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JEE Main Previous Year Questions  
(2021-2025): Units & Measurements 
2025 
 
Q1. A quantity Q is formulated as . 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  [2025] 
(a) 0.6 
(b) 0.8 
(c) 0.7 
(d) 0.1 
Ans: (c)  
The quantity Q is expressed as . The variables X, Y, and Z are 
independent parameters with fractional errors of 0.1, 0.2, and 0.5, respectively. To determine the 
maximum fractional error in Q, we can use the following method: 
Fractional error in  
Substituting the fractional errors into the equation: 
 
Calculating each term gives:  
= 0.2 + 0.3 + 0.2  
Summing these values results in:  
= 0.7 
Thus, the maximum fractional error in Q is 0.7. 
 
Q2: The dimension of is equal to that of: (µ
0
 = Vacuum permeability and ?
0
 = 
Vacuum permittivity)   [2025] 
(a) Voltage 
(b) Inductance 
(c) Resistance 
(d) Capacitance 
Ans: (c)  
Page 2


 
 
JEE Main Previous Year Questions  
(2021-2025): Units & Measurements 
2025 
 
Q1. A quantity Q is formulated as . 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  [2025] 
(a) 0.6 
(b) 0.8 
(c) 0.7 
(d) 0.1 
Ans: (c)  
The quantity Q is expressed as . The variables X, Y, and Z are 
independent parameters with fractional errors of 0.1, 0.2, and 0.5, respectively. To determine the 
maximum fractional error in Q, we can use the following method: 
Fractional error in  
Substituting the fractional errors into the equation: 
 
Calculating each term gives:  
= 0.2 + 0.3 + 0.2  
Summing these values results in:  
= 0.7 
Thus, the maximum fractional error in Q is 0.7. 
 
Q2: The dimension of is equal to that of: (µ
0
 = Vacuum permeability and ?
0
 = 
Vacuum permittivity)   [2025] 
(a) Voltage 
(b) Inductance 
(c) Resistance 
(d) Capacitance 
Ans: (c)  
The dimension of can be understood as follows: 
Vacuum permeability (µ
0
) and vacuum permittivity (?
0
) relate to the properties of inductance and 
capacitance, respectively, in a vacuum. We start by considering the formulas for inductance (L) 
and capacitance (C): 
Inductance (L) is given by: 
 
Capacitance (C) is given by: 
 
From these, the ratio L/C can be expressed as : 
 
Taking the square root of this ratio, we have: 
 
This simplifies further to considering the relationship between time constant (t) and resistance 
(R): 
 
Thus, by taking the square root: 
 
In conclusion, the dimension of is equivalent to the dimension of resistance, R. 
 
Q3: Match List - I with List - II.    [2025] 
 
Choose the correct answer from the options given below : 
Page 3


 
 
JEE Main Previous Year Questions  
(2021-2025): Units & Measurements 
2025 
 
Q1. A quantity Q is formulated as . 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  [2025] 
(a) 0.6 
(b) 0.8 
(c) 0.7 
(d) 0.1 
Ans: (c)  
The quantity Q is expressed as . The variables X, Y, and Z are 
independent parameters with fractional errors of 0.1, 0.2, and 0.5, respectively. To determine the 
maximum fractional error in Q, we can use the following method: 
Fractional error in  
Substituting the fractional errors into the equation: 
 
Calculating each term gives:  
= 0.2 + 0.3 + 0.2  
Summing these values results in:  
= 0.7 
Thus, the maximum fractional error in Q is 0.7. 
 
Q2: The dimension of is equal to that of: (µ
0
 = Vacuum permeability and ?
0
 = 
Vacuum permittivity)   [2025] 
(a) Voltage 
(b) Inductance 
(c) Resistance 
(d) Capacitance 
Ans: (c)  
The dimension of can be understood as follows: 
Vacuum permeability (µ
0
) and vacuum permittivity (?
0
) relate to the properties of inductance and 
capacitance, respectively, in a vacuum. We start by considering the formulas for inductance (L) 
and capacitance (C): 
Inductance (L) is given by: 
 
Capacitance (C) is given by: 
 
From these, the ratio L/C can be expressed as : 
 
Taking the square root of this ratio, we have: 
 
This simplifies further to considering the relationship between time constant (t) and resistance 
(R): 
 
Thus, by taking the square root: 
 
In conclusion, the dimension of is equivalent to the dimension of resistance, R. 
 
