CLASS 11 PHYSICS • UNITS AND MEASUREMENTS

Errors in Measurement

Master absolute error, relative error, percentage error and error propagation with NEET, JEE, CBSE, IB and IGCSE level numericals.

CBSENEETJEE MainJEE AdvancedIBIGCSEA-Level

Need help in Units and Measurements?

For CBSE, NEET, JEE Main, JEE Advanced, IB, IGCSE and A-Level Physics, contact Kumar Sir for one-to-one online Physics classes.

Phone: +91-9958461445Email: kumarsirphysics@gmail.com Website: https://kumarphysicsclasses.com WhatsApp Kumar Sir

1. Errors

Error is the difference between the true value and the measured value of a physical quantity. A mistake is a wrong procedure or careless recording, while error is the unavoidable uncertainty present even in careful experiments.

True Value

The ideal value of a quantity. It is usually approximated by a reliable standard or by the mean of many accurate readings.

Measured Value

The value obtained from an instrument during an experiment.

Approximate Value

Most experimental values are approximate because instruments have finite least count and conditions fluctuate.

Physics numericals use errors to decide reliability, correct significant figures and uncertainty in derived quantities.

2. Systematic Errors

Systematic errors shift all readings in one direction because of a fixed cause. They affect accuracy and cannot be removed simply by taking the mean.

Instrumental

Zero error in screw gauge, wrong calibration or damaged scale.

Environmental

Temperature, humidity, pressure or vibrations changing the measurement.

Observational

Parallax error due to wrong eye position.

Reduction

Calibrate instruments, remove zero error, control surroundings and use correct reading method.

3. Random Errors

Random errors produce unpredictable fluctuations in readings due to small uncontrolled changes. Repeated measurements reduce their effect, so the mean value is used.

4. Instrumental Errors

Least Count Error

Uncertainty due to the smallest division of an instrument. A metre scale cannot reliably measure below 1 mm.

Zero Error

Instrument shows non-zero reading when actual value is zero, common in vernier calipers and screw gauge.

Calibration Error

Instrument markings are not matched with standard values.

Instrument Defect

Loose screw, bent pointer, worn scale or delayed stopwatch response can introduce error.

Instrument	Common Error	Care
Metre scale	Least count and parallax	Keep eye vertically above mark
Vernier calipers	Zero error	Check zero before measuring
Screw gauge	Zero error and backlash	Use ratchet gently
Stopwatch	Reaction time	Repeat and average

5. Personal Errors

Personal errors are caused by the observer: wrong eye position, late reaction, incorrect method or careless recording.

6. Absolute Error

Absolute error is the magnitude of difference between measured value and true or mean value.

Absolute Error = |Measured Value - True Value|

a_mean = (a₁ + a₂ + a₃ + ... + a_n) / n

Δa₁ = |a₁ - a_mean|, Δa₂ = |a₂ - a_mean|

Solved Example 1

Question: A length is measured as 10.2 cm while true length is 10.0 cm. Find absolute error.

Given: Measured = 10.2 cm, true = 10.0 cm

Formula: Absolute error = |measured - true|

Substitution: |10.2 - 10.0| cm

Calculation: 0.2 cm

Final Answer: 0.2 cm

Exam Tip: Absolute error always has the same unit as the measured quantity.

Solved Example 2

Question: Readings are 5.1 cm, 5.2 cm and 5.0 cm. Find mean value.

Given: a₁=5.1 cm, a₂=5.2 cm, a₃=5.0 cm

Formula: a_mean = sum / n

Substitution: (5.1 + 5.2 + 5.0) / 3

Calculation: 15.3 / 3 = 5.1 cm

Final Answer: 5.1 cm

Exam Tip: Use mean value when true value is not given.

7. Mean Absolute Error

Δa_mean = (|Δa₁| + |Δa₂| + |Δa₃| + ... + |Δa_n|) / n

Final result: a = a_mean ± Δa_mean

Step-by-step Example

Question: Readings of length are 2.4 cm, 2.5 cm and 2.6 cm. Write final result.

Given: Readings = 2.4, 2.5, 2.6 cm

Formula: a_mean = sum / 3, Δa_mean = average of absolute deviations

Substitution: a_mean = 7.5 / 3 = 2.5 cm; deviations = 0.1, 0, 0.1 cm

Calculation: Δa_mean = 0.2 / 3 = 0.067 cm ≈ 0.07 cm

Final Answer: a = 2.50 ± 0.07 cm

Exam Tip: Round uncertainty sensibly, then report value to matching decimal place.

Laboratory Example

Question: Mass readings are 20.1 g, 20.0 g, 20.2 g and 20.1 g. Find mean absolute error.

Given: n = 4

Formula: Δm_mean = average absolute deviation from mean

Substitution: m_mean = 80.4 / 4 = 20.1 g; deviations = 0, 0.1, 0.1, 0

Calculation: Δm_mean = 0.2 / 4 = 0.05 g

Final Answer: 20.10 ± 0.05 g

Exam Tip: Mean absolute error measures spread of readings.

8. Relative Error

Relative error compares absolute uncertainty with the measured value. It is dimensionless.

Relative Error = Mean Absolute Error / Mean Value = Δa / a

Relative Error Example

Question: Mean length is 50 cm and mean absolute error is 0.5 cm. Find relative error.

