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Number of solutions of the equation [2x] − 3{2x} = 1 (where [⋅] and {⋅} denotes the greatest integer and fractional part function respectively) is
  • a)
    1
  • b)
    2
  • c)
    3
  • d)
    0
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Number of solutions of the equation [2x] − 3{2x} = 1(where [&sdo...
The equation [2x] = 0 has no solutions if x is not an integer or if x is an integer but not within the range of -0.5 to 0.5.

If x is an integer within the range of -0.5 to 0.5, then [2x] = 0. In this case, there are infinitely many solutions.
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Number of solutions of the equation [2x] − 3{2x} = 1(where [&sdo...
Given [2x] − 3{2x} = 1
Let x = I + f, where I is integral part and f is fractional part.

Case-I

From the Case-I

Case-II

Case-III


So, three solutions are 
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Number of solutions of the equation [2x] − 3{2x} = 1(where [⋅]and {⋅}denotes the greatest integer and fractional part function respectively) isa)1b)2c)3d)0Correct answer is option 'C'. Can you explain this answer?
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Number of solutions of the equation [2x] − 3{2x} = 1(where [⋅]and {⋅}denotes the greatest integer and fractional part function respectively) isa)1b)2c)3d)0Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Number of solutions of the equation [2x] − 3{2x} = 1(where [⋅]and {⋅}denotes the greatest integer and fractional part function respectively) isa)1b)2c)3d)0Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Number of solutions of the equation [2x] − 3{2x} = 1(where [⋅]and {⋅}denotes the greatest integer and fractional part function respectively) isa)1b)2c)3d)0Correct answer is option 'C'. Can you explain this answer?.
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