĻāĻžāĻ¨ā§ Î¸ =āĻā§āĻŖ
92. đˇāϏāĻŽāĻŦā§āϤā§āϤāĻā§āĻŽāĻŋāĻ āϏāĻŋāϞāĻŋāύā§āĻĄāĻžāϰ / āĻŦā§āϞāύđˇ
93. āϏāĻŽāĻŦā§āϤā§āϤāĻā§āĻŽāĻŋāĻ āϏāĻŋāϞāĻŋāύā§āĻĄāĻžāϰā§āϰ āĻā§āĻŽāĻŋāϰ āĻŦā§āϝāĻžāϏāĻžāϰā§āϧ r āĻāĻŦāĻ āĻāĻā§āĻāϤāĻž h āĻāϰ āĻšā§āϞāĻžāύ⧠āϤāϞā§āϰ āĻāĻā§āĻāϤāĻž l āĻšāϞā§,
94. 1.āϏāĻŋāϞāĻŋāύā§āĻĄāĻžāϰā§āϰ āĻāϝāĻŧāϤāύ = Īr²h
95. 2.āϏāĻŋāϞāĻŋāύā§āĻĄāĻžāϰā§āϰ āĻŦāĻā§āϰāϤāϞā§āϰ āĻā§āώā§āϤā§āϰāĻĢāϞ (āϏāĻŋāĻāϏāĻ) = 2ĪrhāĨ¤
96. 3.āϏāĻŋāϞāĻŋāύā§āĻĄāĻžāϰā§āϰ āĻĒā§āώā§āĻ āϤāϞā§āϰ āĻā§āώā§āϤā§āϰāĻĢāϞ (āĻāĻŋāĻāϏāĻ) = 2Īr (h + r)
97. đˇāϏāĻŽāĻŦā§āϤā§āϤāĻā§āĻŽāĻŋāĻ āĻā§āĻŖāĻđˇ
98. āϏāĻŽāĻŦā§āϤā§āϤāĻā§āĻŽāĻŋāĻ āĻā§āĻŽāĻŋāϰ āĻŦā§āϝāĻžāϏāĻžāϰā§āϧ r āĻāĻŦāĻ āĻāĻā§āĻāϤāĻž h āĻāϰ āĻšā§āϞāĻžāύ⧠āϤāϞā§āϰ āĻāĻā§āĻāϤāĻž l āĻšāϞā§,
99. 1.āĻā§āĻŖāĻā§āϰ āĻŦāĻā§āϰāϤāϞā§āϰ āĻā§āώā§āϤā§āϰāĻĢāϞ= Īrl āĻŦāϰā§āĻ āĻāĻāĻ
100. 2.āĻā§āĻŖāĻā§āϰ āϏāĻŽāϤāϞā§āϰ āĻā§āώā§āϤā§āϰāĻĢāϞ= Īr(r+l) āĻŦāϰā§āĻ āĻāĻāĻ
101. 3.āĻā§āĻŖāĻā§āϰ āĻāϝāĻŧāϤāύ= â
Īr²h āĻāύ āĻāĻāĻ
102. đˇâŽāĻŦāĻšā§āĻā§āĻā§āϰ āĻāϰā§āĻŖā§āϰ āϏāĻāĻā§āϝāĻž= n(n-3)/2
103. âŽāĻŦāĻšā§āĻā§āĻā§āϰ āĻā§āĻŖāĻā§āϞāĻŋāϰ āϏāĻŽāώā§āĻāĻŋ=(2n-4)āϏāĻŽāĻā§āĻŖ
104. āĻāĻāĻžāύ⧠n=āĻŦāĻžāĻšā§āϰ āϏāĻāĻā§āϝāĻž
105. â
āĻāϤā§āϰā§āĻā§āĻā§āϰ āĻĒāϰāĻŋāϏā§āĻŽāĻž=āĻāĻžāϰ āĻŦāĻžāĻšā§āϰ āϏāĻŽāώā§āĻāĻŋ
106. đˇāϤā§āϰāĻŋāĻā§āĻŖāĻŽāĻŋāϤāĻŋāϰ āϏā§āϤā§āϰāĻžāĻŦāϞā§āĻđˇ
107. 1. sinθ=⤞āĻŽā§āĻŦ/āĻ
āϤāĻŋāĻā§āĻ
108. 2. cosθ=āĻā§āĻŽāĻŋ/āĻ
āϤāĻŋāĻā§āĻ
109. 3. taneθ=⤞āĻŽā§āĻŦ/āĻā§āĻŽāĻŋ
110. 4. cotθ=āĻā§āĻŽāĻŋ/āϞāĻŽā§āĻŦ