Given: a = 50 cm, Δa = 0.5 cm

Formula: Relative error = Δa / a

Substitution: 0.5 / 50

Calculation: 0.01

Final Answer: 0.01

Exam Tip: Units cancel in relative error.

9. Percentage Error

Percentage error expresses relative error as a percentage.

Percentage Error = (Δa / a) × 100

Percentage Error Example

Question: A current is 2.0 A with uncertainty 0.04 A. Find percentage error.

Given: I = 2.0 A, ΔI = 0.04 A

Formula: Percentage error = (ΔI / I) × 100

Substitution: (0.04 / 2.0) × 100

Calculation: 2%

Final Answer: 2%

Exam Tip: Convert relative error into percent by multiplying by 100.

10. Error Propagation

This is the most important part for NEET and JEE. In derived quantities, individual measurement errors combine according to the mathematical operation.

Addition and Subtraction

If Z = A + B or Z = A - B, then ΔZ = ΔA + ΔB

Multiplication and Division

If Z = AB or Z = A / B, then ΔZ / Z = ΔA / A + ΔB / B

Power Rule

If Z = A^mBⁿ / C^pD^q, then ΔZ / Z = m(ΔA/A) + n(ΔB/B) + p(ΔC/C) + q(ΔD/D)

Power Rule 1

Question: If Y = X³ and percentage error in X is 2%, find percentage error in Y.

Given: Y = X³, error in X = 2%

Formula: % error in Y = 3 × % error in X

Substitution: 3 × 2%

Calculation: 6%

Final Answer: 6%

Exam Tip: Power multiplies percentage error.

Power Rule 2

Question: If Y = P⁴ and error in P is 1%, find error in Y.

Given: Power = 4

Formula: % error = 4 × 1%

Substitution: 4%

Calculation: 4%

Final Answer: 4%

Exam Tip: Exponent directly multiplies relative error.

Power Rule 3

Question: If Y = L² / T, errors in L and T are 1% and 2%. Find error in Y.

Given: Y = L² / T

Formula: % error = 2(%L) + %T

Substitution: 2(1%) + 2%

Calculation: 4%

Final Answer: 4%

Exam Tip: For division, add percentage errors.

Power Rule 4

Question: If Y = A²B³ / C⁴, errors are A=1%, B=2%, C=1%.

Given: A=1%, B=2%, C=1%

Formula: %Y = 2%A + 3%B + 4%C

Substitution: 2(1) + 3(2) + 4(1)

Calculation: 12%

Final Answer: 12%

Exam Tip: All powers contribute positively.

Power Rule 5

Question: If Y = m²gL / T², errors are m=1%, g=0.5%, L=2%, T=1%.

Given: m=1%, g=0.5%, L=2%, T=1%

Formula: %Y = 2%m + %g + %L + 2%T

Substitution: 2 + 0.5 + 2 + 2

Calculation: 6.5%

Final Answer: 6.5%

Exam Tip: Do not subtract denominator error; add it.

Power Rule 6

Question: If Y = P²Q³ / R⁴, errors are P=2%, Q=1%, R=0.5%.

Given: P=2%, Q=1%, R=0.5%

Formula: %Y = 2%P + 3%Q + 4%R

Substitution: 4 + 3 + 2

Calculation: 9%

Final Answer: 9%

Exam Tip: Convert all uncertainties to percentage first.

11. Graphs for Errors

Random Error Scatter Graph

Systematic Error Shift Graph

Accuracy vs Precision Target

Error Bar Diagram

Percentage Error Comparison Bar Graph

12. NEET Question Bank: 60 MCQs

NEET-style practice focused on percentage error, relative error, error propagation, power rule, least count and uncertainty.

NEET MCQ 1

Question: If measured value is 12.4 cm and true value is 12.0 cm, absolute error is

(a) 0.4 cm(b) 24.4 cm(c) 0.04 cm(d) 12.4 cm

Correct Answer: 0.4 cm

Solution: Absolute error = |12.4 - 12.0| = 0.4 cm.

Exam Tip: Use modulus for error.

NEET MCQ 2

Question: Relative error is defined as

(a) absolute error / measured value(b) measured value / absolute error(c) absolute error × value(d) true value + error

Correct Answer: absolute error / measured value

Solution: Relative error = Δa / a.

Exam Tip: It has no unit.

NEET MCQ 3

Question: Percentage error for Δa = 0.2 cm and a = 10 cm is

(a) 2%(b) 20%(c) 0.2%(d) 5%

Correct Answer: 2%

Solution: (0.2 / 10) × 100 = 2%.

Exam Tip: Multiply relative error by 100.

NEET MCQ 4

Question: For Z = A + B, absolute error in Z is

(a) ΔA + ΔB(b) ΔA - ΔB(c) ΔA × ΔB(d) zero

Correct Answer: ΔA + ΔB

Solution: In addition, absolute errors add.

Exam Tip: Never subtract errors.

NEET MCQ 5

Question: For Z = AB, relative error in Z is

(a) ΔA/A + ΔB/B(b) ΔA + ΔB(c) A/ΔA(d) B/ΔB

Correct Answer: ΔA/A + ΔB/B

Solution: Product uses relative error addition.

Exam Tip: Use fractional errors.

NEET MCQ 6

Question: If Y = X² and error in X is 3%, error in Y is

(a) 6%(b) 3%(c) 9%(d) 1.5%

Correct Answer: 6%

Solution: Power 2 doubles percentage error.

