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Percentage error in a quantity given as a product of powers of measured quantities

This type of question, asked 7 times: 19 Apr 2025 S1, 21 Apr 2025 S1, 26 Apr 2025 S2, 11 Apr 2026 S2, 20 Apr 2026 S2, 12 May 2026 S2, 15 May 2026 S2. All 7 questions below, oldest first.

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  1. Question 1

    19 Apr 2025 S1

    1
    The formula for the physical quantity is P=x3yz2P =\frac{x^{3}y}{z^{2}} and the percentage error in the determination of physical quantities x,y,zx,y,z are 0.6%,3%0.6\%,3\% and 1.3%1.3\% respectively. The percentage error in the measurement of PP is

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  2. Question 2

    21 Apr 2025 S1

    5
    A physical quantity A can be determined by measuring parameters B,C,DB,C,D and E using the relation A=BαCβDγEδA =\frac{B^{\alpha}C^{\beta}}{D^{\gamma}E^{\delta}}. If the maximum errors in the measurement are b%,c%, d%b\%,c\%,\text{ }d\% and e%e\% then maximum error in the value of AA is

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  3. Question 3

    26 Apr 2025 S2

    48
    In an experiment four quantities p,q,rp, q, r and ss are measured with percentage errors 3%,2%,3%3\%, 2\%, 3\% and 1%1\% respectively. Quantity 'AA' is calculated as follows A=pq2r2s4A = \frac{pq^2}{r^2s^4}, the percentage error in 'AA' is

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  4. Question 4

    11 Apr 2026 S2

    101
    A quantity P is related as X−2Y−3/2Z2/5X^{-2}Y^{-3/2}Z^{2/5} where X,Y,Z are independent parameters which have fractional errors of 0.1,0.20.1, 0.2 and 0.50.5 respectively in measurement. The maximum fractional error in P is

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  5. Question 5

    20 Apr 2026 S2

    101
    A physical quantity xx is related as x=a b2c3d−4x = \sqrt{a}\,b^2c^3d^{-4}. Relative errors in the quantities a,b,ca, b, c and dd are 2%, 1%, 3% and 4% respectively. Relative error in xx will be

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  6. Question 6

    12 May 2026 S2

    101
    A quantity QQ is formulated X−2Y+32Z−25X^{-2}Y^{+\frac{3}{2}}Z^{-\frac{2}{5}}. X,YX, Y and ZZ are independent parameters which have fractional errors of 0.10.1, 0.20.2 and 0.50.5 respectively in measurement. The maximum fractional error of QQ is

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  7. Question 7

    15 May 2026 S2

    102
    A physical quantity CC is related to four other quantities P,Q,RP, Q, R and SS as C=PQ2R3SC = \dfrac{PQ^2}{R^3\sqrt{S}}. The percentage error in the measurement of P,Q,RP, Q, R and SS are 1%1\%, 2%2\%, 3%3\% and 2%2\% respectively. The percentage error in the measurement of CC will be

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