111. 5. secθ=āĻ
āϤāĻŋāĻā§āĻ/āĻā§āĻŽāĻŋ
112. 6. cosecθ=āĻ
āϤāĻŋāĻā§āĻ/āϞāĻŽā§āĻŦ
113. 7. sinθ=1/cosecθ, cosecθ=1/sinθ
114. 8. cosθ=1/secθ, secθ=1/cosθ
115. 9. tanθ=1/cotθ, cotθ=1/tanθ
116. 10. sin²θ + cos²θ= 1
117. 11. sin²θ = 1 - cos²θ
118. 12. cos²θ = 1- sin²θ
119. 13. sec²θ - tan²θ = 1
120. 14. sec²θ = 1+ tan²θ
121. 15. tan²θ = sec²θ - 1
122. 16, cosec²θ - cot²θ = 1
123. 17. cosec²θ = cot²θ + 1
124. 18. cot²θ = cosec²θ - 1
125. đˇđˇ āĻŦāĻŋāϝāĻŧāĻžā§āĻā§āϰ āϏā§āϤā§āϰāĻžāĻŦāϞāĻŋđˇ
126. 1. āĻŦāĻŋāϝāĻŧāĻžā§āĻāύ-āĻŦāĻŋāϝāĻŧā§āĻā§āϝ =āĻŦāĻŋāϝāĻŧā§āĻāĻĢāϞāĨ¤
127. 2.āĻŦāĻŋāϝāĻŧāĻžā§āĻāύ=āĻŦāĻŋāϝāĻŧāĻžā§āĻāĻĢ + āĻŦāĻŋāϝāĻŧāĻžā§āĻā§āϝ
128. 3.āĻŦāĻŋāϝāĻŧāĻžā§āĻā§āϝ=āĻŦāĻŋāϝāĻŧāĻžā§āĻāύ-āĻŦāĻŋāϝāĻŧāĻžā§āĻāĻĢāϞ
129. đˇđˇ āĻā§āĻŖā§āϰ āϏā§āϤā§āϰāĻžāĻŦāϞāĻŋđˇ
130. 1.āĻā§āĻŖāĻĢāϞ =āĻā§āĻŖā§āϝ à āĻā§āĻŖāĻ
131. 2.āĻā§āĻŖāĻ = āĻā§āĻŖāĻĢāϞ Ãˇ āĻā§āĻŖā§āϝ
132. 3.āĻā§āĻŖā§āϝ= āĻā§āĻŖāĻĢāϞ Ãˇ āĻā§āĻŖāĻ
133. đˇđˇ āĻāĻžāĻā§āϰ āϏā§āϤā§āϰāĻžāĻŦāϞāĻŋđˇ
134. āύāĻŋāĻāĻļā§āώ⧠āĻŦāĻŋāĻāĻžāĻā§āϝ āύāĻž āĻšāϞā§āĨ¤
135. 1.āĻāĻžāĻā§āϝ= āĻāĻžāĻāĻ Ã āĻāĻžāĻāĻĢāϞ + āĻāĻžāĻāĻļā§āώāĨ¤
136. 2.āĻāĻžāĻā§āϝ= (āĻāĻžāĻā§āϝâ āĻāĻžāĻāĻļā§āώ) Ãˇ āĻāĻžāĻāĻĢāϞāĨ¤
137. 3.āĻāĻžāĻāĻĢāϞ = (āĻāĻžāĻā§āϝ â āĻāĻžāĻāĻļā§āώ)Ãˇ āĻāĻžāĻāĻāĨ¤
138. *āύāĻŋāĻāĻļā§āώ⧠āĻŦāĻŋāĻāĻžāĻā§āϝ āĻšāϞā§āĨ¤
139. 4.āĻāĻžāĻāĻ= āĻāĻžāĻā§āĻ¯Ãˇ āĻāĻžāĻāĻĢāϞāĨ¤
140. 5.āĻāĻžāĻāĻĢāϞ = āĻāĻžāĻā§āϝ Ãˇ āĻāĻžāĻāĻāĨ¤
141. 6.āĻāĻžāĻā§āϝ = āĻāĻžāĻāĻ Ã āĻāĻžāĻāĻĢāϞāĨ¤