Exam Tip: Exponent multiplies percent error.

NEET MCQ 7

Question: Systematic error mainly affects

(a) accuracy(b) randomness only(c) mass only(d) SI unit

Correct Answer: accuracy

Solution: It shifts measurements away from true value.

Exam Tip: Calibration removes it.

NEET MCQ 8

Question: Random error can be reduced by

(a) taking mean of repeated readings(b) changing unit only(c) ignoring readings(d) using fewer trials

Correct Answer: taking mean of repeated readings

Solution: Mean smooths random fluctuations.

Exam Tip: Repeat readings.

NEET MCQ 9

Question: Zero error in screw gauge is an example of

(a) instrumental error(b) personal error only(c) random error only(d) percentage error

Correct Answer: instrumental error

Solution: It is caused by the instrument.

Exam Tip: Check zero first.

NEET MCQ 10

Question: Parallax error is reduced by

(a) keeping eye perpendicular to scale(b) using bigger unit(c) rounding to zero(d) heating instrument

Correct Answer: keeping eye perpendicular to scale

Solution: Correct eye position avoids parallax.

Exam Tip: Eye must be normal to mark.

NEET MCQ 11

Question: For Z = A / B, percentage error in Z equals

(a) %A + %B(b) %A - %B(c) %A × %B(d) %A / %B

Correct Answer: %A + %B

Solution: For division relative errors add.

Exam Tip: Denominator error also adds.

NEET MCQ 12

Question: If length has 1% error, area L² has error

(a) 2%(b) 1%(c) 0.5%(d) 4%

Correct Answer: 2%

Solution: Area proportional to L squared.

Exam Tip: Power rule.

NEET MCQ 13

Question: If V = lbh and each dimension has 1% error, error in volume is

(a) 3%(b) 1%(c) 2%(d) 0%

Correct Answer: 3%

Solution: 1% + 1% + 1% = 3%.

Exam Tip: Products add percentage errors.

NEET MCQ 14

Question: Error in density ρ = m / V is

(a) %m + %V(b) %m - %V(c) %V - %m(d) zero

Correct Answer: %m + %V

Solution: Division adds relative errors.

Exam Tip: Use magnitude only.

NEET MCQ 15

Question: Mean absolute error has unit

(a) same as measured quantity(b) no unit(c) percent only(d) second always

Correct Answer: same as measured quantity

Solution: It is an absolute uncertainty.

Exam Tip: Relative error is unitless.

NEET MCQ 16

Question: Least count error is related to

(a) instrument resolution(b) human memory(c) temperature only(d) graph slope only

Correct Answer: instrument resolution

Solution: Smallest measurable division limits precision.

Exam Tip: Better LC means finer reading.

NEET MCQ 17

Question: If a = 20 ± 0.2, percentage error is

(a) 1%(b) 10%(c) 0.1%(d) 20%

Correct Answer: 1%

Solution: (0.2/20) ×100 = 1%.

Exam Tip: Divide uncertainty by value.

NEET MCQ 18

Question: If radius error is 2%, error in area πr² is

(a) 4%(b) 2%(c) 1%(d) 8%

Correct Answer: 4%

Solution: Area depends on r squared.

Exam Tip: Constants have no error.

NEET MCQ 19

Question: If radius error is 1%, error in volume r³ is

(a) 3%(b) 1%(c) 2%(d) 6%

Correct Answer: 3%

Solution: Cube power triples error.

Exam Tip: Exponent is key.

NEET MCQ 20

Question: In Z = A²B / C³, percentage error is

(a) 2%A + %B + 3%C(b) 2%A - %B - 3%C(c) %A + %B + %C(d) 6% always

Correct Answer: 2%A + %B + 3%C

Solution: All relative errors add with powers.

Exam Tip: Ignore signs in denominator.

NEET MCQ 21

Question: A measurement is 50 with absolute uncertainty 0.5. Percentage error is

(a) 1%(b) 10%(c) 0.1%(d) 0%

Correct Answer: 1%

Solution: (0.5 / 50) × 100 = 1%.

Exam Tip: Calculate percentage error directly.

NEET MCQ 22

Question: A measurement is 100 with absolute uncertainty 2. Percentage error is

(a) 2%(b) 20%(c) 0.2%(d) 0%

Correct Answer: 2%

Solution: (2 / 100) × 100 = 2%.

Exam Tip: Calculate percentage error directly.

NEET MCQ 23

Question: A measurement is 25 with absolute uncertainty 0.25. Percentage error is

(a) 1%(b) 10%(c) 0.1%(d) 0%

Correct Answer: 1%

Solution: (0.25 / 25) × 100 = 1%.

Exam Tip: Calculate percentage error directly.

NEET MCQ 24

Question: A measurement is 80 with absolute uncertainty 1.6. Percentage error is

(a) 2%(b) 20%(c) 0.2%(d) 0%

Correct Answer: 2%

Solution: (1.6 / 80) × 100 = 2%.

Exam Tip: Calculate percentage error directly.

NEET MCQ 25

Question: A measurement is 40 with absolute uncertainty 0.8. Percentage error is

(a) 2%(b) 20%(c) 0.2%(d) 0%

Correct Answer: 2%

Solution: (0.8 / 40) × 100 = 2%.

Exam Tip: Calculate percentage error directly.

