Physics · Units and Measurements · PYQ set
Errors in Measurement · JEE PYQ Practice with Solutions
Twenty questions on errors in measurement for JEE Main and Advanced: absolute and mean absolute error, relative and percentage error, and combination of errors, all with detailed solutions.
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20Questions
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In short
Error questions are decided by one habit: track which operation you performed. Absolute errors add when quantities are added or subtracted; relative errors add when they are multiplied or divided, and multiply by the power when a quantity is raised to one. Almost every mark lost here comes from mixing those two rules up.
Contents
Q
Errors in Measurement – 20 MCQs
Single correct answer. Weighted toward absolute and mean absolute error, then relative, percentage and combination of errors. Tagged JEE Main (crimson) or Advanced (teal).
Q1JEE MAINMean Value
In an experiment the period of oscillation of a pendulum is measured five times giving 2.63, 2.56, 2.42, 2.71 and 2.80 s. The mean period is:
A2.72 s
B2.56 s
C2.50 s
D2.62 s
Q2JEE MAINAbsolute Error
For the same pendulum readings (mean 2.62 s), the absolute error in the third reading (2.42 s) is:
A0.18 s
B0.06 s
C0.09 s
D0.20 s
Q3JEE MAINMean Absolute Error
For the pendulum readings (mean 2.62 s), the mean absolute error is closest to:
A0.20 s
B0.02 s
C0.06 s
D0.11 s
Q4JEE MAINReporting
The pendulum result (mean 2.62 s, mean absolute error 0.11 s) should be reported as:
A(2.62 ± 0.53) s
B(2.62 ± 0.04) s
C(2.62 ± 0.11) s
D2.62 s
Q5JEE MAINMean Absolute Error
Four measurements of a length give 1.24, 1.26, 1.28 and 1.22 cm. The mean absolute error is:
A0.04 cm
B0.02 cm
C0.01 cm
D0.06 cm
Q6JEE MAINMean Absolute Error
Five readings of a resistance are 1.23, 1.24, 1.26, 1.25, 1.22 Ω (mean 1.24 Ω). The mean absolute error is:
A0.012 Ω
B0.008 Ω
C0.05 Ω
D0.02 Ω
Q7JEE MAINAbsolute Error
A single measurement of a rod gives 2.56 cm while its true length is 2.50 cm. The absolute error is:
A2.56 cm
B0.6 cm
C0.02 cm
D0.06 cm
Q8JEE MAINConcept
Which statement about mean absolute error is correct?
AIt has the same units as the measured quantity
BIt can be negative
CIt is always dimensionless
DIt equals the sum of the absolute errors
Q9JEE MAINRelative Error
A screw gauge gives a wire diameter with mean 0.500 mm and mean absolute error 0.002 mm. The relative error is:
A0.002
B0.04
C0.004
D0.001
Q10JEE MAINPercentage Error
A measurement is recorded as (5.00 ± 0.05) cm. The percentage error is:
A5%
B1%
C0.5%
D0.05%
Q11JEE MAINPercentage Error
The mean of a quantity is 10.2 units with mean absolute error 0.12 units. The percentage error is about:
A0.12%
B2.4%
C1.2%
D12%
Q12JEE MAINPercentage Error
If the percentage error in a mass is 2% and the mass is 50.0 g, the absolute error is:
A1.0 g
B0.5 g
C0.1 g
D2.0 g
Q13JEE MAINCombination: Sum
For A = (10.0 ± 0.1) and B = (5.0 ± 0.2), the result of A + B is:
A(15.0 ± 0.02)
B(15.0 ± 0.1)
C(15.0 ± 0.15)
D(15.0 ± 0.3)
Q14JEE MAINCombination: Difference
For A = (10.0 ± 0.1) and B = (5.0 ± 0.2), the result of A − B is:
A(5.0 ± 0.3)
B(5.0 ± 0.1)
C(5.0 ± 0.15)
D(5.0 ± 0.02)
Q15JEE MAINCombination: Quotient
V = (100 ± 5) V and I = (10 ± 0.2) A. The percentage error in R = V/I is:
A3%
B7%
C2%
D5%
Q16JEE ADVCombination: Product
A = (10 ± 0.1) and B = (5 ± 0.1) are multiplied, Z = AB. The absolute error in Z is:
A3.0
B0.2
C1.5
D0.03
Q17JEE ADVCombination: Power
g = 4π²L/T². If the percentage error in L is 1% and in T is 2%, the percentage error in g is:
A5%
B3%
C1%
D7%
Q18JEE ADVCombination: Power
Z = A²B³/C. If the percentage errors in A, B and C are each 1%, the percentage error in Z is:
A5%
B6%
C1%
D3%
Q19JEE ADVCombination: Power
The density of a sphere is ρ = m/(⅔πr³). If %error in m is 1% and in r is 0.5%, the %error in density is:
A1.5%
B3.5%
C2.5%
D1%
Q20JEE ADVCombination: Power
For Young's modulus Y = MgL/(πr²l), with %errors M 1%, L 1%, r 0.5%, l 2% (g exact), the maximum %error in Y is:
A6.5%
B5%
C3.5%
D4%
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Answer Key & Solutions
Q1D
Q2D
Q3D
Q4C
Q5B
Q6A
Q7D
Q8A
Q9C
Q10B
Q11C
Q12A
Q13D
Q14A
Q15B
Q16C
Q17A
Q18B
Q19C
Q20B
Q1Correct: D2.62 s
The mean is the arithmetic average: (2.63+2.56+2.42+2.71+2.80)/5 = 13.12/5 = 2.62 s. The mean of repeated readings is the best estimate of the true value.
