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Decay with a known half-life: amount left or time taken

This type of question, asked 6 times: 3 May 2023 S1, 4 May 2023 S1, 4 May 2023 S2, 11 May 2023 S2, 22 Apr 2025 S2, 15 May 2026 S1. All 6 questions below, oldest first.

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  1. Question 1

    3 May 2023 S1

    120
    If the half-life of substance is 5 years, then the total amount of the substance left after 15 years, when initial amount is 64 gms is

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  2. Question 2

    4 May 2023 S1

    146
    A wet substance in the open air loses its moisture at a rate proportional to the moisture content. If a sheet hung in the open air loses half its moisture during the first hour, then the time tt, in which 99% of the moisture will be lost, is

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  3. Question 3

    4 May 2023 S2

    127
    The decay rate of radium is proportional to the amount present at any time t. If initially 60 gms was present and half life period of radium is 1600 years, then the amount of radium present after 3200 years is

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  4. Question 4

    11 May 2023 S2

    104
    An ice ball melts at the rate which is proportional to the amount of ice at that instant. Half of the quantity of ice melts in 15 minutes. x0x_0 is the initial quantity of ice. If after 30 minutes the amount of ice left is kx0kx_0, then the value of k is

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  5. Question 5

    22 Apr 2025 S2

    123
    A wet substance in the open air loses its moisture at a rate proportional to the moisture content. If a sheet, hung in the open air, loses half its moisture during the first hour, then 90%90\% of the moisture will be lost in ____\_\_\_\_ hours.

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  6. Question 6

    15 May 2026 S1

    85
    An ice ball melts. The rate at which it melts is proportional to the amount of the ice at that time. If half quantity of ice melts in 2020 minutes, then the time when (1/8)th(1/8)^{th} part of original amount of the ice is left is:

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