NEET MCQ 26

Question: A measurement is 200 with absolute uncertainty 5. Percentage error is

(a) 2.5%(b) 25%(c) 0.25%(d) 0%

Correct Answer: 2.5%

Solution: (5 / 200) × 100 = 2.5%.

Exam Tip: Calculate percentage error directly.

NEET MCQ 27

Question: A measurement is 60 with absolute uncertainty 0.6. Percentage error is

(a) 1%(b) 10%(c) 0.1%(d) 0%

Correct Answer: 1%

Solution: (0.6 / 60) × 100 = 1%.

Exam Tip: Calculate percentage error directly.

NEET MCQ 28

Question: A measurement is 30 with absolute uncertainty 0.9. Percentage error is

(a) 3%(b) 30%(c) 0.3%(d) 0%

Correct Answer: 3%

Solution: (0.9 / 30) × 100 = 3%.

Exam Tip: Calculate percentage error directly.

NEET MCQ 29

Question: A measurement is 75 with absolute uncertainty 1.5. Percentage error is

(a) 2%(b) 20%(c) 0.2%(d) 0%

Correct Answer: 2%

Solution: (1.5 / 75) × 100 = 2%.

Exam Tip: Calculate percentage error directly.

NEET MCQ 30

Question: A measurement is 120 with absolute uncertainty 3. Percentage error is

(a) 2.5%(b) 25%(c) 0.25%(d) 0%

Correct Answer: 2.5%

Solution: (3 / 120) × 100 = 2.5%.

Exam Tip: Calculate percentage error directly.

NEET MCQ 31

Question: If Y = X² and percentage error in X is 1%, percentage error in Y is

(a) 2%(b) 1%(c) 0.5%(d) 3%

Correct Answer: 2%

Solution: Power rule gives 2 × 1% = 2%.

Exam Tip: Power multiplies percentage error.

NEET MCQ 32

Question: If Y = X³ and percentage error in X is 2%, percentage error in Y is

(a) 6%(b) 2%(c) 0.666667%(d) 5%

Correct Answer: 6%

Solution: Power rule gives 3 × 2% = 6%.

Exam Tip: Power multiplies percentage error.

NEET MCQ 33

Question: If Y = X⁴ and percentage error in X is 0.5%, percentage error in Y is

(a) 2%(b) 0.5%(c) 0.125%(d) 4.5%

Correct Answer: 2%

Solution: Power rule gives 4 × 0.5% = 2%.

Exam Tip: Power multiplies percentage error.

NEET MCQ 34

Question: If Y = X² and percentage error in X is 1.5%, percentage error in Y is

(a) 3%(b) 1.5%(c) 0.75%(d) 3.5%

Correct Answer: 3%

Solution: Power rule gives 2 × 1.5% = 3%.

Exam Tip: Power multiplies percentage error.

NEET MCQ 35

Question: If Y = X² and percentage error in X is 2.5%, percentage error in Y is

(a) 5%(b) 2.5%(c) 1.25%(d) 4.5%

Correct Answer: 5%

Solution: Power rule gives 2 × 2.5% = 5%.

Exam Tip: Power multiplies percentage error.

NEET MCQ 36

Question: If Y = X³ and percentage error in X is 3%, percentage error in Y is

(a) 9%(b) 3%(c) 1%(d) 6%

Correct Answer: 9%

Solution: Power rule gives 3 × 3% = 9%.

Exam Tip: Power multiplies percentage error.

NEET MCQ 37

Question: If Y = X⁴ and percentage error in X is 0.25%, percentage error in Y is

(a) 1%(b) 0.25%(c) 0.0625%(d) 4.25%

Correct Answer: 1%

Solution: Power rule gives 4 × 0.25% = 1%.

Exam Tip: Power multiplies percentage error.

NEET MCQ 38

Question: If Y = X² and percentage error in X is 4%, percentage error in Y is

(a) 8%(b) 4%(c) 2%(d) 6%

Correct Answer: 8%

Solution: Power rule gives 2 × 4% = 8%.

Exam Tip: Power multiplies percentage error.

NEET MCQ 39

Question: If Y = X⁵ and percentage error in X is 1%, percentage error in Y is

(a) 5%(b) 1%(c) 0.2%(d) 6%

Correct Answer: 5%

Solution: Power rule gives 5 × 1% = 5%.

Exam Tip: Power multiplies percentage error.

NEET MCQ 40

Question: If Y = X⁴ and percentage error in X is 2%, percentage error in Y is

(a) 8%(b) 2%(c) 0.5%(d) 6%

Correct Answer: 8%

Solution: Power rule gives 4 × 2% = 8%.

Exam Tip: Power multiplies percentage error.

NEET MCQ 41

Question: For Z = AB, percentage errors in A and B are 1% and 2%. Error in Z is

(a) 3%(b) 1%(c) 2%(d) 0.5%

Correct Answer: 3%

Solution: For product, percentage error = 1% + 2% = 3%.

Exam Tip: Add relative errors for product.

NEET MCQ 42

Question: For Z = AB, percentage errors in A and B are 2% and 2%. Error in Z is

(a) 4%(b) 0%(c) 4%(d) 1%

Correct Answer: 4%

Solution: For product, percentage error = 2% + 2% = 4%.

Exam Tip: Add relative errors for product.

