JEE Main Previous Year Questions (2016-2025) on the topic of Units and Measurements:
Question 1 (JEE Main 2023)
Match List I with List II:
| List I | List II |
| A. Planck'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 ($\phi$) | III. $[M^1 L^2 T^{-1}]$ |
| D. Momentum ($p$) | IV. $[M^1 L^2 T^{-3} A^{-1}]$ |
Choose the correct answer from the options given below:
(1) A-I, B-III, C-IV, D-II
(2) A-III, B-I, C-II, D-IV
(3) A-II, B-IV, C-III, D-I
(4) A-III, B-IV, C-I, D-II
Question 2 (JEE 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:
(1) $ \dfrac{3}{2}, \dfrac{1}{2}, \dfrac{1}{2} $
(2) $ \dfrac{-3}{2}, \dfrac{-1}{2}, \dfrac{1}{2} $
(3) $ \dfrac{-3}{2}, \dfrac{1}{2}, \dfrac{-1}{2} $
(4) $ \dfrac{1}{2}, \dfrac{-3}{2}, \dfrac{1}{2} $
Question 3 (JEE Main 2023)
Match List I with List II:
| List I | List II |
| A. Surface Tension | I. $[M^1 L^2 T^{-2}]$ |
| B. Pressure | II. $[M^1 L^{-1} T^{-2}]$ |
| C. Viscosity | III. $[M^1 L^0 T^{-2}]$ |
| D. Impulse | IV. $[M^1 L^1 T^{-1}]$ |
Choose the correct answer from the options given below:
(1) A-II, B-I, C-III, D-IV
(2) A-IV, B-III, C-I, D-II
(3) A-III, B-IV, C-I, D-II
(4) A-IV, B-III, C-II, D-I
Question 4 (JEE Main 2023)
Match List I with List II:
| List I | List II |
| A. Torque | I. $[M^1 L^1 T^{-1}]$ |
| B. Stress | II. $[M^1 L^2 T^{-2}]$ |
| C. Latent Heat | III. $[M^1 L^{-1} T^{-2}]$ |
| D. Power | IV. $[M^0 L^2 T^{-2}]$ |
Choose the correct answer from the options given below:
(1) A-I, B-II, C-III, D-IV
(2) A-II, B-III, C-IV, D-I
(3) A-I, B-III, C-IV, D-II
(4) A-III, B-I, C-II, D-IV
Question 5 (JEE Main 2023)
Match List I with List II:
| List I | List II |
| A. Young's Modulus | I. $[M^1 L^2 T^{-1}]$ |
| B. Planck's Constant | II. $[M^1 L^{-1} T^{-2}]$ |
| C. Work Function | III. $[M^1 L^2 T^{-2}]$ |
| D. Coefficient of Viscosity | IV. $[M^1 L^{-1} T^{-1}]$ |
Choose the correct answer from the options given below:
(1) A-II, B-III, C-I, D-IV
(2) A-II, B-III, C-IV, D-I
(3) A-III, B-II, C-IV, D-I
(4) A-III, B-II, C-I, D-IV
Question 6 (JEE Main 2022)
Match List I with List II:
| List I | List II |
| A. Torque | I. $\text{Nms}^{-1}$ |
| B. Stress | II. $\text{J kg}^{-1}$ |
| C. Latent Heat | III. $\text{Nm}$ |
| D. Power | IV. $\text{Nm}^{-2}$ |
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
Question 7 (JEE Main 2022)
In an experiment to find out the diameter of wire using a screw gauge, the following observations were noted:
-
(A) Screw moves 0.5 mm on main scale in one complete rotation.
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(B) Total divisions on circular scale = 50.
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(C) Main scale reading is 2.5 mm.
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(D) 45th division of circular scale is in the pitch line.
-
(E) Instrument has 0.03 mm negative error.
Then the diameter of wire is:
(a) 2.92 mm
(b) 2.54 mm
(c) 2.98 mm
(d) 3.45 mm
Question 8 (JEE Main 2022)
A travelling microscope has 20 divisions per cm on the main scale while its vernier scale has total 50 divisions and 25 vernier scale divisions are equal to 24 main scale divisions. What is the least count of the travelling microscope?
(a) 0.001 cm
(b) 0.002 mm
(c) 0.002 cm
(d) 0.005 cm
Question 9 (JEE Main 2022)
Consider the efficiency of Carnot's engine is given by $\eta = \frac{\alpha \beta}{\sin \theta} e^{\frac{\alpha x}{kT}}$, where $\alpha$ and $\beta$ are constants. If $T$ is temperature, $k$ is Boltzmann 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 $\beta$.
