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.
I. \({\left( {\frac{{1024 \times 36}}{{900}}} \right)^p} = \frac{{32}}{5}\)
II. q2+ 2 × √2 × √2 × q + 2 × √2 × √2 = 0
Solution
Correct Answer: Option A
We will solve both the equations separately.
Equation I:
\(\begin{array}{l} {\left( {\frac{{1024 \times 36}}{{900}}} \right)^p} = \frac{{32}}{5}\\ \Rightarrow \;{\left( {\frac{{{2^{10}} \times 1}}{{25}}} \right)^p} = \frac{{{2^{10\; \times \frac{1}{2}}}}}{{{{25}^{\frac{1}{2}}}}}\\ \Rightarrow \;\frac{{{2^{10 \times p}}}}{{{{25}^p}}} = \frac{{{2^{10\; \times \frac{1}{2}}}}}{{{{25}^{\frac{1}{2}}}}} \end{array}\)
On comparing both sides, we get
⇒ p = 1/2
Equation II:
q2 + 2 × √2 × √2 × q + 2 × √2 × √2 = 0
⇒ q2 + 2 × 2× q + 22 = 0
By using formula: (a + b)2= a2 + 2ab + b2
⇒ (q + 2)2 = 0
⇒ q = -2, -2
Comparing the values of p and q we get,
p > q
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