Errors — JEE Main Physics MCQs with Solutions
Free JEE Main Physics Errors MCQs with step-by-step solutions (36 questions). Part of Units and Dimensions. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Errors · easy · theory
The absolute error in a measurement is
A. The magnitude of the difference between the measured and true (mean) value ✓ Correct
B. Always zero
C. The measured value itself
D. The ratio of error to true value
Solution: Absolute error $= |a_{measured} - a_{true}|$.
Q2 — Errors · medium · theory
The relative (fractional) error is defined as
A. Absolute error itself
B. Absolute error × mean value
C. Mean value ÷ absolute error
D. Mean absolute error ÷ mean value ✓ Correct
Solution: Relative error $= \frac{\Delta a}{a}$ (dimensionless).
Q3 — Errors · medium · theory
The percentage error equals
A. Mean value × 100
B. Absolute error × 100%
C. Relative error ÷ 100
D. Relative error × 100% ✓ Correct
Solution: Percentage error $= \frac{\Delta a}{a}×100\%$.
Q4 — Errors · medium · numerical
A length has mean value 25.0 cm with mean absolute error 0.1 cm. The percentage error is
A. 0.04%
B. 4%
C. 0.4% ✓ Correct
D. 2.5%
Solution: $\frac{0.1}{25.0}×100 = 0.4\%$.
Q5 — Errors · easy · theory
When two quantities are ADDED (or subtracted), the ABSOLUTE errors
A. Cancel
B. Multiply
C. Add up ✓ Correct
D. Subtract
Solution: For $Z = A ± B$, the maximum absolute error is $\Delta Z = \Delta A + \Delta B$.
Q6 — Errors · medium · theory
When two quantities are MULTIPLIED (or divided), the RELATIVE errors
A. Are ignored
B. Subtract
C. Multiply
D. Add up ✓ Correct
Solution: For $Z = AB$ or $A/B$, $\frac{\Delta Z}{Z} = \frac{\Delta A}{A} + \frac{\Delta B}{B}$.
Q7 — Errors · medium · theory
If $Z = A^2$, the relative error in $Z$ is
A. $\frac{\Delta A}{A}$
B. $\frac{1}{2}\frac{\Delta A}{A}$
C. $4\frac{\Delta A}{A}$
D. $2\frac{\Delta A}{A}$ ✓ Correct
Solution: For a power $A^n$, the relative error is multiplied by $|n|$; here $n = 2$.
Q8 — Errors · medium · theory
If $Z = \frac{A^2 B}{C}$, the percentage error in $Z$ is
A. $\%_A + \%_B + \%_C$
B. $\%_A - \%_B - \%_C$
C. $2\%_A + \%_B - \%_C$
D. $2\%_A + \%_B + \%_C$ ✓ Correct
Solution: Powers multiply, and both multiplication and division ADD relative errors: $2\%_A + \%_B + \%_C$.
Q9 — Errors · medium · numerical
A and B are measured with 2% and 3% error. The percentage error in the product $A×B$ is
A. 6%
B. 2.5%
C. 1%
D. 5% ✓ Correct
Solution: For a product, relative errors add: 2% + 3% = 5%.
Q10 — Errors · medium · numerical
A and B are measured with 2% and 3% error. The percentage error in $A/B$ is
A. 1%
B. −1%
C. 5% ✓ Correct
D. 6%
Solution: Even for division, relative errors ADD (worst case): 2% + 3% = 5%.
Q11 — Errors · medium · numerical
The side of a cube is measured with 1% error. The percentage error in its volume is
A. 2%
B. 6%
C. 3% ✓ Correct
D. 1%
Solution: Volume $= a^3$, so the relative error is tripled: 3×1% = 3%.
Q12 — Errors · medium · numerical
The radius of a sphere is measured with 2% error. The percentage error in its surface area ($4\pi r^2$) is
A. 6%
B. 2%
C. 4% ✓ Correct
D. 8%
Solution: Area $\propto r^2$, so error = 2×2% = 4%.
Q13 — Errors · easy · theory
A resistor gives readings 10.1, 10.2, 10.0, 10.3 Ω. The mean value is
A. 10.1 Ω
B. 10.2 Ω
C. 10.0 Ω
D. 10.15 Ω ✓ Correct
Solution: Mean $= \frac{10.1+10.2+10.0+10.3}{4} = \frac{40.6}{4} = 10.15$ Ω.
Q14 — Errors · easy · theory
The mean absolute error of readings 10.1, 10.2, 10.0, 10.3 (mean 10.15) is
A. 0.05 Ω
B. 0.20 Ω
C. 0.10 Ω ✓ Correct
D. 0.15 Ω
Solution: Deviations: 0.05, 0.05, 0.15, 0.15; mean $= \frac{0.40}{4} = 0.10$ Ω.