142. đˇđˇāĻāĻā§āύāĻžāĻāĻļā§āϰ āϞ.āϏāĻž.āĻā§ āĻ āĻ.āϏāĻž.āĻā§ āϏā§āϤā§āϰāĻžāĻŦāϞ⧠đˇ
143. 1.āĻāĻā§āύāĻžāĻāĻļā§āϰ āĻ.āϏāĻž.āĻā§ = āϞāĻŦāĻā§āϞāĻžā§āϰ āĻ.āϏāĻž.āĻā§ / āĻšāϰāĻā§āϞāĻžā§āϰ āϞ.āϏāĻž.āĻā§
144. 2.āĻāĻā§āύāĻžāĻāĻļā§āϰ āϞ.āϏāĻž.āĻā§ =āϞāĻŦāĻā§āϞāĻžā§āϰ āϞ.āϏāĻž.āĻā§ /āĻšāϰāĻā§āϞāĻžāϰ āĻ.āϏāĻž.āĻā§
145. 3.āĻāĻā§āύāĻžāĻāĻļāĻĻā§āĻŦāϝāĻŧā§āϰ āĻā§āĻŖāĻĢāϞ = āĻāĻā§āύāĻžāĻāĻļāĻĻā§āĻŦāϝāĻŧā§āϰ āϞ.āϏāĻž.āĻā§ Ã āĻāĻā§āύāĻžāĻāĻļāĻĻā§āĻŦāϝāĻŧā§āϰ āĻ.āϏāĻž.āĻā§.
146. đˇāĻāĻĄāĻŧ āύāĻŋāϰā§āĻŖāϝāĻŧ đˇ
147. 1.āĻāĻĄāĻŧ = āϰāĻžāĻļāĻŋ āϏāĻŽāώā§āĻāĻŋ /āϰāĻžāĻļāĻŋ āϏāĻāĻā§āϝāĻž
148. 2.āϰāĻžāĻļāĻŋāϰ āϏāĻŽāώā§āĻāĻŋ = āĻāĻĄāĻŧ ÃāϰāĻžāĻļāĻŋāϰ āϏāĻāĻā§āϝāĻž
149. 3.āϰāĻžāĻļāĻŋāϰ āϏāĻāĻā§āϝāĻž = āϰāĻžāĻļāĻŋāϰ āϏāĻŽāώā§āĻāĻŋ Ãˇ āĻāĻĄāĻŧ
150. 4.āĻāϝāĻŧā§āϰ āĻāĻĄāĻŧ = āĻŽāĻžā§āĻ āĻāϝāĻŧā§āϰ āĻĒāϰāĻŋāĻŽāĻžāĻŖ / āĻŽāĻžā§āĻ āϞāĻžā§āĻā§āϰ āϏāĻāĻā§āϝāĻž
151. 5.āϏāĻāĻā§āϝāĻžāϰ āĻāĻĄāĻŧ = āϏāĻāĻā§āϝāĻžāĻā§āϞāĻžā§āϰ āϝāĻžā§āĻāĻĢāϞ /āϏāĻāĻā§āϝāĻžāϰ āĻĒāϰāĻŋāĻŽāĻžāύ āĻŦāĻž āϏāĻāĻā§āϝāĻž
152. 6.āĻā§āϰāĻŽāĻŋāĻ āϧāĻžāϰāĻžāϰ āĻāĻĄāĻŧ =āĻļā§āώ āĻĒāĻĻ +ā§§āĻŽ āĻĒāĻĻ /2
153. đˇđˇāϏā§āĻĻāĻāώāĻžāϰ āĻĒāϰāĻŋāĻŽāĻžāύ āύāĻŋāϰā§āύāϝāĻŧā§āϰ āϏā§āϤā§āϰāĻžāĻŦāϞā§đˇ
154. 1. āϏā§āĻĻ = (āϏā§āĻĻā§āϰ āĻšāĻžāϰÃāĻāϏāϞÃāϏāĻŽāϝāĻŧ) Ãˇā§§ā§Ļā§Ļ
155. 2. āϏāĻŽāϝāĻŧ = (100à āϏā§āĻĻ)Ãˇ (āĻāϏāϞÃāϏā§āĻĻā§āϰ āĻšāĻžāϰ)
156. 3. āϏā§āĻĻā§āϰ āĻšāĻžāϰ = (100ÃāϏā§āĻĻ)Ãˇ(āĻāϏāϞÃāϏāĻŽāϝāĻŧ)
157. 4. āĻāϏāϞ = (100ÃāϏā§āĻĻ)Ãˇ(āϏāĻŽāϝāĻŧÃāϏā§āĻĻā§āϰ āĻšāĻžāϰ)
