(a³ + b³) / (a² - ab + b²)
= (a + b) (a² - ab + b²)/(a² - ab + b²)
= a + b

Correct Option: C

[725 x 725 x 725 + 371 x 371 x 371] / [725 x 725 - 725 x 371 + 371 x 371]
= 725 + 371 = 1096
[∵ (a³ + b³) / (a² - ab + b²) = (a + b) (a² - ab + b²)/(a² - ab + b²) = a + b ]

(?)^1/2 = (5568 ÷ 87)^1/3 + (72 x 2)^1/2
= (64)^1/3 + (144)^1/2
∴ ? = (4 + 12)² = 256

Correct Option: A

(?)^1/2 = (5568 ÷ 87)^1/3 + (72 x 2)^1/2
= (64)^1/3 + (144)^1/2
∴ ? = (4 + 12)² = 256

(70 ÷ 100) ^{? + 3} = (0.49)⁴ x (0.343)⁴ ÷ (0.2401)⁴
(0.7) ^{? + 3} = (0.49 x 0.343/0.2401)⁴
(0.7)^{? + 3} = (0.7)⁴
On comparing the exponents both sides, we get
? + 3 = 4
∴ ? = 4 - 3 = 1

Correct Option: B

(70 ÷ 100) ^{? + 3} = (0.49)⁴ x (0.343)⁴ ÷ (0.2401)⁴
(0.7) ^{? + 3} = (0.49 x 0.343/0.2401)⁴
(0.7)^{? + 3} = (0.7)⁴
On comparing the exponents both sides, we get
? + 3 = 4
∴ ? = 4 - 3 = 1

Given expression
= a³+ b³ + c³ - 3abc/a² + b² + c² - ab - bc - ca
= a + b + c

Correct Option: A

Given expression
= a³+ b³ + c³ - 3abc/a² + b² + c² - ab - bc - ca
= a + b + c
= 0.5 + 0.2 + 0.3
where, a = 0.5, b = 0.2, c = 0.3

Given expression = 2x² + 2/3x² + 3 + 5x
On dividing numerator and denominator by x, we get
= 2(x + 1/x)/3(x + 1/x) + 5 = 2 x 2/3 x 2 + 5 = 4/11
[given x + 1/x = 2]

Correct Option: A

Given expression = 2x² + 2/3x² + 3 + 5x
On dividing numerator and denominator by x, we get
= 2(x + 1/x)/3(x + 1/x) + 5 = 2 x 2/3 x 2 + 5 = 4/11
[given x + 1/x = 2]