How much of JEE Main comes from Units and Measurements?

JEEGenie estimates about 2% of JEE Main marks come from Units and Measurements, based on recent papers. The share varies from year to year.

Which formulas matter most in Units and Measurements?

The Units and Measurements sheet on this page has 23 formula entries, starting with Physical Quantity and Unit, Fundamental and Derived Units, SI Prefixes, Dimensional Formula, Dimensional Analysis for Equation Consistency. Each one comes with when to use it and the trap to avoid.

What topics does Units and Measurements cover for JEE?

Units and Measurements covers Units and Dimensions, Dimensional Analysis, Significant Figures, Errors in Measurement, Vernier and Screw Gauge.

How should I revise Units and Measurements before the exam?

Learn each formula together with its condition of use, read the trap listed beside it, then practise questions and review every mistake. The practice link on this page opens Units and Measurements questions on JEEGenie.

How many previous-year questions are there on Units and Measurements?

JEEGenie has 566 previous-year questions on Units and Measurements, and this page shows a few with worked explanations.

Is practice on Units and Measurements free on JEEGenie?

Sign-up is free and includes a 7-day Pro trial. After the trial, free accounts keep a limited daily quota.

Units and Measurements for JEE Main & Advanced — formulas, what is asked, and traps

JEEGenie estimates about 2% of JEE Main marks come from Units and Measurements. This page covers 23 formula entries, each with when to use it, what JEE asks and the traps. A common slip: Confusing fundamental and derived quantities (e.g., area is derived, not fundamental).

Key points to know

Physical Quantity and Unit. A physical quantity is a measurable property of a system; its measurement requires a standard called a unit. Every physical quantity = numerical value × unit.
Fundamental and Derived Units. Fundamental units (mass, length, time, etc.) are independent; derived units (e.g., velocity, force) are combinations of fundamental units.
SI Prefixes. SI prefixes denote powers of 10 (e.g., kilo = $10^{3}$ , milli = $10^{- 3}$ , micro = $10^{- 6}$ , nano = $10^{- 9}$ ).
Dimensional Formula. Dimensional formula expresses a physical quantity in terms of fundamental dimensions: mass (M), length (L), time (T), etc. (e.g., velocity = $[L T^{- 1}]$ ).
Significant Figures. Significant figures are the digits in a measurement that are known reliably plus one uncertain digit. Rules: non-zero digits are always significant; zeros between non-zero digits are significant; leading zeros are not; trailing zeros after decimal are significant.
Accuracy and Precision. Accuracy is how close a measurement is to the true value; precision is how close repeated measurements are to each other. High precision does not guarantee high accuracy.
Error in Measurement. Error = measured value - true value. Types: systematic (consistent bias) and random (fluctuations). Absolute error = $∣ Δ a ∣$ ; relative error = $Δ a / a_{mean}$ ; percentage error = relative error $\times 100 %$ .
Least Count and Instrument Error. Least count is the smallest measurement an instrument can make (e.g., vernier caliper: 0.01 cm, screw gauge: 0.001 cm). Instrument error is often taken as half the least count or as specified.
Order of Magnitude. Order of magnitude of a number is the power of 10 nearest to it (NCERT rule: round $a$ to 1 if $a \leq 5$ , to 10 if $a > 5$ ). For example, $4 \times 10^{4}$ has order $10^{4}$ and $8 \times 10^{4}$ has order $10^{5}$ .
Common Physical Constants and Their Dimensions. Memorize dimensions of key constants: Planck's constant $h = [M L^{2} T^{- 1}]$ , gravitational constant $G = [M^{- 1} L^{3} T^{- 2}]$ , Boltzmann constant $k = [M L^{2} T^{- 2} K^{- 1}]$ , permittivity $ϵ_{0} = [M^{- 1} L^{- 3} T^{4} A^{2}]$ .
Conversion of Units Using Dimensions. To convert a quantity from one system of units to another, use the dimensional formula: $n_{2} = n_{1} {(\frac{M_{1}}{M_{2}})}^{a} {(\frac{L_{1}}{L_{2}})}^{b} {(\frac{T_{1}}{T_{2}})}^{c}$ .
Parallax Method for Distance Measurement. Parallax angle $θ$ (in radians) = baseline $b$ / distance $D$ . For distant stars, $D = b / θ$ (with $b$ as Earth's orbit diameter).
Range of Lengths and Orders of Magnitude. Know typical orders: atomic size $\sim 10^{- 10}$ m, nucleus $\sim 10^{- 15}$ m, Earth radius $\sim 10^{7}$ m, distance to nearest star $\sim 10^{16}$ m.
Range of Masses and Orders of Magnitude. Typical masses: electron $\sim 10^{- 31}$ kg, proton $\sim 10^{- 27}$ kg, human $\sim 10^{2}$ kg, Earth $\sim 10^{24}$ kg, Sun $\sim 10^{30}$ kg.
Range of Time Intervals and Orders of Magnitude. Typical times: light crossing a nuclear distance $\sim 10^{- 22}$ s (NCERT value; direct estimate $\sim 10^{- 24}$ s), molecular vibration $\sim 10^{- 13}$ s, human heartbeat $\sim 1$ s, age of universe $\sim 10^{17}$ s.

