How many questions from Units and Measurements appear in JEE?

Units and Measurements has appeared in 149 of the last 186 JEE Main and JEE Advanced papers — about 80% of them — contributing 193 questions in total across those papers.

Is Units and Measurements an important chapter for JEE?

Judged by how often it is actually tested, it appears in roughly 80% of papers. Chapters above about 50% are effectively guaranteed to show up every session, so they repay thorough preparation; lower-frequency chapters are better treated as targeted revision.

Where do these Units and Measurements questions come from?

Every question is from an official JEE Main or JEE Advanced paper, transcribed from the original paper and tagged to this chapter. Answers follow the official answer key.

Units and Measurements JEE Previous Year Questions with Answers

Q1·PhysicsNumericalJEE Advanced 2026

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

\mu_{0}

and

\epsilon_{0}

are the permeability and permittivity of free space, respectively, then in this new system of units, the magnitude of one SI unit of

\sqrt{\mu_{0}/\epsilon_{0}}

, is:

Q2·PhysicsNumericalJEE Advanced 2026

In a single slit diffraction experiment, a slit of width

(0.016 \pm 0.002)

mm is used to measure the wavelength of a monochromatic light source. In the diffraction pattern, the angular distance between the central maximum and first minimum is measured to be

(2° \pm 40')

. The value of the fractional error in the measurement of wavelength is: [Given:

\sin(2°) = 0.035

]

Q3·PhysicsSingle correctJEE Main 2026

A new unit

(\alpha)

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

\alpha

units if light takes 6 min. 40 s to cover this distance?

(A) $200\,\alpha$
(B) $400\,\alpha$
(C) $300\,\alpha$
(D) $500\,\alpha$

Q4·PhysicsSingle correctJEE Main 2026

Consider the equation

H = \dfrac{x^p \epsilon^q E^r}{t^s}

, where

H

= magnetic field;

E

= electric field,

\epsilon

= permittivity,

x

= distance,

t

= time. The values of

p, q, r

and

s

respectively are:

(A) $1, 1, 1, 1$
(B) $-1, 1, 2, 1$
(C) $1, -1, -2, 1$
(D) $-1, -2, -2, 1$

Q5·PhysicsSingle correctJEE Main 2026

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

List - I	List - II
A.Boltzmann constant	I. $[M^{-1}L^{3}T^{-2}]$
B.Stefan's constant	II. $[ML^{2}T^{-1}]$
C.Planck's constant	III. $[ML^{2}T^{-2}K^{-1}]$
D.Gravitational constant	IV. $[ML^{0}T^{-3}K^{-4}]$

(A)A-I, B-II, C-III, D-IV
(B)A-IV, B-III, C-II, D-I
(C)A-III, B-IV, C-II, D-I
(D)A-II, B-I, C-IV, D-III

Q6·PhysicsSingle correctJEE Main 2026

The potential energy of a particle changes with distance x from a fixed origin as

V = \frac{A\sqrt{x}}{x + B}

, where A and B are constant with appropriate dimensions. The dimensions of AB are ________.

(A) $[M^{1}L^{5/2}T^{-2}]$
(B) $[M^{3/2}L^{5/2}T^{-2}]$
(C) $[M^{1}L^{2}T^{-2}]$
(D) $[M^{1}L^{7/2}T^{-2}]$

Q7·PhysicsSingle correctJEE Main 2026

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

(A)1
(B)2
(C)6
(D)8

Q8·PhysicsSingle correctJEE Main 2026

The density ρ of a uniform cylinder is determined by measuring its mass m, length l and diameter d. The measured values of m, l and d are 97.42 ± 0.02 g, 8.35 ± 0.05 mm and 20.20 ± 0.02 mm, respectively. Calculated percentage fractional error in ρ is ________.

(A)0.63%
(B)0.82%
(C)0.72%
(D)0.25%

Q9·PhysicsSingle correctJEE Main 2026

L

,

C

and

R

represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula

ML^2T^{-4}A^{-2}

corresponds to __________.

(A) $\frac{R}{\sqrt{LC}}$
(B) $\frac{R}{LC}$
(C) $\frac{C}{\sqrt{LR}}$
(D) $\frac{1}{R}\sqrt{\frac{L}{C}}$

Q10·PhysicsSingle correctJEE Main 2026

Match List-I with List-II. where h (Planck's constant), G (gravitational constant) and c (speed of light in vacuum) as fundamental units. Choose the correct answer from the options given below :

List-I	List-II
A.Meter (L)	I. $\sqrt{\dfrac{hc}{G}}$
B.Second (S)	II. $\sqrt{\dfrac{Gh}{c^{5}}}$
C.Kilogram (M)	III. $\sqrt{\dfrac{K^{2}L^{2}c^{3}}{Gh}}$
D.Kelvin (K)	IV. $\sqrt{\dfrac{Gh}{c^{3}}}$

(A)A-II, B-IV, C-I, D-III
(B)A-IV, B-II, C-I, D-III
(C)A-IV, B-I, C-II, D-III
(D)A-III, B-I, C-II, D-IV

Q11·PhysicsSingle correctJEE Main 2026

In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as 10 V and 5 A, respectively. The least counts of voltmeter and ammeter are 500 mV and 200 mA, respectively. The estimated error in the resistance measurement is ________ Ω.

(A)0.25
(B)2
(C)2.5
(D)0.18

Q12·PhysicsSingle correctJEE Main 2026

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

List-I	List-II
A.Planck's constant	I. $ML^{2}T^{-2}$
B.Stopping potential	II. $T^{-1}$
C.Work function	III. $ML^{2}T^{-1}$
D.Threshold frequency	IV. $ML^{2}T^{-3}A^{-1}$

(A)A-III, B-IV, C-I, D-II
(B)A-I, B-II, C-III, D-IV
(C)A-IV, B-III, C-I, D-II
(D)A-I, B-IV, C-III, D-II

Q13·PhysicsSingle correctJEE Main 2026

The dimensional formula of

\frac{1}{2}\epsilon_{0}E^{2}

(

\epsilon_{0}

= permittivity of vacuum and

E

= electric field) is

M^{a}L^{b}T^{c}

. The value of

2a - b + c

= ______.

(A)0
(B)1
(C)−1
(D)2

Q14·PhysicsSingle correctJEE Main 2026

The diameter of a wire measured by a screw gauge of least count 0.001 cm is 0.08 cm. The length measured by a scale of least count 0.1 cm is 150 cm. When a weight of 100 N is applied to the wire, the extension in length is 0.5 cm, measured by a micrometer of least count 0.001 cm. The error in the measured Young's modulus is

\alpha \times 10^{9}

N/m

^{2}

. The value of

\alpha

is ______. (Ignore the contribution of the load to Young's modulus error calculation)

(A)1.3
(B)1.65
(C)0.13
(D)0.25

Q15·PhysicsSingle correctJEE Main 2026

Dimensions of universal gravitational constant

(G)

in terms of Planck's constant

(h)

, distance

(L)

, mass

(M)

and time

(T)

are ______.

(A) $[hTLM^{-2}]$
(B) $[hT^{-1}LM^{-2}]$
(C) $[hTL^{2}M^{-2}]$
(D) $[h^{-1}T^{-1}LM^{-2}]$

Q16·PhysicsSingle correctJEE Main 2026

The time period of a simple harmonic oscillator is

T = 2\pi\sqrt{\dfrac{k}{m}}

. The measured value of mass (m) of the object is 10 g with an accuracy of 10 mg, and time for 50 oscillations of the spring is found to be 60 s using a watch of 2 s resolution. Percentage error in determination of spring constant(k) is _______%.

(A)3.43
(B)3.35
(C)7.60
(D)6.76

Q17·PhysicsSingle correctJEE Main 2026

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

List-I	List-II
A.Coefficient of viscosity	I.[ML $^{–1}$ T $^{–2}$ ]
B.Surface tension	II.[ML $^{2}$ T $^{–2}$ ]
C.Pressure	III.[ML $^{0}$ T $^{–2}$ ]
D.Surface energy	IV.[ML $^{–1}$ T $^{–1}$ ]

(A)A-I, B-II, C-IV, D-III
(B)A-IV,B-III,C-I,D-II
(C)A-I, B-III, C-II, D-IV
(D)A-IV, B-I, C-II, D-III

Q18·PhysicsSingle correctJEE Main 2026

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

List-I	List-II
A.Magnetic induction	I. $\mathrm{M\,L\,T^{-2}A^{-2}}$
B.Magnetic flux	II. $\mathrm{M\,L^{2}\,T^{-2}A^{-2}}$
C.Magnetic permeability	III. $\mathrm{M\,L^{0}\,T^{-2}A^{-1}}$
D.Self inductance	IV. $\mathrm{M\,L^{2}\,T^{-2}A^{-1}}$

(A)A-IV,B-III,C-I,D-II
(B)A-III,B-IV,C-II,D-I
(C)A-I,B-III,C-IV,D-II
(D)A-III,B-IV,C-I,D-II

Q19·PhysicsNumericalJEE Main 2026

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

\rho^{a}

r^{b}

\eta^{c}

\sigma^{d}

, where A is a constant and a, b c and d are integers. The value of

\frac{b+c}{a+d}

is ______.

Q20·PhysicsSingle correctJEE Main 2026

Four persons measure the length of a rod as 20.00 cm, 19.75 cm, 17.01 cm and 18.25 cm. The relative error in the measurement of average length of the rod is :

(A)0.24
(B)0.18
(C)0.06
(D)0.08

Q21·PhysicsSingle correctJEE Main 2026

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

List-I	List-II
A.Spring constant	I. $ML^2T^{-2}K^{-1}$
B.Thermal conductivity	II. $ML^0T^{-2}$
C.Boltzmann constant	III. $ML^2T^{-3}A^{-2}$
D.Inductive reactance	IV. $MLT^{-3}K^{-1}$

(A)A-II, B-I, C-IV, D-III
(B)A-I, B-IV, C-II, D-III
(C)A-III, B-II, C-IV, D-I
(D)A-II, B-IV, C-I, D-III

Q22·PhysicsSingle correctJEE Main 2026

Consider a modified Bernoulli equation.

\left(P + \frac{A}{Bt^{2}}\right) + \rho g(h + Bt) + \frac{1}{2}\rho V^{2} = \mathrm{constant}

If t has the dimension of time then the dimensions of A and B are ______, ______respectively.

