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JEE Units and Dimensions PYQs with Solutions

364 previous year questions from Units and Dimensions (JEE Main & Advanced Physics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

364 questionsPhysics2002–2026Answers + solutions

About Units and Dimensions PYQs

Units and Dimensions has 364 previous year questions in the Quantrex Academy JEE Main & Advanced Physics bank. The 220 questions in this list come from JEE Main (148), NTA Abhyas JEE Main (54) and JEE Advanced (18), spanning 2002 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2026: 16
  • 2025: 26
  • 2024: 17
  • 2023: 20
  • 2022: 16
  • 2021: 18
  • 2020: 64
  • 2019: 10
  • 2018: 3
  • 2017: 2
  • 2016: 3
  • 2015: 5

Units and Dimensions questions with solutions

1

In a new system of units, the units of mass, length, time and current are 5 kg, 5 m, 5 s and 5 A, respectively. If μ_0 and ε_0 are the permeability and permittivity of free space

JEE Advanced 2026 Solution View → 2

A new unit (α) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of α units if light takes 6 min. 40

JEE Main 2026 Solution View → 3

Consider the equation H = (x^p ε^q E^r)/(t^s) , where H= magnetic field; E= electric field, ε= permittivity, x= distance, t= time. The values of p, q, r and s respectively are:

JEE Main 2026 Solution View → 4

The percentage error in the calculated volume of a sphere, if there is 2\% error in its diameter measurement, is __________.

JEE Main 2026 Solution View → 5

Match List - I with List - II. List - I List - II A. Boltzmann constant I. [M^ -1 L^3T^ -2 ] B. Stefan's constant II. [ML^2T^ -1 ] C. Planck's constant III. [ML^2T^ -2 K^ -1 ] D.

JEE Main 2026 Solution View → 6

The potential energy of a particle changes with distance x from a fixed origin as V = A x x + B , where A and B are constant with appropriate dimensions. The dimensions of AB are

JEE Main 2026 Solution View → 7

Match List-I with List-II. List-I List-II A. Meter (L) I. (hc)/(G) B. Second (S) II. (Gh)/(c^5) C. Kilogram (M) III. (K^2L^2c^3)/(Gh) D. Kelvin (K) IV. (Gh)/(c^3) where h

JEE Main 2026 Solution View → 8

L , C and R represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula ML^2 T^ -4 A^ -2 corresponds to __________.

JEE Main 2026 Solution View → 9

Dimensions of universal gravitational constant (G) in terms of Planck's constant (h) , distance (L) , mass (M) and time (T) are _______.

JEE Main 2026 Solution View → 10

Match List - I with List - II. \( List - I List - II A. Coefficient of viscosity I. [M L^ -1 T^ -1 ] B. Surface tension II. [M L^ 0 T^ -2 ] C. Pressure III. [M L^ -1 T^ -2 ] D.

JEE Main 2026 Solution View → 11

Match the List-I with List-II \( List-I List-II A. Magnetic induction I. M L T^ -2 A^ -2 B. Magnetic flux II. M L^ 2 T^ -2 A^ -2 C. Magnetic permeability III. M L^ 0 T^ -2 A^ -1

JEE Main 2026 Solution View → 12

A ball of radius r and density ρ dropped through a viscous liquid of density σ and viscosity η attains its terminal velocity at time t , given by t=A ρ^ a r^ b η^ c σ^ d , where A

JEE Main 2026 Solution View → 13

If ε, E and t represent the free space permittivity, electric field and time respectively, then the unit of (ε E)/(t) will be :

JEE Main 2026 Solution View → 14

Match the List-I with List-II \( List-I List-II A. Spring constant I. M L^ 2 T^ -2 K^ -1 B. Thermal conductivity II. M L^ 0 T^ -2 C. Boltzmann constant III. M L^ 2 T^ -3 A^ -2 D.

