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BITSAT2016MathematicsBinomial TheoremActual

If the third term in the expansion of [ x + x ^ ₁₀ x ]⁵ is 10⁶, then x may be

Options

  1. A1
  2. B10
  3. C10
  4. D10^ -2 / 5

Correct answer

C. 10

Step-by-step solution

Put ₁₀ x=y, the given expression becomes (x+x^ y )⁵ T ₃= ⁵ C ₂ x ³ ( x ^ y )²=10 x ^ 3+2 y =10⁶ (given) (3+2 y ) ₁₀ x =5 ₁₀ 10=5 (3+2 y ) y =5 y =1,- 5 2 ₁₀ x =1 or ₁₀ x =- 5 2 x =10 or x =(10)^ -5 / 2

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