(A) $[ML^{0}T^{-1}]$ and $[M^{0}LT]$
(B) $[ML^{0}T^{-1}]$ and $[M^{0}LT^{-1}]$
(C) $[ML^{0}T^{-2}]$ and $[M^{0}LT^{-2}]$
(D) $[ML^{0}T^{-2}]$ and $[M^{0}LT^{-1}]$

Q23·PhysicsSingle correctJEE Main 2026

In an experiment the values of two spring constants were measured as

k_{1} = (10 \pm 0.2)

N/m and

k_{2} = ( 20 \pm 0.3)

N/m. If these springs are connected in parallel, then the percentage error in equivalent spring constant is :

(A)2.67%
(B)2.33%
(C)1.33%
(D)1.67%

Q24·PhysicsSingle correctJEE Main 2026

A spherical body of radius r and density σ falls freely through a viscous liquid having density ρ and viscosity η and attains a terminal velocity

v_0

. Estimated maximum error in the quantity η is : (Ignore errors associated with σ, ρ and g, gravitational acceleration)

(A) $2\frac{\Delta r}{r} - \frac{\Delta v_0}{v_0}$
(B) $\frac{2\Delta r}{r} + \frac{\Delta v_0}{v_0}$
(C) $2\left[\frac{\Delta r}{r} + \frac{\Delta v_0}{v_0}\right]$
(D) $2\left[\frac{\Delta r}{r} - \frac{\Delta v_0}{v_0}\right]$

Q25·PhysicsSingle correctJEE Main 2026

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

(A)205 m
(B)205.333 m
(C)205.33 m
(D)205.3 m

Q26·PhysicsMultiple correctJEE Advanced 2025

Length, breadth and thickness of a strip having a uniform cross section are measured to be 10.5 cm , 0.05 mm , and 6.0 μm, respectively. Which of the following option(s) give(s) the volume of the strip in

\text{cm}^{3}

with correct significant figures:

(A) $3.2 \times 10^{-5}$
(B) $32.0 \times 10^{-6}$
(C) $3.0 \times 10^{-5}$
(D) $3 \times 10^{-5}$

Q27·PhysicsSingle correctJEE Advanced 2025

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 conductivity and κ the thermal conductivity of the material of the wire. Taking M, L, T, I and K as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity

Z = \frac{S^2\sigma}{\kappa}

is:

(A) $[M^0L^0T^0I^0K^0]$
(B) $[M^0L^0T^0I^0K^{-1}]$
(C) $[M^1L^2T^{-2}I^{-1}K^{-1}]$
(D) $[M^1L^2T^{-4}I^{-1}K^{-1}]$

Q28·PhysicsSingle correctJEE Main 2025

A quantity

Q

is formulated as

X^{-2}Y^{3/2}Z^{-2/5}

.

X

,

Y

and

Z

are independent parameters which have fractional errors of 0.1, 0.2 and 0.5, respectively in measurement. The maximum fractional error of

Q

is:

(A) $0.1$
(B) $0.8$
(C) $0.7$
(D) $0.6$

Q29·PhysicsSingle correctJEE Main 2025

Match the LIST-I (Mechanical quantity) with LIST-II (Dimensional formula). Choose the correct answer from the options given below:

LIST-I (Mechanical quantity)	LIST-II (Dimensional formula)
A.Mass density	I. $[ML^2T^{-3}]$
B.Impulse	II. $[MLT^{-1}]$
C.Power	III. $[ML^2T^0]$
D.Moment of inertia	IV. $[ML^{-3}T^0]$

(A)(A)-(IV), (B)-(II), (C)-(III), (D)-(I)
(B)(A)-(I), (B)-(III), (C)-(IV), (D)-(II)
(C)(A)-(IV), (B)-(II), (C)-(I), (D)-(III)
(D)(A)-(II), (B)-(III), (C)-(IV), (D)-(I)

Q30·PhysicsSingle correctJEE Main 2025

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

(A) $(3,-5)$
(B) $(-2,2)$
(C) $(-2,1)$
(D) $(1,-1)$

Q31·PhysicsSingle correctJEE Main 2025

In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of

[M^P\,L^Q\,T^A]

. The value of P and Q are:

(A)1, 0
(B) $-1, 1$
(C) $1, -1$
(D) $0, -1$

Q32·PhysicsSingle correctJEE Main 2025

For the determination of refractive index of glass slab, a travelling microscope is used whose main scale contains 300 equal divisions equals to 15 cm. The vernier scale attached to the microscope has 25 divisions equals to 24 divisions of main scale. The least count (LC) of the travelling microscope is (in cm):

(A)0.001
(B)0.002
(C)0.0005
(D)0.0025

Q33·PhysicsIntegerJEE Main 2025

A physical quantity C is related to four other quantities p, q, r and s as follows

C=\dfrac{pq^2}{r^3\sqrt s}

. The percentage errors in the measurement of p, q, r and s are 1%, 2%, 3% and 2% respectively. The percentage error in the measurement of C will be __________ %.

Q34·PhysicsSingle correctJEE Main 2025

Match the LIST-I (Physical quantities and constants) with LIST-II (Dimensional formula). Choose the correct answer from the options given below:

LIST-I (Physical quantities and constants)	LIST-II (Dimensional formula)
A.Boltzmann constant	I. $ML^2T^{-1}$
B.Coefficient of viscosity	II. $MLT^{-3}K^{-1}$
C.Planck's constant	III. $ML^2T^{-2}K^{-1}$
D.Thermal conductivity	IV. $ML^{-1}T^{-1}$

(A)A-III, B-IV, C-I, D-II
(B)A-II, B-III, C-IV, D-I
(C)A-III, B-II, C-I, D-IV
(D)A-III, B-IV, C-II, D-I

Q35·PhysicsSingle correctJEE Main 2025

A person measures the 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 addition of the masses of the 3 particles will be:

(A)661.845 g
(B)662 g
(C)661.8 g
(D)661.84 g

Q36·PhysicsSingle correctJEE Main 2025

Match the LIST-I (Physical quantity) with LIST-II (Dimensional formula). Choose the correct answer from the options given below:

LIST-I (Physical quantity)	LIST-II (Dimensional formula)
A.Gravitational constant	I. $[LT^{-2}]$
B.Gravitational potential energy	II. $[L^2T^{-2}]$
C.Gravitational potential	III. $[ML^2T^{-2}]$
D.Acceleration due to gravity	IV. $[M^{-1}L^3T^{-2}]$

(A)(A)-IV, (B)-III, (C)-II, (D)-I
(B)(A)-III, (B)-II, (C)-I, (D)-IV
(C)(A)-II, (B)-IV, (C)-III, (D)-I
(D)(A)-I, (B)-III, (C)-IV, (D)-II

Q37·PhysicsSingle correctJEE Main 2025

The equation for real gas is given by

\left(P+\dfrac{a}{V^2}\right)(V-b)=RT

, where

P,V,T

and

R

are the pressure, volume, temperature and gas constant, respectively. The dimension of

ab^{-2}

is equivalent to that of:

(A)Planck’s constant
(B)Compressibility
(C)Strain
(D)Energy density

Q38·PhysicsSingle correctJEE Main 2025

Match List-I (physical quantities) with List-II (dimensional formulae). Choose the correct answer from the options given below:

List-I	List-II
A.Coefficient of viscosity	I. $[ML^0T^{-3}]$
B.Intensity of wave	II. $[ML^{-2}T^{-2}]$
C.Pressure gradient	III. $[M^{-1}LT^2]$
D.Compressibility	IV. $[ML^{-1}T^{-1}]$

(A)(A)-(I), (B)-(IV), (C)-(III), (D)-(II)
(B)(A)-(IV), (B)-(I), (C)-(II), (D)-(III)
(C)(A)-(IV), (B)-(II), (C)-(I), (D)-(III)
(D)(A)-(II), (B)-(III), (C)-(IV), (D)-(I)

Q39·PhysicsSingle correctJEE Main 2025

Given a charge

q

, current

I

and permeability of vacuum

\mu_0

. Which of the following quantity has the dimension of momentum?

(A) $qI/\mu_0$
(B) $q\mu_0 I$
(C) $q^2\mu_0 I$
(D) $q\mu_0/I$

Q40·PhysicsSingle correctJEE Main 2025

The pair of physical quantities not having same dimensions is:

(A)Torque and energy
(B)Surface tension and impulse
(C)Angular momentum and Planck’s constant
(D)Pressure and Young’s modulus

Q41·PhysicsIntegerJEE Main 2025

A physical quantity Q is related to four observables a, b, c, d as follows:

Q=\dfrac{ab^4}{cd}

, where

a=(60\pm 3)

Pa;

b=(20\pm 0.1)

m;

c=(40\pm 0.2)

Nsm⁻² and

d=(50\pm 0.1)

m, then the percentage error in Q is

\dfrac{x}{1000}

, where

x=

______.

Q42·PhysicsSingle correctJEE Main 2025

Match List-I (Mechanical Quantity) with List-II (Dimensional Formula). Choose the correct answer from the options given below:

List-I (Mechanical Quantity)	List-II (Dimensional Formula)
A.Young’s Modulus	I. $ML^{-1}T^{-1}$
B.Torque	II. $ML^{-1}T^{-2}$
C.Coefficient of Viscosity	III. $M^{-1}L^{3}T^{-2}$
D.Gravitational Constant	IV. $ML^{2}T^{-2}$

(A)(A)-(I), (B)-(III), (C)-(II), (D)-(IV)
(B)(A)-(II), (B)-(I), (C)-(IV), (D)-(III)
(C)(A)-(IV), (B)-(II), (C)-(III), (D)-(I)
(D)(A)-(II), (B)-(IV), (C)-(I), (D)-(III)

Q43·PhysicsSingle correctJEE Main 2025

The expression given below shows the variation of velocity (v) with time (t),

v=At^2+\dfrac{Bt}{C+t}

. The dimension of ABC is:

(A) $[M^0 L^2 T^{-3}]$
(B) $[M^0 L^1 T^{-3}]$
(C) $[M^0 L^1 T^{-2}]$
(D) $[M^0 L^2 T^{-2}]$

Q44·PhysicsIntegerJEE Main 2025

A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm, respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be

\frac{x}{100}

where x is______

Q45·PhysicsSingle correctJEE Main 2025

Match List-I (Physical Quantity) with List-II (Dimensional Formula). Choose the correct answer from the options given below:

List-I (Physical Quantity)	List-II (Dimensional Formula)
A.Angular Impulse	I. $[M^0L^2T^{-2}]$
B.Latent Heat	II. $[ML^2T^{-3}A^{-1}]$
C.Electrical resistivity	III. $[ML^2T^{-1}]$
D.Electromotive force	IV. $[ML^3T^{-3}A^{-2}]$

(A)(A)-(III), (B)-(I), (C)-(IV), (D)-(II)
(B)(A)-(I), (B)-(III), (C)-(IV), (D)-(II)
(C)(A)-(III), (B)-(I), (C)-(II), (D)-(IV)
(D)(A)-(II), (B)-(I), (C)-(IV), (D)-(III)

Q46·PhysicsSingle correctJEE Main 2025

For an experimental expression

y=\dfrac{32.3\times1125}{27.4}

, where all the digits are significant. Then to report the value of y we should write :-

(A) $y=1326.2$
(B) $y=1326.19$
(C) $y=1326.186$
(D) $y=1330$

Q47·PhysicsSingle correctJEE Main 2025

The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light, identify the correct equation.