158. 5. āĻāϏāϞ = {100Ã(āϏā§āĻĻ-āĻŽā§āϞ)}Ãˇ(100+āϏā§āĻĻā§āϰ āĻšāĻžāϰÃāϏāĻŽāϝāĻŧ )
159. 6. āϏā§āĻĻāĻžāϏāϞ = āĻāϏāϞ + āϏā§āĻĻ
160. 7. āϏā§āĻĻāĻžāϏāϞ = āĻāϏāϞ Ã(1+ āϏā§āĻĻā§āϰ āĻšāĻžāϰ)à āϏāĻŽāϝāĻŧ |[āĻāĻā§āϰāĻŦā§āĻĻā§āϧāĻŋ āϏā§āĻĻā§āϰ āĻā§āώā§āϤā§āϰā§]āĨ¤
161. đˇđˇāϞāĻžāĻ-āĻā§āώāϤāĻŋāϰ āĻāĻŦāĻ āĻā§āϰāϝāĻŧ-āĻŦāĻŋāĻā§āϰāϝāĻŧā§āϰ āϏā§āϤā§āϰāĻžāĻŦāϞā§đˇ
162. 1. āϞāĻžāĻ = āĻŦāĻŋāĻā§āϰāϝāĻŧāĻŽā§āϞā§āϝ-āĻā§āϰāϝāĻŧāĻŽā§āϞā§āϝ
163. 2.āĻā§āώāϤāĻŋ = āĻā§āϰāϝāĻŧāĻŽā§āϞā§āϝ-āĻŦāĻŋāĻā§āϰāϝāĻŧāĻŽā§āϞā§āϝ
164. 3.āĻā§āϰāϝāĻŧāĻŽā§āϞā§āϝ = āĻŦāĻŋāĻā§āϰāϝāĻŧāĻŽā§āϞā§āϝ-āϞāĻžāĻ
165. āĻ
āĻĨāĻŦāĻž
166. āĻā§āϰāϝāĻŧāĻŽā§āϞā§āϝ = āĻŦāĻŋāĻā§āϰāϝāĻŧāĻŽā§āϞā§āϝ + āĻā§āώāϤāĻŋ
167. 4.āĻŦāĻŋāĻā§āϰāϝāĻŧāĻŽā§āϞā§āϝ = āĻā§āϰāϝāĻŧāĻŽā§āϞā§āϝ + āϞāĻžāĻ
169. āĻŦāĻŋāĻā§āϰāϝāĻŧāĻŽā§āϞā§āϝ = āĻā§āϰāϝāĻŧāĻŽā§āϞā§āϝ-āĻā§āώāϤāĻŋ
đˇđˇ1-100 āĻĒāϰā§āϝāύā§āϤ āĻŽā§āϞāĻŋāĻ āϏāĻāĻā§āϝāĻžāĻŽāύ⧠āϰāĻžāĻāĻžāϰ āϏāĻšāĻ āĻāĻĒāĻžāϝāĻŧāĻđˇ
āĻļāϰā§āĻāĻāĻžāĻ :- 44 -22 -322-321
â
1āĻĨā§āĻā§100āĻĒāϰā§āϝāύā§āϤ āĻŽā§āϞāĻŋāĻ āϏāĻāĻā§āϝāĻž=25āĻāĻŋ
â
1āĻĨā§āĻā§10āĻĒāϰā§āϝāύā§āϤ āĻŽā§āϞāĻŋāĻ āϏāĻāĻā§āϝāĻž=4āĻāĻŋ 2,3,5,7
â
11āĻĨā§āĻā§20āĻĒāϰā§āϝāύā§āϤ āĻŽā§āϞāĻŋāĻ āϏāĻāĻā§āϝāĻž=4āĻāĻŋ 11,13,17,19
â
21āĻĨā§āĻā§30āĻĒāϰā§āϝāύā§āϤ āĻŽā§āϞāĻŋāĻ āϏāĻāĻā§āϝāĻž=2āĻāĻŋ 23,29
â
31āĻĨā§āĻā§40āĻĒāϰā§āϝāύā§āϤ āĻŽā§āϞāĻŋāĻ āϏāĻāĻā§āϝāĻž=2āĻāĻŋ 31,37
â
41āĻĨā§āĻā§50āĻĒāϰā§āϝāύā§āϤ āĻŽā§āϞāĻŋāĻ āϏāĻāĻā§āϝāĻž=3āĻāĻŋ 41,43,47
â