JEE Main 2026 Solution View → 15

Keeping the significant figures in view, the sum of the physical quantities 52.01 ~m, 153.2 ~m and 0.123 m is :

JEE Main 2026 Solution View → 16

Consider a modified Bernoulli equation. (P+ A B t^ 2 )+ρ g(h+B t)+(1)/(2) ρ V^ 2 = constant If t has the dimension of time then the dimensions of A and B are \_\_\_\_ , \_\_\_\_

JEE Main 2026 Solution View → 17

A temperature difference can generate e.m.f. in some materials. Let S be the e.m.f. produced per unit temperature difference between the ends of a wire, σ the electrical

JEE Advanced 2025 Solution View → 18

The dimension of (μ_0)/(ε_0) is equal to that of : ( μ_0= Vacuum permeability and ε_0= Vacuum permittivity)

JEE Main 2025 Solution View → 19

Match List-I with List-II. List-I List-II (A) Mass density (I) [ ML^2 T^ -3 ] (B) Impulse (II) [ MLT^ -1 ] (C) Power (III) [ ML^2 T⁰] (D) Moment of inertia (IV) [ ML^ -3 T⁰]

JEE Main 2025 Solution View → 20

If ε_0 denotes the permittivity of free space and Φ_ E is the flux of the electric field through the area bounded by the closed surface, then dimension of (ε_0 ~d φ_ E dt ) are

JEE Main 2025 Solution View → 21

Given below are two statements : Statement (I) : The dimensions of Planck's constant and angular momentum are same. Statement (II) : In Bohr's model electron revolve around the

JEE Main 2025 Solution View → 22

In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of [M^P L^ ∘ T^ R A^ S ] . The value of P and Q

JEE Main 2025 Solution View → 23

In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of M^ P L^ Q T^ R A^ S , where value of ' Q ' and ' R ' are

JEE Main 2025 Solution View → 24

Match the LIST-I with LIST-II Choose the correct answer from the options given below :

JEE Main 2025 Solution View → 25

A person measures mass of 3 different particles as 435.42 ~g, 226.3 ~g and 0.125 g. According to the rules for arithmetic operations with significant figures, the additions of the

JEE Main 2025 Solution View → 26

Match the List-I with List-II List-I List-II A. Gravitational constant I. [ LT^ -2 ] B. Gravitational potential energy II. [ L^2 T^ -2 ] C. Gravitational potential III. [ ML^2 T^

JEE Main 2025 Solution View → 27

If μ_0 and ε_0 are the permeability and permittivity of free space, respectively, then the dimension of ((1)/(μ_0 ε_0)) is :

JEE Main 2025 Solution View → 28

Match List-I with List-II. List-I List-II (A) Heat capacity of body (I) J kg^ -1 (B) Specific heat capacity of body (II) JK^ -1 (C) Latent heat (III) J kg^ -1 K^ -1 (D) Thermal

JEE Main 2025 Solution View → 29

Given a charge q , current I and permeability of vacuum μ_0 . Which of the following quantity has the dimension of momentum?

JEE Main 2025 Solution View → 30

The equation for real gas is given by (P+ a V^2 )(V-b)=RT , where P, V, T and R are the pressure, volume, temperature and gas constant, respectively. The dimension of ab^ -2 is

JEE Main 2025 Solution View → 31

Match List-I with List-II. List-I List-II (A) Coefficient of viscosity (I) [ ML^0 T^ -3 ] (B) Intensity of wave (II)[ ML^ -2 T^ -2 ] (C) Pressure gradient (III) [M^ -1 LT^2] (D)

JEE Main 2025 Solution View → 32

Match List - I with List - II. Choose the correct answer from the options given below :

JEE Main 2025 Solution View → 33

Match List - I with List - II. Choose the correct answer from the options given below :

JEE Main 2025 Solution View → 34

The expression given below shows the variation of velocity \((v)\) with time (t), \(v=At^2+ Bt C+t \). The dimension of ABC is :

JEE Main 2025 Solution View → 35

The pair of physical quantities not having same dimensions is :

JEE Main 2025 Solution View → 36

Match List - I with List - II.