(A) $E^2=pc^2+m^2c^4$
(B) $E^2=pc^2+m^2c^2$
(C) $E^2=p^2c^2+m^2c^2$
(D) $E^2=p^2c^2+m^2c^4$

Q48·PhysicsSingle correctJEE Main 2025

The energy of a system is given as

E(t)=\alpha^3 e^{-\beta t}

, where

t

is the time and

\beta=0.3\ \mathrm{s^{-1}}

. The errors in the measurement of

\alpha

and

t

are

1.2\%

and

1.6\%

, respectively. At

t=5

s, maximum percentage error in the energy is :

(A) $4\%$
(B) $11.6\%$
(C) $6\%$
(D) $8.4\%$

Q49·PhysicsSingle correctJEE Main 2025

Match List-I (Electromagnetic Quantity) with List-II (Dimensional Formula). Choose the correct answer from the options given below:

List-I (Electromagnetic Quantity)	List-II (Dimensional Formula)
A.Permeability of free space	I. $[\mathrm{M\,L^2\,T^{-2}}]$
B.Magnetic field	II. $[\mathrm{M\,T^{-2}\,A^{-1}}]$
C.Magnetic moment	III. $[\mathrm{M\,L\,T^{-2}\,A^{-2}}]$
D.Torsional constant	IV. $[\mathrm{L^2\,A}]$

(A)(A)-(I), (B)-(IV), (C)-(II), (D)-(III)
(B)(A)-(II), (B)-(I), (C)-(III), (D)-(IV)
(C)(A)-(IV), (B)-(III), (C)-(I), (D)-(II)
(D)(A)-(III), (B)-(II), (C)-(IV), (D)-(I)

Q50·PhysicsSingle correctJEE Main 2025

The position of a particle moving on x-axis is given by

x(t)=A\sin t+B\cos^2 t+Ct^2+D

, where

t

is time. The dimension of

\dfrac{ABC}{D}

is-

(A)L
(B) $L^3T^{-2}$
(C) $L^2T^{-2}$
(D) $L^2$

Q51·PhysicsSingle correctJEE Main 2025

If B is the magnetic field and μ₀ is the permeability of free space, then the dimensions of (B/μ₀) are:

(A)M T⁻¹ A⁻¹
(B)L⁻¹ A
(C)L T⁻¹ A⁻¹
(D)M L T⁻¹ A⁻¹

Q52·PhysicsSingle correctJEE Main 2025

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,

(A) $[F]=[C^{2}M^{-2}L^{2}T^{2}]$
(B) $[F]=[CM^{-2}L^{-2}T^{-2}]$
(C) $[F]=[CM^{-1}L^{-2}T^{2}]$
(D) $[F]=[C^{2}M^{-1}L^{-2}T^{2}]$

Q53·PhysicsSingle correctJEE Main 2025

The maximum percentage error in the measurement of density of a wire is [Given, mass of wire

=(0.60\pm0.003)

g, radius of wire

=(0.50\pm0.01)

cm, length of wire

=(10.00\pm0.05)

cm]

(A)4
(B)5
(C)8
(D)7

Q54·PhysicsNumericalJEE Advanced 2024

The dimensions of a cone are measured using a scale with a least count of 2mm . The diameter of the base and the height are both measured to be 20.0cm . The maximum percentage error in the determination of the volume is -

Q55·PhysicsSingle correctJEE Advanced 2024

A dimensionless quantity is constructed in terms of electronic charge

e

, permittivity of free space

\varepsilon_{0}

, Planck's constant

h

, and speed of light

c

. If the dimensionless quantity is written as

e^{\alpha}\varepsilon_{0}^{\beta}h^{\gamma}c^{\delta}

and

n

is a non-zero integer, then

(\alpha, \beta, \gamma, \delta)

is given by

(A) $(2n, -n, -n, -n)$
(B) $(n, -n, -2n, -n)$
(C) $(n, -n, -n, -2n)$
(D) $(2n, -n, -2n, -2n)$

Q56·PhysicsSingle correctJEE Main 2024

The dimensional formula of latent heat is:

(A) $[M^0 L T^{-2}]$
(B) $[M L T^{-2}]$
(C) $[M^0 L^2 T^{-2}]$
(D) $[M L^2 T^{-2}]$

Q57·PhysicsSingle correctJEE Main 2024

The de-Broglie wavelength associated with a particle of mass

m

and energy

E

is

h/\sqrt{2mE}

. The dimensional formula for Planck's constant is:

(A) $[ML^{-1}T^{-1}]$
(B) $[ML^{2}T^{-1}]$
(C) $[MLT^{-1}]$
(D) $[M^{4}L^{2}T^{-3}]$

Q58·PhysicsSingle correctJEE Main 2024

There are 100 divisions on the circular scale of a screw gauge of pitch 1 mm. With no measuring quantity in between the jaws, the zero of the circular scale lies 5 divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found that 4 linear scale divisions are clearly visible while 60 divisions on circular scale coincide with the reference line. The diameter of the wire is:

(A)4.65 mm
(B)4.55 mm
(C)4.60 mm
(D)3.35 mm

Q59·PhysicsSingle correctJEE Main 2024

In an expression

a\times10^b

:

(A) $a$ is order of magnitude for $b\le5$
(B) $b$ is order of magnitude for $a\le5$
(C) $b$ is order of magnitude for $5<a\le10$
(D) $b$ is order of magnitude for $a\ge5$

Q60·PhysicsSingle correctJEE Main 2024

Young's modulus is determined by the equation

Y=49000\dfrac{m}{\ell}\dfrac{\text{dyne}}{cm^2}

where

M

is the mass and

\ell

is the extension of wire used in the experiment. Now error in Young modulus

(Y)

is estimated by taking data from M-

\ell

plot in graph paper. The smallest scale divisions are

5\,g

and

0.02\,cm

along load axis and extension axis respectively. If the value of

M

and

\ell

are

500\,g

and

2\,cm

respectively then percentage error of

Y

is:

(A) $0.2\%$
(B) $0.02\%$
(C) $2\%$
(D) $0.5\%$

Q61·PhysicsSingle correctJEE Main 2024

Least count of a vernier caliper is

\dfrac{1}{20N}

cm. The value of one division on the main scale is 1 mm. Then the number of divisions of main scale that coincide with N divisions of vernier scale is:

(A) $\left(\dfrac{2N-1}{20N}\right)$
(B) $\left(\dfrac{2N-1}{2}\right)$
(C) $(2N-1)$
(D) $\left(\dfrac{2N-1}{2N}\right)$

Q62·PhysicsSingle correctJEE Main 2024

If

\varepsilon_0

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

\varepsilon_0 E^2

has the dimensions:

(A) $[M^0L^{-2}TA]$
(B) $[ML^{-1}T^{-2}]$
(C) $[M^{-1}L^{-3}T^4A^2]$
(D) $[ML^2T^{-2}]$

Q63·PhysicsSingle correctJEE Main 2024

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}]

.

(A)Statement (I) is incorrect but statement (II) is correct
(B)Both statement (I) and statement (II) are incorrect
(C)Statement (I) is correct but statement (II) is incorrect
(D)Both statement (I) and statement (II) are correct

Q64·PhysicsSingle correctJEE Main 2024

To find the spring constant (

k

) of a spring experimentally, a student commits 2% positive error in the measurement of time and 1% negative error in the measurement of mass. The percentage error in determining the value of

k

is:

(A) $3\%$
(B) $1\%$
(C) $4\%$
(D) $5\%$

Q65·PhysicsSingle correctJEE Main 2024

Match List-I (physical quantities) with List-II (their dimensional formulae). Choose the correct answer from the options given below:

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. $[M^{1}T^{-2}A^{-1}]$
D.Permeability of free space	IV. $[M^{1}L^{2}T^{-2}]$

(A)A-I, B-III, C-II, D-IV
(B)A-IV, B-III, C-II, D-I
(C)A-III, B-I, C-II, D-IV
(D)A-IV, B-II, C-III, D-I

Q66·PhysicsSingle correctJEE Main 2024

What is the dimensional formula of

ab^{-1}

in the equation

\left(P+\dfrac{a}{V^2}\right)(V-b)=RT

, where the letters have their usual meaning?

(A) $[M^0L^3T^{-2}]$
(B) $[ML^2T^{-2}]$
(C) $[M^{-1}L^5T^3]$
(D) $[M^6L^7T^4]$

Q67·PhysicsSingle correctJEE Main 2024

If G is the gravitational constant and

u

is the energy density then which of the following quantity has the same dimensions as

\sqrt{uG}

:

(A)Pressure gradient per unit mass
(B)Force per unit mass
(C)Gravitational potential
(D)Energy per unit mass

Q68·PhysicsSingle correctJEE Main 2024

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.

(A) $T^2=\tfrac{4\pi^2 r}{GM^2}$
(B) $T^2=4\pi^2 r^3$
(C) $T^2=\tfrac{4\pi^2 r^3}{GM}$
(D) $T^2=\tfrac{4\pi^2 r^2}{GM}$

Q69·PhysicsSingle correctJEE Main 2024

The dimensional formula of angular impulse is:

(A) $[ML^{-2}T^{-1}]$
(B) $[ML^2T^{-1}]$
(C) $[MLT^{-1}]$
(D) $[ML^2T^{-2}]$

Q70·PhysicsSingle correctJEE Main 2024

The radius

(r)

, length

(l)

and resistance

(R)

of a metal wire was measured in the laboratory as

r=(0.35\pm0.05)\,cm

,

R=(100\pm10)

ohm,

l=(15\pm0.2)\,cm

. The percentage error in resistivity of the material of the wire is:

(A) $25.6\%$
(B) $39.9\%$
(C) $37.3\%$
(D) $35.6\%$

Q71·PhysicsSingle correctJEE Main 2024

Match List-I (Number) with List-II (Significant figures). Choose the correct answer from the options given below:

List-I (Number)	List-II (Significant figure)
A.1001	I.3
B.010.1	II.4
C.100.100	III.5
D.0.0010010	IV.6

(A)(A)-(III), (B)-(IV), (C)-(II), (D)-(I)
(B)(A)-(IV), (B)-(III), (C)-(I), (D)-(II)
(C)(A)-(II), (B)-(I), (C)-(IV), (D)-(III)
(D)(A)-(I), (B)-(II), (C)-(III), (D)-(IV)

Q72·PhysicsSingle correctJEE Main 2024

If the percentage errors in measuring the length and the diameter of a wire are 0.1% each. The percentage error in measuring its resistance will be :

(A) $0.2\%$
(B) $0.3\%$
(C) $0.1\%$
(D) $0.144\%$

Q73·PhysicsSingle correctJEE Main 2024

Consider two physical quantities A and B related to each other as

E=\dfrac{B-x^2}{At}

where E,

x

and

t

have dimensions of energy, length and time respectively. The dimension of AB is

(A) $L^{-2}M^1T^0$
(B) $L^2M^{-1}T^1$
(C) $L^{-2}M^{-1}T^1$
(D) $L^0M^1T^{-1}$

Q74·PhysicsSingle correctJEE Main 2024

A force is represented by

F=ax^2+bt^{1/2}

where x = distance and t = time. The dimensions of

\dfrac{b^2}{a}

are :

(A) $[ML^3T^{-3}]$
(B) $[MLT^{-2}]$
(C) $[ML^{-1}T^{-1}]$
(D) $[ML^2T^{-3}]$

Q75·PhysicsSingle correctJEE Main 2024

The measured value of the length of a simple pendulum is 20 cm with 2 mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is N%. The value of N is:

(A)4
(B)8
(C)6
(D)5

Q76·PhysicsSingle correctJEE Main 2024

Match List-I (physical quantities) with List-II (their dimensional formulae). Choose the correct answer:

