Given exp. = [ a² + ab + b² ] / [a³ - b³] where a = 137, b = 133
= 1/(a - b)

Correct Option: C

Given exp. = [ a² + ab + b² ] / [a³ - b³] where a = 137, b = 133
= 1/(a - b)
= 1/(137- 133)
=1/4

Given expression = (a³ - b³) / (a² + ab + b²), where a=117, b =98
= [(a-b)(a² + ab + b²)] / (a²+ab+b²)

Correct Option: C

Given expression = (a³ - b³) / (a² + ab + b²), where a=117, b =98
= [(a-b)(a² + ab + b²)] / (a²+ab+b²)
=(a-b)
=117 - 98
= 19.

Given Exp. = ( a³ + b³ ) / ( a² - ab + b² ), where a =3 42, b = 257
= [(a + b )(a² - ab +b²)] / (a² - ab + b²)
= a + b

Correct Option: C

Given Exp. = ( a³ + b³ ) / ( a² - ab + b² ), where a =3 42, b = 257
= [(a + b )(a² - ab +b²)] / (a² - ab + b²)
= a + b
= 343+257
= 600.

Given expression = 3 ÷ [(8 - 5) ÷ {(4 - 2) ÷ (2 + 8/13)}]
= 3 ÷ [3 ÷ { 2 ÷ 34/13}]
= 3 ÷ [3 ÷ { 2 x 13/34}]
= 3 ÷ [ 3 x 17/13]
= 3 x 13/51

Correct Option: A

Given expression = 3 ÷ [(8 - 5) ÷ {(4 - 2) ÷ (2 + 8/13)}]
= 3 ÷ [3 ÷ { 2 ÷ 34/13}]
= 3 ÷ [3 ÷ { 2 x 13/34}]
= 3 ÷ [ 3 x 17/13]
= 3 x 13/51
= 13/17

Given expression = 15/2 + 1/2 ÷ 1/8 - 2/5 x 7/3 ÷ 15/8 x (7/5 - 4/3)
= 15/2 + 4 - 2/5 x 7/3 ÷ 15/8 x 1/15
= 15/2 + 4 - 2/5 x 7/3 ÷ 1/8
= 15/2 + 4 - 2/5 x 7/3 x 8/1

Correct Option: C

Given expression = 15/2 + 1/2 ÷ 1/8 - 2/5 x 7/3 ÷ 15/8 x (7/5 - 4/3)
= 15/2 + 4 - 2/5 x 7/3 ÷ 15/8 x 1/15
= 15/2 + 4 - 2/5 x 7/3 ÷ 1/8
= 15/2 + 4 - 2/5 x 7/3 x 8/1
= 15/2 + 4 - 112/15
= 23/2 - 112/15
= 121/30
= 4¹/₃₀