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Class 11 • Physics
Units , Dimensions and Error Analysis
Chapter-1
319 Questions
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109 Easy209 Medium1 Hard
Practice Questions
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1
MediumCOMEDK2025
Two physical quantities having the same dimensional formula \left[\mathrm{M}^1 \mathrm{~L}^{-1} \mathrm{~T}^{-2}\right] are
Options:
A) Thrust and Strain
B) Moment of force and Thrust
C) Stress and Pressure
D) Work and thrust
2
MediumCOMEDK2025
In the expression \mathrm{P}=\mathrm{El}^2 \mathrm{~m}^{-5} \mathrm{G}^{-2} where \mathrm{E}, 1, \mathrm{~m} and G represent Energy, Angular Momentum, Mass and Gravitational Constant, the dimensions of P are
Options:
A) \left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]
B) \left[\mathrm{M}^0 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]
C) \left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^0\right]
D) \left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^{-2}\right]
3
MediumCOMEDK2025
The nuclear forces a. are central forces, independent of the spin of the nucleons. b. have a short-range dominant over a distance of about a few fermi c. are stronger being hundred times stronger than that of electromagnetic forces. d. are independent of the nuclear charge. Which of the above is not true?
Options:
A) c
B) a
C) b
D) d
4
MediumCOMEDK2025
Two light rays A and B travel from a medium into air at angles of incidence 15 degrees and 42 degrees respectively. In the medium, light travels 3 cm in 0.2 ns . Will there be total internal reflection? If so, which ray?
Options:
A) No
B) Yes, A
C) Yes, B
D) Yes, Both A and B
5
MediumCOMEDK2025
An electric field E=3 x^2 i N C^{-1} exists in a certain region of space. The potential difference between the origin and at x=4 m, V_0-V_4 is
Options:
A) -20 V
B) -40 V
C) -64 V
D) 64 V
6
MediumCOMEDK2025
A symmetric double convex lens is cut into two equal parts by a plane perpendicular to the principal axis. If the power of the original lens is 4D, the difference between the powers of the original lens and the cut lens is
Options:
A) zero
B) 3D
C) D
D) 2D
7
MediumCOMEDK2025
Three identical conducting balls \mathrm{A}, \mathrm{B} and C , each of mass m , are thrown upward at an angle \Theta to the horizontal with an initial speed v in a region of space that has a uniform electric field E downward along with the gravitational field g . A is positively charged, B is uncharged and C is negatively charged. Rank the ranges R of these three balls in increasing order.
Options:
A) R_A< R_B< R_C
B) R_B< R_C< R_A
C) R_A=R_B< R_C
D) R_C< R_B< R_A
8
MediumCOMEDK2025
A wooden block floats with \frac{3}{5} of its volume submerged in a tank of water. If a denser liquid is poured into the tank, the wooden block floats with half its volume in the liquid and the remaining half in water. The relative density of the liquid is:
Options:
A) \frac{1}{2}
B) \frac{1}{3}
C) \frac{1}{6}
D) \frac{1}{5}
9
MediumCOMEDK2025
A particle starts from rest and moves along the x -axis with a velocity that varies as \mathrm{v}=\sqrt{100+4 x} \mathrm{~ms}^{-1}. The acceleration of the particle is:
Options:
A) 25 \mathrm{~ms}^{-2}
B) 5 \mathrm{~ms}^{-2}
C) 4 \mathrm{~ms}^{-2}
D) 2 \mathrm{~ms}^{-2}
10
MediumCOMEDK2025
If E is the amplitude of the electric field of the waves starting from the slits in a double slit experiment and \theta is the phase difference between the waves reaching a point on the screen, the ratio of the amplitude of the resultant electric field at that point on the screen to the amplitude at one of the slits is
Options:
A) \cos (\theta)
B) 2 \cos (\theta)
C) \cos \left(\frac{\theta}{2}\right)
D) 2 \cos \left(\frac{\theta}{2}\right)
11
MediumCOMEDK2025
Two simple harmonic motions are represented by equations y_1=0.5 \sin \left[200 \pi \mathrm{t}+\frac{\pi}{3}\right] and y_1=0.5 \cos \pi \mathrm{t}. The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is :
Options:
A) \frac{\pi}{2}
B) \frac{\pi}{6}
C) \frac{-\pi}{6}
D) \frac{-\pi}{2}
12
MediumCOMEDK2025
A vertical spring of spring constant 24 \mathrm{Nm}^{-1} is fixed on a table. A ball of mass 0.5 kg at a height 2 m above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance of 50 cm . The net work done in the process is:
Options:
A) 6.5 J
B) 10.5 J
C) 12.5 J
D) 9.5 J
13
MediumCOMEDK2025
A sonometer string vibrates with a frequency of 400 Hz . When the length of the string is halved and the tension is altered, it begins to vibrate with a frequency of 200 Hz . The ratio of the new tension to the original tension in the string is:
Options:
A) 4: 1
B) 16: 1
C) 1: 4
D) 1: 16
14
MediumCOMEDK2025
In an experiment to measure the density of the material of a sphere, an error of 2 \% occurred while measuring the radius of a sphere and an error of 3 \% occurred while measuring the mass of the sphere. What is the maximum percentage error in the measurement of density?