List-I (Physical quantity)	List-II (Dimensional formula)
A.Coefficient of viscosity	I. $[M\,L^2\,T^{-2}]$
B.Surface Tension	II. $[M\,L^2\,T^{-1}]$
C.Angular momentum	III. $[M\,L^{-1}\,T^{-1}]$
D.Rotational kinetic energy	IV. $[M\,L^0\,T^{-2}]$

(A)A-II, B-I, C-IV, D-III
(B)A-I, B-II, C-III, D-IV
(C)A-III, B-IV, C-II, D-I
(D)A-IV, B-III, C-II, D-I

Q77·PhysicsSingle correctJEE Main 2024

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)

(A) $\dfrac{1}{2}$
(B) $\dfrac{1}{3}$
(C)2
(D) $-\dfrac{1}{3}$

Q78·PhysicsSingle correctJEE Main 2024

A physical quantity

Q

is found to depend on quantities

a

,

b

,

c

by the relation

Q=\dfrac{a^{4}b^{3}}{c^{2}}

. The percentage error in

a

,

b

and

c

are 3%, 4% and 5% respectively. Then, the percentage error in

Q

is:

(A)66%
(B)43%
(C)34%
(D)14%

Q79·PhysicsSingle correctJEE Main 2024

The resistance

R=\dfrac{V}{I}

where

V=(200\pm5)

V and

I=(20\pm0.2)

A, the percentage error in the measurement of R is :

(A) $3.5\%$
(B) $7\%$
(C) $3\%$
(D) $5.5\%$

Q80·PhysicsSingle correctJEE Main 2024

Statement (I): Planck’s constant and angular momentum have same dimensions. Statement (II): Linear momentum and moment of force have same dimensions. In the light of the above statements, choose the correct answer from the options given below:

(A)Statement I is true but Statement II is false
(B)Both Statement I and Statement II are false
(C)Both Statement I and Statement II are true
(D)Statement I is false but Statement II is true

Q81·PhysicsSingle correctJEE Advanced 2023

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, as

Y = c^{\alpha} h^{\beta} G^{\gamma}

. Which of the following is the correct option?

(A) $\alpha = 7, \beta = -1, \gamma = -2$
(B) $\alpha = -7, \beta = -1, \gamma = -2$
(C) $\alpha = 7, \beta = -1, \gamma = 2$
(D) $\alpha = -7, \beta = 1, \gamma = -2$

Q82·PhysicsNumericalJEE Advanced 2023

In an experiment for determination of the focal length of a thin convex lens, the distance of the object from the lens is 10

\pm

0.1 cm and the distance of its real image from the lens is 20

\pm

0.2 cm. The error in the determination of focal length of the lens is n%. The value of n is ________.

Q83·PhysicsSingle correctJEE Main 2023

The speed of a wave produced in water is given by

v = \lambda^a g^b \rho^c

. Where

\lambda

,

g

and

\rho

are wavelength of wave, acceleration due to gravity and density of water respectively. The values of a, b and c respectively, are :

(A) $\frac{1}{2}, \frac{1}{2}, 0$
(B) $1, 1, 0$
(C) $1, -1, 0$
(D) $\frac{1}{2}, 0, \frac{1}{2}$

Q84·PhysicsSingle correctJEE Main 2023

In the equation

\left[X + \dfrac{a}{Y^2}\right][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

\dfrac{a}{b}

is:

(A)Energy
(B)Impulse
(C)Pressure gradient
(D)Coefficient of viscosity

Q85·PhysicsSingle correctJEE Main 2023

Match List I (physical quantities: spring constant, angular speed, angular momentum, moment of inertia) with List II (dimensional formulae). Choose the correct answer from the options given below:

List I	List II
A.Spring constant	I. $[T^{-1}]$
B.Angular speed	II. $[MT^{-2}]$
C.Angular momentum	III. $[ML^2]$
D.Moment of Inertia	IV. $[ML^2T^{-1}]$

(A)A-II, B-I, C-IV, D-III
(B)A-IV, B-I, C-III, D-II
(C)A-II, B-III, C-I, D-IV
(D)A-II, B-III, C-II, D-IV

Q86·PhysicsSingle correctJEE Main 2023

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

\text{Au} < \text{Parsec (Pc)} < \text{ly}

. In the light of the above statements. choose the most appropriate answer from the options given below:

(A)Both Statements I and Statements II are correct.
(B)Statements I is correct but Statements II is incorrect.
(C)Both Statements I and Statements II are incorrect.
(D)Statements I is incorrect but statements II is correct.

Q87·PhysicsSingle correctJEE Main 2023

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

(A) $FV^{-2}T^{2}$
(B) $FV^{-4}T^{-2}$
(C) $FV^{4}T^{-6}$
(D) $F^{2}V^{-2}T^{6}$

Q88·PhysicsSingle correctJEE Main 2023

A physical quantity P is given as

P=\dfrac{a^2 b^3}{c\sqrt d}

. The percentage error in the measurement of a, b, c and d are

1\%, 2\%, 3\%

and

4\%

respectively. The percentage error in the measurement of quantity P will be

(A)13%
(B)14%
(C)15%
(D)16%

Q89·PhysicsSingle correctJEE Main 2023

In an experiment with Vernier callipers of least count

0.1

mm, when the two jaws are joined together the zero of the Vernier scale lies to the right of the zero of the main scale and the

6^{th}

division of the Vernier scale coincides with a main scale division. While measuring the diameter of a spherical bob, the zero of the Vernier scale lies in between

3.2

cm and

3.3

cm marks, and the

4^{th}

division of the Vernier scale coincides with a main scale division. The diameter of the bob is measured as:

(A) $3.18$ cm
(B) $3.25$ cm
(C) $3.26$ cm
(D) $3.22$ cm

Q90·PhysicsSingle correctJEE Main 2023

A cylindrical wire of mass

(0.4\pm0.01)\,\text{g}

has length

(8\pm0.04)\,\text{cm}

and radius

(6\pm0.03)\,\text{mm}

. The maximum error in its density will be

(A) $1\%$
(B) $3.5\%$
(C) $4\%$
(D) $5\%$

Q91·PhysicsSingle correctJEE Main 2023

Match List-I (physical quantity) with List-II (dimensional formula). Choose the correct answer from the options given below:

List-I (Physical quantity)	List-II (Dimensional formula)
A.Torque	I. $ML^{-2}T^{-2}$
B.Stress	II. $ML^{2}T^{-2}$
C.Pressure gradient	III. $ML^{-1}T^{-1}$
D.Coefficient of viscosity	IV. $ML^{-1}T^{-2}$

(A)A-III, B-IV, C-I, D-II
(B)A-IV, B-II, C-III, D-I
(C)A-II, B-IV, C-I, D-III
(D)A-II, B-I, C-IV, D-III

Q92·PhysicsSingle correctJEE Main 2023

Dimension of

\dfrac{1}{\mu_{0}\,\epsilon_{0}}

should be equal to

(A) $T^{2}/L^{2}$
(B) $L/T$
(C) $L^{2}/T^{2}$
(D) $T/L$

Q93·PhysicsSingle correctJEE Main 2023

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

(A) $[h^{1/2}c^{-1/2}G^2]$
(B) $[h^{-1/2}c^{1/2}G^{1/2}]$
(C) $[h^{1/2}c^{1/2}G^{-1/2}]$
(D) $[h^{1}c^{1}G^{-1}]$

Q94·PhysicsSingle correctJEE Main 2023

\left(P+\tfrac{a}{V^2}\right)(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 physical quantity, which has dimensional formula as that of

\tfrac{b^2}{a}

, will be:

(A)Compressibility
(B)Energy density
(C)Modulus of rigidity
(D)Bulk modulus

Q95·PhysicsSingle correctJEE Main 2023

Match List I (physical quantities) with List II (dimensional formulae). Choose the correct answer from the options given below:

List I	List II
A.Angular momentum	I. $[ML^2T^{-2}]$
B.Torque	II. $[ML^{-2}T^{-2}]$
C.Stress	III. $[ML^2T^{-1}]$
D.Pressure gradient	IV. $[ML^{-1}T^{-2}]$

(A)A-III, B-I, C-IV, D-II
(B)A-III, B-II, C-IV, D-I
(C)A-IV, B-II, C-I, D-III
(D)A-I, B-IV, C-III, D-II

Q96·PhysicsSingle correctJEE Main 2023

Match List-I (physical quantities) with List-II (their dimensional formulae). Choose the correct answer from the options given below:

List-I	List-II
A.Torque	I. $kg\,m^{-1}\,s^{-2}$
B.Energy density	II. $kg\,m\,s^{-1}$
C.Pressure gradient	III. $kg\,m^{-2}\,s^{-2}$
D.Impulse	IV. $kg\,m^{2}\,s^{-2}$

(A)A-IV, B-I, C-III, D-II
(B)A-IV, B-III, C-I, D-II
(C)A-IV, B-I, C-II, D-III
(D)A-I, B-IV, C-III, D-II

Q97·PhysicsSingle correctJEE Main 2023

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 dimensions of

A

and

B

in a new equation:

(x-At)^2+\left(y-\dfrac{t}{B}\right)^2=a^2

. The dimensions of

t

is given as

[T^{-1}]

.

(A) $A=[LT],\,B=[L^{-1}T^{-1}]$
(B) $A=[L^{-1}T^{-1}],\,B=[LT]$
(C) $A=[L^{-1}T],\,B=[LT^{-1}]$
(D) $A=[L^{-1}T^{-1}],\,B=[LT^{-1}]$

Q98·PhysicsSingle correctJEE Main 2023

Match List I with List II and choose the correct answer from the options given below:

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. $[M^1 L^{-2} T^{-2}]$
D.Latent heat	IV. $[M^1 L^1 T^{-3} A^{-1}]$

(A)A-II, B-III, C-I, D-IV
(B)A-II, B-III, C-IV, D-I
(C)A-III, B-II, C-IV, D-I
(D)A-III, B-II, C-I, D-IV

Q99·PhysicsSingle correctJEE Main 2023

Match List I (physical quantities) with List II (their dimensional formulae) and choose the correct answer.