NEET MCQ 43

Question: For Z = AB, percentage errors in A and B are 1.5% and 0.5%. Error in Z is

(a) 2%(b) 1%(c) 0.75%(d) 3%

Correct Answer: 2%

Solution: For product, percentage error = 1.5% + 0.5% = 2%.

Exam Tip: Add relative errors for product.

NEET MCQ 44

Question: For Z = AB, percentage errors in A and B are 3% and 1%. Error in Z is

(a) 4%(b) 2%(c) 3%(d) 3%

Correct Answer: 4%

Solution: For product, percentage error = 3% + 1% = 4%.

Exam Tip: Add relative errors for product.

NEET MCQ 45

Question: For Z = AB, percentage errors in A and B are 0.5% and 0.5%. Error in Z is

(a) 1%(b) 0%(c) 0.25%(d) 1%

Correct Answer: 1%

Solution: For product, percentage error = 0.5% + 0.5% = 1%.

Exam Tip: Add relative errors for product.

NEET MCQ 46

Question: For Z = AB, percentage errors in A and B are 2.5% and 1.5%. Error in Z is

(a) 4%(b) 1%(c) 3.75%(d) 1.66667%

Correct Answer: 4%

Solution: For product, percentage error = 2.5% + 1.5% = 4%.

Exam Tip: Add relative errors for product.

NEET MCQ 47

Question: For Z = AB, percentage errors in A and B are 4% and 2%. Error in Z is

(a) 6%(b) 2%(c) 8%(d) 2%

Correct Answer: 6%

Solution: For product, percentage error = 4% + 2% = 6%.

Exam Tip: Add relative errors for product.

NEET MCQ 48

Question: For Z = AB, percentage errors in A and B are 1% and 3%. Error in Z is

(a) 4%(b) 2%(c) 3%(d) 0.333333%

Correct Answer: 4%

Solution: For product, percentage error = 1% + 3% = 4%.

Exam Tip: Add relative errors for product.

NEET MCQ 49

Question: For Z = AB, percentage errors in A and B are 3% and 3%. Error in Z is

(a) 6%(b) 0%(c) 9%(d) 1%

Correct Answer: 6%

Solution: For product, percentage error = 3% + 3% = 6%.

Exam Tip: Add relative errors for product.

NEET MCQ 50

Question: For Z = AB, percentage errors in A and B are 0.75% and 1.25%. Error in Z is

(a) 2%(b) 0.5%(c) 0.9375%(d) 0.6%

Correct Answer: 2%

Solution: For product, percentage error = 0.75% + 1.25% = 2%.

Exam Tip: Add relative errors for product.

NEET MCQ 51

Question: For Z = A - B with ΔA = 5 and ΔB = 2, absolute error in Z is

(a) 7(b) 3(c) 10(d) 2.5

Correct Answer: 7

Solution: For subtraction absolute errors add: 5 + 2 = 7.

Exam Tip: Errors add even in subtraction.

NEET MCQ 52

Question: For Z = A - B with ΔA = 10 and ΔB = 1, absolute error in Z is

(a) 11(b) 9(c) 10(d) 10

Correct Answer: 11

Solution: For subtraction absolute errors add: 10 + 1 = 11.

Exam Tip: Errors add even in subtraction.

NEET MCQ 53

Question: For Z = A - B with ΔA = 8 and ΔB = 3, absolute error in Z is

(a) 11(b) 5(c) 24(d) 2.66667

Correct Answer: 11

Solution: For subtraction absolute errors add: 8 + 3 = 11.

Exam Tip: Errors add even in subtraction.

NEET MCQ 54

Question: For Z = A - B with ΔA = 6 and ΔB = 0.5, absolute error in Z is

(a) 6.5(b) 5.5(c) 3(d) 12

Correct Answer: 6.5

Solution: For subtraction absolute errors add: 6 + 0.5 = 6.5.

Exam Tip: Errors add even in subtraction.

NEET MCQ 55

Question: For Z = A - B with ΔA = 12 and ΔB = 2, absolute error in Z is

(a) 14(b) 10(c) 24(d) 6

Correct Answer: 14

Solution: For subtraction absolute errors add: 12 + 2 = 14.

Exam Tip: Errors add even in subtraction.

NEET MCQ 56

Question: For Z = A - B with ΔA = 20 and ΔB = 4, absolute error in Z is

(a) 24(b) 16(c) 80(d) 5

Correct Answer: 24

Solution: For subtraction absolute errors add: 20 + 4 = 24.

Exam Tip: Errors add even in subtraction.

NEET MCQ 57

Question: For Z = A - B with ΔA = 7 and ΔB = 1, absolute error in Z is

(a) 8(b) 6(c) 7(d) 7

Correct Answer: 8

Solution: For subtraction absolute errors add: 7 + 1 = 8.

Exam Tip: Errors add even in subtraction.

NEET MCQ 58

Question: For Z = A - B with ΔA = 15 and ΔB = 5, absolute error in Z is

(a) 20(b) 10(c) 75(d) 3

Correct Answer: 20

Solution: For subtraction absolute errors add: 15 + 5 = 20.

Exam Tip: Errors add even in subtraction.

NEET MCQ 59

Question: For Z = A - B with ΔA = 9 and ΔB = 2, absolute error in Z is

(a) 11(b) 7(c) 18(d) 4.5

Correct Answer: 11

Solution: For subtraction absolute errors add: 9 + 2 = 11.