Question 10 (JEE Main 2022)
The dimensions of $\frac{B^2}{2\mu_0}$ will be (if $\mu_0$ is permeability of free space and $B$ is magnetic field):
(a) $[M^1 L^2 T^{-2}]$
(b) $[M^1 L^1 T^{-2}]$
(c) $[M^1 L^{-1} T^{-2}]$
(d) $[M^1 L^2 T^{-2} A^{-1}]$
Question 11 (JEE Main 2022)
An expression of energy density is given by $u = \frac{\alpha}{\beta} \sin\left(\frac{\alpha x}{kt}\right)$, where $\alpha, \beta$ are constants, $x$ is displacement, $k$ is Boltzmann constant and $t$ is the temperature. The dimensions of $\beta$ will be:
(a) $[M^1 L^2 T^{-2} \theta^{-1}]$
(b) $[M^0 L^2 T^{-2}]$
(c) $[M^0 L^0 T^0]$
(d) $[M^0 L^2 T^0]$
Question 12 (JEE 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%
Question 13 (JEE Main 2022)
In a Vernier Calipers, 10 divisions of Vernier scale is equal to the 9 divisions of main scale. When both jaws touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and 4th Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to 1 mm. While measuring the diameter of a spherical body, the zero of the Vernier scale lies between 30 and 31 divisions of main scale and 6th Vernier scale division coincides. The diameter of the spherical body will be:
(a) 3.02 cm
(b) 3.06 cm
(c) 3.10 cm
(d) 3.20 cm
Question 14 (JEE Main 2022)
A screw gauge of pitch 0.5 mm and 50 divisions on its circular scale is used to measure the diameter of a uniform wire of length 6.8 cm. The main scale reading is 1.5 mm and circular scale reading is 7. The calculated curved surface area of the wire to appropriate significant figures is:
(a) $6.8\text{ cm}^2$
(b) $3.4\text{ cm}^2$
(c) $3.9\text{ cm}^2$
(d) $2.4\text{ cm}^2$
Question 15 (JEE Main 2022)
The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are 1%, 2% and 3% respectively. The maximum percentage error in the detection of the dissipated heat ($H = I^2Rt$) will be:
(a) 2%
(b) 4%
(c) 6%
(d) 8%
Question 16 (JEE 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) $[PA^{-1} T^0]$
(b) $[PA T^{-1}]$
(c) $[PA^{-1} T]$
(d) $[PA^{-1} T^{-1}]$
Question 17 (JEE Main 2022)
If $n$ main scale divisions coincide with $(n + 1)$ vernier scale divisions. The least count of vernier callipers, when each centimetre on the main scale is divided into five equal parts, will be:
(a) $\frac{2}{n+1}\text{ mm}$
(b) $\frac{5}{n+1}\text{ mm}$
(c) $\frac{1}{2n}\text{ mm}$
(d) $\frac{1}{5n}\text{ mm}$
Question 18 (JEE 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
Question 19 (JEE 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
Question 20 (JEE Main 2022)
If $Z = \frac{A^2 B^3}{C^4}$, then the relative error in $Z$ will be:
(a) $\frac{\Delta A}{A} + \frac{\Delta B}{B} + \frac{\Delta C}{C}$
(b) $2\frac{\Delta A}{A} + 3\frac{\Delta B}{B} - 4\frac{\Delta C}{C}$
(c) $2\frac{\Delta A}{A} + 3\frac{\Delta B}{B} + 4\frac{\Delta C}{C}$
(d) $\frac{\Delta A}{A} + \frac{\Delta B}{B} - \frac{\Delta C}{C}$
Question 21 (JEE Main 2022)
The dimension of mutual inductance is:
(a) $[M^1 L^2 T^{-2} A^{-1}]$
(b) $[M^1 L^2 T^{-3} A^{-1}]$
(c) $[M^1 L^2 T^{-2} A^{-2}]$
(d) $[M^1 L^2 T^{-3} A^{-2}]$
Question 22 (JEE 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 $\alpha$ and $\beta$ are constants, $x$ is distance, $k$ is Boltzmann constant and $t$ is the temperature. Then the dimensions of $\alpha$ will be:
(a) $[M^0 L^{-1} T^0]$
(b) $[M^1 L^0 T^{-2}]$
(c) $[M^1 L^1 T^{-2}]$
(d) $[M^1 L^2 T^{-2}]$
Question 23 (JEE Main 2022)
A silver wire has a mass $(0.6 \pm 0.006)\text{ g}$, radius $(0.5 \pm 0.005)\text{ mm}$ and length $(4 \pm 0.04)\text{ cm}$. The maximum percentage error in the measurement of its density will be:
(a) 4%
(b) 3%
(c) 6%
(d) 7%
Question 24 (JEE Main 2022)
The SI unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be:
(a) $[M^1 L^{-1} T^{-1}]$
(b) $[M^1 L^{-1} T^{-2}]$
(c) $[M^1 L^2 T^{-1}]$
(d) $[M^{-1} L^3 T^0]$
Question 25 (JEE Advanced 2022)
Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is 0.05 mm. The circular scale has 100 divisions and for one full rotation of the circular scale, the main scale shifts by two divisions. The measured readings are listed below. What are the diameter and cross-sectional area of the wire measured using the screw gauge?