Q15 — Errors · medium · theory
Systematic errors are those that
A. Cannot be identified
B. Occur randomly
C. Always cancel out on averaging
D. Occur consistently in the same direction and can often be corrected ✓ Correct
Solution: Systematic errors have a definite cause and direction (e.g. zero error), so they can be reduced or corrected.
Q16 — Errors · easy · theory
Random errors can be reduced by
A. Ignoring them
B. Using the same faulty instrument
C. Taking many readings and averaging ✓ Correct
D. Reading only once
Solution: Averaging many trials reduces the effect of random fluctuations.
Q17 — Errors · medium · theory
A "zero error" of an instrument is an example of a
A. Least-count error
B. Gross error
C. Systematic error ✓ Correct
D. Random error
Solution: A zero error is constant and directional, hence systematic.
Q18 — Errors · medium · theory
The least count of an instrument determines its
A. Accuracy of the true value
B. Smallest measurable value (precision) ✓ Correct
C. Zero error
D. Maximum reading
Solution: Least count is the smallest division measurable, setting the instrument's precision.
Q19 — Errors · easy · numerical
If $Z = A + B$ with $A = 4.0 ± 0.1$ and $B = 6.0 ± 0.2$, then $Z$ is
A. $2.0 ± 0.3$
B. $10.0 ± 0.5$
C. $10.0 ± 0.1$
D. $10.0 ± 0.3$ ✓ Correct
Solution: Value adds (10.0); absolute errors add (0.1 + 0.2 = 0.3).
Q20 — Errors · easy · numerical
If $Z = A − B$ with $A = 8.0 ± 0.2$ and $B = 3.0 ± 0.1$, then $Z$ is
A. $11.0 ± 0.3$
B. $5.0 ± 0.3$ ✓ Correct
C. $5.0 ± 0.1$
D. $5.0 ± 0.2$
Solution: Even for subtraction, ABSOLUTE errors add: 0.2 + 0.1 = 0.3.
Q21 — Errors · easy · theory
The accuracy of a measurement refers to
A. The least count
B. How reproducible it is
C. How close it is to the true value ✓ Correct
D. The number of decimal places
Solution: Accuracy = closeness to the true value; precision = reproducibility.
Q22 — Errors · easy · theory
The precision of a measurement refers to
A. Closeness to the true value
B. How reproducible/close together repeated readings are ✓ Correct
C. The percentage error
D. The mean value
Solution: Precision is about consistency of repeated readings, independent of accuracy.
Q23 — Errors · medium · numerical
In $g = \frac{4\pi^2 l}{T^2}$, if $l$ has 1% error and $T$ has 2% error, the percentage error in $g$ is
A. 3%
B. 4%
C. 5% ✓ Correct
D. 1%
Solution: $\%_g = \%_l + 2\%_T = 1\% + 2(2\%) = 5\%$.
Q24 — Errors · medium · numerical
A quantity $Z = \sqrt{A}$. If $A$ has 4% error, the error in $Z$ is
A. 8%
B. 1%
C. 4%
D. 2% ✓ Correct
Solution: A square root is a power of ½, so error = ½×4% = 2%.
Q25 — Errors · easy · theory
The most reliable estimate of the true value from several readings is the
A. First reading
B. Smallest reading
C. Arithmetic mean ✓ Correct
D. Largest reading
Solution: The arithmetic mean of repeated measurements best estimates the true value.
Q26 — Errors · medium · theory
Which measurement is more precise: 2.5 cm or 2.53 cm?
A. Cannot say
B. Both equal
C. 2.53 cm ✓ Correct
D. 2.5 cm
Solution: More decimal places (smaller least count) means greater precision.
Q27 — Errors · medium · numerical
A current of 5.0 A is measured with an absolute error of 0.1 A. The relative error is
A. 0.02 ✓ Correct
B. 0.2
C. 0.5
D. 0.05
Solution: Relative error $= \frac{0.1}{5.0} = 0.02$ (i.e. 2%).
Q28 — Errors · medium · numerical
If the percentage errors in mass, length and time are 1%, 1% and 1%, the percentage error in density (mass/volume, volume = length³) is
A. 4% ✓ Correct
B. 3%
C. 1%
D. 6%
Solution: $\%_{density} = \%_m + 3\%_L = 1\% + 3\% = 4\%$.
Q29 — Errors · easy · theory
Errors due to carelessness or misreading a scale are called
A. Random errors
B. Least-count errors
C. Systematic errors
D. Gross errors ✓ Correct
Solution: Gross errors arise from human mistakes and cannot be treated statistically.
Q30 — Errors · medium · theory
To reduce the percentage error in a quantity raised to a power, one should measure that quantity
A. Less accurately
B. In different units
C. Only once
D. More accurately (its error is magnified by the power) ✓ Correct
Solution: Since errors in powered quantities are multiplied by the exponent, they must be measured most carefully.