Exam Tip: Errors add even in subtraction.

NEET MCQ 60

Question: For Z = A - B with ΔA = 11 and ΔB = 3, absolute error in Z is

(a) 14(b) 8(c) 33(d) 3.66667

Correct Answer: 14

Solution: For subtraction absolute errors add: 11 + 3 = 14.

Exam Tip: Errors add even in subtraction.

13. JEE Main Question Bank

JEE Main Style 1

Question: If x = 10.0 ± 0.1 and y = 5.0 ± 0.2, find percentage error in xy.

Given: x error =1%, y error=4%

Formula: % error in xy = %x + %y

Substitution: 1% + 4%

Calculation: 5%

Final Answer: 5%

Exam Tip: Convert absolute errors to percentages first.

JEE Main Style 2

Question: The time period T = 2π√(l/g). If error in l is 2%, find error in T assuming g exact.

Given: T proportional to l^1/2

Formula: %T = (1/2)%l

Substitution: (1/2) × 2%

Calculation: 1%

Final Answer: 1%

Exam Tip: Square root means power 1/2.

JEE Main Style 3

Question: For resistance R = V / I, errors in V and I are 1% and 2%. Find error in R.

Given: %V=1%, %I=2%

Formula: %R = %V + %I

Substitution: 1 + 2

Calculation: 3%

Final Answer: 3%

Exam Tip: Division adds percentage errors.

JEE Main Style 4

Question: A graph slope is y/x. If y has 3% uncertainty and x has 2%, find uncertainty in slope.

Given: slope = y/x

Formula: %slope = %y + %x

Substitution: 3 + 2

Calculation: 5%

Final Answer: 5%

Exam Tip: Slope uncertainty follows division rule.

JEE Main Style 5

Question: If kinetic energy K = mv²/2, errors in m and v are 1% and 2%, find error in K.

Given: constant 1/2 exact

Formula: %K = %m + 2%v

Substitution: 1 + 4

Calculation: 5%

Final Answer: 5%

Exam Tip: Constants do not contribute.

14. JEE Advanced Conceptual Questions

JEE Advanced Conceptual 1

Question: Why are errors in denominator added, not subtracted, in percentage error propagation?

Given: Maximum possible uncertainty is required.

Formula: Use logarithmic differentiation and take magnitudes.

Substitution: For Z=A/B, ΔZ/Z = ΔA/A + ΔB/B

Calculation: Both uncertainties can increase final spread.

Final Answer: They are added in magnitude.

Exam Tip: Exam asks maximum error.

JEE Advanced Conceptual 2

Question: A quantity is constant in a formula. Does it contribute to percentage error?

Given: Constants like 2, π and 1/2 are exact.

Formula: Exact constants have zero uncertainty.

Substitution: Δπ/π = 0

Calculation: Only measured variables contribute.

Final Answer: No contribution.

Exam Tip: Do not add error of exact constants.

JEE Advanced Conceptual 3

Question: How does uncertainty in graph slope change when both x and y axes have uncertainties?

Given: slope = Δy/Δx

Formula: Treat slope like division.

Substitution: % slope = %y interval + %x interval

Calculation: Both axis uncertainties affect slope.

Final Answer: Add relative uncertainties of intervals.

Exam Tip: Use extreme slopes for graph method.

JEE Advanced Conceptual 4

Question: Can a reading be precise but inaccurate? Explain.

Given: Repeated values can be close but shifted.

Formula: Precision concerns repeatability; accuracy concerns true value.

Substitution: Zero error gives close shifted readings.

Calculation: Systematic error causes this situation.

Final Answer: Yes, precise but inaccurate.

Exam Tip: Separate accuracy from precision.

15. CBSE School Exam Questions

1 Mark

Question: Define absolute error.

Answer: Magnitude of difference between measured value and true or mean value.

2 Mark

Question: Differentiate systematic and random errors.

Answer: Systematic error has fixed cause and direction; random error fluctuates unpredictably and is reduced by repeated readings.

3 Mark

Question: Derive percentage error from relative error.

Answer: Relative error = Δa/a. Multiplying by 100 gives percentage error = (Δa/a) × 100.

5 Mark

Question: Explain error propagation rules with examples.

Answer: For addition/subtraction, absolute errors add. For multiplication/division, relative errors add. For powers, percentage error is multiplied by the power.

16. IB Physics Questions

IB 1

Question: Repeated readings reduce which type of uncertainty?

Solution: Random uncertainty. Mean reading is more reliable.

IB 2

Question: What are error bars?

Solution: Graphical representation of uncertainty in plotted data.

IB 3

Question: How is percentage uncertainty found?

Solution: Absolute uncertainty divided by measured value multiplied by 100.

17. IGCSE Questions

IGCSE 1

Question: Why should the eye be placed perpendicular to a scale?

Solution: To avoid parallax error.

IGCSE 2

Question: Why repeat a timing experiment?

Solution: To reduce random error and find a reliable average.

IGCSE 3

Question: What is precision?

Solution: Closeness of repeated readings to each other.

18. A-Level Questions

A-Level 1

Question: A slope is found from a graph. How can uncertainty be estimated?

Solution: Draw maximum and minimum acceptable slopes using error bars.

A-Level 2

Question: For P = IV, find percentage uncertainty in P.

Solution: %P = %I + %V.

A-Level 3

Question: Why does a systematic error not vanish by averaging?

