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Errors in Products, Quotients and Powers for JEE: 31 solved questions

Real JEE paper questions on errors in products, quotients and powers, part of units and measurements. Each opens with the options, the correct answer and a step-by-step solution. Papers run from 2012 to 2026. No sign-in needed to read them.

What this topic asks

• Percentage error in a derived quantity — 16 questions
• Error in a power — 15 questions

All 31 questions with solutions

• The density ρ of a uniform cylinder is determined by measuring its mass m, length l and diameter d. The measu… JEE Main 6th April 1st Shift 2026
• The percentage error in the calculated volume of a sphere, if there is 2% error in its diameter measurement,… JEE Main 6th April 2nd Shift 2026
• A quantity Q is formulated as X⁻²Y^3/2Z^-2/5. X, Y and Z are independent parameters which have fractional err… JEE Main 8th April 2nd Shift 2025
• The maximum percentage error in the measurement of density of a wire is [Given, mass of wire =(0.60±0.003) g,… JEE Main 22nd Jan 2nd Shift 2025
• The energy of system is given as E(t)=α³e^-β t, where t is the time and β=0.3 s⁻¹. The errors in the measurem… JEE Main 23rd Jan 2nd Shift 2025
• The resistance R=V/I where V=(200±5) V and I=(20±0.2) A, the percentage error in the measurement of R is JEE Main 29th Jan 1st Shift 2024
• A physical quantity Q is found to depend on quantities a, b, c by the relation Q=(a⁴b³)/(c²). The percentage… JEE Main 29th Jan 2nd Shift 2024
• If the percentage errors in measuring the length and the diameter of a wire are 0.1% each. The percentage err… JEE Main 31st Jan 1st Shift 2024
• A cylindrical wire of mass (0.4±0.01) g has length (8±0.04) cm and radius (6±0.03) mm. The maximum error in i… JEE Main 8th April 1st Shift 2023
• A physical quantity P is given as, P=(a²b³)/(c√d). The percentage errors in the measurement of a, b, c and d… JEE Main 10th April 1st Shift 2023
• A body of mass (5±0.5) kg is moving with a velocity of (20±0.4) m/s. Its kinetic energy will be JEE Main 13th April 1st Shift 2023
• The maximum error in the measurement of resistance, current and time for which current flows in an electrical… JEE Main 25th July 2nd Shift 2022
• A torque meter is calibrated to reference standards of mass, length and time each with 5% accuracy. After cal… JEE Main 27th July 1st Shift 2022
• If Z=(A²B³)/(C⁴), then the relative error in Z will be JEE Main 25th June 1st Shift 2022
• A silver wire has a mass (0.6±0.006) g, radius (0.5±0.005) mm and length (4±0.04) cm. The maximum percentage… JEE Main 27th June 1st Shift 2022
• A physical quantity y is represented by the formula y=m²r⁻⁴g^xl^-3/2. If the percentage errors found in y, m,… JEE Main 27th July 2nd Shift 2021
• A physical quantity z depends on four observables a, b, c and d, as z=(a²b^2/3)/(√c d³). The percentages of e… JEE Main 5th Sept 1st Shift 2020
• In the density measurement of a cube, the mass and edge length are measured as (10.00±0.10) kg and (0.10±0.01… JEE Main 9th April 1st Shift 2019
• The density of a material in the shape of a cube is determined by measuring three sides of the cube and its m… JEE Main 2018
• The relative error in the determination of the surface area of a sphere is α. Then the relative error in the… JEE Main Online 2018
• The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5% respectively in measurement of a… JEE Main Online 2018
• The relative uncertainty in the period of a satellite orbiting around the earth is 10⁻². If the relative unce… JEE Main Online 2018
• A physical quantity P is described by the relation P=a^1/2 b² c³ d⁻⁴. If the relative errors in the measureme… JEE Main Online 2017
• Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference appl… AIEEE 2012
• The amount of heat produced in an electric circuit depends upon the current (I), resistance (R) and time (t).… AIEEE Online 2012
• A physical quantity C is related to four other quantities p, q, r and s as follows C=(pq²)/(r³√s). The percen… JEE Main 3rd April 2nd Shift 2025
• A physical quantity Q is related to four observables a, b, c, d as follows: Q=(ab⁴)/(cd) where, a=(60±3) Pa;… JEE Main 29th Jan 2nd Shift 2025
• For z=a²x³y^1/2, where a is a constant. If percentage error in measurement of x and y are 4% and 12%, respect… JEE Main 25th June 2nd Shift 2022
• The resistance R=V/I, where V=(50±2) V and I=(20±0.2) A. The percentage error in R is x%. The value of x to t… JEE Main 16th March 1st Shift 2021
• The radius of a sphere is measured to be (7.50±0.85) cm. Suppose the percentage error in its volume is x. The… JEE Main 18th March 2nd Shift 2021
• The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error i… JEE Main 6th Sept 1st Shift 2020