In the following question, one or two equation(s) is/are given. You have to solve both the equations and find the relation between ‘l’ and ‘m’ and mark correct answer. I. (125)1/3 l – (1331)1/3 = 4 × (729)1/6 + (1024)1/10 II. (m)2

In the following question, one or two equation(s) is/are given. You have to solve both the equations and find the relation between ‘l’ and ‘m’ and mark correct answer.

I. (125)^1/3 l – (1331)^1/3 = 4 × (729)^1/6 + (1024)^1/10

II. (m)² – (15625)^1/3 = 0

A l > m

B l ≥ m

C l < m

D l ≤ m

E l = m or the relation cannot be determined

Solution

Correct Answer: Option B

We solve both equations separately

Equation I:

(125)^1/3 l – (1331)^1/3 = 4 × (729)^1/6 + (1024)^1/10

⇒ 5l – 11 = 4 × 3 + 2

⇒ 5l = 14 + 11

⇒ l = 25/5

⇒ l = 5

Equation II:

(m)² – (15625)^1/3 = 0

⇒ (m)² = (15625)^1/3

⇒ m² = 25

⇒ m² – 25 = 0

By using the formula: a² – b² = (a + b) (a – b)

⇒ m = ± 5

Comparing values of l and m, we obtain

l ≥ m

Solution

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