Let 50 / N = N / (25/2)
⇒ N² = 50 x 25/2 = 625

Correct Option: D

Let 50 / N = N / (25/2)
⇒ N² = 50 x 25/2 = 625
∴ N = √625 = 25

Given Exp. = 4/7 + (2y - x)/(2y + x)
= 4/7 + [(2 - (x/y)] / [2 + (x/y)]
= 4/7 + [2 - 4/5] / [2 + 4/5]
= 4/7 + ( 6/5 x 5/14 )

Correct Option: B

Given Exp. = 4/7 + (2y - x)/(2y + x)
= 4/7 + [(2 - (x/y)] / [2 + (x/y)]
= 4/7 + [2 - 4/5] / [2 + 4/5]
= 4/7 + ( 6/5 x 5/14 )
= 4/7 + 3/7
= 1

Given expression = 2x + y / x - 2y
Dividing Num and Denom by y we get.
= [2(x/y) + 1] / [(x/y) - 2] = (2 x 3 + 1) / (3 - 2) = 7/1 = 7
[ ∵ x/2y = 3 / 2 ⇒x/y = (3 / 2 x 2) = 3 ]

Correct Option: B

Given expression = 2x + y / x - 2y
Dividing Num and Denom by y we get.
= [2(x/y) + 1] / [(x/y) - 2] = (2 x 3 + 1) / (3 - 2) = 7/1 = 7
[ ∵ x/2y = 3 / 2 ⇒x/y = (3 / 2 x 2) = 3 ]

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

Correct Option: D

Given expression = (a³ + b³) / (a² + b² - ab)
= (a + b)(a² + b² - ab) / (a² + b² - ab)
= (a + b) = (885 + 115)
= 1000

Give expression
= 70/17 ÷ 7/5 x 68/33
= 70/17 x 5/7 x 68/33
= 200/33

Correct Option: B

Give expression
= 70/17 ÷ 7/5 x 68/33
= 70/17 x 5/7 x 68/33
= 200/33
= 6²/₃₃