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JEE Mains · Maths · STD 11 - basic of algoritham
The coefficient of \({x^5}\) in the expansion of \({{{x^2} + 1} \over {({x^2} + 4)(x - 2)}}\) is
- A \(1/256\)
- B \(1/562\)
- C \(1/265\)
- D \(-1/256\)
Answer & Solution
Correct Answer
(D) \(-1/256\)
Step-by-step Solution
Detailed explanation
(d) \({{{x^2} + 1} \over {({x^2} + 4)\,(x - 2)}} = {{Ax + B} \over {{x^2} + 4}} + {C \over {x - 2}}\) \( \Rightarrow \)\({x^2} + 1 = (Ax + B)\,(x - 2)\, + C({x^2} + 4)\)\( \Rightarrow \)\(1 = A + C\) \( - 2A + B = 0\), \(1 = - 2B + 4C\)…
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