In the following question, one or two equation(s) is/are given. You have to solve both the equations and find the relation between ‘p’ and ‘q’ and mark correct answer. 1. \(\frac{{135}}{{\sqrt p }} - 22\sqrt p = 23\sqrt p\) 2. \(\frac{{2 \times 324 \div \sqrt q }}{{108}}

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

1. \(\frac{{135}}{{\sqrt p }} - 22\sqrt p = 23\sqrt p\)

2. \(\frac{{2 \times 324 \div \sqrt q }}{{108}} - 2\sqrt q = 0\)

A p > q

B p ≥ q

C p < q

D p ≤ q

E p = q or the relation cannot be determined

Solution

Correct Answer: Option E

We will solve both the equations separately.

Equation I:

\(\frac{{135}}{{\sqrt p }} - 22\sqrt p = 23\sqrt p\)

Multiplying both sides by √p, we get

⇒ 135 – 22p = 23p

⇒ 23p + 22p = 135

⇒ 45p = 135

⇒ p = 135/45

⇒ p = 3

Equation II:

\(\begin{array}{l} \frac{{2 \times 324 \div \sqrt q }}{{108}} - 2\sqrt q = 0\\ \Rightarrow \frac{{2 \times 324}}{{108 \times \sqrt q }} = 2\sqrt q \end{array}\)

Multiplying both sides by √q, we get

\(\Rightarrow q = \;\frac{{2 \times 324}}{{108 \times 2}}\)

⇒ q = 3

Comparing the values of p and q, we notice that p = q

Solution

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