L. C. M of 3, 4, 5, 6, 8 is 120
Now, 120 = 2 x 2 x 2 x 3 x 5

Correct Option: D

L. C. M of 3, 4, 5, 6, 8 is 120
Now, 120 = 2 x 2 x 2 x 3 x 5
∴ Required number = (2 x 2 x 2 x 3 x 5) x (2 x 3 x 5)
= 3600

a = [(√5 + 1) / (√5-1)] x [(√5 + 1) / (√5 + 1)]
= (√5 + 1)² / (5 - 1)
= (5 + 1 + 2 √5) / 4
= (3 + √5) / 2

b = [(√5 - 1) / (√5 + 1)] x [(√5 - 1 ) / (√5 -1)]
= (√5 - 1 )² / (5 - 1)
= (5 + 1 - 2√5) / 4
= (3 - √5) / 2

Now a² + b² = [(3 + √5)² + (3 - √5)²] / 4
= [2 x (9 + 5 )] / 4
= 7

ab = 1

Correct Option: B

a = [(√5 + 1) / (√5-1)] x [(√5 + 1) / (√5 + 1)]
= (√5 + 1)² / (5 - 1)
= (5 + 1 + 2 √5) / 4
= (3 + √5) / 2

b = [(√5 - 1) / (√5 + 1)] x [(√5 - 1 ) / (√5 -1)]
= (√5 - 1 )² / (5 - 1)
= (5 + 1 - 2√5) / 4
= (3 - √5) / 2

Now a² + b² = [(3 + √5)² + (3 - √5)²] / 4
= [2 x (9 + 5 )] / 4
= 7

ab = 1

∴ (a² + ab + b²) / (a² - ab + b²)
= (7 + 1) / (7 - 1)
= 8/6
= 4 / 3

(√5 - √3)/ (√5 + √3)
= (√5 - √3) / (√5 + √3)
= (√5 - √3)² / (5 - 3)
= (5 + 3 - 2√5 x 3) / 2
= 2 (4 - √15) / 2
= (4 - √15)

Correct Option: B

(√5 - √3)/ (√5 + √3)
= (√5 - √3) / (√5 + √3)
= (√5 - √3)² / (5 - 3)
= (5 + 3 - 2√5 x 3) / 2
= 2 (4 - √15) / 2
= (4 - √15)

216 = 2 x 2 x 2 x 3 x 3 x 3
= (2 x 2) x 2 x ( 3 x 3) x 3

Clearly, in order to make it a perfect square, it must be divided by 2 x 3 i.e., 6 .

Correct Option: C

216 = 2 x 2 x 2 x 3 x 3 x 3
= (2 x 2) x 2 x ( 3 x 3) x 3

Clearly, in order to make it a perfect square, it must be divided by 2 x 3 i.e., 6 .

√0.04 x 0.4 x a = 0.4 x 0.04 x √b
⇒ √0.016 a = 0.016 x √b
⇒ √a / √b = 0.016/√0.016 = √0.016

Correct Option: A

√0.04 x 0.4 x a = 0.4 x 0.04 x √b
⇒ √0.016 a = 0.016 x √b
⇒ √a / √b = 0.016/√0.016 = √0.016
∴ √a/b = √0.016
So a/b = 0.016