Solution: All readings are shifted in the same direction.

19. Assertion Reason Questions

Options: (a) Both A and R are true and R explains A. (b) Both are true but R does not explain A. (c) A true, R false. (d) A false, R true.

Assertion Reason 1

Assertion: Systematic error affects accuracy.

Reason: It shifts all readings in one direction.

Answer: (a)

Explanation: Both are true and reason explains assertion.

Assertion Reason 2

Assertion: Random error is reduced by repeated readings.

Reason: Averaging reduces fluctuations.

Answer: (a)

Explanation: Both are true and reason explains assertion.

Assertion Reason 3

Assertion: Least count error is a personal error.

Reason: Least count depends on instrument resolution.

Answer: (d)

Explanation: Assertion false, reason true.

Assertion Reason 4

Assertion: Relative error has no unit.

Reason: It is ratio of two quantities with same unit.

Answer: (a)

Explanation: Units cancel.

Assertion Reason 5

Assertion: Percentage error equals relative error multiplied by 100.

Reason: Percentage means per hundred.

Answer: (a)

Explanation: Correct relation.

Assertion Reason 6

Assertion: In subtraction, absolute errors are subtracted.

Reason: Maximum uncertainty requires adding magnitudes.

Answer: (d)

Explanation: Assertion false, reason true.

Assertion Reason 7

Assertion: In a product, relative errors are added.

Reason: Logarithmic differentiation gives fractional uncertainties.

Answer: (a)

Explanation: Correct explanation.

Assertion Reason 8

Assertion: A zero error is random error.

Reason: Zero error remains fixed unless corrected.

Answer: (d)

Explanation: Zero error is systematic.

Assertion Reason 9

Assertion: Parallax error is observational.

Reason: It occurs due to wrong eye position.

Answer: (a)

Explanation: Both true.

Assertion Reason 10

Assertion: Constants such as π add percentage error.

Reason: Exact constants have zero uncertainty.

Answer: (d)

Explanation: Assertion false, reason true.

Assertion Reason 11

Assertion: Systematic error affects accuracy.

Reason: It shifts all readings in one direction.

Answer: (a)

Explanation: Both are true and reason explains assertion.

Assertion Reason 12

Assertion: Random error is reduced by repeated readings.

Reason: Averaging reduces fluctuations.

Answer: (a)

Explanation: Both are true and reason explains assertion.

Assertion Reason 13

Assertion: Least count error is a personal error.

Reason: Least count depends on instrument resolution.

Answer: (d)

Explanation: Assertion false, reason true.

Assertion Reason 14

Assertion: Relative error has no unit.

Reason: It is ratio of two quantities with same unit.

Answer: (a)

Explanation: Units cancel.

Assertion Reason 15

Assertion: Percentage error equals relative error multiplied by 100.

Reason: Percentage means per hundred.

Answer: (a)

Explanation: Correct relation.

Assertion Reason 16

Assertion: In subtraction, absolute errors are subtracted.

Reason: Maximum uncertainty requires adding magnitudes.

Answer: (d)

Explanation: Assertion false, reason true.

Assertion Reason 17

Assertion: In a product, relative errors are added.

Reason: Logarithmic differentiation gives fractional uncertainties.

Answer: (a)

Explanation: Correct explanation.

Assertion Reason 18

Assertion: A zero error is random error.

Reason: Zero error remains fixed unless corrected.

Answer: (d)

Explanation: Zero error is systematic.

Assertion Reason 19

Assertion: Parallax error is observational.

Reason: It occurs due to wrong eye position.

Answer: (a)

Explanation: Both true.

Assertion Reason 20

Assertion: Constants such as π add percentage error.

Reason: Exact constants have zero uncertainty.

Answer: (d)

Explanation: Assertion false, reason true.

Assertion Reason 21

Assertion: Systematic error affects accuracy.

Reason: It shifts all readings in one direction.

Answer: (a)

Explanation: Both are true and reason explains assertion.

Assertion Reason 22

Assertion: Random error is reduced by repeated readings.

Reason: Averaging reduces fluctuations.

Answer: (a)

Explanation: Both are true and reason explains assertion.

Assertion Reason 23

Assertion: Least count error is a personal error.

Reason: Least count depends on instrument resolution.

Answer: (d)

Explanation: Assertion false, reason true.

Assertion Reason 24

Assertion: Relative error has no unit.

Reason: It is ratio of two quantities with same unit.

Answer: (a)

Explanation: Units cancel.

Assertion Reason 25

Assertion: Percentage error equals relative error multiplied by 100.

Reason: Percentage means per hundred.

Answer: (a)

Explanation: Correct relation.

Assertion Reason 26

Assertion: In subtraction, absolute errors are subtracted.

Reason: Maximum uncertainty requires adding magnitudes.

Answer: (d)

Explanation: Assertion false, reason true.

Assertion Reason 27

Assertion: In a product, relative errors are added.

Reason: Logarithmic differentiation gives fractional uncertainties.

Answer: (a)

Explanation: Correct explanation.

Assertion Reason 28

Assertion: A zero error is random error.

Reason: Zero error remains fixed unless corrected.

Answer: (d)

Explanation: Zero error is systematic.

Assertion Reason 29

Assertion: Parallax error is observational.

Reason: It occurs due to wrong eye position.

Answer: (a)

Explanation: Both true.