51āĻĨā§āĻā§ 60āĻĒāϰā§āϝāύā§āϤ āĻŽā§āϞāĻŋāĻ āϏāĻāĻā§āϝāĻž=2āĻāĻŋ 53,59
â
61āĻĨā§āĻā§70āĻĒāϰā§āϝāύā§āϤ āĻŽā§āϞāĻŋāĻ āϏāĻāĻā§āϝāĻž=2āĻāĻŋ 61,67
â
71āĻĨā§āĻā§80 āĻĒāϰā§āϝāύā§āϤ āĻŽā§āϞāĻŋāĻ āϏāĻāĻā§āϝāĻž=3āĻāĻŋ 71,73,79
â
81āĻĨā§āĻā§ 90āĻĒāϰā§āϝāύā§āϤ āĻŽā§āϞāĻŋāĻ āϏāĻāĻā§āϝāĻž=2āĻāĻŋ 83,89
â
91āĻĨā§āĻā§100āĻĒāϰā§āϝāύā§āϤ āĻŽā§āϞāĻŋāĻ āϏāĻāĻā§āϝāĻž=1āĻāĻŋ 97
đˇ1-100 āĻĒāϰā§āϝāύā§āϤ āĻŽā§āϞāĻŋāĻ āϏāĻāĻā§āϝāĻž 25 āĻāĻŋāĻ
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97
đˇ1-100āĻĒāϰā§āϝāύā§āϤ āĻŽā§āϞāĻŋāĻ āϏāĻāĻā§āϝāĻžāϰ āϝā§āĻāĻĢāϞ
1060āĨ¤
đˇ1.āĻā§āύ āĻāĻŋāĻā§āϰ
āĻāϤāĻŋāĻŦā§āĻ= āĻ
āϤāĻŋāĻā§āϰāĻžāύā§āϤ āĻĻā§āϰāϤā§āĻŦ/āϏāĻŽāϝāĻŧ
2.āĻ
āϤāĻŋāĻā§āϰāĻžāύā§āϤ āĻĻā§āϰāϤā§āĻŦ = āĻāϤāĻŋāĻŦā§āĻÃāϏāĻŽāϝāĻŧ
3.āϏāĻŽāϝāĻŧ= āĻŽā§āĻ āĻĻā§āϰāϤā§āĻŦ/āĻŦā§āĻ
4.āϏā§āϰā§āϤā§āϰ āĻ
āύā§āĻā§āϞ⧠āύā§āĻāĻžāϰ āĻāĻžāϰā§āϝāĻāϰ⧠āĻāϤāĻŋāĻŦā§āĻ = āύā§āĻāĻžāϰ āĻĒā§āϰāĻā§āϤ āĻāϤāĻŋāĻŦā§āĻ + āϏā§āϰā§āϤā§āϰ āĻāϤāĻŋāĻŦā§āĻāĨ¤
5.āϏā§āϰā§āϤā§āϰ āĻĒā§āϰāϤāĻŋāĻā§āϞ⧠āύā§āĻāĻžāϰ āĻāĻžāϰā§āϝāĻāϰ⧠āĻāϤāĻŋāĻŦā§āĻ = āύā§āĻāĻžāϰ āĻĒā§āϰāĻā§āϤ āĻāϤāĻŋāĻŦā§āĻ - āϏā§āϰā§āϤā§āϰ āĻāϤāĻŋāĻŦā§āĻ
đˇāϏāϰāϞ āϏā§āĻĻđˇ
āϝāĻĻāĻŋ āĻāϏāϞ=P, āϏāĻŽāϝāĻŧ=T, āϏā§āĻĻā§āϰ āĻšāĻžāϰ=R, āϏā§āĻĻ-āĻāϏāϞ=A āĻšāϝāĻŧ, āϤāĻžāĻšāϞā§
1.āϏā§āĻĻā§āϰ āĻĒāϰāĻŋāĻŽāĻžāĻŖ= PRT/100
2.āĻāϏāϞ= 100ÃāϏā§āĻĻ-āĻāϏāϞ(A)/100+TR
đˇđˇāύā§āĻāĻžāϰ āĻāϤāĻŋ āϏā§āϰā§āϤā§āϰ āĻ
āύā§āĻā§āϞ⧠āĻāύā§āĻāĻžāϝāĻŧ 10 āĻāĻŋ.āĻŽāĻŋ. āĻāĻŦāĻ āϏā§āϰā§āϤā§āϰ āĻĒā§āϰāϤāĻŋāĻā§āϞ⧠2 āĻāĻŋ.āĻŽāĻŋ.āĨ¤ āϏā§āϰā§āϤā§āϰ āĻŦā§āĻ āĻāϤ?