List-I	List-II
A.Young's Modulus (Y)	I. $[M\,L^{-1}\,T^{-1}]$
B.Co-efficient of Viscosity ( $\eta$ )	II. $[M\,L^2\,T^{-1}]$
C.Planck's Constant (h)	IV. $[M\,L^2\,T^{-2}]$
D.Work Function ( $\varphi$ )	III. $[M\,L^{-1}\,T^{-2}]$

(A)A-I, B-II, C-III, D-IV
(B)A-II, B-III, C-IV, D-I
(C)A-I, B-III, C-IV, D-II
(D)A-III, B-I, C-II, D-IV

Q100·PhysicsSingle correctJEE Main 2023

The graph between two temperature scales

P

and

Q

is shown in the figure. Between upper fixed point and lower fixed point there are

150

equal divisions of scale P and

100

divisions on scale Q. The relationship for conversion between the two scales is given by:

(A) $\frac{t_P}{100} = \frac{t_Q - 180}{150}$
(B) $\frac{t_Q}{150} = \frac{t_P - 180}{100}$
(C) $\frac{t_P}{180} - \frac{t_Q - 40}{100}$
(D) $\frac{t_Q}{100} = \frac{t_P - 30}{150}$

Q101·PhysicsSingle correctJEE Main 2023

Match List-I (physical quantity) with List-II (SI base-unit dimensional form). Choose the correct answer from the options given below:

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. $kg\,s^{-2}$

(A)A-II, B-I, C-III, D-IV
(B)A-IV, B-III, C-I, D-II
(C)A-III, B-IV, C-I, D-II
(D)A-IV, B-III, C-II, D-I

Q102·PhysicsSingle correctJEE Main 2023

The frequency

(\nu)

of an oscillating liquid drop may depend upon radius

(r)

of the drop, density

(\rho)

of liquid and the surface tension

(s)

of the liquid as:

\nu=r^a\rho^b s^c

. The values of

a

,

b

and

c

respectively are

(A) $\left(-\dfrac32,\dfrac12,\dfrac12\right)$
(B) $\left(\dfrac32,-\dfrac12,\dfrac12\right)$
(C) $\left(-\dfrac32,-\dfrac12,\dfrac12\right)$
(D) $\left(\dfrac32,\dfrac12,-\dfrac12\right)$

Q103·PhysicsSingle correctJEE Main 2023

Match List I (physical quantities) with List II (their dimensional formulae). Choose the correct answer from the options given below:

List I	List II
A.Planck's constant (h)	I. $[M^1L^2T^{-2}]$
B.Stopping potential ( $V_s$ )	II. $[M^1L^1T^{-1}]$
C.Work function ( $\phi$ )	III. $[M^1L^2T^{-1}]$
D.Momentum (p)	IV. $[M^1L^2T^{-3}A^{-1}]$

(A)A-I, B-III, C-IV, D-II
(B)A-III, B-I, C-II, D-IV
(C)A-II, B-IV, C-III, D-I
(D)A-III, B-IV, C-I, D-II

Q104·PhysicsIntegerJEE Advanced 2022

In a particular system of units, a physical quantity can be expressed in terms of the electric charge e , electron mass m

_e

, Planck's constant h , and Coulomb's constant

k = \frac{1}{4\pi\epsilon_0}

, where ε

_0

is the permittivity of vacuum. In terms of these physical constants, the dimension of the magnetic field is [B] = [e]

^{\alpha}

[m

_e

]

^{\beta}

[h]

^{\gamma}

[k]

^{\delta}

. The value of α + β + γ + δ is ______________.

Q105·PhysicsSingle correctJEE Main 2022

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 tension (S), if density of the liquid is p and radius of the drop is r, then

T = k\sqrt{\frac{pr^{3}}{S^{3/2}}}

is dimensionally correct, where K is dimensionless. Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period. In the light of above statements, choose the correct answer from the options given below.

(A)Both (A) and (R) are true and (R) is the correct explanation of (A)
(B)Both (A) and (R) are true but (R) is not the correct explanation of (A)
(C)(A) is true but (R) is false
(D)(A) is false but (R) is true

Q106·PhysicsSingle correctJEE Main 2022

Match List I with List II. List I A. Torque B. Stress C. Latent Heat D. Power List II I. Nms

^{-1}

II. J kg

^{-1}

III. Nm IV. Nm

^{-2}

Choose the correct answer from the options given below:

(A)A-III, B-II, C-I, D-IV
(B)A-III, B-IV, C-II, D-I
(C)A-IV, B-I, C-III, D-II
(D)A-II, B-III, C-I, D-IV

Q107·PhysicsSingle correctJEE Main 2022

Consider the efficiency of Carnot's engine is given by

\eta = \dfrac{\alpha\beta}{\sin\theta}\log_e \dfrac{\beta x}{kT}

, where

\alpha

and

\beta

are constants. If T is temperature, k is Boltzman constant,

\theta

is angular displacement and x has the dimensions of length. Then, choose the incorrect option.

(A)Dimensions of $\beta$ is same as that of force.
(B)Dimensions of $\alpha^{-1}$ x is same as that of energy.
(C)Dimensions of $\eta^{-1}\sin\theta$ is same as that of $\alpha\beta$
(D)Dimensions of $\alpha$ is same as that of $\beta$

Q108·PhysicsSingle correctJEE Main 2022

The dimensions of

\left(\frac{B^{2}}{\mu_{0}}\right)

will be : (if μ

_{0}

: permeability of free space and B : magnetic field)

(A)[M L $^{2}$ T $^{-2}$ ]
(B)[M L T $^{-2}$ ]
(C)[M L $^{-1}$ T $^{-2}$ ]
(D)[M L $^{2}$ T $^{-2}$ A $^{-1}$ ]

Q109·PhysicsNumericalJEE Main 2022

In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of 0.5 s is measured from time of 100 oscillation with a watch of 1s resolution. If measured value of length is 10 cm known to 1mm accuracy. The accuracy in the determination of g is found to be x %. The value of x is

Q110·PhysicsSingle correctJEE Main 2022

A torque meter is calibrated to reference standards of mass, length and time each with 5% accuracy. After calibration, the measured torque with this torque meter will have net accuracy of :

(A)15%
(B)25%
(C)75%
(D)5%

Q111·PhysicsSingle correctJEE Main 2022

An expression of energy density is given by

u = \frac{\alpha}{\beta}\sin\left(\frac{\alpha x}{kt}\right)

, where α, β are constants, x is displacement, k is Boltzmann constant and t is the temperature. The dimensions of β will be :

(A) $[ML^{2}T^{-2}\theta^{-1}]$
(B) $[M^{0}L^{2}T^{-2}]$
(C) $[M^{0}L^{0}T^{0}]$
(D) $[M^{0}L^{2}T^{0}]$

Q112·PhysicsNumericalJEE Main 2022

In an experiment of determine the Young's modulus of wire of a length exactly 1m, the extension in the length of the wire is measured as 0.4mm with an uncertainty of ±0.02 mm when a load of 1kg is applied. The diameter of the wire is measured as 0.4mm with an uncertainty of ±0.01 mm. The error in the measurement of Young's modulus (ΔY) is found to be x × 10

^{10}

Nm

^{-2}

. The value of x is ______ [Take g = 10m/s

^{2}

]

Q113·PhysicsSingle correctJEE Main 2022

Which of the following physical quantities have the same dimensions ?

(A)Electric displacement $(\vec{D})$ and surface charge density
(B)Displacement current and electric field
(C)Current density and surface charge density
(D)Electric potential and energy

Q114·PhysicsSingle correctJEE Main 2022

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

(A) $[P\ A^{-1}\ T^{0}]$
(B) $[P\ A\ T^{-1}]$
(C) $[P\ A^{-1}\ T]$
(D) $[P\ A^{-1}\ T^{-1}]$

Q115·PhysicsSingle correctJEE Main 2022

In Vander Waals equation

\left[P+\frac{a}{V^2}\right][V-b]=RT

; P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants

\frac{a}{b}

is dimensionally equal to :

(A) $\frac{P}{V}$
(B) $\frac{V}{P}$
(C)PV
(D) $PV^3$

Q116·PhysicsSingle correctJEE Main 2022

Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as

v_2 = \frac{n}{m^2} v_1

and

a_2 = \frac{a_1}{mn}

respectively. Here m and n are constants. The relations for distance and time in two systems respectively are:

(A) $\frac{n^3}{m^3} L_1 = L_2$ and $\frac{n^2}{m} T_1 = T_2$
(B) $L_1 = \frac{n^4}{m^2} L_2$ and $T_1 = \frac{n^2}{m} T_2$
(C) $L_1 = \frac{n^2}{m} L_2$ and $T_1 = \frac{n^4}{m^2} T_2$
(D) $\frac{n^2}{m} L_1 = L_2$ and $\frac{n^4}{m^2} T_1 = T_2$

Q117·PhysicsNumericalJEE Main 2022

A student in the laboratory measures thickness of a wire using screw gauge. The readings are 1.22 mm, 1.23 mm, 1.19 mm and 1.20 mm. The percentage error is

\frac{x}{121}

% . The value of x is ___

Q118·PhysicsSingle correctJEE Main 2022

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Product of Pressure (P) and time (t) has the same dimension as that of coefficient of viscosity. Reason R: Coefficient of viscosity

= \frac{\text{Force}}{\text{Velocity gradient}}

Question: Choose the correct answer from the options given below :

(A)Both A and R true, and R is correct explanation of A.
(B)Both A and R are true but R is NOT the correct explanation of A.
(C)A is true but R is false.
(D)A is false but R is true.

Q119·PhysicsSingle correctJEE Main 2022

The distance of the Sun from earth is

1.5\times10^{11}

m and its angular diameter is (2000) s when observed from the earth. The diameter of the Sun will be :

(A) $2.45\times10^{10}$ m
(B) $1.45\times10^{10}$ m
(C) $1.45\times10^{9}$ m
(D) $0.14\times10^{9}$ m

Q120·PhysicsSingle correctJEE Main 2022

A sliver wire has mass

(0.6 \pm 0.006)

g, radius

(0.5 \pm 0.005)

mm and length

(4 \pm 0.04)

cm. The maximum percentage error in the measurement of its density will be :

(A)4%
(B)3%
(C)6%
(D)7%

Q121·PhysicsSingle correctJEE Main 2022

The SI unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be

(A) $[ML^{-1}T^{-1}]$
(B) $[ML^{-1}T^{-2}]$
(C) $[ML^{2}T^{-1}]$
(D) $[M^{-1}L^{3}T^{0}]$

Q122·PhysicsSingle correctJEE Main 2022

An expression for a dimensionless quantity P is given by

P = \frac{\alpha}{\beta}\log_{e}\left(\frac{kt}{\beta x}\right)

; where α and β are constants, x is distance ; k is Boltzmann constant and t is the temperature. Then the dimensions of α will be :

(A) $[M^{0}L^{-1}T^{0}]$
(B) $[ML^{0}T^{-2}]$
(C) $[MLT^{-2}]$
(D) $[ML^{2}T^{-2}]$

Q123·PhysicsSingle correctJEE Main 2022

The dimension of mutual inductance is :

(A) $[ML^2 T^{-2} A^{-1}]$
(B) $[ML^2T^{-3}A^{-1}]$
(C) $[ML^2T^{-2}A^{-2}]$
(D) $[ML^2T^{-3}A^{-2}]$

Q124·PhysicsSingle correctJEE Main 2022

If

Z=\frac{A^2B^3}{C^4}

, then the relative error in Z will be :

(A) $\frac{\Delta A}{A}+\frac{\Delta B}{B}+\frac{\Delta C}{C}$
(B) $\frac{2\Delta A}{A}+\frac{3\Delta B}{B}-\frac{4\Delta C}{C}$
(C) $\frac{2\Delta A}{A}+\frac{3\Delta B}{B}+\frac{4\Delta C}{C}$
(D) $\frac{\Delta A}{A}+\frac{\Delta B}{B}-\frac{\Delta C}{C}$

Q125·PhysicsNumericalJEE Main 2022

For

z = a^2 x^3 y^{\frac{1}{2}}

, where 'a' is a constant. If percentage error in measurement of 'x' and 'y' are 4% and 12%, respectively, then the percentage error for 'z' will be %.

