Errors — NEET Physics MCQs with Solutions
Free NEET 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 ratio of error to true value
B. The measured value itself
C. Always zero
D. The magnitude of the difference between the measured and true (mean) value ✓ Correct
Solution: Absolute error $= |a_{measured} - a_{true}|$.
Q2 — Errors · medium · theory
The relative (fractional) error is defined as
A. Absolute error itself
B. Mean value ÷ absolute error
C. Mean absolute error ÷ mean value ✓ Correct
D. Absolute error × mean value
Solution: Relative error $= \frac{\Delta a}{a}$ (dimensionless).
Q3 — Errors · medium · theory
The percentage error equals
A. Relative error ÷ 100
B. Mean value × 100
C. Relative error × 100% ✓ Correct
D. Absolute error × 100%
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. 4%
B. 2.5%
C. 0.04%
D. 0.4% ✓ Correct
Solution: $\frac{0.1}{25.0}×100 = 0.4\%$.
Q5 — Errors · easy · theory
When two quantities are ADDED (or subtracted), the ABSOLUTE errors
A. Add up ✓ Correct
B. Subtract
C. Multiply
D. Cancel
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. Subtract
B. Multiply
C. Are ignored
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. $4\frac{\Delta A}{A}$
B. $2\frac{\Delta A}{A}$ ✓ Correct
C. $\frac{1}{2}\frac{\Delta A}{A}$
D. $\frac{\Delta A}{A}$
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. $2\%_A + \%_B - \%_C$
C. $\%_A - \%_B - \%_C$
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. 1%
B. 2.5%
C. 6%
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. 6%
B. 1%
C. 5% ✓ Correct
D. −1%
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. 3% ✓ Correct
B. 1%
C. 6%
D. 2%
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. 4% ✓ Correct
B. 6%
C. 8%
D. 2%
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. 10.15 Ω ✓ Correct
B. 10.0 Ω
C. 10.2 Ω
D. 10.1 Ω
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. 0.15 Ω
D. 0.10 Ω ✓ Correct
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. Occur consistently in the same direction and can often be corrected ✓ Correct
B. Cannot be identified
C. Occur randomly
D. Always cancel out on averaging
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. Reading only once
B. Using the same faulty instrument
C. Ignoring them
D. Taking many readings and averaging ✓ Correct
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. Random error
C. Systematic error ✓ Correct
D. Gross error
Solution: A zero error is constant and directional, hence systematic.
Q18 — Errors · medium · theory
The least count of an instrument determines its
A. Maximum reading
B. Accuracy of the true value
C. Zero error
D. Smallest measurable value (precision) ✓ Correct
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. $10.0 ± 0.5$
B. $2.0 ± 0.3$
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. $5.0 ± 0.3$ ✓ Correct
B. $11.0 ± 0.3$
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 number of decimal places
B. How close it is to the true value ✓ Correct
C. The least count
D. How reproducible it is
Solution: Accuracy = closeness to the true value; precision = reproducibility.
Q22 — Errors · easy · theory
The precision of a measurement refers to
A. How reproducible/close together repeated readings are ✓ Correct
B. The percentage error
C. The mean value
D. Closeness to the true 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. 5% ✓ Correct
B. 4%
C. 3%
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. 2% ✓ Correct
B. 1%
C. 4%
D. 8%
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. Arithmetic mean ✓ Correct
C. Smallest reading
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. 2.53 cm ✓ Correct
B. 2.5 cm
C. Cannot say
D. Both equal
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. 0.5
B. 0.02 ✓ Correct
C. 0.05
D. 0.2
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. 1%
B. 6%
C. 3%
D. 4% ✓ Correct
Solution: $\%_{density} = \%_m + 3\%_L = 1\% + 3\% = 4\%$.
Q29 — Errors · easy · theory
Errors due to carelessness or misreading a scale are called
A. Gross errors ✓ Correct
B. Random errors
C. Systematic errors
D. Least-count errors
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. More accurately (its error is magnified by the power) ✓ Correct
B. Less accurately
C. In different units
D. Only once
Solution: Since errors in powered quantities are multiplied by the exponent, they must be measured most carefully.