â
āĻā§āĻāύāĻŋāĻ-
āϏā§āϰā§āϤā§āϰ āĻŦā§āĻ = (āϏā§āϰā§āϤā§āϰ āĻ
āύā§āĻā§āϞ⧠āύā§āĻāĻžāϰ āĻŦā§āĻ - āϏā§āϰā§āϤā§āϰ āĻĒā§āϰāϤāĻŋāĻā§āϞ⧠āύā§āĻāĻžāϰ āĻŦā§āĻ) /2
= (10 - 2)/2=
= 4 āĻāĻŋ.āĻŽāĻŋ.
đˇāĻāĻāĻāĻŋ āύā§āĻāĻž āϏā§āϰā§āϤā§āϰ āĻ
āύā§āĻā§āϞ⧠āĻāύā§āĻāĻžāϝāĻŧ 8 āĻāĻŋ.āĻŽāĻŋ.āĻāĻŦāĻ āϏā§āϰā§āϤā§āϰ āĻĒā§āϰāϤāĻŋāĻā§āϞ⧠āĻāύā§āĻāĻžāϝāĻŧ 4 āĻāĻŋ.āĻŽāĻŋ.
āϝāĻžāϝāĻŧāĨ¤ āύā§āĻāĻžāϰ āĻŦā§āĻ āĻāϤ?
â
āĻā§āĻāύāĻŋāĻ-
āύā§āĻāĻžāϰ āĻŦā§āĻ = (āϏā§āϰā§āϤā§āϰ āĻ
āύā§āĻā§āϞ⧠āύā§āĻāĻžāϰ āĻŦā§āĻ+āϏā§āϰā§āϤā§āϰ āĻĒā§āϰāϤāĻŋāĻā§āϞ⧠āύā§āĻāĻžāϰ āĻŦā§āĻ)/2
= (8 + 4)/2
=6 āĻāĻŋ.āĻŽāĻŋ.
đˇāύā§āĻāĻž āĻ āϏā§āϰā§āϤā§āϰ āĻŦā§āĻ āĻāύā§āĻāĻžāϝāĻŧ āϝāĻĨāĻžāĻā§āϰāĻŽā§ 10 āĻāĻŋ.āĻŽāĻŋ. āĻ 5 āĻāĻŋ.āĻŽāĻŋ.āĨ¤ āύāĻĻā§āĻĒāĻĨā§ 45 āĻāĻŋ.āĻŽāĻŋ. āĻĒāĻĨ āĻāĻāĻŦāĻžāϰ āĻāĻŋāϝāĻŧā§ āĻĢāĻŋāϰ⧠āĻāϏāϤ⧠āĻāϤ āϏāĻŽāϝāĻŧ āϞāĻžāĻāĻŦā§?
āĻā§āĻāύāĻŋāĻ-
â
āĻŽāĻžā§āĻ āϏāĻŽāϝāĻŧ = [(āĻŽāĻžā§āĻ āĻĻā§āϰāϤā§āĻŦ/ āĻ
āύā§āĻā§āϞ⧠āĻŦā§āĻ) + (āĻŽāĻžā§āĻ āĻĻā§āϰāϤā§āĻŦ/āĻĒā§āϰāϤāĻŋāĻā§āϞ⧠āĻŦā§āĻ)]
āĻāϤā§āϤāϰ:āϏā§āϰā§āϤā§āϰ āĻ
āύā§āĻā§āϞ⧠āύā§āĻāĻžāϰāĻŦā§āĻ = (10+5) = 15 āĻāĻŋ.āĻŽāĻŋ.
āϏā§āϰā§āϤā§āϰ āĻĒā§āϰāϤāĻŋāĻā§āϞ⧠āύā§āĻāĻžāϰ āĻŦā§āĻ = (10-5) = 5āĻāĻŋ.āĻŽāĻŋ.