JEE Main 2025 Solution View → 37

In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of [M^a L^b T^c] . If b=-3 , the value of c

JEE Main 2025 Solution View → 38

Match List - I with List - II. array llll & - I & & - II (A) & Permeability of free space & (I) [M L^2 T^ -2 ] (B) & Magnetic field & (II) [M T^ -2 A^ -1 ] (C) & Magnetic moment &

JEE Main 2025 Solution View → 39

The position of a particle moving on x -axis is given by x(t)=A t+B ^2 t+C t^2+D , where t is time. The dimension of (A B C)/(D) is

JEE Main 2025 Solution View → 40

The electric flux is φ=α σ+β λ where λ and σ are linear and surface charge density, respectively. ((α)/(β)) represents

JEE Main 2025 Solution View → 41

Which one of the following is the correct dimensional formula for the capacitance in F ? M, L, T and C stand for unit of mass, length, time and charge,

JEE Main 2025 Solution View → 42

If B is magnetic field and μ_0 is permeability of free space, then the dimensions of (B / μ_0) is

JEE Main 2025 Solution View → 43

A dimensionless quantity is constructed in terms of electronic charge e , permittivity of free space ε_0 , Planck's constant h and speed of light c . If the dimensionless quantity

JEE Advanced 2024 Solution View → 44

The de-Broglie wavelength associated with a particle of mass m and energy E is h / 2 m E . The dimensional formula for Planck's constant is :

JEE Main 2024 Solution View → 45

The dimensional formula of latent heat is :

JEE Main 2024 Solution View → 46

If ε_0 is the permittivity of free space and E is the electric field, then ε_0 E^2 has the dimensions :

JEE Main 2024 Solution View → 47

Given below are two statements : Statement (I) : Dimensions of specific heat is [L^2 ~T^ -2 ~K^ -1 ] . Statement (II) : Dimensions of gas constant is [M L^2 ~T^ -1 ~K^ -1 ] . In

JEE Main 2024 Solution View → 48

Match List I with List II -I -II A. Torque I. [M^1 L^1 T^ -2 A^ -2 ] B. Magnetic field II. [L^2 A^1] C. Magnetic moment III. [M^1 T^ -2 A^ -1 ] D. Permeability of free space IV.

JEE Main 2024 Solution View → 49

What is the dimensional formula of a b^ -1 in the equation (P+ a V^2 )(V-b)=RT , where letters have their usual meaning.

JEE Main 2024 Solution View → 50

If G be the gravitational constant and u be the energy density then which of the following quantity have the dimensions as that of the uG :

JEE Main 2024 Solution View → 51

Applying the principle of homogeneity of dimensions, determine which one is correct, where T is time period, G is gravitational constant, M is mass, r is radius of orbit.

JEE Main 2024 Solution View → 52

The equation of stationary wave is : y=2 a ((2 π n t)/(λ)) ((2 π x)/(λ)) . Which of the following is NOT correct :

JEE Main 2024 Solution View → 53

The dimensional formula of angular impulse is :

JEE Main 2024 Solution View → 54

Consider two physical quantities A and B related to each other as E = B - x ^ 2 At where E, x and t have dimensions of energy, length and time respectively. The dimension of AB is

JEE Main 2024 Solution View → 55

A force is represented by F = a x ^ 2 + bt(1)/(2) , where x = distance and t = time. The dimensions of b ^ 2 a are :

JEE Main 2024 Solution View → 56

If mass is written as m = k c ^ P G ^ - 1 / 2 h ^ 1 / 2 , then the value of P will be : (Constants have their usual meaning with k a dimensionless constant)

JEE Main 2024 Solution View → 57

Match List-I with List-II. cases & -I & & -II A. & Coefficient of viscosity & I. & [ ML ^ 2 T ^ - 2 ] B. & Surface Tension & II. & [ ML ^ 2 T ^ - 1 ] C. & Angular momentum & III.