Formula sheet

Name	Formula	When to use
Physical Quantity and Unit	$Physical Quantity = n \times u$	Whenever converting between units or expressing measurements.
Fundamental and Derived Units	$Derived unit = [M^{a} L^{b} T^{c} \dots]$	When analyzing dimensional formulas or checking consistency of equations.
SI Prefixes	$1 km = 10^{3} m$ , $1 mm = 10^{- 3} m$ , $1 μ m = 10^{- 6} m$ , $1 nm = 10^{- 9} m$	When converting between metric units or expressing very large/small quantities.
Dimensional Formula	$[Velocity] = [M^{0} L^{1} T^{- 1}]$	To check equation consistency, derive relations, or convert units.
Dimensional Analysis for Equation Consistency	$[L H S] = [R H S]$	When verifying derived formulas or checking if an equation is plausible.
Deriving Relations Using Dimensional Analysis	$T = k l^{a} g^{b}$ → $[T] = [L]^{a} [L T^{- 2}]^{b}$ → $a = 1 / 2, b = - 1 / 2$	When you need to guess the formula for a new quantity based on known dependencies.
Significant Figures	Example: $0.00450$ has 3 significant figures (4,5,0).	When reporting measurements or performing calculations with limited precision.
Arithmetic with Significant Figures	Example: $12.11 + 0.3 = 12.4$ (one decimal). $2.5 \times 3.42 = 8.6$ (two sig figs).	When performing calculations with measured values to avoid false precision.
Accuracy and Precision	No formula, but concept: accurate = small systematic error; precise = small random error.	When evaluating experimental data or instrument quality.
Error in Measurement	$Relative error = \frac{Δ a}{a_{mean}}$ , $Percentage error = \frac{Δ a}{a_{mean}} \times 100 %$	When analyzing experimental data or estimating uncertainty.
Propagation of Errors (Addition/Subtraction)	$Δ Z = Δ A + Δ B$	When combining measurements through addition or subtraction.
Propagation of Errors (Multiplication/Division)	$\frac{Δ Z}{Z} = \frac{Δ A}{A} + \frac{Δ B}{B}$	When combining measurements through multiplication or division.
Propagation of Errors (Powers and Functions)	$\frac{Δ Z}{Z} = n \frac{Δ A}{A}$ (for $Z = A^{n}$ ); $Δ Z = ∣ \frac{d Z}{d A} ∣ Δ A$ (general)	When dealing with powers, roots, or trigonometric functions of measured quantities.
Least Count and Instrument Error	$Least count = \frac{value of 1 main scale division}{number of vernier divisions}$ (for vernier)	When reading measurements from instruments or calculating instrument precision.
Vernier Caliper Reading	$Reading = MSR + (VCD \times LC)$ ; $Corrected reading = Reading - Zero error$	When measuring length with a vernier caliper.
Screw Gauge Reading	$Reading = MSR + (CSR \times LC)$ ; $LC = \frac{pitch}{number of circular divisions}$	When measuring small thicknesses (e.g., wire diameter).
Order of Magnitude	$N = a \times 10^{b}$ with $1 \leq a < 10$ ; order $= 10^{b}$ if $a \leq 5$ , else $10^{b + 1}$ (NCERT convention)	When estimating or comparing very large/small quantities.
Common Physical Constants and Their Dimensions	$[h] = [M L^{2} T^{- 1}]$ , $[G] = [M^{- 1} L^{3} T^{- 2}]$ , $[k] = [M L^{2} T^{- 2} K^{- 1}]$ , $[ϵ_{0}] = [M^{- 1} L^{- 3} T^{4} A^{2}]$	When using dimensional analysis or deriving formulas involving these constants.
Conversion of Units Using Dimensions	$n_{2} = n_{1} {(\frac{M_{1}}{M_{2}})}^{a} {(\frac{L_{1}}{L_{2}})}^{b} {(\frac{T_{1}}{T_{2}})}^{c}$	When converting between different unit systems (e.g., CGS to SI).
Parallax Method for Distance Measurement	$θ = \frac{b}{D}$ (small angle approximation); $D = \frac{b}{θ}$	When estimating astronomical distances (e.g., distance to a star).
Range of Lengths and Orders of Magnitude	No formula; memorize approximate values.	When estimating or comparing scales in physics problems.
Range of Masses and Orders of Magnitude	No formula; memorize approximate values.	When estimating masses in problems (e.g., number of atoms in a sample).
Range of Time Intervals and Orders of Magnitude	No formula; memorize approximate values.	When estimating time scales in physics (e.g., period of oscillation).