Q3: Match List - I with List - II.    [2025] 
 
Choose the correct answer from the options given below : 
(a) (A)-(IV), (B)-(II), (C)-(III), (D)-(I) 
(b) (A)-(II), (B)-(III), (C)-(IV), (D)-(I) 
(c) (A)-(IV), (B)-(III), (C)-(I), (D)-(II) 
(d) (A)-(IV), (B)-(II), (C)-(I), (D)-(III) 
Ans: (d) 
(A) Mass density: 
Mass density is defined as mass per unit volume. 
The dimension of mass is [M]. 
The dimension of volume is [L
3
]. 
Therefore, the dimension of mass density is   
Matches with (IV). 
(B) Impulse: 
Impulse is defined as the change in momentum, or force multiplied by time. 
Impulse = Force x Time 
The dimension of force is [MLT
-2
]. 
The dimension of time is [T]. 
Therefore, the dimension of impulse is [MLT
-2
] ·[T] = [MLT
-1
]. 
Matches with (II). 
(C) Power: 
Power is defined as the rate of doing work or energy per unit time. 
Power = Work / Time 
The dimension of work (or energy) is [ML
2
T
-2
] 
The dimension of time is [T]. 
Therefore, the dimension of power is  
Matches with (I). 
(D) Moment of inertia: 
Moment of inertia is defined as I = m
2
, where m is mass and r is the distance from the axis of 
rotation. 
The dimension of mass is [M]. 
The dimension of distance squared is [
2
]. 
Therefore, the dimension of moment of inertia is [ML
2
T
0
] 
Matches with (III). 
So, the correct matches are: 
(A) - (IV) 
(B) - (II) 
(C) - (I) 
(D) - (III) 
Therefore, the correct option is D. 
 
Q4: 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
R
A
S
] . The value of P and 
Page 4


 
 
JEE Main Previous Year Questions  
(2021-2025): Units & Measurements 
2025 
 
Q1. A quantity Q is formulated as . 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  [2025] 
(a) 0.6 
(b) 0.8 
(c) 0.7 
(d) 0.1 
Ans: (c)  
The quantity Q is expressed as . The variables X, Y, and Z are 
independent parameters with fractional errors of 0.1, 0.2, and 0.5, respectively. To determine the 
maximum fractional error in Q, we can use the following method: 
Fractional error in  
Substituting the fractional errors into the equation: 
 
Calculating each term gives:  
= 0.2 + 0.3 + 0.2  
Summing these values results in:  
= 0.7 
Thus, the maximum fractional error in Q is 0.7. 
 
Q2: The dimension of is equal to that of: (µ
0
 = Vacuum permeability and ?
0
 = 
Vacuum permittivity)   [2025] 
(a) Voltage 
(b) Inductance 
(c) Resistance 
(d) Capacitance 
Ans: (c)  
The dimension of can be understood as follows: 
Vacuum permeability (µ
0
) and vacuum permittivity (?
0
) relate to the properties of inductance and 
capacitance, respectively, in a vacuum. We start by considering the formulas for inductance (L) 
and capacitance (C): 
Inductance (L) is given by: 
 
Capacitance (C) is given by: 
 
From these, the ratio L/C can be expressed as : 
 
Taking the square root of this ratio, we have: 
 
This simplifies further to considering the relationship between time constant (t) and resistance 
(R): 
 
Thus, by taking the square root: 
 
In conclusion, the dimension of is equivalent to the dimension of resistance, R. 
 
Q3: Match List - I with List - II.    [2025] 
 
Choose the correct answer from the options given below : 
(a) (A)-(IV), (B)-(II), (C)-(III), (D)-(I) 
(b) (A)-(II), (B)-(III), (C)-(IV), (D)-(I) 
(c) (A)-(IV), (B)-(III), (C)-(I), (D)-(II) 
(d) (A)-(IV), (B)-(II), (C)-(I), (D)-(III) 
Ans: (d) 
(A) Mass density: 
Mass density is defined as mass per unit volume. 
The dimension of mass is [M]. 
The dimension of volume is [L
3
]. 
Therefore, the dimension of mass density is   
Matches with (IV). 
(B) Impulse: 
Impulse is defined as the change in momentum, or force multiplied by time. 
Impulse = Force x Time 
The dimension of force is [MLT
-2
]. 
The dimension of time is [T]. 
Therefore, the dimension of impulse is [MLT
-2
] ·[T] = [MLT
-1
]. 
Matches with (II). 
(C) Power: 
Power is defined as the rate of doing work or energy per unit time. 
Power = Work / Time 
The dimension of work (or energy) is [ML
2
T
-2
] 
The dimension of time is [T]. 
Therefore, the dimension of power is  
Matches with (I). 
(D) Moment of inertia: 
Moment of inertia is defined as I = m
2
, where m is mass and r is the distance from the axis of 
rotation. 
The dimension of mass is [M]. 
The dimension of distance squared is [
2
]. 
Therefore, the dimension of moment of inertia is [ML
2
T
0
] 
Matches with (III). 
So, the correct matches are: 
(A) - (IV) 
(B) - (II) 
(C) - (I) 
(D) - (III) 
Therefore, the correct option is D. 
 