Assertion Reason 30

Assertion: Constants such as π add percentage error.

Reason: Exact constants have zero uncertainty.

Answer: (d)

Explanation: Assertion false, reason true.

20. Case Study Questions

Case Study: Repeated Measurements

A student measures the time period of a pendulum five times and obtains slightly different values because of reaction time and small disturbances.

Questions: Why are readings repeated?; Which error is reduced?; What value should be reported?; Why is mean useful?

Answers: To improve reliability; random error; mean value with uncertainty; it balances fluctuations.

Explanation: This case connects experimental uncertainty with correct error handling.

Case Study: Vernier Calipers Zero Error

A vernier calipers shows +0.02 cm when jaws are closed. The observed reading of a cylinder diameter is 2.36 cm.

Questions: What type of error is this?; What correction is applied?; What is corrected reading?; Is averaging enough?

Answers: Instrumental systematic; subtract +0.02 cm; 2.34 cm; no, zero correction is required.

Explanation: This case connects experimental uncertainty with correct error handling.

Case Study: Screw Gauge Error

A screw gauge has least count 0.01 mm and zero error -0.03 mm. A wire reading is 0.58 mm.

Questions: Name the error; Find correction; Correct reading; Why is screw gauge used?

Answers: Zero error; +0.03 mm; 0.61 mm; for small diameters.

Explanation: This case connects experimental uncertainty with correct error handling.

Case Study: Percentage Error in Derived Quantity

A quantity Q = A²B / C is measured. Percentage errors in A, B and C are 1%, 2% and 3%.

Questions: Which rule applies?; Find % error in Q; Does denominator error subtract?; Final answer?

Answers: Power rule; 2(1)+2+3 = 7%; no, it adds; 7%.

Explanation: This case connects experimental uncertainty with correct error handling.

Case Study: Error Bar and Graph

A student plots data points with vertical error bars and finds several possible straight lines passing within the bars.

Questions: What do bars show?; Why multiple slopes?; How to estimate slope uncertainty?; What is best line?

Answers: Uncertainty; data has limits; use maximum and minimum slopes; line passing best through points.

Explanation: This case connects experimental uncertainty with correct error handling.

21. PYQ and Exam-style Questions

Authentic year is mentioned only where certain; otherwise the item is clearly marked Exam-style Question.

CBSE Exam-style Question

Question: Why is percentage error more useful than absolute error when comparing two measurements?

Solution: It compares uncertainty relative to the size of the quantity, so different measurements can be compared fairly.

Final Answer: It compares uncertainty relative to the size of the quantity, so different measurements can be compared fairly.

Exam Tip: Use the correct uncertainty rule before calculation.

NEET Exam-style Question

Question: If radius has 2% error, find percentage error in area of circle.

Solution: Area = πr², so error = 2 × 2% = 4%.

Final Answer: Area = πr², so error = 2 × 2% = 4%.

Exam Tip: Use the correct uncertainty rule before calculation.

JEE Main Exam-style Question

Question: For y = a²b³/c, percentage errors are 1%, 2%, 3%. Find error in y.

Solution: 2(1) + 3(2) + 3 = 11%.

Final Answer: 2(1) + 3(2) + 3 = 11%.

Exam Tip: Use the correct uncertainty rule before calculation.

JEE Advanced Exam-style Question

Question: Explain why signs are ignored while adding errors in derived quantities.

Solution: Maximum possible uncertainty is estimated, so magnitudes of fractional errors are added.

Final Answer: Maximum possible uncertainty is estimated, so magnitudes of fractional errors are added.

Exam Tip: Use the correct uncertainty rule before calculation.

IB Physics Exam-style Question

Question: How are error bars used in graph analysis?

Solution: They show uncertainty range and help estimate maximum and minimum possible slopes.

Final Answer: They show uncertainty range and help estimate maximum and minimum possible slopes.

Exam Tip: Use the correct uncertainty rule before calculation.

IGCSE Exam-style Question

Question: State one way to reduce random error in a stopwatch experiment.

Solution: Repeat the timing several times and calculate mean.

Final Answer: Repeat the timing several times and calculate mean.

Exam Tip: Use the correct uncertainty rule before calculation.

A-Level Exam-style Question

Question: For P = Fv, percentage uncertainties in F and v are 4% and 3%. Find uncertainty in P.

Solution: %P = 4% + 3% = 7%.

Final Answer: %P = 4% + 3% = 7%.

Exam Tip: Use the correct uncertainty rule before calculation.

22. Quick Revision Notes

One Page Revision Sheet

Error = measured value - true value
Absolute error has unit
Relative error has no unit
Percentage error = relative error × 100

Error Formula Sheet

Δa = |a - a_mean|
a = a_mean ± Δa_mean
Relative error = Δa / a
% error = (Δa/a) × 100

Propagation Summary

Add/subtract: absolute errors add
Multiply/divide: relative errors add
Power: multiply percentage error by power
Constants have zero error

Most important NEET/JEE tricks: denominator errors are also added; powers multiply percentage error; convert absolute error to percentage before using product or quotient rules; never invent precision beyond uncertainty.

Need help in Physics Numericals?

Contact Kumar Sir for one-to-one online Physics classes.

Phone: +91-9958461445Email: kumarsirphysics@gmail.com Website: https://kumarphysicsclasses.com WhatsApp Kumar Sir