Practice portal › JEE › Units and Measurements

Dimensions of Constants in Physical Relations for JEE: 20 solved questions

Real JEE paper questions on dimensions of constants in physical relations, part of units and measurements. Each opens with the options, the correct answer and a step-by-step solution. Papers run from 2019 to 2026. No sign-in needed to read them.

What this topic asks

• Constants in a given relation — 20 questions

All 20 questions with solutions

• The potential energy of a particle changes with distance x from a fixed origin as V=(A√x)/(x+B), where A and… JEE Main 6th April 1st Shift 2026
• Consider a modified Bernoulli equation. (P+A/(Bt²))+ρ g(h+Bt)+1/2ρ V²= constant. If t has the dimension of ti… JEE Main 21st Jan 1st Shift 2026
• The position of a particle moving on x-axis is given by x(t)=A sin t+B cos²t+Ct²+D, where t is time. The dime… JEE Main 23rd Jan 1st Shift 2025
• The expression given below shows the variation of velocity (v) with time (t), v=At²+(Bt)/(C+t). The dimension… JEE Main 29th Jan 1st Shift 2025
• What is the dimensional formula of ab⁻¹ in the equation (P+a/(V²))(V-b)=RT, where letters have their usual me… JEE Main 5th April 2nd Shift 2024
• The equation of state of a real gas is given by (P+a/(V²))(V-b)=RT, where P, V and T are pressure, volume and… JEE Main 27th Jan 2nd Shift 2024
• A force is represented by F=ax²+bt^1/2 where x= distance and t= time. The dimensions of (b²)/a are JEE Main 31st Jan 1st Shift 2024
• Consider two physical quantities A and B related to each other as E=(B-x²)/(At) where E, x and t have dimensi… JEE Main 31st Jan 2nd Shift 2024
• In the equation [X+a/(Y²)][Y-b]=RT, X is pressure, Y is volume, R is universal gas constant and T is temperat… JEE Main 13th April 2nd Shift 2023
• The equation of a circle is given by x²+y²=a², where a is the radius. If the equation is modified to change t… JEE Main 29th Jan 2nd Shift 2023
• An expression of energy density is given by u=α/β sin ((α x)/(kt)), where α, β are constants, x is displaceme… JEE Main 27th July 2nd Shift 2022
• Consider the efficiency of engine is given by η=(αβ)/(sin θ)logₑ(β x)/(kT), where α and β are constants. If T… JEE Main 28th July 2nd Shift 2022
• An expression for a dimensionless quantity P is given by P=α/β logₑ((kt)/(β x)); where α and β are constants,… JEE Main 26th June 1st Shift 2022
• In van der Waal equation [P+a/(V²)][V-b]=RT; P is pressure, V is volume, R is universal gas constant and T is… JEE Main 29th June 1st Shift 2022
• The entropy of any system is given by S=α²β ln [(μ kR)/(Jβ²)+3] where α and β are the constants. μ, J, K and… JEE Main 20th July 1st Shift 2021
• The force is given in terms of time t and displacement x by the equation F=A cos Bx+C sin Dt. The dimensional… JEE Main 25th July 2nd Shift 2021
• The workdone by a gas molecule in an isolated system is given by W=αβ²e^-(x²)/(α kT), where x is the displace… JEE Main 24th Feb 2nd Shift 2021
• In a typical combustion engine the work done by a gas molecule is given by W=α²β e^(-β x²)/(kT), where x is t… JEE Main 26th Feb 1st Shift 2021
• In the formula X=5YZ², X and Z have dimensions of capacitance and magnetic field, respectively. What are the… JEE Main 10th April 2nd Shift 2019
• The force of interaction between two atoms is given by F=αβ exp (-(x²)/(α kT)); where x is the distance, k is… JEE Main 11th Jan 1st Shift 2019