Q126·PhysicsSingle correctJEE Main 2022

Identify the pair of physical quantities that have same dimensions :

(A)velocity gradient and decay constant
(B)wien's constant and Stefan constant
(C)angular frequency and angular momentum
(D)wave number and Avogadro number

Q127·PhysicsSingle correctJEE Main 2022

Identify the pair of physical quantities which have different dimensions :

(A)Wave number and Rydberg's constant
(B)Stress and Coefficient of elasticity
(C)Coercivity and Magnetisation
(D)Specific heat capacity and Latent heat

Q128·PhysicsMultiple correctJEE Advanced 2021

A physical quantity

\vec{S}

is defined as

\vec{S} = (\vec{E} \times \vec{B}) / \mu_0

, where

\vec{E}

is electric field,

\vec{B}

is magnetic field and

\mu_0

is the permeability of free space. The dimensions of

\vec{S}

are the same as the dimensions of which of the following quantity (ies) ?

(A) $\frac{\text{Energy}}{\text{charge} \times \text{current}}$
(B) $\frac{\text{Force}}{\text{Length} \times \text{Time}}$
(C) $\frac{\text{Energy}}{\text{Volume}}$
(D) $\frac{\text{Power}}{\text{Area}}$

Q129·PhysicsSingle correctJEE Main 2021

A student determined Young's Modulus of elasticity using the formula

Y = \frac{MgL^{3}}{4bd^{3}\delta}

. The value of g is taken to be 9.8 m/s

^{2}

, without any significant error, his observation are as following. Then the fractional error in the measurement of Y is :

Physical Quantity	Least count of the Equipment used for measurement	Observed value
Mass (M)	1 g	2 kg
Length of bar (L)	1 mm	1 m
Breadth of bar (b)	0.1 mm	4 cm
Thickness of bar (d)	0.01 mm	0.4 cm
Depression (δ)	0.01 mm	5 mm

(A)0.0083
(B)0.0155
(C)0.155
(D)0.083

Q130·PhysicsSingle correctJEE Main 2021

Two resistors R

_{1}

= (4 ± 0.8) Ω and R

_{2}

= (4 ± 0.4) Ω are connected in parallel. The equivalent resistance of their parallel combination will be :

(A)(4 ± 0.4) Ω
(B)(2 ± 0.4) Ω
(C)(2 ± 0.3) Ω
(D)(4 ± 0.3) Ω

Q131·PhysicsSingle correctJEE Main 2021

Which of the following equations is dimensionally incorrect ? Where t = time, h = height, s = surface tension,

\theta

= angle,

\rho

= density, a, r = radius, g = acceleration due to gravity, v = volume , p = pressure, W = work done,

\Gamma

= torque,

\in

= permittivity, E = electric field, J = current density, L = length.

(A) $v=\frac{\pi\,p\,a^{4}}{8\eta\,L}$
(B) $h=\frac{2s\cos\theta}{\rho\,r\,g}$
(C) $J=\in\frac{\partial E}{\partial t}$
(D) $W=\Gamma\theta$

Q132·PhysicsSingle correctJEE Main 2021

Match List-I with List-II. List-I (a) Torque (b) Impulse (c) Tension (d) Surface Tension List-II (i)

MLT^{-1}

(ii)

MT^{-2}

(iii)

ML^{2}T^{-2}

(iv)

MLT^{-2}

Choose the most appropriate answer from the option given below :

(A)(a)–(iii), (b)–(i), (c)–(iv), (d)–(ii)
(B)(a)–(ii), (b)–(i), (c)–(iv), (d)–(iii)
(C)(a)–(i), (b)–(iii), (c)–(iv), (d)–(ii)
(D)(a)–(iii), (b)–(iv), (c)–(i), (d)–(ii)

Q133·PhysicsSingle correctJEE Main 2021

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

(A) $[FT^{-1} V^{-1}]$
(B) $[FTV^{-1}]$
(C) $[FT^{2} V]$
(D) $[FVT^{-1}]$

Q134·PhysicsSingle correctJEE Main 2021

A huge circular arc of length 4.4 ly subtends an angle '4s' at the centre of the circle. How long it would take for a body to complete 4 revolution if its speed is 8 AU per second ? Given : 1 ly =

9.46 \times 10^{15}

m

\qquad

1 AU =

1.5 \times 10^{11}

m

(A) $4.1 \times 10^{8}$ s
(B) $4.5 \times 10^{10}$ s
(C) $3.5 \times 10^{6}$ s
(D) $7.2 \times 10^{8}$ s

Q135·PhysicsSingle correctJEE Main 2021

Which of the following is not a dimensionless quantity ?

(A)Relative magnetic permeability ( $\mu_r$ )
(B)Power factor
(C)Permeability of free space ( $\mu_0$ )
(D)Quality factor

Q136·PhysicsSingle correctJEE Main 2021

Match List-I (physical quantity) with List-II (SI unit). Choose the most appropriate answer from the options given below :

List-I	List-II
a. $R_{H}$ (Rydberg constant)	i.kg m $^{-1}$ s $^{-1}$
b.h (Planck's constant)	ii.kg m $^{2}$ s $^{-1}$
c. $\mu_{B}$ (Magnetic field energy density)	iii.m $^{-1}$
d.η (coefficient of viscocity)	iv.kg m $^{-1}$ s $^{-2}$

(A)(a)–(ii), (b)–(iii), (c)–(iv), (d)–(i)
(B)(a)–(iii), (b)–(ii), (c)–(iv), (d)–(i)
(C)(a)–(iv), (b)–(ii), (c)–(i), (d)–(iii)
(D)(a)–(iii), (b)–(ii), (c)–(i), (d)–(iv)

Q137·PhysicsSingle correctJEE Main 2021

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

(A)[FL $^{-4}$ T $^{2}$ ]
(B)[FL $^{-3}$ T $^{2}$ ]
(C)[FL $^{-5}$ T $^{2}$ ]
(D)[FL $^{-3}$ T $^{3}$ ]

Q138·PhysicsSingle correctJEE Main 2021

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

(A)ohm
(B)mho
(C)joule
(D)newton

Q139·PhysicsSingle correctJEE Main 2021

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 =

EL^{2}M^{-5}G^{-2}

are :-

(A) $[M^{0}\,L^{1}\,T^{0}]$
(B) $[M^{-1}\,L^{-1}\,T^{2}]$
(C) $[M^{1}\,L^{1}\,T^{-2}]$
(D) $[M^{0}\,L^{0}\,T^{0}]$

Q140·PhysicsSingle correctJEE Main 2021

Match List–I with List–II. Choose the most appropriate answer from the options given below :

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	iv. $MLT^{-2}A^{-2}$

(A)(a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)
(B)(a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)
(C)(a)-(iii), (b)-(ii), (c)-(iv), (d)-(i)
(D)(a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)

Q141·PhysicsNumericalJEE Main 2021

The acceleration due to gravity is found upto an accuracy of 4% on a planet. The energy supplied to a simple pendulum to known mass 'm' to undertake oscillations of time period T is being estimated. If time period is measured to an accuracy of 3%, the accuracy to which E is known as ..........%

Q142·PhysicsSingle correctJEE Main 2021

Match List I with List II. List I (a) Capacitance, C (b) Permittivity of free space,

\varepsilon_0

(c) Permeability of free space,

\mu_0

(d) Electric field, E List II (i) M

^1

L

^1

T

^{-3}

A

^{-1}

(ii) M

^{-1}

L

^{-3}

T

^4

A

^2

(iii) M

^{-1}

L

^{-2}

T

^4

A

^2

(iv) M

^1

L

^1

T

^{-2}

A

^{-2}

Choose the correct answer from the options given below :

(A)(a) → (iii), (b) → (ii), (c) → (iv), (d) → (i)
(B)(a) → (iii), (b) → (iv), (c) → (ii), (d) → (i)
(C)(a) → (iv), (b) → (ii), (c) → (iii), (d) → (i)
(D)(a) → (iv), (b) → (iii), (c) → (ii), (d) → (i)

Q143·PhysicsSingle correctJEE Main 2021

A physical 'y' is represented by the formula y = m

^2

r

^{-4}

g

^x

\ell^{-\frac{3}{2}}

if the percentage errors found in y, m, r,

\ell

and g are 18, 1, 0.5, 4 and p respectively, then find the value of x and p.

(A)5 and ± 2
(B) $\frac{16}{3}$ and ± $\frac{3}{2}$
(C)8 and ± 2
(D)4 and ± 3

Q144·PhysicsSingle correctJEE Main 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 formula of

\frac{AD}{B}

is :

(A) $\left[\mathrm{M}^2\mathrm{L}^2\mathrm{T}^{-3}\right]$
(B) $\left[\mathrm{M}^1\mathrm{L}^1\mathrm{T}^{-2}\right]$
(C) $\left[\mathrm{M}\mathrm{L}^2\mathrm{T}^{-3}\right]$
(D) $\left[\mathrm{M}^0\mathrm{L}\mathrm{T}^{-1}\right]$

Q145·PhysicsSingle correctJEE Main 2021

Two vectors

\vec{X}

and

\vec{Y}

have equal magnitude. The magnitude of

\left(\vec{X}-\vec{Y}\right)

is n times the magnitude of

\left(\vec{X}+\vec{Y}\right)

. The angle between

\vec{X}

and

\vec{Y}

is :

(A) $\cos^{-1}\left(\frac{n^2+1}{n^2-1}\right)$
(B) $\cos^{-1}\left(\frac{-n^2-1}{n^2-1}\right)$
(C) $\cos^{-1}\left(\frac{n^2-1}{-n^2-1}\right)$
(D) $\cos^{-1}\left(\frac{n^2+1}{-n^2-1}\right)$

Q146·PhysicsSingle correctJEE Main 2021

The entropy of any system is given by

S = \alpha^2\beta\ \ell n\left[\frac{\mu kR}{J\beta^2}+3\right]

Where

\alpha

and

\beta

are the constants. μ, J, k and R no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant respectively . [ Take

S = \frac{dQ}{T}

] Choose the incorrect option from the following :

(A)S, β, k and μR have the same dimensions.
(B)α and k have the same dimensions.
(C)S and α have different dimensions.
(D)α and J have the same dimensions.

Q147·PhysicsSingle correctJEE Main 2021

If time

(t)

, velocity

(\upsilon)

, and angular momentum

(\ell)

are taken as the fundamental units. Then the dimension of mass

(m)

in terms of

t, \upsilon,

and

\ell

is :

(A) $\left[ t^{-2}\,\upsilon^{-1}\,\ell^{1} \right]$
(B) $\left[ t^{-1}\,\upsilon^{1}\,\ell^{-2} \right]$
(C) $\left[ t^{-1}\,\upsilon^{-2}\,\ell^{1} \right]$
(D) $\left[ t^{1}\,\upsilon^{2}\,\ell^{-1} \right]$

Q148·PhysicsSingle correctJEE Main 2021

The time period of a simple pendulum is given by

T = 2\pi\sqrt{\dfrac{\ell}{g}}

. The measured value of the length of pendulum is 10 cm known to a 1mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using a clock of 1s resolution. The percentage accuracy in the determination of 'g' using this pendulum is 'x'. The value of 'x' to the nearest integer is:-

(A)2%
(B)3%
(C)5%
(D)4%

Q149·PhysicsNumericalJEE Main 2021

Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes 0.01 cm

^{3}

of oleic acid per cm

^{3}

of the solution. Then you make a thin film of this solution (monomolecular thickness) of area 4 cm

^{2}

by considering 100 spherical drops of radius

\left(\frac{3}{40\pi}\right)^{\frac{1}{3}} \times 10^{-3}

cm. Then the thickness of oleic acid layer will be x × 10

^{-14}

m. Where x is___________.