Options:
A) 8
B) 6
C) 7
D) 9
15
MediumCOMEDK2025
If the binding energy per nucleon in 3 \mathrm{Li}^7 and { }_2 \mathrm{He}^4 nuclei are respectively 5.60 MeV and 7.06 MeV , then energy of p in the reaction p+{ }_3 \mathrm{Li}^7 \rightarrow 2{ }_2 \mathrm{He}^4 is
Options:
A) 12.28 MeV
B) 13.28 MeV
C) 28.28 MeV
D) 17.28 MeV
16
MediumCOMEDK2025
A long solenoid has 400 turns. When a current of 100 A is passed through it, the resulting magnetic flux linked with each turn of the solenoid is 4 mWb . The self-inductance of the solenoid is
Options:
A) 1.6 mH
B) 16 mH
C) 16 H
D) 0.16 mH
17
MediumCOMEDK2025
Which of the following is not true for a perfect conductor?
Options:
A) Electric field inside a conductor is zero
B) The electric field just outside a conductor is always perpendicular to the surface.
C) The surface of a conductor is an equipotential surface.
D) The charge carried by a conductor is always uniformly distributed over the surface of the conductor irrespective of the shape of the conductor.
18
MediumCOMEDK2025
Young's modulus of the material of wires X and Y are in the ratio 4:1 and the areas of cross sections of the wires X and Y are in the ratio 2: 1. If the same amount of load is applied to both the wires, the ratio of elongation produced in the wires X and Y will be: (Assume length of the wires X and Y initially are the same)
Options:
A) 1: 8
B) 1: 1
C) 8: 1
D) 1: 2
19
MediumCOMEDK2024
The dimension [\mathrm{ML}^{-1} \mathrm{~T}^{-2}] is the physical quantity of
Options:
A) Pressure \times Area
B) \mathrm{\frac{Force}{Pressure}}
C) Power \times Time
D) Energy density
20
MediumCOMEDK2024
If units of mass, length and gravitational constant are chosen to fundamental units, the dimensions of time would be
Options:
A)
\mathrm{M}^{1 / 2} \mathrm{~L}^{1 / 2} \mathrm{G}^{-1 / 2}
B)
\mathrm{M}^1 \mathrm{~L}^{1 / 2} \mathrm{G}^2
C)
\mathrm{M}^{-1 / 2} \mathrm{~L}^{3 / 2} \mathrm{G}^{-1 / 2}
D)
\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{G}^{-1}
21
MediumCOMEDK2024
Which of the given dimensional formula represents heat capacity
Options:
A) \left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]
B) \left[\mathrm{ML}^2 \mathrm{~T}^{-1} \mathrm{~K}^{-1}\right]
C) \left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-2}\right]
D) \left[\mathrm{MLT}^{-2} \mathrm{~K}^{-1}\right]
22
MediumCOMEDK2024
Find the value of 'n' in the given equation P=\rho^n v^2 where 'P' is the pressure, '\rho' density and 'v' velocity.
Options:
A) \mathrm{n}=\frac{1}{2}
B) \mathrm{n}=1
C) \mathrm{n}=3
D) \mathrm{n}=2
23
MediumCOMEDK2023
The time dependence of a physical quantity P is give by \mathrm{P=P}_0 \exp \left(-\alpha t^2\right) where \alpha is a constant and t is time. The constant \alpha will
Options:
A) Have dimensions as that of \mathrm{P}
B) Have dimensions equal to that of \mathrm{Pt}^2
C) Have no dimensions
D) Have dimensions of t^{-2}
24
MediumCOMEDK2023
A tentative explanation of observations without assuming that it is true is called
Options:
A) hypothesis
B) physical laws
C) theory
D) model
25
MediumCOMEDK2021
Which of the following statement is incorrect?