Q4: 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
R
A
S
] . The value of P and 
Q are :   [2025] 
(a) -1, 0 
(b) 0, -1 
(c) -1, 1 
(d) 1, -1 
Ans: (b) 
 
After compering values of P & Q are 0 , - 1  
 
Q5: 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):    [2025] 
(a) 0.002 
(b) 0.0025 
(c) 0.0005 
(d) 0.001 
Ans: (a) 
Determine one main scale division (msd): 
300 msd = 15 cm 
Therefore, 
1 msd = 15/300 cm = 0.05 cm 
Determine one vernier scale division (vsd): 
25 vsd = 24 vsd 
Therefore, 
1 vsd = 24/25 msd 
Calculate the least count (LC): 
The least count is given by the difference between one main scale division and one vernier 
scale division: 
LC = 1 msd - 1 vsd 
Substitute the expression for 1 vsd: 
 
This simplifies to: 
Page 5


 
 
JEE Main Previous Year Questions  
(2021-2025): Units & Measurements 
2025 
 
Q1. A quantity Q is formulated as . 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  [2025] 
(a) 0.6 
(b) 0.8 
(c) 0.7 
(d) 0.1 
Ans: (c)  
The quantity Q is expressed as . The variables X, Y, and Z are 
independent parameters with fractional errors of 0.1, 0.2, and 0.5, respectively. To determine the 
maximum fractional error in Q, we can use the following method: 
Fractional error in  
Substituting the fractional errors into the equation: 
 
Calculating each term gives:  
= 0.2 + 0.3 + 0.2  
Summing these values results in:  
= 0.7 
Thus, the maximum fractional error in Q is 0.7. 
 
Q2: The dimension of is equal to that of: (µ
0
 = Vacuum permeability and ?
0
 = 
Vacuum permittivity)   [2025] 
(a) Voltage 
(b) Inductance 
(c) Resistance 
(d) Capacitance 
Ans: (c)  
The dimension of can be understood as follows: 
Vacuum permeability (µ
0
) and vacuum permittivity (?
0
) relate to the properties of inductance and 
capacitance, respectively, in a vacuum. We start by considering the formulas for inductance (L) 
and capacitance (C): 
Inductance (L) is given by: 
 
Capacitance (C) is given by: 
 
From these, the ratio L/C can be expressed as : 
 
Taking the square root of this ratio, we have: 
 
This simplifies further to considering the relationship between time constant (t) and resistance 
(R): 
 
Thus, by taking the square root: 
 
In conclusion, the dimension of is equivalent to the dimension of resistance, R. 
 
Q3: Match List - I with List - II.    [2025] 
 
Choose the correct answer from the options given below : 
(a) (A)-(IV), (B)-(II), (C)-(III), (D)-(I) 
(b) (A)-(II), (B)-(III), (C)-(IV), (D)-(I) 
(c) (A)-(IV), (B)-(III), (C)-(I), (D)-(II) 
(d) (A)-(IV), (B)-(II), (C)-(I), (D)-(III) 
Ans: (d) 
(A) Mass density: 
Mass density is defined as mass per unit volume. 
The dimension of mass is [M]. 
The dimension of volume is [L
3
]. 
Therefore, the dimension of mass density is   
Matches with (IV). 
(B) Impulse: 
Impulse is defined as the change in momentum, or force multiplied by time. 
Impulse = Force x Time 
The dimension of force is [MLT
-2
]. 
The dimension of time is [T]. 
Therefore, the dimension of impulse is [MLT
-2
] ·[T] = [MLT
-1
]. 
Matches with (II). 
(C) Power: 
Power is defined as the rate of doing work or energy per unit time. 
Power = Work / Time 
The dimension of work (or energy) is [ML
2
T
-2
] 
The dimension of time is [T]. 
Therefore, the dimension of power is  
Matches with (I). 
(D) Moment of inertia: 
Moment of inertia is defined as I = m
2
, where m is mass and r is the distance from the axis of 
rotation. 
The dimension of mass is [M]. 
The dimension of distance squared is [
2
]. 
Therefore, the dimension of moment of inertia is [ML
2
T
0
] 
Matches with (III). 
So, the correct matches are: 
(A) - (IV) 
(B) - (II) 
(C) - (I) 
(D) - (III) 
Therefore, the correct option is D. 
 
