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CDS Maths Previous Paper 9 (Held On: 2 Feb 2020)

Option 2 : -1

Electric charges and coulomb's law (Basic)

48838

10 Questions
10 Marks
10 Mins

**Given:**

\(\frac{1}{{{{\rm{a}}^{{\rm{m}} - {\rm{n}}}} - 1}} + \frac{1}{{{{\rm{a}}^{{\rm{n}} - {\rm{m}}}} - 1}}\)

**Concept Used:**

x^{-1 }= 1/x

**Calculation:**

Let, x = a^{m – n}

⇒ a^{n – m} = a^{– (m – n)} = x^{– 1} = 1/x

Hence, we can write,

\(\frac{1}{{{a^{m - n}} - 1}} + \frac{1}{{{a^{n - m}} - 1}}\)

\(\frac{1}{{x - 1}} + \frac{1}{{\frac{1}{x} - 1}}\)

\( = - \frac{1}{{1 - x}} + \frac{x}{{1 - x\;}}\)

\( = - \left( {\frac{{1 - x}}{{1 - x}}} \right)\)

= -1

**∴ The value of \(\frac{1}{{{{\rm{a}}^{{\rm{m}} - {\rm{n}}}} - 1}} + \frac{1}{{{{\rm{a}}^{{\rm{n}} - {\rm{m}}}} - 1}}\) is - 1.**