Options:
A) Classical Physics deals with macroscopic phenomena and includes subject like mechanics, electrodynamics, optics and thermodynamics.
B) All Physics and also mathematics is based on assumptions each of which is variously called hypothesis or axiom or postulate etc.
C) A hypothesis is a supposition with assuming that is true.
D) An axiom is a self-evident truth, while a model is a theory proposed to explain observed phenomena.
26
MediumCOMEDK2021
Which of the following technique is not used for measuring small time intervals?
Options:
A) Electronic oscillator
B) Decay of elementary particles
C) Atomic clock
D) Spring oscillator
27
MediumCOMEDK2021
The relative errors in the measurement of two lengths 1.02 cm \pm 0.01 cm and 9.89 cm \pm 0.01 cm is
Options:
A) \pm1% and \pm0.1%
B) \pm1% and \pm0.2%
C) \pm1% and \pm1%
D) \pm0.1% and \pm1%
28
MediumCOMEDK2020
Suppose refractive index \alpha is given as \alpha = A + {B \over {{\lambda ^2}}}, where A and B are constants and \lambda is wavelength, then dimensions of B are same as that of
Options:
A) wavelength
B) volume
C) pressure
D) area
29
MediumJEE Mains2026
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?
Options:
A) 200 \alpha
B) 400 \alpha
C) 300 \alpha
D) 500 \alpha
30
MediumJEE Mains2026
Consider the equation H=\frac{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 :
Options:
A) 1, 1, 1, 1
B) -1,1,2,1
C) 1, -1, -2, 1
D) -1,-2,-2,1
31
MediumJEE Mains2026
The percentage error in the calculated volume of a sphere, if there is 2 \% error in its diameter measurement, is \_\_\_\_ .
Options:
A) 1
B) 2
C) 6
D) 8
32
MediumJEE Mains2026
\text { Match List - I with List - II. } \text { List - I } \text { List - II } A. Boltzmann constant I. \left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right] B. Stefan's constant II. \left[\mathrm{M} \mathrm{~L}^2 \mathrm{~T}^{-1}\right] C. Planck's constant III. \left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right] D. Gravitational constant IV. \left[\mathrm{M} \mathrm{~L}^0 \mathrm{~T}^{-3} \mathrm{~K}^{-4}\right] Choose the correct answer from the options given below :
Options:
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
33
MediumJEE Mains2026
The density \rho 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 \pm 0.02 \mathrm{~g}, 8.35 \pm 0.05 \mathrm{~mm} and 20.20 \pm 0.02 \mathrm{~mm}, respectively. Calculated percentage fractional error in \rho is \_\_\_\_ .
Options:
A) 0.63%
B) 0.82%
C) 0.72%
D) 0.25%
34
MediumJEE Mains2026
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 A B are \_\_\_\_
Options:
A) \left[\mathrm{M}^1 \mathrm{~L}^{5 / 2} \mathrm{~T}^{-2}\right]
B) \left[\mathrm{M}^{3 / 2} \mathrm{~L}^{5 / 2} \mathrm{~T}^{-2}\right]
C) \left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]
D) \left[\mathrm{M}^1 \mathrm{~L}^{7 / 2} \mathrm{~T}^{-2}\right]
35
MediumJEE Mains2026
\text { Match List - I with List - II. } \text { List - I } \text { List - II } A. Meter (L) I. \sqrt{\frac{h c}{G}} B. Second (S) II. \sqrt{\frac{G h}{c^5}} C. Kilogram (M) III. \sqrt{\frac{K^2 L^2 c^3}{G h}} D. Kelvin (K) IV. \sqrt{\frac{G h}{c^3}} 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 :
Options:
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
36
MediumJEE Mains2026
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 \_\_\_\_ \Omega
Options:
A) 0.25
B) 2
C) 2.5
D) 0.18
37
MediumJEE Mains2026
In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and 7^{\text {th }} Vernier division coincides with a main scale reading. If the value of 1 main scale division is 1 mm and there are 10 Vernier scale divisions, then the Vernier caliper has
Options:
A) 0.07 cm negative zero error
B) 0.7 cm negative zero error
C) 0.07 cm positive zero error
D) 0.7 cm positive zero error
38
MediumJEE Mains2026
L, C and R represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula \mathrm{ML}^2 \mathrm{~T}^{-4} \mathrm{~A}^{-2} corresponds to \_\_\_\_ .