Open the Units and Measurements formula page

What JEE asks

Physical Quantity and Unit. JEE often asks unit conversion problems where you must apply $n_{1} u_{1} = n_{2} u_{2}$ .
Fundamental and Derived Units. JEE tests identification of derived units (e.g., unit of pressure = ${kg m}^{- 1} s^{- 2}$ ).
SI Prefixes. JEE often includes prefix conversions in numerical problems (e.g., $1 nm = 10^{- 9} m$ ).
Dimensional Formula. JEE asks to find dimensional formula of a given quantity (e.g., pressure gradient).
Dimensional Analysis for Equation Consistency. JEE often gives an equation and asks if it is dimensionally correct (e.g., $v = \sqrt{2 g h}$ ).
Deriving Relations Using Dimensional Analysis. JEE may ask to derive the expression for frequency of a vibrating string using dimensions.
Significant Figures. JEE asks to determine the number of significant figures in a given value (e.g., $3.00 \times 10^{8}$ has 3).
Arithmetic with Significant Figures. JEE may give a calculation and ask the result with correct significant figures.
Accuracy and Precision. JEE may ask to identify whether a set of measurements is precise or accurate.
Error in Measurement. JEE often asks to compute percentage error from given absolute errors.
Propagation of Errors (Addition/Subtraction). JEE may give two lengths with errors and ask the error in their sum or difference.
Propagation of Errors (Multiplication/Division). JEE often asks error in derived quantities like density ( $ρ = m / V$ ) or resistance ( $R = V / I$ ).
Propagation of Errors (Powers and Functions). JEE may ask error in $T = 2 π \sqrt{l / g}$ given errors in $l$ and $g$ .
Least Count and Instrument Error. JEE often asks to compute least count of vernier caliper or screw gauge from given data.
Vernier Caliper Reading. JEE often gives a diagram of vernier scale and asks the reading.
Screw Gauge Reading. JEE may give a screw gauge diagram and ask the thickness including zero error.
Order of Magnitude. JEE may ask the order of magnitude of physical constants (e.g., speed of light $\sim 10^{8}$ m/s).
Common Physical Constants and Their Dimensions. JEE often asks to find dimensions of a constant from a given equation (e.g., $E = h ν$ ).
Conversion of Units Using Dimensions. JEE may ask to convert 1 N (SI) to dyne (CGS) using dimensions.
Parallax Method for Distance Measurement. JEE may give parallax angle and baseline, ask distance in parsec or light-years.
Range of Lengths and Orders of Magnitude. JEE may ask the order of magnitude of a given length (e.g., wavelength of light $\sim 10^{- 7}$ m).
Range of Masses and Orders of Magnitude. JEE may ask the order of magnitude of mass of a given object (e.g., a virus $\sim 10^{- 15}$ kg).
Range of Time Intervals and Orders of Magnitude. JEE may ask the order of magnitude of a time interval (e.g., half-life of a radioactive element).