JEE Main 2024 Solution View → 58

The equation of state of a real gas is given by (P + a V ^ 2 ) ( V - b ) = RT , where P, V and T are pressure, volume and temperature respectively and R is the universal gas

JEE Main 2024 Solution View → 59

Given below are two statements: Statement (I) : Planck's constant and angular momentum have the same dimensions. Statement (II) : Linear momentum and moment of force have the same

JEE Main 2024 Solution View → 60

Young’s modulus of elasticity Y is expressed in terms of three derived quantities, namely, the gravitational constant G , Planck’s constant h and the speed of light c

JEE Advanced 2023 Solution View → 61

The speed of a wave produced in water is given by ν = λ ^ a g ^ b ρ ^ c . Where λ, g and ρ are wavelength of wave, acceleration due to gravity and density of water respectively.

JEE Main 2023 Solution View → 62

In the equation [X + a Y ^ 2 ] [ Y - b ] = RT, X is pressure, Y is volume, R is universal gas constant and T is temperature. The physical quantity equivalent to the ratio (a)/(b)

JEE Main 2023 Solution View → 63

Match List I with List II List-I List-II A Spring constant I [ T ^ – 1 ] B Angular speed II [ M T ^ – 2 ] C Angular momentum III [ M L ^ 2 ] D Moment of Inertia IV [ M L ^ 2 T ^ –

JEE Main 2023 Solution View → 64

If force ( F ) , velocity ( V ) and time ( T ) are considered as fundamental physical quantity, then dimensional formula of density will be :

JEE Main 2023 Solution View → 65

Given below are two statements : Statement I : Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances. Statement II : Au < Parsec

JEE Main 2023 Solution View → 66

Match List I with List II List I List II A. Torque I. M L ^ - 2 T ^ - 2 B. Stress II. M L ^ 2 T ^ - 2 C. Pressure gradient III. M L ^ - 1 T ^ - 1 D. Coefficient of viscosity IV. M

JEE Main 2023 Solution View → 67

Dimension of 1 μ _ 0 ε _ 0 should be equal to

JEE Main 2023 Solution View → 68

If the velocity of light c , universal gravitational constant G and planck&#39;s constant h are chosen as fundamental quantities. The dimensions of mass in the new system is:

JEE Main 2023 Solution View → 69

(P + a V ^ 2 )(V - b) = RT represents the equation of state of some gases. Where P is the pressure, V is the volume, T is the temperature and a, b, R are the constants. The

JEE Main 2023 Solution View → 70

Match List I with List II List I List II A Angular momentum I [ ML ^ 2 T ^ - 2 ] B Torque II [ ML ^ - 2 T ^ - 2 ] C Stress III [ ML ^ 2 T ^ - 1 ] D Pressure gradient IV [ ML ^ - 1

JEE Main 2023 Solution View → 71

If R, X _ L and X _ C represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:

JEE Main 2023 Solution View → 72

Match List I with List II List I List II A Torque I kg m ^ – 1 s ^ – 2 B Energy density II kgm s ^ – 1 C Pressure gradient III kg m ^ – 2 s ^ – 2 D Impulse IV kg m ^ 2 s ^ – 2

JEE Main 2023 Solution View → 73

Electric field in a certain region is given by → E = ( A x ^ 2 ^ i + B y ^ 3 ^ j ) . The SI unit of A and B are :

JEE Main 2023 Solution View → 74

The equation of a circle is given by x ^ 2 + y ^ 2 = a ^ 2 , where a is the radius. If the equation is modified to change the origin other than ( 0, 0 ) , then find out the

JEE Main 2023 Solution View → 75

Match List I with List II : List-I (Physical Quantity) List-II (Dimensional Formula) A Pressure gradient I [ M ^ 0 L ^ 2 T ^ - 2 ] B Energy density II [ M ^ 1 L ^ - 1 T ^ - 2 ] C

JEE Main 2023 Solution View → 76

Match List I with List II List List II A Young&#39;s Modulus ( Y ) I [ ML ^ – 1 T ^ – 1 ] B Co-efficient of Viscosity ( η ) II [ ML ^ 2 T ^ – 1 ] C Planck&#39;s Constant ( h ) III

JEE Main 2023 Solution View → 77

Match List I with List II List - I List - II A Surface tension I. kg m ^ - 1 s ^ - 1 B Pressure II. kgm s ^ - 1 C Viscosity III. kg m ^ - 1 s ^ - 2 D Impulse IV. kg s ^ - 2 Choose

JEE Main 2023 Solution View → 78

The frequency (ν) of an oscillating liquid drop may depend upon radius (r) of the drop, density (ρ) of liquid and the surface tension (s) of the liquid as: ν = r ^ a ρ ^ b s ^ c .