Options:
A) \frac{R}{\sqrt{L C}}
B) \frac{R}{L C}
C) \frac{C}{\sqrt{L R}}
D) \frac{1}{R} \sqrt{\frac{L}{C}}
39
MediumJEE Mains2026
\text { Match the LIST-I with LIST-II } List - I List - II A. Planck's constant I. \mathrm{ML}^2 \mathrm{~T}^{-2} B. Stopping potential II. \mathrm{T}^{-1} C. Work function III. \mathrm{ML}^2 \mathrm{~T}^{-1} D. Threshold frequency IV. \mathrm{ML}^2 \mathrm{~T}^{-3} \mathrm{~A}^{-1} Choose the correct answer from the options given below:
Options:
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
40
MediumJEE Mains2026
In a screw gauge when the circular scale is given five complete rotations it moves linearly by 2.5 mm . If the circular scale has 100 divisions, the least count of screw gauge is \_\_\_\_ mm.
Options:
A) 1 \times 10^{-2}
B) 1 \times 10^{-3}
C) 5 \times 10^{-2}
D) 5 \times 10^{-3}
41
MediumJEE Mains2026
Dimensions of universal gravitational constant (G) in terms of Planck's constant (h), distance (L), mass (M) and time (T) are _______.
Options:
A) [h T L M^{-2}]
B) [h T^{-1} L M^{-2}]
C) [h T L^2 M^{-2}]
D) [h^{-1} T^{-1} L M^{-2}]
42
MediumJEE Mains2026
In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are 100 divisions in circular scale and pitch of screw gauge is 0.1 mm. When diameter of a sphere is measured, the reading of main scale is 5 mm and 50 th division of circular scale coincides with the reference line of main scale. The diameter of sphere is ______ mm.
Options:
A) 5.045
B) 5.055
C) 5.450
D) 5.550
43
MediumJEE Mains2026
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 = ________.
Options:
A) 0
B) 1
C) -1
D) 2
44
MediumJEE Mains2026
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 \ \mathrm{N/m}^2. The value of \alpha is ________. (Ignore the contribution of the load to Young’s modulus error calculation)
Options:
A) 1.3
B) 1.65
C) 0.13
D) 0.25
45
MediumJEE Mains2026
The time period of a simple harmonic oscillator is T = 2\pi \sqrt{\frac{k}{m}}. 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 ________%.
Options:
A) 3.43
B) 7.60
C) 3.35
D) 6.76
46
MediumJEE Mains2026
The speed of a longitudinal wave in a metallic bar is 400 m/s. If the density and Young's modulus of the bar material are increased by 0.5% and 1%, respectively then the speed of the wave is changed approximately to ______ m/s.
Options:
A) 398
B) 402
C) 401
D) 399
47
EasyJEE Mains2026
Match List - I with List - II . List – I List – II A. Coefficient of viscosity B. Surface tension C. Pressure D. Surface energy I. [ML −1 T −2 ] II. [ML 2 T −2 ] III. [ML 0 T −2 ] IV. [ML −1 T −1 ] Choose the correct answer from the options given below :
Options:
A) A-I, B-II, C-IV, D-III
B) A-IV, B-III, C-I, D-II
C) A-IV, B-I, C-II, D-III
D) A-I, B-III, C-II, D-IV
48
EasyJEE Mains2026
In an experiment, a set of reading are obtained as follows - 1.24 mm, 1.25 mm, 1.23 mm, 1.21 mm. The expected least count of the instrument used in recording these readings is _______ mm.
Options:
A) 0.01
B) 0.05
C) 0.001
D) 0.1
49
EasyJEE Mains2026
When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, 4{ }^{\text {th }} mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes 15 divisions on main scale and 5^{\text {th }} division of vernier scale coincides with a main scale division. Measured length of cylinder is \_\_\_\_ mm. (Least count of Vernier calliper =0.1 \mathrm{~mm} )
Options:
A) 15.5
B) 15.4
C) 15.9
D) 15.1
50
EasyJEE Mains2026
In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions. If one main scale division =0.05 \mathrm{~mm}, then the least count of the vernier callipers is \_\_\_\_ mm.