(a) $2.22 \pm 0.02\text{ mm}$, $\pi(1.23 \pm 0.02)\text{ mm}^2$
(b) $2.22 \pm 0.01\text{ mm}$, $\pi(1.23 \pm 0.01)\text{ mm}^2$
(c) $2.14 \pm 0.02\text{ mm}$, $\pi(1.14 \pm 0.02)\text{ mm}^2$
(d) $2.14 \pm 0.01\text{ mm}$, $\pi(1.14 \pm 0.01)\text{ mm}^2$
Question 26 (JEE Main 2021)
A student determined Young's Modulus of elasticity ($Y$) using the formula $Y = \frac{MgL}{\pi r^2 l}$. The value of $g$ is taken to be $9.8\text{ m/s}^2$ without any significant error. His observations are as follows: (Mass $M$, Length $L$, radius $r$, elongation $l$). Then the fractional error in the measurement of $Y$ is:
(a) 0.0083
(b) 0.0155
(c) 0.155
(d) 0.083
Question 27 (JEE 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) $[FVT^{-1}]$
Question 28 (JEE 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, $T$ = torque, $\epsilon$ = permittivity, $E$ = electric field, $J$ = current density, $L$ = length).
(a) $h = \frac{2s \cos \theta}{\rho r g}$
(b) $v = \frac{\pi p a^4}{8 \eta L}$
(c) $J = \sigma E$
(d) $W = T\theta$
Question 29 (JEE Main 2021)
Match List I with List II:
| List I | List II |
| A. Torque ($\tau$) | I. $[M^1 L^1 T^{-1}]$ |
| B. Impulse ($I$) | II. $[M^1 L^0 T^{-2}]$ |
| C. Tension force | III. $[M^1 L^2 T^{-2}]$ |
| D. Surface Tension | IV. $[M^1 L^1 T^{-2}]$ |
Choose the most appropriate answer from the options 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
Question 30 (JEE Main 2021)
An object is placed at the focus of a concave lens having focal length $f$. What is the magnification and distance of the image from the optical centre of the lens?
(a) $1, \infty$
(b) Very high, $\infty$
(c) $1/2, f/2$
(d) $1/4, f/4$
Question 30 (JEE Main 2021)
An object is placed at the focus of a concave lens having focal length $f$. What is the magnification and distance of the image from the optical centre of the lens?
(a) $1, \infty$
(b) Very high, $\infty$
(c) $1/2, f/2$
(d) $1/4, f/4$
Question 31 (JEE 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) $[FL^{-3} T^3]$
Question 32 (JEE Main 2021)
Match List I with List II:
| List I | List II |
| A. Rydberg Constant | I. $\text{kg m}^2 \text{s}^{-1}$ |
| B. Planck's Constant | II. $\text{m}^{-1}$ |
| C. Magnetic Field Energy Density | III. $\text{kg m}^{-1} \text{s}^{-1}$ |
| D. Coefficient of Viscosity | IV. $\text{kg m}^{-1} \text{s}^{-2}$ |
Choose the most appropriate answer from the options given below:
(a) A-II, B-III, C-IV, D-I
(b) A-II, B-I, C-IV, D-III
(c) A-IV, B-II, C-I, D-III
(d) A-III, B-II, C-I, D-IV
Question 33 (JEE Main 2021)
If $E$ and $H$ represent 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
Question 34 (JEE 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
Question 35 (JEE Main 2021)
If the length of the pendulum in a pendulum clock increases by 0.1%, then the error in time per day is:
(a) 86.4 s
(b) 4.32 s
(c) 43.2 s
(d) 8.64 s
Question 36 (JEE Main 2021)
Match List I with List II:
| List I | List II |
| A. Magnetic Induction | I. $[ML^2 T^{-2} A^{-1}]$ |
| B. Magnetic Flux | II. $[MT^{-2} A^{-1}]$ |
| C. Magnetic Permeability | III. $[M^0 L^{-1} A]$ |
| D. Magnetization | IV. $[MLT^{-2} A^{-2}]$ |
Choose the correct answer from the options given below:
(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
Question 37 (JEE 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) $[M^0 L^0 T^0]$
Question 38 (JEE Main 2021)
In a Screw Gauge, the fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are 50 divisions on the circular scale, and the main scale moves by 0.5 mm on a complete rotation. For a particular observation, the reading on the main scale is 5 mm and the 20th division of the circular scale coincides with the reference line. Calculate the true reading:
(a) 5.00 mm
(b) 5.25 mm
(c) 5.15 mm
(d) 5.20 mm
Question 39 (JEE Main 2021)
A physical quantity $y$ is represented by the formula $y = m^2 r^{-4} g^x l^{3/2}$. If the percentage errors found in $y, m, r, l$ and $g$ are 18, 1, 0.5, 4 and p respectively, then find the value of $x$ and $p$:
(a) 5 and $\pm 2$
(b) 4 and $\pm 3$
(c) $16/3$ and $\pm 3/2$
(d) 8 and $\pm 2$
Question 40 (JEE Main 2021)
Assertion A: If in five complete rotations of the circular scale, the distance travelled on the main scale of the screw gauge is 5 mm and there are 50 total divisions on the circular scale, then the least count is 0.001 cm.
