Q.42 Physics ⭐ 360° Option Elimination Active

NEET 2025 Physics Question 42 Solution

Topic: Units and Measurements · Official NTA Booklet Code 45

Question

A physical quantity P is related to four observations a, b, c and d as follows: P = a³b²/(c√d). The percentage errors of measurement in a, b, c and d are 1%, 3%, 2%, and 4% respectively. The percentage error in the quantity P is

✓

Verified Against NTA Final Answer Key

Option (3) : 13%

📚 Units and Measurements Easy

📋 Given Parameters & Problem Setup

Functional Relation P = a³ b² / (c √d) = a³ b² c⁻¹ d⁻¹/²

Percentage Error in a (Δa/a × 100) 1%

Percentage Error in b (Δb/b × 100) 3%

Percentage Error in c (Δc/c × 100) 2%

Percentage Error in d (Δd/d × 100) 4%

⚡

The 30-Second Exam Hall Shortcut: ⚡ Power Multiplier Error Rule

⏱️ Save ~25 seconds

ΔP/P = 3(%a) + 2(%b) + 1(%c) + (1/2)(%d) = 3(1%) + 2(3%) + 1(2%) + 0.5(4%) = 3 + 6 + 2 + 2 = 13%!

1 In error analysis, errors always add in the worst-case scenario: fractional error equals sum of powers times fractional errors.

2 Multiply percentage error of each variable by the absolute value of its exponent:

3 Contribution of a³: 3 × 1% = 3%.

4 Contribution of b²: 2 × 3% = 6%.

5 Contribution of c⁻¹: 1 × 2% = 2%.

6 Contribution of √d (d^(1/2)): (1/2) × 4% = 2%.

7 Sum all contributions: 3% + 6% + 2% + 2% = 13%.

8 Match Option (3) in under 10 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Propagation of Fractional Errors (NCERT Physics · Units and Measurements: ΔX/X = Σ a_i (ΔA_i/A_i)).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Formula for Maximum Fractional Error in a Power Product

For a physical quantity defined by P = a^p b^q c^r d^s, logarithmic differentiation gives the maximum fractional error:

\frac{\Delta P}{P} = |p| \frac{\Delta a}{a} + |q| \frac{\Delta b}{b} + |r| \frac{\Delta c}{c} + |s| \frac{\Delta d}{d}

• Here p = 3, q = 2, r = -1, s = -1/2.
• The negative signs become positive because errors compound in the worst-case direction.

Step 2

Substitute Numerical Percentage Errors

Multiply both sides by 100 to convert to percentage errors:

\left(\frac{\Delta P}{P} \times 100\right) = 3 \left(\frac{\Delta a}{a}\%\right) + 2 \left(\frac{\Delta b}{b}\%\right) + 1 \left(\frac{\Delta c}{c}\%\right) + \frac{1}{2} \left(\frac{\Delta d}{d}\%\right)

• Substitute given values: a = 1%, b = 3%, c = 2%, d = 4%.

Step 3

Calculate Total Percentage Error

Compute the algebraic sum:

\%\text{ error in } P = 3(1\%) + 2(3\%) + 1(2\%) + \frac{1}{2}(4\%) = 3\% + 6\% + 2\% + 2\% = 13\%

• Matches Option (3) exactly.

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 A

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Omits contribution from c or miscalculates powers.

⚠️

Student Fallacy (Why candidates pick this trap): Subtracting errors instead of adding.

2 B

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Forgetting to multiply by exponents.

⚠️

Student Fallacy (Why candidates pick this trap): Subtracting denominator errors: (3+6) - (2+2) = 5% or similar.

3 C

✓ 100% Correct

Verdict & Scientific Reason:

100% correct. 3(1) + 2(3) + 1(2) + 0.5(4) = 3 + 6 + 2 + 2 = 13%.

💡

Why this is airtight: None; standard error propagation.

4 D

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Using power 1 for d instead of 1/2 (giving 4% instead of 2% ⟹ 15%).

⚠️

Student Fallacy (Why candidates pick this trap): Forgetting that √d has power 1/2, multiplying by 4% directly.

⚠️

NTA Trap Alert: Treating √d as Having Exponent 1

A very common slip is taking the error of √d as 4% instead of (1/2) × 4% = 2%. Doing so yields 3 + 6 + 2 + 4 = 15% (Option 4)!

🛡️ How to avoid the -1 mark: Always rewrite roots as fractional powers: √d = d^(1/2) ⟹ multiply error by 1/2.

📖

Core NEET Syllabus Standard

NEET Physics Core Syllabus · Units and Measurements Standard Benchmark

Core Scientific Principle Tested:

"Relative error in a quantity raised to the power n is n times the relative error in the individual quantity."

Syllabus Focus: Propagation of Errors in Powers of Quantities

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Powers multiply: 3(1) + 2(3) + 1(2) + 0.5(4) = 3 + 6 + 2 + 2 = 13%!

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NEET 2025 Physics Question 42 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Power Multiplier Error Rule

Step-by-Step Rigorous Workflow & Mathematical Proof

Formula for Maximum Fractional Error in a Power Product

Substitute Numerical Percentage Errors

Calculate Total Percentage Error

360° Option Elimination Engine Key Feature

NTA Trap Alert: Treating √d as Having Exponent 1

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Units and Measurements

Vernier Calliper Negative Zero Error & Full Marks Bonus Audit

Dimensional Analysis of Combined Thermal Radiation Constants (sigma_s * k_B^-1 * b)

Vernier Constant of Vernier Calipers with Variable Divisions

Dimensionless Physical Quantities Matching Solid Angle

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