Q4: 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
R
A
S
] . The value of P and 
Q are :   [2025] 
(a) -1, 0 
(b) 0, -1 
(c) -1, 1 
(d) 1, -1 
Ans: (b) 
 
After compering values of P & Q are 0 , - 1  
 
Q5: 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):    [2025] 
(a) 0.002 
(b) 0.0025 
(c) 0.0005 
(d) 0.001 
Ans: (a) 
Determine one main scale division (msd): 
300 msd = 15 cm 
Therefore, 
1 msd = 15/300 cm = 0.05 cm 
Determine one vernier scale division (vsd): 
25 vsd = 24 vsd 
Therefore, 
1 vsd = 24/25 msd 
Calculate the least count (LC): 
The least count is given by the difference between one main scale division and one vernier 
scale division: 
LC = 1 msd - 1 vsd 
Substitute the expression for 1 vsd: 
 
This simplifies to: 
 
Calculate the LC in cm: 
Substituting the value of 1 msd: 
 
Hence, the least count of the traveling microscope is 0.002 cm. 
 
Q6: 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   [2025] 
(a) (3, -5) 
(b) (-2, 1) 
(c) (-2, 2) 
(d) (1, -1) 
Ans: (d) 
To solve this problem, we need to find the dimensions of the electric flux and the magnetic flux, 
and then take their ratio. 
Determine the dimension of electric flux (F?) 
Electric flux is defined as 
 
The electric field E has dimensions: 
 
Since force has dimensions MLT
-2
 , and charge (in SI) has dimensions AT, we get: 
 
The area element dA has dimensions L
2
.  
Thus, the electric flux has dimensions: 
  
Determine the dimension of magnetic flux (F_B):  
Magnetic flux is defined as 
 
The magnetic field B has dimensions determined via the Lorentz force law (using F = q v B), 
giving:

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FAQs on JEE Main Previous Year Questions (2021-2025): Units & Measurements - Physics for JEE Main & Advanced

1. What are the fundamental units of measurement in the International System of Units (SI)?

Ans. The fundamental units of measurement in the International System of Units (SI) include: 1. Meter (m) for length 2. Kilogram (kg) for mass 3. Second (s) for time 4. Ampere (A) for electric current 5. Kelvin (K) for temperature 6. Mole (mol) for the amount of substance 7. Candela (cd) for luminous intensity. These units serve as the foundation for all other derived units in scientific measurements.

2. How do you convert units in measurements effectively?

Ans. To convert units effectively, you can use the factor-label method (also known as dimensional analysis). This involves multiplying the quantity you want to convert by a conversion factor that relates the old unit to the new unit. The conversion factor should equal 1 (e.g., 1 inch = 2.54 cm). Be sure to cancel out the units appropriately to ensure that the final answer is in the desired unit.

3. What is the significance of significant figures in measurements?

Ans. Significant figures are important in measurements because they indicate the precision of a measurement. They help convey how much uncertainty is associated with a given value. When performing calculations, the number of significant figures in the result should reflect the measurement with the least number of significant figures to ensure the result is not over-precise.

4. How can one determine the accuracy and precision of a measurement?

Ans. Accuracy refers to how close a measured value is to the true or accepted value, while precision refers to the repeatability or consistency of the measurement. One can determine accuracy by comparing the measured value to a known standard or accepted value. Precision can be assessed by taking multiple measurements and calculating the standard deviation or range of the values. A high level of precision does not guarantee accuracy.

5. What common errors occur in measurements and how can they be minimized?

Ans. Common errors in measurements include systematic errors (consistent bias due to measurement methods) and random errors (fluctuations due to unpredictable factors). To minimize these errors, one can calibrate measuring instruments regularly, use proper techniques, take multiple measurements and average them, and maintain environmental controls (e.g., temperature, humidity) that may affect readings.

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