- Option : D
- Explanation : Let HCF be h and LCM be l.
**I.**Let, numbers be ah and bh. Then abh = and (a + b)h = m

=> (a — b)h = n

Using these ah and bh can be uniquely determined. Thus, I is true II.**II.**If HCF = LCM, then two numbers are equal and same as HCF or LCM. Thus, II is true.**III.**LCM/HCF = prime i.e. l/h =P Then one of the numbers is equal to h and other is equal to E. Thus, III is true.

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- Option : D
- Explanation : Number = (555+445)*(555-445)*2+30

= (555+445)*2*110+30

= 220000+30 = 220030

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14. HCF of y^{3} - 4y and 4y (y^{3} + 8) is

- Option : A
- Explanation : y
^{3}-4y = y(y^{2}-4)

= y(y-2)(y+2)

4y(y^{3}+8)

=4y(y+2)(y^{2}-2y+4)

∴ HCF = y(y + 2).

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- Option : A
- Explanation :
Total distance travelled by the ball before coming to rest

= 12 + 2 (6 + 3 + 1.5 +...to?)

= 12 + 2. ( 6/ (1-1/2))

= 12 + 2(12)

= 36m

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