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Units and Dimensions — JEE Main & Advanced Physics PYQs

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

364 questionsPhysicsSolutions on every page
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 ₀ and ₀ are the permeability and permittivity of free space, resp

JEE Advanced 2026 Solution View → 2

A new unit ( ) 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 units if light takes 6 min. 40 s

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

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

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

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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 _

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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 (Planck's constant), G (g

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 _______.

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Match List - I with List - II. ( array llll & List - I & & List - II A. & Coefficient of viscosity & I. & [M L⁻¹ T⁻¹] B. & Surface tension & II. & [M L⁰ T⁻²] C. & Pressure & III. &

JEE Main 2026 Solution View → 11

Match the List-I with List-II ( array ||c|l||c|l|| & List-I & & List-II A. & Magnetic induction & I. & M ,L ,T⁻² ,A⁻² B. & Magnetic flux & II. & M ,L² ,T⁻² ,A⁻² C. & Magnetic perme

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

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

JEE Main 2026 Solution View → 14

Match the List-I with List-II ( array ||c|l||c||l|| & List-I & & List-II A. & Spring constant & I. & M L² T⁻² K⁻¹ B. & Thermal conductivity & II. & M L⁰ T⁻² C. & Boltzmann constant

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 :

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Consider a modified Bernoulli equation. ( P + A B t² )+ g(h+B t)+ 1 2 V²= constant If t has the dimension of time then the dimensions of A and B are _ _ _ _ , _ _ _ _ respectively.

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, the electrical conductivity

JEE Advanced 2025 Solution View → 18

The dimension of ₀ ₀ is equal to that of : ( ₀= Vacuum permeability and ₀= Vacuum permittivity)

JEE Main 2025 Solution View → 19

Match List-I with List-II. array |l|l|l|l| & List-I & & List-II (A) & Mass density & (I) & [ ML ^2 ~T ⁻³ ] (B) & Impulse & (II) & [ MLT ⁻¹ ] (C) & Power & (III) & [ ML ^2 ~T ^0 ] (

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If ₀ denotes the permittivity of free space and _ E is the flux of the electric field through the area bounded by the closed surface, then dimension of ( ₀ ~d _ E dt ) are that of

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 nuc

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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 are

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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

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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 array |l|l|l|l| & List-I & & List-II A. & Gravitational constant & I. & [ LT ⁻² ] B. & array l Gravitational potential energy array & II. & [ L ^2 ~T

JEE Main 2025 Solution View → 27

If ₀ and ₀ are the permeability and permittivity of free space, respectively, then the dimension of ( 1 ₀ ₀ ) is :

JEE Main 2025 Solution View → 28

Match List-I with List-II. array ll 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 (

JEE Main 2025 Solution View → 29

Given a charge q , current I and permeability of vacuum 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

JEE Main 2025 Solution View → 31

Match List-I with List-II. array ll 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) [

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 & List - I & & List - II (A) & Permeability of free space & (I) [ M ~L ^2 ~T ⁻² ] (B) & Magnetic field & (II) [ M ~T ⁻² ~A ⁻¹ ] (C) & Magn

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 = + where and are linear and surface charge density, respectively. ( ) 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 ₀ is permeability of free space, then the dimensions of (B / ₀ ) is

JEE Main 2025 Solution View → 43

A dimensionless quantity is constructed in terms of electronic charge e , permittivity of free space ₀ , Planck's constant h and speed of light c . If the dimensionless quantity is

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 ₀ is the permittivity of free space and E is the electric field, then 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 th

JEE Main 2024 Solution View → 48

Match List I with List-II array |l|l|r|l| List-I & List-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 ]

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 n t ) ( 2 x ) . 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 A t where E , x and t have dimensions of energy, length and time respectively. The dimension of A B is

JEE Main 2024 Solution View → 55

A force is represented by F = a x 2 + b t 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. List-I List-II A. Coefficient of viscosity I. ML 2 T - 2 B. Surface Tension II. ML 2 T - 1 C. Angular momentum III. ML - 1 T - 1 D. Rotational kinetic en

