State True or False: If a ∝ b, b ∝ 1/c, and c ∝ d, then a ∝ 1/d.

If x ∝ √y and y = a², when x = 2a then find x² : y

If x\over2 = y\over3 = z\over4 then find the value of (3x + 4y + 8z) / (x + 3y).

If b ∝ a³ and a increase in the ratio of 2 : 3, then find in what ratio b will be increasesed .

If 15 farmers can cultivate 18 bighas of land in 5 days, determine by using the theory of variation the number of days required by 10 farmers to cultivate 12 bighas of land.

If x³ - ∝ x³ + , then show that x ∝ .

If = = , then show that each ratio is or -1.

If (√a + √b) ∝ (√a-√b) then show that (a + b) ∝ √(ab)

If x ∝ y, y ∝ z and z ∝ x, then find the relation between the constants of variations.

If = = = 1, then show that + + = 1

If x ∝ y and y ∝ z, then show that + + ∝ + + .

State True/False: “The equal chords of a circle are at equal distances from the centre of the circle.”