PYQ Vault

Percentage error in a quantity given as a product of powers

This type of question, asked 10 times: 2021 Paper 17, 25 Jun 2022, 25 Jul 2022, 27 Jul 2022, 10 Apr 2023, 13 Apr 2023, 29 Jan 2024, 29 Jan 2025, 3 Apr 2025, 6 Apr 2026 S2. All 11 questions below, oldest first.

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  1. Question 1

    2021 Paper 17

    16
    A physical quantity ' yy ' is represented by the formula y=m2r−4 gxl−32y =m^{2}r^{- 4}{\text{ }g}^{x}l^{-\frac{3}{2}} If the percentage errors found in y,m,r,ly,m,r,l and gg are 18,1,0.5,418,1,0.5,4 and pp respectively, then find the value of xx and pp.

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  2. Question 2

    25 Jun 2022

    111
    For z=a2x3y12z=a^{2}x^{3}y^{\frac{1}{2}}, where aa is a constant. If percentage error in measurement of ' xx ' and ' yy ' are 4%4\% and 12%12\%, respectively, then the percentage error for ' zz ' will be ____ %\_\_\_\_\ \%.
  3. Question 3

    25 Jun 2022

    1
    If Z=A2B3C4Z=\frac{A^{2}B^{3}}{C^{4}}, then the relative error in ZZ will be:

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  4. Question 4

    25 Jul 2022

    109
    The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are 1%,2% and 3% respectively. The maximum percentage error in the detection of the dissipated heat will be:

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  5. Question 5

    27 Jul 2022

    1
    A torque meter is calibrated to reference standards of mass, length and time each with 5%5\% accuracy. After calibration, the measured torque with this torque meter will have net accuracy of:

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  6. Question 6

    10 Apr 2023

    1
    A physical quantity PP is given as
    P=a2b3cdP =\frac{a^{2}b^{3}}{c\sqrt{d}}
    The percentage error in the measurement of a, b, c and dd are 1%,2%,3%1\%,2\%,3\% and 4%4\% respectively. The percentage error in the measurement of quantity PP will be

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  7. Question 7

    13 Apr 2023

    14
    A body of mass (5±0.5)kg(5 \pm 0.5)kg is moving with a velocity of (20±0.4)m/s(20 \pm 0.4)m/s. Its kinetic energy will be

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  8. Question 8

    29 Jan 2024

    93
    A physical quantity QQ is found to depend on quantities a,b,ca,b,c by the relation Q=a4 b3c2Q =\frac{a^{4}{\text{ }b}^{3}}{c^{2}}. The percentage error in a,ba,b and cc are 3%,4%3\%,4\% and 5%5\% respectively. Then, the percentage error in QQ is:

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  9. Question 9

    29 Jan 2025

    98
    A physical quantity Q is related to four observables a, b,c,db,c,d as follows : Q=ab4cdQ = \frac{ab^{4}}{cd} where, a=(60±3)Pa;b=(20±0.1)ma = (60 \pm 3)Pa;b = (20 \pm 0.1)m; c=(40±0.2)Nsm−2c = (40 \pm 0.2)Nsm^{- 2} and d=(50±0.1)md = (50 \pm 0.1)m, then the percentage error in Q is x1000\frac{x}{1000}, where x=x =  ____\ \_\_\_\_ .
  10. Question 10

    3 Apr 2025

    100
    A physical quantity C is related to four other quantities p,q,rp,q,r and s as follows C=pq2r3 sC = \frac{{pq}^{2}}{r^{3}\sqrt{\text{ }s}}.The percentage errors in the measurement of p, q, r and ss are 1%,2%,3%1\%, 2\%, 3\% and 2%2\% respectively. The percentage error in the measurement of CC will be ____ %\_\_\_\_\ \%.
  11. Question 11

    6 Apr 2026 S2

    1
    The percentage error in the calculated volume of a sphere, if there is 2%2\% error in its diameter measurement, is ____\_\_\_\_ .

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