JEE Mains · Maths · STD 11 - 7. binomial theoram
If \(n\) is the degree of the polynomial, \({\left[ {\frac{1}{{\sqrt {5{x^3} + 1} - \sqrt {5{x^3} - 1} }}} \right]^8} \)\(+ {\left[ {\frac{1}{{\sqrt {5{x^3} + 1} + \sqrt {5{x^3} - 1} }}} \right]^8}\) and \(m\) is the coefficient of \(x^{12}\) in it, then the ordered pair \((n, m)\) is equal to
- A \(\left( {12,{{\left( {20} \right)}^4}} \right)\)
- B \(\left( {8,5{{\left( {10} \right)}^4}} \right)\)
- C \(\left( {24,{{\left( {10} \right)}^8}} \right)\)
- D \(\left( {12,8{{\left( {10} \right)}^4}} \right)\)
Answer & Solution
Correct Answer
(D) \(\left( {12,8{{\left( {10} \right)}^4}} \right)\)
Step-by-step Solution
Detailed explanation
\(\left[\frac{1}{\sqrt{5 x^{3}+1}-\sqrt{5 x^{3}-1}}\right]^{8}+\left[\frac{1}{\sqrt{5 x^{3}+1}+\sqrt{5 x^{3}-1}}\right]^{8}\) After rationalise the polynomial we get =…
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