[(45/15) +(45/5)]
= 3+9
=12 āĻāύā§āĻāĻž
đˇâ
āϏāĻŽāĻžāύā§āϤāϰ āϧāĻžāϰāĻžāϰ āĻā§āϰāĻŽāĻŋāĻ āϏāĻāĻā§āϝāĻžāϰ āϝā§āĻāĻĢāϞ-
(āϝāĻāύ āϏāĻāĻā§āϝāĻžāĻāĻŋ1 āĻĨā§āĻā§ āĻļā§āϰā§)1+2+3+4+......+n āĻšāϞ⧠āĻāϰā§āĻĒ āϧāĻžāϰāĻžāϰ āϏāĻŽāώā§āĻāĻŋ= [n(n+1)/2]
n=āĻļā§āώ āϏāĻāĻā§āϝāĻž āĻŦāĻž āĻĒāĻĻ āϏāĻāĻā§āϝāĻž s=āϝā§āĻāĻĢāϞ
đˇ āĻĒā§āϰāĻļā§āύāĻ 1+2+3+....+100 =?
đˇ āϏāĻŽāĻžāϧāĻžāύāĻ[n(n+1)/2]
= [100(100+1)/2]
= 5050
đˇâ
āϏāĻŽāĻžāύā§āϤāϰ āϧāĻžāϰāĻžāϰ āĻŦāϰā§āĻ āϝā§āĻ āĻĒāĻĻā§āϧāϤāĻŋāϰ āĻā§āώā§āϤā§āϰā§,-
āĻĒā§āϰāĻĨāĻŽ n āĻĒāĻĻā§āϰ āĻŦāϰā§āĻā§āϰ āϏāĻŽāώā§āĻāĻŋ
S= [n(n+1)2n+1)/6]
(āϝāĻāύ 1² + 2²+ 3² + 4²........ +n²)
đˇāĻĒā§āϰāĻļā§āύāĻ(1² + 3²+ 5² + ....... +31²) āϏāĻŽāĻžāύ āĻāϤ?
đˇāϏāĻŽāĻžāϧāĻžāύāĻ S=[n(n+1)2n+1)/6]
= [31(31+1)2Ã31+1)/6]
=31
đˇâ
āϏāĻŽāĻžāύā§āϤāϰ āϧāĻžāϰāĻžāϰ āĻāύāϝā§āĻ āĻĒāĻĻā§āϧāϤāĻŋāϰ āĻā§āώā§āϤā§āϰā§-
āĻĒā§āϰāĻĨāĻŽ n āĻĒāĻĻā§āϰ āĻāύā§āϰ āϏāĻŽāώā§āĻāĻŋ S= [n(n+1)/2]2
(āϝāĻāύ 1Âŗ+2Âŗ+3Âŗ+.............+nÂŗ)
đˇāĻĒā§āϰāĻļā§āύāĻ1Âŗ+2Âŗ+3Âŗ+4Âŗ+âĻâĻâĻâĻ+10Âŗ=?
đˇāϏāĻŽāĻžāϧāĻžāύāĻ [n(n+1)/2]2
= [10(10+1)/2]2
= 3025
đˇâ
āĻĒāĻĻ āϏāĻāĻā§āϝāĻž āĻ āĻĒāĻĻ āϏāĻāĻā§āϝāĻžāϰ āϏāĻŽāώā§āĻāĻŋ āύāĻŋāϰā§āύāϝāĻŧā§āϰ āĻā§āώā§āϤā§āϰā§āĻ
āĻĒāĻĻ āϏāĻāĻā§āϝāĻž N= [(āĻļā§āώ āĻĒāĻĻ â āĻĒā§āϰāĻĨāĻŽ āĻĒāĻĻ)/āĻĒā§āϰāϤāĻŋ āĻĒāĻĻā§ āĻŦā§āĻĻā§āϧāĻŋ] +1
đˇāĻĒā§āϰāĻļā§āύāĻ5+10+15+âĻâĻâĻâĻ+50=?