Options:
A) 0.002
B) 0.02
C) 0.05
D) 0.005
51
EasyJEE Mains2026
In a screw gauge, the zero of the circular scale lies 3 divisions above the horizontal pitch line when their metallic studs are brought in contact. Using this instrument thickness of a sheet is measured. If pitch scale reading is 1 mm and the circular scale reading is 51 then the correct thickness of the sheet is \_\_\_\_ mm. [Assume least count is 0.01 mm ]
Options:
A) 1.54
B) 1.50
C) 1.51
D) 1.48
52
EasyJEE Mains2026
Four persons measure the length of a rod as 20.00 \mathrm{~cm}, 19.75 \mathrm{~cm}, 17.01 \mathrm{~cm} and 18.25 cm . The relative error in the measurement of average length of the rod is :
Options:
A) 0.18
B) 0.24
C) 0.06
D) 0.08
53
EasyJEE Mains2026
If \epsilon, E and t represent the free space permittivity, electric field and time respectively, then the unit of \frac{\epsilon E}{t} will be :
Options:
A) Am
B) \mathrm{A} / \mathrm{m}
C) \mathrm{A} / \mathrm{m}^2
D) \mathrm{Am}^2
54
EasyJEE Mains2026
\text { Match the LIST-I with LIST-II } List-I List-II A. Spring constant I. M L 2 T − 2 K − 1 M L 2 T − 2 K − 1 ML^(2)T^(-2)K^(-1) B. Thermal conductivity II. ML 0 T − 2 ML 0 T − 2 ML^(0)T^(-2) C. Boltzmann constant III. M L 2 T − 3 A − 2 M L 2 T − 3 A − 2 ML^(2)T^(-3)A^(-2) D. Inductive reactance IV. M L T − 3 K − 1 M L T − 3 K − 1 MLT^(-3)K^(-1) Choose the correct answer from the options given below:
Options:
A) A-III, B-II, C-IV, D-I
B) A-I, B-IV, C-II, D-III
C) A-II, B-I, C-IV, D-III
D) A-II, B-IV, C-I, D-III
55
MediumJEE Mains2026
A spherical body of radius r and density \sigma falls freely through a viscous liquid having density \rho and viscosity \eta and attains a terminal velocity v_0. Estimated maximum error in the quantity \eta is : (Ignore errors associated with \sigma, \rho and g, gravitational acceleration)
Options:
A) 2 \left[ \frac{\Delta r}{r} - \frac{\Delta v_0}{v_0} \right]
B) 2 \left[ \frac{\Delta r}{r} + \frac{\Delta v_0}{v_0} \right]
C) \frac{2 \Delta r}{r} + \frac{\Delta v_0}{v_0}
D) 2 \frac{\Delta r}{r} - \frac{\Delta v_0}{v_0}
56
EasyJEE Mains2026
Keeping the significant figures in view, the sum of the physical quantities 52.01 m, 153.2 m and 0.123 m is :
Options:
A) 205.3 m
B) 205 m
C) 205.333 m
D) 205.33 m
57
EasyJEE Mains2026
In an experiment the values of two spring constants were measured as k_1=(10 \pm 0.2) \mathrm{N} / \mathrm{m} and k_2=(20 \pm 0.3) \mathrm{N} / \mathrm{m}. If these springs are connected in parallel, then the percentage error in equivalent spring constant is :
Options:
A) 1.33%
B) 2.67 \%
C) 1.67%
D) 2.33 \%
58
EasyJEE Mains2026
Consider a modified Bernoulli equation. \left(\mathrm{P}+\frac{A}{B t^2}\right)+\rho g(h+B t)+\frac{1}{2} \rho V^2=\text { constant } If t has the dimension of time then the dimensions of A and B are \_\_\_\_ , \_\_\_\_ respectively.