Common traps

Confusing fundamental and derived quantities (e.g., area is derived, not fundamental). Physical Quantity and Unit
Mistaking radian or steradian as fundamental (they are supplementary). Fundamental and Derived Units
Confusing micro ( $μ$ ) with milli (m) or nano (n). SI Prefixes
Forgetting that dimensionless constants (like $π$ , $e$ ) have no dimensions. Dimensional Formula
Assuming dimensional correctness implies physical correctness (it only checks consistency). Dimensional Analysis for Equation Consistency
Forgetting that dimensionless constants (like $2 π$ ) cannot be determined by dimensions. Deriving Relations Using Dimensional Analysis
Counting leading zeros as significant (e.g., $0.002$ has 1, not 3). Significant Figures
Rounding incorrectly (e.g., $2.5 \times 3.42 = 8.55$ rounded to 8.6, not 8.5). Arithmetic with Significant Figures
Using the terms interchangeably (they are distinct). Accuracy and Precision
Confusing absolute error with relative error. Error in Measurement
Using relative error instead of absolute error for addition/subtraction. Propagation of Errors (Addition/Subtraction)
Using absolute errors instead of relative errors. Propagation of Errors (Multiplication/Division)
Forgetting to convert angles to radians for trigonometric functions. Propagation of Errors (Powers and Functions)
Confusing least count with accuracy (least count is a limit, not the actual error). Least Count and Instrument Error

Topics in Units and Measurements

Units and Dimensions
Dimensional Analysis
Significant Figures
Errors in Measurement
Vernier and Screw Gauge

Previous-year questions on Units and Measurements

JEEGenie has 566 previous-year questions on Units and Measurements. A few worked examples follow.

Year	Questions
2026	53
2025	49
2024	75
2023	65
2022	59
2021	65
2020	35
2019	36
2018	18
2017	10
2016	9
2015	6
2014	7
2013	7
2012	8
2011	3
2010	4
2009	3
2008	6
2007	4
2006	5
2005	6
2004	4
2003	11
2002	4
2001	1
2000	1
1998	2
1997	2
1995	2
1986	1
1985	1
1984	1
1982	1
1981	1
1980	1

Question 1 easy

The dimensional formula of

\frac{1}{2} ϵ_{0} E^{2}

(

ϵ_{0}

= permittivity of vacuum and

E

= electric field) is

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

. The value of

2 a - b + c =

________.

0
1
-1
2

Answer: B

Explanation.

\frac{1}{2} ϵ_{0} E^{2}

is the energy density of the electric field. Energy density

= \frac{Energy}{Volume}

. Dimensional formula of energy is

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

. Dimensional formula of volume is

[L^{3}]

. Therefore, dimensions of energy density:

[\frac{1}{2} ϵ_{0} E^{2}] = \frac{[M L^{2} T^{- 2}]}{[L^{3}]} = [M L^{- 1} T^{- 2}]

Comparing with

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

, we get:

a = 1, b = - 1, c = - 2

Now compute:

2 a - b + c = 2 (1) - (- 1) + (- 2) = 2 + 1 - 2 = 1

Thus, the value is:

1

**Answer: B**

From NTA/IIT papers: JEE Main 2026 · 2 Apr Shift 1

Question 2 medium

Considering Bohr's atomic model for hydrogen atom : (A) the energy of H atom in ground state is same as energy of

{H e}^{+}

ion in its first excited state. (B) the energy of H atom in ground state is same as that for

{L i}^{+ +}

ion in its second excited state. (C) the energy of H atom in its ground state is same as that of

{H e}^{+}

ion for its ground state. (D) the energy of

{H e}^{+}

ion in its first excited state is same as that for

{L i}^{+ +}

ion in its ground state. Choose the correct answer from the options given below :

(A), (B) only
(A), (D) only
(A), (C) only
(B), (D) only

Answer: A

Explanation. Energy in Bohr model:

E_{n} = - 13.6 \frac{Z^{2}}{n^{2}}

eV. For H (

Z = 1

), ground state (

n = 1

E = - 13.6

eV. (A) He

^{+}

(

Z = 2

), first excited state (

n = 2

E = - 13.6 \cdot \frac{4}{4} = - 13.6

eV. Matches H ground. True. (B) Li

^{+ +}

(

Z = 3

), second excited state (

n = 3

E = - 13.6 \cdot \frac{9}{9} = - 13.6

eV. Matches H ground. True. (C) He

^{+}

ground state (

n = 1

E = - 13.6 \cdot 4 = - 54.4

eV. Not equal. False. (D) He

^{+}

first excited (

n = 2

- 13.6

eV. Li

^{+ +}

ground (

n = 1

- 13.6 \cdot 9 = - 122.4

eV. Not equal. False. Thus only (A) and (B) are correct. Answer is option A.

From NTA/IIT papers: JEE Main 2025 · 2 Apr Shift 1

Question 3 hard

A hydrogen atom changes its state from

n = 3

n = 2

. Due to recoil, the percentage change in the wave length of emitted light is approximately

1 \times 10^{- n}

. The value of

n

is _______. [Given Rhc

= 13.6 e V, h c = 1242 e V n m, h = 6.6 \times 10^{- 34} J s

mass of the hydrogenatom

= 1.6 \times 10^{- 27} k g

]

Answer: 7

Explanation. **Step 1: Energy of the emitted photon** For a hydrogen atom transition from

n = 3

n = 2

Δ E = 13.6 (\frac{1}{2^{2}} - \frac{1}{3^{2}}) = 13.6 (\frac{1}{4} - \frac{1}{9})

= 13.6 (\frac{9 - 4}{36}) = 13.6 \times \frac{5}{36}

Δ E = \frac{68}{36} = 1.8889 eV

The photon wavelength is

λ = \frac{h c}{Δ E} = \frac{1242}{1.8889} nm

λ \approx 657.6 nm

**Step 2: Momentum of the emitted photon** The photon momentum is

p = \frac{E}{c}

The hydrogen atom recoils with equal and opposite momentum. If

M

is the mass of the hydrogen atom, the recoil kinetic energy is

K = \frac{p^{2}}{2 M} = \frac{E^{2}}{2 M c^{2}}

**Step 3: Energy lost to recoil** The actual photon energy is slightly less than

Δ E

because the atom recoils. The recoil energy is

K = \frac{(Δ E)^{2}}{2 M c^{2}}

Using

Δ E = 1.8889 eV

K = \frac{(1.8889)^{2}}{2 M c^{2}}

Now

M c^{2}

for the hydrogen atom:

M = 1.6 \times 10^{- 27} kg

M c^{2} = (1.6 \times 10^{- 27}) (3 \times 10^{8})^{2}

= 1.6 \times 10^{- 27} \times 9 \times 10^{16} = 1.44 \times 10^{- 10} J

Convert to eV:

1 eV = 1.6 \times 10^{- 19} J

M c^{2} = \frac{1.44 \times 10^{- 10}}{1.6 \times 10^{- 19}} = 9.0 \times 10^{8} eV

Thus

K = \frac{(1.8889)^{2}}{2 (9.0 \times 10^{8})}

(1.8889)^{2} \approx 3.568

K = \frac{3.568}{1.8 \times 10^{9}} \approx 1.982 \times 10^{- 9} eV

**Step 4: Fractional change in wavelength** Since

E = \frac{h c}{λ}

a small change in energy gives

\frac{Δ λ}{λ} \approx \frac{Δ E}{E}

Here the photon energy is reduced by the recoil energy

K

, so

\frac{Δ λ}{λ} \approx \frac{K}{Δ E}

\frac{Δ λ}{λ} \approx \frac{1.982 \times 10^{- 9}}{1.8889}

\approx 1.049 \times 10^{- 9}

**Step 5: Percentage change** Percentage change is

\frac{Δ λ}{λ} \times 100 \approx 1.049 \times 10^{- 7} %

This is approximately

1 \times 10^{- 7} %

Comparing with the given form

1 \times 10^{- n}

, we get

n = 7

7.0

From NTA/IIT papers: JEE Main 2024 · 4 Apr Shift 1

Question 4 easy

The radius of fifth orbit of the

{L i}^{+ +}

is __________

\times 10^{- 12} m

. Take: radius of hydrogen atom

= 0.51 \overset{o}{A}

Answer: 425

Explanation. For a hydrogen-like ion, the radius of the

n

-th orbit is given by

r_{n} = \frac{n^{2}}{Z} a_{0}

where: -

a_{0}

is the Bohr radius for hydrogen, -

Z

is the atomic number, -

n

is the principal quantum number. For

{L i}^{+ +}

Z = 3

For the fifth orbit:

n = 5

Given:

a_{0} = 0.51 \overset{˚}{A} = 0.51 \times 10^{- 10} m

So,

r_{5} = \frac{5^{2}}{3} \times 0.51 \times 10^{- 10}

r_{5} = \frac{25}{3} \times 0.51 \times 10^{- 10}

r_{5} = 25 \times 0.17 \times 10^{- 10}

r_{5} = 4.25 \times 10^{- 10} m

Now convert to the required form:

4.25 \times 10^{- 10} m = 425 \times 10^{- 12} m

Thus, the radius is

425.0

Final answer: **425.0**

From NTA/IIT papers: JEE Main 2023 · 6 Apr Shift 1

Question 5 hard

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 π ϵ_{0}}

, where

ϵ_{0}

is the permittivity of vacuum. In terms of these physical constants, the dimension of the magnetic field is

[B] = [e]^{α} [m_{e}]^{β} [h]^{γ} [k]^{δ}

. The value of

α + β + γ + δ

is _____.

Answer: 4

Explanation. We use dimensional analysis. Dimensions of the given constants:

[e] = [I T], [m_{e}] = [M], [h] = [M L^{2} T^{- 1}], [k] = [M L^{3} T^{- 4} I^{- 2}]

Magnetic field dimensions:

[B] = [M T^{- 2} I^{- 1}]

Assume

[B] = [e]^{α} [m_{e}]^{β} [h]^{γ} [k]^{δ}

Substitute dimensions:

[M T^{- 2} I^{- 1}] = (I T)^{α} M^{β} (M L^{2} T^{- 1})^{γ} (M L^{3} T^{- 4} I^{- 2})^{δ}

Combine exponents: - Mass:

β + γ + δ = 1

- Length:

2 γ + 3 δ = 0

- Time:

α - γ - 4 δ = - 2

- Current:

α - 2 δ = - 1

From length:

2 γ = - 3 δ \Rightarrow γ = - \frac{3}{2} δ

From current:

α = 2 δ - 1

From time:

(2 δ - 1) - (- \frac{3}{2} δ) - 4 δ = - 2

2 δ - 1 + \frac{3}{2} δ - 4 δ = - 2

- \frac{1}{2} δ - 1 = - 2

- \frac{1}{2} δ = - 1 \Rightarrow δ = 2

Then

γ = - \frac{3}{2} (2) = - 3

α = 2 (2) - 1 = 3

Mass equation:

β + (- 3) + 2 = 1 \Rightarrow β = 2

α + β + γ + δ = 3 + 2 - 3 + 2 = 4

4

From NTA/IIT papers: JEE Advanced 2022

Frequently asked questions

How much of JEE Main comes from Units and Measurements?: JEEGenie estimates about 2% of JEE Main marks come from Units and Measurements, based on recent papers. The share varies from year to year.
Which formulas matter most in Units and Measurements?: The Units and Measurements sheet on this page has 23 formula entries, starting with Physical Quantity and Unit, Fundamental and Derived Units, SI Prefixes, Dimensional Formula, Dimensional Analysis for Equation Consistency. Each one comes with when to use it and the trap to avoid.
What topics does Units and Measurements cover for JEE?: Units and Measurements covers Units and Dimensions, Dimensional Analysis, Significant Figures, Errors in Measurement, Vernier and Screw Gauge.
How should I revise Units and Measurements before the exam?: Learn each formula together with its condition of use, read the trap listed beside it, then practise questions and review every mistake. The practice link on this page opens Units and Measurements questions on JEEGenie.
How many previous-year questions are there on Units and Measurements?: JEEGenie has 566 previous-year questions on Units and Measurements, and this page shows a few with worked explanations.
Is practice on Units and Measurements free on JEEGenie?: Sign-up is free and includes a 7-day Pro trial. After the trial, free accounts keep a limited daily quota.