Q2Correct: D0.20 s
Absolute error = |reading − mean| = |2.42 − 2.624| = 0.20 s. Absolute error is always taken as a positive magnitude.
Q3Correct: D0.11 s
Absolute errors: 0.006, 0.064, 0.204, 0.086, 0.176. Mean = 0.536/5 = 0.11 s. The mean absolute error is the average of the individual absolute errors.
Q4Correct: C(2.62 ± 0.11) s
A measured quantity is reported as mean ± mean absolute error, so the period is (2.62 ± 0.11) s.
Q5Correct: B0.02 cm
Mean = 5.00/4 = 1.25 cm. Absolute errors: 0.01, 0.01, 0.03, 0.03. Mean absolute error = 0.08/4 = 0.02 cm.
Q6Correct: A0.012 Ω
Absolute errors from 1.24: 0.01, 0.00, 0.02, 0.01, 0.02. Mean = 0.06/5 = 0.012 Ω.
Q7Correct: D0.06 cm
With a known true value, absolute error = |measured − true| = |2.56 − 2.50| = 0.06 cm.
Q8Correct: AIt has the same units as the measured quantity
Mean absolute error is an average of |reading − mean| values, so it carries the same units as the quantity. It is an average (not a sum) of magnitudes, so never negative.
Q9Correct: C0.004
Relative error = mean absolute error / mean = 0.002/0.500 = 0.004 (a pure number). Times 100 gives 0.4%.
Q10Correct: B1%
Percentage error = (0.05/5.00) × 100 = 1%.
Q11Correct: C1.2%
Percentage error = (0.12/10.2) × 100 ≈ 1.2%.
Q12Correct: A1.0 g
Absolute error = (2/100) × 50.0 = 1.0 g. The reverse of the usual calculation.
Q13Correct: D(15.0 ± 0.3)
For a sum, absolute errors add: Δ = 0.1 + 0.2 = 0.3, so (15.0 ± 0.3). Same rule for a difference.
Q14Correct: A(5.0 ± 0.3)
For a difference the absolute errors still add: Δ = 0.3, so (5.0 ± 0.3). The error grew while the value shrank, so a difference of near-equal values has a large percentage error.
Q15Correct: B7%
For a quotient, percentage errors add: 5% + 2% = 7%. Products and quotients combine by adding relative errors.
Q16Correct: C1.5
Relative errors add: ΔZ/Z = 0.01 + 0.02 = 0.03. Then ΔZ = 0.03 × 50 = 1.5. Find the relative error, then multiply by Z.
Q17Correct: A5%
A power contributes its exponent times the error: %g = %L + 2(%T) = 1 + 4 = 5%. T is squared, so its error counts double.
Q18Correct: B6%
Each factor contributes exponent × error: %Z = 2(1) + 3(1) + 1(1) = 6%. Exponents add regardless of numerator or denominator.
Q19Correct: C2.5%
%ρ = %m + 3(%r) = 1 + 1.5 = 2.5%. The radius is cubed, so its error is tripled.
Q20Correct: B5%
%Y = %M + %L + 2(%r) + %l = 1 + 1 + 1 + 2 = 5%. The r term doubles because r is squared; all contributions add in a maximum-error problem.
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Error Analysis: Quick Revision
Everything for revision day.ABSOLUTE ERROR
|reading − mean|
always positive
same units as quantity
MEAN ABS ERROR
average of |errors|
report mean ± MAE
e.g. pendulum 0.11 s
RELATIVE / %
rel = MAE/mean
% = rel × 100
dimensionless
SUM / DIFFERENCE
absolute errors ADD
even for a difference
Δ(A±B)=ΔA+ΔB
PRODUCT / QUOTIENT
relative errors ADD
%(AB)=%A+%B
%(A/B)=%A+%B
POWERS
%(A^n)=n×%A
g: %L+2%T
density: %m+3%r
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