JEE Main 2023 Solution View → 79

Match List I with List II List I List II A . Planck&#39;s constant (h) I . [ M ^ 1 L ^ 2 T ^ - 2 ] B . Stopping potential ( V _ s ) II . [ M ^ 1 L ^ 1 T ^ - 1 ] C . Work function

JEE Main 2023 Solution View → 80

In a particular system of units, a physical quantity can be expressed in terms of the electric charge e , electron mass m _ e . Planck&#39;s constant h , and Coulomb&#39;s

JEE Advanced 2022 Solution View → 81

Match List I with List II. List I List II (A) Torque (I) Nms ^ - 1 (B) Stress (II) Jkg ^ - 1 (C) Latent Heat (III) Nm (D) Power (IV) Nm ^ - 2 Choose the correct answer from the

JEE Main 2022 Solution View → 82

Given below are two statements: One is labelled as Assertion (A) and other is labelled as Reason (R) Assertion (A) : Time period of oscillation of a liquid drop depends on surface

JEE Main 2022 Solution View → 83

Consider the efficiency of Carnot&#39;s engine is given by η = (αβ)/(sinθ) _ e ( )/(kT) , where α and β are constants. If T is temperature, k is Boltzman constant, θ is angular

JEE Main 2022 Solution View → 84

The dimensions of ( B ^ 2 μ _ 0 ) will be (if μ _ 0 : permeability of free space and B: magnetic field)

JEE Main 2022 Solution View → 85

An expression of energy density is given by u = (α)/(β)sin(( )/(kt)) , where α, β are constants, x is displacement, k is Boltzmann constant and t is the temperature. The

JEE Main 2022 Solution View → 86

If momentum [P] , area [A] and time [T] are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is

JEE Main 2022 Solution View → 87

Which of the following physical quantities have the same dimensions?

JEE Main 2022 Solution View → 88

In van dar Wall equation [P + a V ^ 2 ][V - b] = RT; P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants (a)/(b) is dimensionally

JEE Main 2022 Solution View → 89

Assertion A: Product of Pressure (P) and time (t) has the same dimension as that of coefficient of viscosity. Reason: Coefficient of viscosity = (Force)/(Velocitygradient)

JEE Main 2022 Solution View → 90

The SI unit of a physical quantity is Pascal ‐ sec . The dimensional formula of this quantity will be

JEE Main 2022 Solution View → 91

If L, C and R are the self inductance, capacitance and resistance respectively, which of the following does not have the dimension of time?

JEE Main 2022 Solution View → 92

The dimension of mutual inductance is

JEE Main 2022 Solution View → 93

An expression for a dimensionless quantity P is given by P = (α)/(β) _ e ((kT)/( )) ; where α and β are constants, x is distance; k is Boltzmann constant and T is the temperature.

JEE Main 2022 Solution View → 94

Identify the pair of physical quantities that have same dimensions:

JEE Main 2022 Solution View → 95

Identify the pair of physical quantities which have different dimensions:

JEE Main 2022 Solution View → 96

A physical quantity → S is defined as → S = ( → E × → B ) μ _ 0 . where → E is electric field, → B is magnetic field and μ _ 0 is the permeability of free space. The dimensions of

JEE Advanced 2021 Solution View → 97

If velocity [V] time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will be :

JEE Main 2021 Solution View → 98

Which of the following equations is dimensionally incorrect? Where t = time, h = height, s = surface tension, θ = angle, ρ = density , a, r = radius, g = the acceleration due to

JEE Main 2021 Solution View → 99

Match List - I with List - II. List - I List - II a Torque i MLT ^ - 1 b Impulse ii MT ^ - 2 c Tension iii ML ^ 2 T ^ - 2 d Surface Tension iv MLT ^ - 2 Choose the most