Q150·PhysicsSingle correctJEE Main 2021

In order to determine the Young's Modulus of a wire of radius 0.2 cm (measured using a scale of least count = 0.001 cm) and length 1m (measured using a scale of least count = 1 mm), a weight of mass 1kg (measured using a scale of least count = 1g) was hanged to get the elongation of 0.5 cm (measured using a scale of least count 0.001 cm). What will be the fractional error in the value of Young's Modulus determined by this experiment ?

(A)0.14%
(B)0.9%
(C)9%
(D)1.4%

Q151·PhysicsNumericalJEE Main 2021

The resistance R =

\dfrac{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 the nearest integer is _________.

Q152·PhysicsSingle correctJEE Main 2021

In a typical combustion engine the workdone by a gas molecule is given by

W = \alpha^{2}\beta e^{\frac{-\beta x^{2}}{kT}}

, where x is the displacement, k is the Boltzmann constant and T is the temperature. If α and β are constants, dimensions of α will be :

(A) $[M^{0}\,L\,T^{0}]$
(B) $[M^{2}\,L\,T^{-2}]$
(C) $[M\,L\,T^{-2}]$
(D) $[M\,L\,T^{-1}]$

Q153·PhysicsSingle correctJEE Main 2021

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

(A) $\left[M^{-2}L^{-4}I^{3}T^{7}\right]$
(B) $\left[M^{-2}L^{-3}I^{2}T^{6}\right]$
(C) $\left[M^{-1}L^{-3}I^{-2}T^{-7}\right]$
(D) $\left[M^{-3}L^{-4}I^{3}T^{7}\right]$

Q154·PhysicsSingle correctJEE Main 2021

If e is the electronic charged, c is the speed of light in free space and h is planck's constant, the 1e

^{2}

quantity has dimensions of : 4πε

_{0}

hc

(A)[ LC $^{-1}$ ]
(B)[M $^{0}$ L $^{0}$ T $^{0}$ ]
(C)[ M L T $^{0}$ ]
(D)[M L T $^{-1}$ ]

Q155·PhysicsSingle correctJEE Main 2021

Match List –I with List- II : List-I (a)h (Planck's constant) (b)E (kinetic energy) (c)V (electric potential) (d)P (linear momentum) List-II (i)

[M\,L\,T^{-1}]

(ii)

[M\,L^2\,T^{-1}]

(iii)

[M\,L^2\,T^{-2}]

(iv)

[ML^2I^{-1}\,T^{-3}]

Choose the correct answer from the options given below :

(A)(a) → (ii), (b) → (iii), (c) → (iv), (d) → (i)
(B)(a) → (i), (b) → (ii), (c) → (iv), (d) → (iii)
(C)(a) → (iii), (b) → (ii), (c) → (iv), (d) → (i)
(D)(a) → (iii), (b) → (iv), (c) → (ii), (d) → (i)

Q156·PhysicsSingle correctJEE Main 2021

The period of oscillation of a simple pendulum is

T=2\pi\sqrt{\frac{L}{g}}

. Measured value of 'L' is 1.0 m from meter scale having a minimum division of 1 mm and time of one complete oscillation is 1.95 s measured from stopwatch of 0.01 s resolution. The percentage error in the determination of 'g' will be :

(A)1.33 %
(B)1.30 %
(C)1.13 %
(D)1.03 %

Q157·PhysicsSingle correctJEE Main 2021

The workdone by a gas molecule in an isolated system is given by,

W = \alpha\beta^2 e^{-\frac{x^2}{\alpha kT}}

, where x is the displacement, k is the Boltzmann constant and T is the temperature.

\alpha

and

\beta

are constants. Then the dimensions of

\beta

will be -

(A) $[M^0LT^0]$
(B) $[M^2LT^2]$
(C) $[MLT^{-2}]$
(D) $[ML^2T^{-2}]$

Q158·PhysicsMultiple correctJEE Advanced 2020

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 different quantities are given in terms of a quantity X as follows: [position] =

[X^{\alpha}]

; [speed] =

[X^{\beta}]

; [acceleration] =

[X^{p}]

; [linear momentum] =

[X^{q}]

; [force] =

[X^{r}]

. Then -

(A) $\alpha + p = 2\beta$
(B) $p + q - r = \beta$
(C) $p - q + r = \alpha$
(D) $p + q + r = \beta$

Q159·PhysicsNumericalJEE Advanced 2020

Two capacitors with capacitance values

C_1 = 2000 \pm 10

pF and

C_2 = 3000 \pm 15

pF are connected in series. The voltage applied across this combination is

V = 5.00 \pm 0.02

V. The percentage error in the calculation of the energy stored in this combination of capacitors is ________.

Q160·PhysicsSingle correctJEE Main 2020

A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings 5.50 mm, 5.55 mm, 5.45 mm ; 5.65 mm. The average of these four readings is 5.5375 mm and the standard deviation of the data is 0.07395 mm. The average diameter of the pencil should therefore be recorded as:

(A)(5.5375 ± 0.0739) mm
(B)(5.5375 ± 0.0740) mm
(C)(5.538 ± 0.074) mm
(D)(5.54 ± 0.07) mm

Q161·PhysicsNumericalJEE Main 2020

The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is

\left(\dfrac{x}{100}\right)\%

. If the relative errors in measuring the mass and the diameter are 6.0% and 1.5% respectively, the value of x is __________.

Q162·PhysicsSingle correctJEE Main 2020

Assume that the displacement (s) of air is proportional to the pressure difference

(\Lambda p)

created by a sound wave. Displacement (s) further depends on the speed of sound (v), density of air (ρ) and the frequency (f). If

\Lambda p \sim 10\text{Pa}

,

\upsilon \sim 300

m/s,

\rho \sim \pi 1 \text{ lg} / \text{m}^3

and f ∼ 1000 Hz, then s will be of the order of (take the multiplicative constant to be 1)

(A) $\dfrac{1}{10}$ mm
(B)10 mm
(C) $\dfrac{3}{100}$ mm
(D)1 mm

Q163·PhysicsSingle correctJEE Main 2020

A physical quantity z depends on four observables a, c, c and d, as z =

\dfrac{a^{2}b^{\frac{2}{3}}}{\sqrt{c}\,d^{3}}

. The percentages of error in the measurement of a, b, c and d are 2%, 1.5%, 4% and 2.5% respectively. The percentage of error in z is:

(A)13.5%
(B)16.5%
(C)12.25%
(D)14.5%

Q164·PhysicsSingle correctJEE Main 2020

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

(A) $MLT^{-3}K^{-1}$
(B) $MLT^{-2}K^{-2}$
(C) $MLT^{-2}K$
(D) $MLT^{-3}K$

Q165·PhysicsSingle correctJEE Main 2020

A quantity X is given by

(IF\upsilon^{2}/WL^{4})

in terms of moment of inertia I, force F, velocity υ, work W and Length L. The dimensional formula for x is same as that of:

(A)coefficient of viscosity
(B)planck's constant
(C)energy density
(D)force constant

Q166·PhysicsSingle correctJEE Main 2020

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

(A) $M^{2}L^{0}T^{-1}$
(B) $ML^{2}T^{-2}$
(C) $ML^{0}T^{-3}$
(D) $MLT^{-2}$

Q167·PhysicsSingle correctJEE Main 2020

A quantity f is given by

f=\sqrt{\dfrac{hc^{5}}{G}}

where c is speed of light, G universal gravitational constant and h is the Planck's constant. Dimension of f is that of:

(A)energy
(B)momentum
(C)area
(D)volume

Q168·PhysicsSingle correctJEE Main 2020

A simple pendulum is being used to determine the vale of gravitational acceleration g at a certain place. The length of the pendulum is 25.0 cm and a stop watch with 1 s resolution measures the time taken for 40 oscillations to be 50 s. The accuracy in g is:

(A)4.40%
(B)2.40%
(C)3.40%
(D)5.40%

Q169·PhysicsSingle correctJEE Main 2020

The dimension of

\frac{B^{2}}{2\mu_{0}}

, where B is magnetic field and

\mu_{0}

is the magnetic permeability of vacuum, is

(A)ML $^{2}$ T $^{-1}$
(B)ML $^{2}$ T $^{-2}$
(C)ML $^{-1}$ T $^{-2}$
(D)MLT $^{-2}$

Q170·PhysicsMultiple correctJEE Advanced 2019

Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of L, which of the following statement(s) is/are correct?

(A)The dimension of energy is $L^{-2}$
(B)The dimension of force is $L^{-3}$
(C)The dimension of power is $L^{-5}$
(D)The dimension of linear momentum is $L^{-1}$

Q171·PhysicsSingle correctJEE Main 2019

Which of the following combinations has the dimension of electrical resistance (

\epsilon_0

is the permittivity of vacuum and

\mu_0

is the permeability of vacuum)?

(A) $\sqrt{\dfrac{\epsilon_0}{\mu_0}}$
(B) $\dfrac{\mu_0}{\epsilon_0}$
(C) $\dfrac{\epsilon_0}{\mu_0}$
(D) $\sqrt{\dfrac{\mu_0}{\epsilon_0}}$

Q172·PhysicsSingle correctJEE Main 2019

The formula

X = 5YZ^{2}

X and Z have dimensions of capacitance and magnetic field respectively. What are the dimensions of Y in SI units?