đˇāϏāĻŽāĻžāϧāĻžāύāĻ āĻĒāĻĻāϏāĻāĻā§āϝāĻž = [(āĻļā§āώ āĻĒāĻĻ â āĻĒā§āϰāĻĨāĻŽāĻĒāĻĻ)/āĻĒā§āϰāϤāĻŋ āĻĒāĻĻā§ āĻŦā§āĻĻā§āϧāĻŋ]+1
= [(50 â 5)/5] + 1
=10
āϏā§āϤāϰāĻžāĻ āĻĒāĻĻ āϏāĻāĻā§āϝāĻžāϰ āϏāĻŽāώā§āĻāĻŋ
= [(5 + 50)/2] Ã10
= 275
đˇâ
n āϤāĻŽ āĻĒāĻĻ=a + (n-1)d
āĻāĻāĻžāύā§, n =āĻĒāĻĻāϏāĻāĻā§āϝāĻž, a = 1āĻŽ āĻĒāĻĻ, d= āϏāĻžāϧāĻžāϰāĻŖ āĻ
āύā§āϤāϰ
đˇāĻĒā§āϰāĻļā§āύāĻ 5+8+11+14+.......āϧāĻžāϰāĻžāĻāĻŋāϰ āĻā§āύ āĻĒāĻĻ 302?
đˇ āϏāĻŽāĻžāϧāĻžāύāĻ āϧāϰāĻŋ, n āϤāĻŽ āĻĒāĻĻ =302
āĻŦāĻž, a + (n-1)d=302
āĻŦāĻž, 5+(n-1)3 =302
āĻŦāĻž, 3n=300
āĻŦāĻž, n=100
đˇâ
6)āϏāĻŽāĻžāύā§āϤāϰ āϧāĻžāϰāĻžāϰ āĻā§āϰāĻŽāĻŋāĻ āĻŦāĻŋāĻā§āĻĄāĻŧ āϏāĻāĻā§āϝāĻžāϰ āϝā§āĻāĻĢāϞ-S=M² āĻāĻāĻžāύā§,M=āĻŽāϧā§āϝā§āĻŽāĻž=(1āĻŽ āϏāĻāĻā§āϝāĻž+āĻļā§āώ āϏāĻāĻā§āϝāĻž)/2
đˇāĻĒā§āϰāĻļā§āύāĻ1+3+5+.......+19=āĻāϤ?
đˇ āϏāĻŽāĻžāϧāĻžāύāĻ S=M²
={(1+19)/2}²
=(20/2)²
=100
đˇđˇ1. āĻā§āĻĄāĻŧ āϏāĻāĻā§āϝāĻž + āĻā§āĻĄāĻŧ āϏāĻāĻā§āϝāĻž = āĻā§āĻĄāĻŧ
āϏāĻāĻā§āϝāĻžāĨ¤
āϝā§āĻŽāύāĻ 2 + 6 = 8.
đˇ2. āĻā§āĻĄāĻŧ āϏāĻāĻā§āϝāĻž + āĻŦāĻŋāĻā§āĻĄāĻŧ āϏāĻāĻā§āϝāĻž =
āĻŦāĻŋāĻā§āĻĄāĻŧ āϏāĻāĻā§āϝāĻžāĨ¤
āϝā§āĻŽāύāĻ 6 + 7 = 13.
đˇ3. āĻŦāĻŋāĻā§āĻĄāĻŧ āϏāĻāĻā§āϝāĻž + āĻŦāĻŋāĻā§āĻĄāĻŧ āϏāĻāĻā§āϝāĻž =
āĻā§āĻĄāĻŧ āϏāĻāĻā§āϝāĻžāĨ¤
āϝā§āĻŽāύāĻ 3 + 5 = 8.
đˇ4. āĻā§āĻĄāĻŧ āϏāĻāĻā§āϝāĻž à āĻā§āĻĄāĻŧ āϏāĻāĻā§āϝāĻž = āĻā§āĻĄāĻŧ
āϏāĻāĻā§āϝāĻžāĨ¤
āϝā§āĻŽāύāĻ 6 à 8 = 48.
đˇ5.āĻā§āĻĄāĻŧ āϏāĻāĻā§āϝāĻž à āĻŦāĻŋāĻā§āĻĄāĻŧ āϏāĻāĻā§āϝāĻž = āĻā§āĻĄāĻŧ
āϏāĻāĻā§āϝāĻžāĨ¤
āϝā§āĻŽāύāĻ 6 à 7 = 42
đˇ6.āĻŦāĻŋāĻā§āĻĄāĻŧ āϏāĻāĻā§āϝāĻž à āĻŦāĻŋāĻā§āĻĄāĻŧ āϏāĻāĻā§āϝāĻž =
āĻŦāĻŋāĻā§āĻĄāĻŧ āϏāĻāĻā§āϝāĻžāĨ¤
āϝā§āĻŽāύāĻ 3 à 9 = 27