JEE Main 2021 Solution View → 100

Match List- (I) with List- (II) . List- (I) List- (II) a R _ H (Rydberg constant) i kg m ^ - 1 s ^ - 1 b h (Planck&#39;s constant) ii kg m ^ 2 s ^ - 1 c μ _ B (Magnetic field

JEE Main 2021 Solution View → 101

If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density:

JEE Main 2021 Solution View → 102

If E and H represents the intensity of electric field and magnetizing field respectively, then the unit of (E)/(H) will be:

JEE Main 2021 Solution View → 103

Which of the following is not a dimensionless quantity?

JEE Main 2021 Solution View → 104

Match List - I with List - II : List - I List - II a Magnetic induction i ML ^ 2 T ^ - 2 A ^ - 1 b Magnetic flux ii M ^ 0 L ^ - 1 A c Magnetic permeability iii MT ^ - 2 A ^ - 1 d

JEE Main 2021 Solution View → 105

If E, L, M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of P in the formula P = E L ^ 2 M ^ - 5 G ^

JEE Main 2021 Solution View → 106

Match List I with List II. List-I List-II a Capacitance, C i M ^ 1 L ^ 1 T ^ - 3 A ^ - 1 b Permittivity of free space, ε _ 0 ii M ^ - 1 L ^ - 3 T ^ 4 A ^ 2 c Permeability of free

JEE Main 2021 Solution View → 107

The force is given in terms of time t and displacement x by the equation F = AcosBx + CsinDt The dimensional formula of (AD)/(B) is:

JEE Main 2021 Solution View → 108

If time (t), velocity (v), and angular momentum (l) are taken as the fundamental units. Then the dimension of mass ( m ) in terms of t, v and l is:

JEE Main 2021 Solution View → 109

If C and V represent capacity and voltage respectively then what are the dimensions of λ where C / V = λ ?

JEE Main 2021 Solution View → 110

In a typical combustion engine the workdone by a gas molecule is given by W = α ^ 2 - β x ^ 2 kT , where x is the displacement, k is the Boltzmann constant and T is the

JEE Main 2021 Solution View → 111

If e is the electronic charge, c is the speed of light in free space and h is Planck&#39;s constant, the quantity 1 4π ε _ 0 |e| ^ 2 hc has dimensions of :

JEE Main 2021 Solution View → 112

Match List - I with List - II : List - I List - II (a) h (Planck&#39;s constant) (i) [ MLT ^ - 1 ] (b) E (kinetic energy) (ii) [ ML ^ 2 T ^ - 1 ] (c) V (electric potential) (iii)

JEE Main 2021 Solution View → 113

The work done by a gas molecule in an isolated system is given by, W = α β ^ 2 e ^ - x ^ 2 , where x is the displacement, k is the Boltzmann constant and T is the temperature. α

JEE Main 2021 Solution View → 114

Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of

JEE Advanced 2020 Solution View → 115

The quantities x = 1 μ _ 0 ∈ _ 0 , y = (E)/(B) and z = (l)/(CR) are defined where C-capacitance, R-Resistance, ℓ - length, E-Electric field, B-magnetic field and ∈ 0, μ0, - free

JEE Main 2020 Solution View → 116

A quantity x is given by ( 1F v ^ 2 / W L ^ 4 ) in terms of moment of inertia I , force F , velocity v , work W and length L . The dimensional formula for x is same as that of :

JEE Main 2020 Solution View → 117

Dimensional formula for thermal conductivity is (here K denotes the temperature):

JEE Main 2020 Solution View → 118

Amount of solar energy received on the earth&#39;s surface per unit area per unit time is defined a solar constant. Dimension of solar constant is:

JEE Main 2020 Solution View → 119

If momentum ( P ) , area ( A ) and time ( T ) are taken to be the fundamental quantities then the dimensional formula for energy is :

JEE Main 2020 Solution View → 120

If speed V , area A and force F are chosen as fundamental units, then the dimension of Young&#39;s modulus will be :

JEE Main 2020 Solution View →
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