(A) $[M^{-2} L^{0} T^{-4} A^{-2}]$
(B) $[M^{-3} L^{-2} T^{8} A^{-1}]$
(C) $[M^{-2} L^{-2} T^{6} A^{3}]$
(D) $[M^{-1} L^{-2} T^{4} A^{2}]$

Q173·PhysicsSingle correctJEE Main 2019

In SI units, the dimensions of

\sqrt{\dfrac{\epsilon_0}{\mu_0}}

is:

(A) $AT^{-3}ML^{3/2}$
(B) $A^{-1}TML^{3}$
(C) $A^{2}T^{3}M^{-1}L^{-2}$
(D) $AT^{2}M^{-1}L^{-1}$

Q174·PhysicsSingle correctJEE Main 2019

If Surface tension (S), Moment of Inertia (I) and Planck's constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be:

(A) $S^{1/2}I^{1/2}h^{0}$
(B) $S^{1/2}I^{3/2}h^{-1}$
(C) $S^{3/2}I^{1/2}h^{0}$
(D) $S^{1/2}I^{1/2}h^{-1}$

Q175·PhysicsSingle correctJEE Main 2019

The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5

\mu

m diameter of a wire is:

(A)50
(B)200
(C)100
(D)500

Q176·PhysicsSingle correctJEE Main 2019

If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young's modulus will be:

(A) $V^{-2}A^{2}F^{-2}$
(B) $V^{-2}A^{2}F^{2}$
(C) $V^{-4}A^{-2}F$
(D) $V^{-4}A^{2}F$

Q177·PhysicsSingle correctJEE Main 2019

The force of interaction between two atoms is given by

F = \alpha\beta\, exp\left(-\dfrac{x^{2}}{\alpha kt}\right)

; where x is the distance, k is the Boltzmann constant and T is temperature and α and β are two constants. The dimension of β is:

(A)M⁰L²T⁻⁴
(B)M²LT⁻⁴
(C)MLT⁻²
(D)M²L²T⁻²

Q178·PhysicsSingle correctJEE Main 2019

The density of a material in SI units is 128 kg m

^{-3}

. In certain units in which the unit of length is 25 cm and the unit of mass 50 g, the numerical value of density of the material is:

(A)40
(B)16
(C)640
(D)410

Q179·PhysicsSingle correctJEE Main 2019

Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to:

(A) $\sqrt{\dfrac{hc^{5}}{G}}$
(B) $\sqrt{\dfrac{c^{3}}{Gh}}$
(C) $\sqrt{\dfrac{Gh}{c^{5}}}$
(D) $\sqrt{\dfrac{Gh}{c^{3}}}$

Q180·PhysicsSingle correctJEE Advanced 2018

PARAGRAPH "A" If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation

z = x/y

. If the errors in

x, y

and

z

are

\Delta x

,

\Delta y

and

\Delta z

, respectively, then

z \pm \Delta z = \frac{x \pm \Delta x}{y \pm \Delta y} = \frac{x}{y}\left(1 \pm \frac{\Delta x}{x}\right)\left(1 \pm \frac{\Delta y}{y}\right)^{-1}.

The series expansion for

\left(1 \pm \frac{\Delta y}{y}\right)^{-1}

, to first power in

\Delta y/y

, is

1 \mp (\Delta y/y)

. The relative errors in independent variables are always added. So the error in

z

will be

\Delta z = z\left(\frac{\Delta x}{x} + \frac{\Delta y}{y}\right).

The above derivation makes the assumption that

\Delta x/x \ll 1

,

\Delta y/y \ll 1

. Therefore, the higher powers of these quantities are neglected. (There are two questions based on PARAGRAPH "A", the question given below is one of them) Consider the ratio

r = \frac{(1 - a)}{(1 + a)}

to be determined by measuring a dimensionless quantity

a

. If the error in the measurement of

a

is

\Delta a

(\Delta a/a \ll 1)

, then what is the error

\Delta r

in determining

r

?

(A) $\frac{\Delta a}{(1 + a)^{2}}$
(B) $\frac{2\Delta a}{(1 + a)^{2}}$
(C) $\frac{2\Delta a}{(1 - a^{2})}$
(D) $\frac{2a\Delta a}{(1 - a^{2})}$

Q181·PhysicsSingle correctJEE Advanced 2018

PARAGRAPH "X" In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below,

[E]

and

[B]

stand for dimensions of electric and magnetic fields respectively, while

[\in_{0}]

and

[\mu_{0}]

stand for dimensions of the permittivity and permeability of free space respectively.

[L]

and

[T]

are dimensions of length and time respectively. All the quantities are given in SI units. (There are two questions based on PARAGRAPH "X", the question given below is one of them) The relation between

[E]

and

[B]

is

(A) $[E] = [B]\,[L]\,[T]$
(B) $[E] = [B]\,[L]^{-1}\,[T]$
(C) $[E] = [B]\,[L]\,[T]^{-1}$
(D) $[E] = [B]\,[L]^{-1}\,[T]^{-1}$

Q182·PhysicsSingle correctJEE Advanced 2018

PARAGRAPH "X" In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below,

[E]

and

[B]

stand for dimensions of electric and magnetic fields respectively, while

[\in_{0}]

and

[\mu_{0}]

stand for dimensions of the permittivity and permeability of free space respectively.

[L]

and

[T]

are dimensions of length and time respectively. All the quantities are given in SI units. (There are two questions based on PARAGRAPH "X", the question given below is one of them) The relation between

[\in_{0}]

and

[\mu_{0}]

is

(A) $[\mu_{0}] = [\in_{0}]\,[L]^{2}\,[T]^{-2}$
(B) $[\mu_{0}] = [\in_{0}]\,[L]^{-2}\,[T]^{2}$
(C) $[\mu_{0}] = [\in_{0}]^{-1}\,[L]^{2}\,[T]^{-2}$
(D) $[\mu_{0}] = [\in_{0}]^{-1}\,[L]^{-2}\,[T]^{2}$

Q183·PhysicsSingle correctJEE Advanced 2018

PARAGRAPH "A" If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation

z = x/y

. If the errors in

x, y

and

z

are

\Delta x

,

\Delta y

and

\Delta z

, respectively, then

z \pm \Delta z = \frac{x \pm \Delta x}{y \pm \Delta y} = \frac{x}{y}\left(1 \pm \frac{\Delta x}{x}\right)\left(1 \pm \frac{\Delta y}{y}\right)^{-1}.

The series expansion for

\left(1 \pm \frac{\Delta y}{y}\right)^{-1}

, to first power in

\Delta y/y

, is

1 \mp (\Delta y/y)

. The relative errors in independent variables are always added. So the error in

z

will be

\Delta z = z\left(\frac{\Delta x}{x} + \frac{\Delta y}{y}\right).

The above derivation makes the assumption that

\Delta x/x \ll 1

,

\Delta y/y \ll 1

. Therefore, the higher powers of these quantities are neglected. (There are two questions based on PARAGRAPH "A", the question given below is one of them) In an experiment the initial number of radioactive nuclei is 3000. It is found that

1000 \pm 40

nuclei decayed in the first

1.0s

. For

|x| \ll 1

,

\ln(1 + x) = x

up to first power in

x

. The error

\Delta\lambda

, in the determination of the decay constant

\lambda

, in

s^{-1}

, is

(A)0.04
(B)0.03
(C)0.02
(D)0.01

Q184·PhysicsSingle correctJEE Advanced 2017

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is

\delta T = 0.01

seconds and he measures the depth of the well to be

L = 20

meters. Take the acceleration due to gravity

g = 10\ \text{ms}^{-2}

and the velocity of sound is

300\ \text{ms}^{-1}

. Then the fractional error in the measurement,

\delta L/L

, is closest to

(A) $0.2\ \%$
(B) $1\ \%$
(C) $3\ \%$
(D) $5\ \%$

Q185·PhysicsMultiple correctJEE Advanced 2016

In an experiment to determine the acceleration due to gravity g, the formula used for the time period of a periodic motion is

T = 2\pi\sqrt{\frac{7(R-r)}{5g}}

. The values of R and r are measured to be (60 ± 1) mm and (10 ± 1) mm, respectively. In five successive measurements, the time period is found to be 0.52 s, 0.56 s, 0.57 s, 0.54 s and 0.59 s. The least count of the watch used for the measurement of time period is 0.01 s. Which of the following statement(s) is(are) true?

(A)The error in the measurement of r is 10%
(B)The error in the measurement of T is 3.57%
(C)The error in the measurement of T is 2%
(D)The error in the determined value of g is 11%

Q186·PhysicsMultiple correctJEE Advanced 2016

A length-scale (

\ell

) depends on the permittivity (

\varepsilon

) of a dielectric material, Boltzmann constant (

k_B

), the absolute temperature (T), the number per unit volume (n) of certain charged particles, and the charge (q) carried by each of the particles. Which of the following expression(s) for

\ell

is(are) dimensionally correct?

(A) $\ell = \sqrt{\left(\frac{nq^{2}}{\varepsilon k_B T}\right)}$
(B) $\ell = \sqrt{\left(\frac{\varepsilon k_B T}{nq^{2}}\right)}$
(C) $\ell = \sqrt{\left(\frac{q^{2}}{\varepsilon n^{2/3} k_B T}\right)}$
(D) $\ell = \sqrt{\left(\frac{q^{2}}{\varepsilon n^{1/3} k_B T}\right)}$

Q187·PhysicsMultiple correctJEE Advanced 2015

Planck's constant h, speed of light c and gravitational constant G are used to form a unit of length L and a unit of mass M. Then the correct option(s) is(are)

(A) $M \propto \sqrt{c}$
(B) $M \propto \sqrt{G}$
(C) $L \propto \sqrt{h}$
(D) $L \propto \sqrt{G}$

Q188·PhysicsMultiple correctJEE Advanced 2015

In terms of potential difference V, electric current I, permittivity

\varepsilon_{0}

, permeability

\mu_{0}

and speed of light c, the dimensionally correct equation(s) is(are)

(A) $\mu_{0}I^{2} = \varepsilon_{0}V^{2}$
(B) $\varepsilon_{0}I = \mu_{0}V$
(C) $I = \varepsilon_{0}cV$
(D) $\mu_{0}cI = \varepsilon_{0}V$

Q189·PhysicsIntegerJEE Advanced 2015

The energy of a system as a function of time t is given as

E(t) = A^{2}\exp(-\alpha t)

, where

\alpha = 0.2

s

^{-1}

. The measurement of A has an error of 1.25 %. If the error in the measurement of time is 1.50 %, the percentage error in the value of

E(t)

at

t = 5

s is

Q190·PhysicsIntegerJEE Advanced 2014

To find the distance

d

over which a signal can be seen clearly in foggy conditions, a railways engineer uses dimensional analysis and assumes that the distance depends on the mass density

\rho

of the fog, intensity (power/area)

S

of the light from the signal and its frequency

f

. The engineer finds that

d

is proportional to

S^{1/n}

. The value of

n

is

Q191·PhysicsSingle correctJEE Advanced 2013

The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm. The 24

^{th}

division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is

(A)5.112 cm
(B)5.124 cm
(C)5.136 cm
(D)5.148 cm

Q192·PhysicsSingle correctJEE Advanced 2013

Match List I with List II and select the correct answer using the codes given below the lists:

List I	List II
P.Boltzmann Constant	1. $[\mathrm{ML^{2}T^{-1}}]$
Q.Coefficient of viscosity	2. $[\mathrm{ML^{-1}T^{-1}}]$
R.Plank Constant	3. $[\mathrm{MLT^{-3}K^{-1}}]$
S.Thermal conductivity	4. $[\mathrm{ML^{2}T^{-2}K^{-1}}]$

(A)P-3, Q-1, R-2, S-4
(B)P-3, Q-2, R-1, S-4
(C)P-4, Q-2, R-1, S-3
(D)P-4, Q-1, R-2, S-3

Q193·PhysicsMultiple correctJEE Advanced 2013

Using the expression

2d\sin\theta = \lambda

, one calculates the values of

d

by measuring the corresponding angles

\theta

in the range

0

to

90^{\circ}

. The wavelength

\lambda

is exactly known and the error in

\theta

is constant for all values of

\theta

. As

\theta

increases from

0^{\circ}

,

(A)the absolute error in $d$ remains constant.
(B)the absolute error in $d$ increases
(C)the fractional error in $d$ remains constant.
(D)the fractional error in $d$ decreases.

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