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Equations in the greatest integer function

This type of question, asked 5 times: May 2022 S1, 11 May 2023 S1, 15 May 2023 S2, 26 Apr 2025 S1, 14 May 2026 S1. All 5 questions below, oldest first.

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  1. Question 1

    May 2022 S1

    143
    If [x][x] is greatest integer function and 2[2x−5]−1=72[2x-5] - 1 = 7, then xx lies in

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  2. Question 2

    11 May 2023 S1

    115
    If [x]2−5[x]+6=0[x]^2 - 5[x] + 6 = 0, where [x][x] denotes the greatest integer function, then

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  3. Question 3

    15 May 2023 S2

    133
    If [x]2−5[x]+6=0[x]^2-5[x]+6=0, where [⋅][\cdot] denotes the greatest integer function, then

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  4. Question 4

    26 Apr 2025 S1

    114
    If [x]2−5[x]+6=0\lbrack x\rbrack^{2}- 5\lbrack x\rbrack + 6 = 0, where [⋅]\lbrack \cdot \rbrack denotes the greatest integer function, then

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  5. Question 5

    14 May 2026 S1

    51
    If [⋅][\cdot] represents the greatest integer function of less than or equal to type then the solution set of the equation [x]2−5[x]+6=0[x]^2 - 5[x] + 6 = 0 is

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