JEE Main 2024 Solution View → 58

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

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 wa

JEE Main 2023 Solution View → 62

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

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 (P

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 L - 1 T - 2

JEE Main 2023 Solution View → 67

Dimension of 1 &#956; 0 &#949; 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 = R T 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 physical q

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 T - 2 Choose the correct ans

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 &#8211; 1 s &#8211; 2 B Energy density II kg m s &#8211; 1 C Pressure gradient III kg m &#8211; 2 s &#8211; 2 D Impulse IV

JEE Main 2023 Solution View → 73

Electric field in a certain region is given by E &#8594; = 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 correct dime

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 Electric Field III M

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Match List I with List II List List II A Young&#39;s Modulus ( Y ) I [ ML &#8211; 1 T &#8211; 1 ] B Co-efficient of Viscosity ( &#951; ) II [ ML 2 T &#8211; 1 ] C Planck&#39;s Cons

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. kg m s - 1 C Viscosity III. kg m - 1 s - 2 D Impulse IV. kg s - 2 Choose the correct

JEE Main 2023 Solution View → 78

The frequency &#957; of an oscillating liquid drop may depend upon radius r of the drop, density &#961; of liquid and the surface tension s of the liquid as: &#957; = r a &#961; b

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 &#981; III . M 1 L 2 T - 1 D

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 constant k

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 options g

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

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Consider the efficiency of Carnot&#39;s engine is given by &#951; = &#945; &#946; sin &#952; log e &#946; x k T , where &#945; and &#946; are constants. If T is temperature, k is B

JEE Main 2022 Solution View → 84

The dimensions of B 2 &#956; 0 will be (if &#956; 0 : permeability of free space and B : magnetic field)

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An expression of energy density is given by u = &#945; &#946; sin &#945; x k t , where &#945; , &#946; are constants, x is displacement, k is Boltzmann constant and t is the temper

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 = R T ; P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants a b is dimensionally equal to

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 Velocity gradient

JEE Main 2022 Solution View → 90

The SI unit of a physical quantity is Pascal &#8208; 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

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An expression for a dimensionless quantity P is given by P = &#945; &#946; log e k T &#946; x ; where &#945; and &#946; are constants, x is distance; k is Boltzmann constant and T

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 &#8594; is defined as S &#8594; = E &#8594; &#215; B &#8594; &#956; 0 . where E &#8594; is electric field, B &#8594; is magnetic field and &#956; 0 is the per

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, &#952; = angle, &#961; = density , a , r = radius, g = the acceleratio

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 appropriate answer fr

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 &#956; B (Magnetic field energy density) iii

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 Magnetization i

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 - 2 a

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, &#949; 0 ii M - 1 L - 3 T 4 A 2 c Permeability of free space, &#956;

JEE Main 2021 Solution View → 107

The force is given in terms of time t and displacement x by the equation F = A cos B x + C sin D t The dimensional formula of A D 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 &#955; where C / V = &#955; ?

JEE Main 2021 Solution View → 110

In a typical combustion engine the workdone by a gas molecule is given by W = &#945; 2 &#946; e - &#946; x 2 k T , where x is the displacement, k is the Boltzmann constant and T is

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 4 &#960; &#949; 0 e 2 h c 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 ML 2 T - 2 d P (linear mome

JEE Main 2021 Solution View → 113

The work done by a gas molecule in an isolated system is given by, W = &#945; &#946; 2 e - x 2 &#945; k T , where x is the displacement, k is the Boltzmann constant and T is the te

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 differen

JEE Advanced 2020 Solution View → 115

The quantities x = 1 &#956; 0 &#8712; 0 , y = E B and z = l C R are defined where C-capacitance, R-Resistance, &#8467; - length, E-Electric field, B-magnetic field and &#8712; 0 ,

JEE Main 2020 Solution View → 116

A quantity x is given by ( 1 F 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 :

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