Reason R: Least Count = Pitch / Total divisions on circular scale.
In the light of the above statements, choose the most appropriate answer:
(a) A is not correct but R is correct.
(b) Both A and R are correct and R is the correct explanation of A.
(c) A is correct but R is not correct.
(d) Both A and R are correct and R is NOT the correct explanation of A.
Question 41 (JEE 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 $AD/B$ is:
(a) $[M^0 L^1 T^{-1}]$
(b) $[M^1 L^2 T^{-3}]$
(c) $[M^1 L^1 T^{-2}]$
(d) $[M^2 L^2 T^{-3}]$
Question 42 (JEE Main 2021)
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:
(a) $[t^{-1} v^1 l^1]$
(b) $[t^1 v^2 l^1]$
(c) $[t^{-1} v^{-1} l^1]$
(d) $[t^{-1} v^{-2} l^1]$
Question 43 (JEE Main 2021)
The vernier scale used for measurement has a positive zero error of 0.2 mm. If while taking a measurement it was noted that '0' on the vernier scale lies between 8.5 cm and 8.6 cm, vernier coincidence is 6, then the correct value of measurement is ___________ cm. (least count = 0.01 cm)
(a) 8.58 cm
(b) 8.54 cm
(c) 8.56 cm
(d) 8.36 cm
Question 44 (JEE 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 1 m (measured using a scale of least count = 1 mm), a weight of mass 1 kg (measured using a scale of least count = 1 g) 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) 9%
(c) 1.4%
(d) 0.9%
Question 45 (JEE Main 2021)
One main scale division of a vernier callipers is '$a$' cm and $n^{th}$ division of the vernier scale coincide with $(n - 1)^{th}$ division of the main scale. The least count of the callipers in mm is:
(a) $\frac{10a}{n}$
(b) $\frac{a}{n}$
(c) $\frac{10n}{a}$
(d) $\frac{n}{10a}$
Question 46 (JEE Main 2021)
If '$C$' and '$V$' represent capacity and voltage respectively, then what are the dimensions of $\lambda$ where $C/V = \lambda$?
(a) $[M^{-3} L^{-4} I^3 T^7]$
(b) $[M^{-2} L^{-3} I^2 T^6]$
(c) $[M^{-2} L^{-4} I^3 T^7]$
(d) $[M^{-1} L^{-3} I^{-2} T^{-7}]$
Question 47 (JEE Main 2021)
In a typical combustion engine the work done by a gas molecule is given by $W = \alpha^2 \beta e^{-\beta x^2 / kT}$, where $x$ is the displacement, $k$ is the Boltzmann constant and $T$ is the temperature. If $\alpha$ and $\beta$ are constants, dimensions of $\alpha$ will be:
(a) $[M^0 L^1 T^0]$
(b) $[M^1 L^1 T^{-1}]$
(c) $[M^1 L^1 T^{-2}]$
(d) $[M^2 L^1 T^{-2}]$
Question 48 (JEE Main 2021)
If $e$ is the electronic charge, $c$ is the speed of light in free space and $h$ is Planck's constant, the quantity $\frac{e^2}{4\pi \epsilon_0 hc}$ has dimensions of:
(a) $[M^1 L^1 T^{-1}]$
(b) $[M^1 L^1 T^0]$
(c) $[M^0 L^0 T^0]$
(d) $[L^1 C^{-1}]$
Question 49 (JEE Main 2021)
The pitch of the screw gauge is 1 mm and there are 100 divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies 8 divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while 72nd division on circular scale coincides with the reference line. The radius of the wire is:
(a) 1.80 mm
(b) 0.90 mm
(c) 0.82 mm
(d) 1.64 mm
Question 50 (JEE Main 2021)
Match List I with List II:
| List I | List II |
| A. Kinetic Energy | I. $[M^1 L^2 T^{-1}]$ |
| B. Momentum | II. $[M^1 L^2 T^{-2}]$ |
| C. Planck Constant | III. $[M^1 L^1 T^{-1}]$ |
| D. Power | IV. $[M^1 L^2 T^{-3}]$ |
Choose the correct answer from the options given below:
(a) A-II, B-III, C-I, D-IV
(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