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MHT CET202618 April 2026Evening ShiftMathematicsInverse Trigonometric FunctionsActual

If ⁻¹ax + ⁻¹3x = 4 , where 3ax^2 < 1 , then value of a for x = 1 6 is

Options

  1. A2
  2. B3
  3. C4
  4. D9

Correct answer

A. 2

Step-by-step solution

Given ⁻¹ax + ⁻¹3x = 4 Using the formula ⁻¹A + ⁻¹B = ⁻¹ ( A+B 1-AB ) for AB ⁻¹ ( ax + 3x 1 - 3ax^2 ) = 4 ax + 3x 1 - 3ax^2 = ( 4 ) = 1 ax + 3x = 1 - 3ax^2 Substituting x = 1 6 : a ( 1 6 ) + 3 ( 1 6 ) = 1 - 3a ( 1 6 )^2 a 6 + 1 2 = 1 - 3a 36 a 6 + a 12 = 1 - 1 2 3a 12 = 1 2 a 4 = 1 2 a = 2 Answer: 2

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