Options:
A) \left[\mathrm{ML}^0 \mathrm{~T}^{-1}\right] and \left[\mathrm{M}^0 \mathrm{LT}\right]
B) \left[\mathrm{ML}^0 \mathrm{~T}^{-2}\right] and \left[\mathrm{M}^0 \mathrm{LT}^{-1}\right]
C) \left[\mathrm{ML}^0 \mathrm{~T}^{-2}\right] and \left[\mathrm{M}^0 \mathrm{LT}^{-2}\right]
D) \left[\mathrm{ML}^0 \mathrm{~T}^{-1}\right] and \left[\mathrm{M}^0 \mathrm{LT}^{-1}\right]
59
MediumJEE Mains2025
A quantity Q is formulated as X^{-2}Y^{+\frac{3}{2}}Z^{-\frac{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
Options:
A) 0.6
B) 0.8
C) 0.7
D) 0.1
60
EasyJEE Mains2025
The dimension of \sqrt{\frac{\mu_0}{\epsilon_0}} is equal to that of: ( \mu_0 = Vacuum permeability and \epsilon_0 = Vacuum permittivity)
Options:
A) Voltage
B) Inductance
C) Resistance
D) Capacitance
61
EasyJEE Mains2025
Match List - I with List - II . List - I List - II (A) Mass density (I) [ML 2 T −3 ] (B) Impulse (II) [MLT −1 ] (C) Power (III) [ML 2 T 0 ] (D) Moment of inertia (IV) [ML −3 T 0 ] Choose the correct answer from the options given below :
Options:
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)
62
MediumJEE Mains2025
In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of \left[\mathrm{M}^{\mathrm{P}} \mathrm{L}^{\mathrm{Q}} \mathrm{T}^R A^{\mathrm{S}}\right]. The value of P and Q are :
Options:
A) -1,0
B) 0,-1
C) -1,1
D) 1,-1
63
EasyJEE Mains2025
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 ) :
Options:
A) 0.002
B) 0.0025
C) 0.0005
D) 0.001
64
MediumJEE Mains2025
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
Options:
A) (3,-5)
B) (-2,1)
C) (-2,2)
D) (1,-1)
65
EasyJEE Mains2025
\text { Match the LIST-I with LIST-II } LIST-I LIST-II A. \text { Boltzmann constant } I \mathrm{ML}^2 \mathrm{~T}^{-1} B \text { Coefficient of viscosity } II \mathrm{MLT}^{-3} \mathrm{~K}^{-1} C \text { Planck's constant } III \mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1} D \text { Thermal conductivity } IV \mathrm{ML}^{-1} \mathrm{~T}^{-1} Choose the correct answer from the options given below:
Options:
A) A - III, B - IV, C - I, D - II
B) A - III, B - IV, C - II, D - I
C) A - III, B - II, C - I, D - IV
D) A - II, B - III, C - IV, D - I
66
EasyJEE Mains2025
A person measures mass of 3 different particles as 435.42 \mathrm{~g}, 226.3 \mathrm{~g} and 0.125 g . According to the rules for arithmetic operations with significant figures, the addition of the masses of 3 particles will be.
Options:
A) 661.845 g
B) 661.84 g
C) 662 g
D) 661.8 g
67
EasyJEE Mains2025
If \mu_0 and \epsilon_0 are the permeability and permittivity of free space, respectively, then the dimension of \left(\frac{1}{\mu_0 \epsilon_0}\right) is :
Options:
A) \mathrm{T}^2 / \mathrm{L}
B) \mathrm{L}^2 / \mathrm{T}^2
C) \mathrm{T}^2 / \mathrm{L}^2
D) \mathrm{L} / \mathrm{T}^2
68
MediumJEE Mains2025
Given a charge q , current I and permeability of vacuum \mu_{\mathrm{o}^*}. Which of the following quantity has the dimension of momentum ?
Options:
A) { } q I / \mu_o
B) q^2 \mu_o I
C) q \mu_0 / I
D) \mathrm{q} \mu_{\mathrm{o}} \mathrm{I}
69
EasyJEE Mains2025
Match List I with List II. List - I List - II (A) Coefficient of viscosity (I) \left[\mathrm{ML}^0 \mathrm{~T}^{-3}\right] (B) Intensity of wave (II) \left[\mathrm{ML}^{-2} \mathrm{~T}^{-2}\right] (C) Pressure gradient (III) \left[\mathrm{M}^{-1} \mathrm{LT}^2\right] (D) Compressibility (IV) \left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right] Choose the correct answer from the options given below:
Options:
A) (A)-(II), (B)-(III), (C)-(IV), (D)-(I)
B) (A)-(IV), (B)-(II), (C)-(I), (D)-(III)
C) (A)-(IV), (B)-(I), (C)-(II), (D)-(III)
D) (A)-(I), (B)-(IV), (C)-(III), (D)-(II)
70
EasyJEE Mains2025
Match List - I with List - II . List - I List - II (A) Young’s Modulus (I) M L -1 T -1 (B) Torque (II) M L -1 T -2 (C) Coefficient of Viscosity (III) M -1 L 3 T -2 (D) Gravitational Constant (IV) M L 2 T -2 Choose the correct answer from the options given below :
Options:
A) (A)-(I), (B)-(III), (C)-(II), (D)-(IV)
B) (A)-(IV), (B)-(II), (C)-(III), (D)-(I)
C) (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
D) (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
71
EasyJEE Mains2025
The pair of physical quantities not having the same dimensions is :
Options:
A) Angular momentum and Planck's constant
B) Torque and energy
C) Surface tension and impulse
D) Pressure and Young's modulus
72
EasyJEE Mains2025
The expression given below shows the variation of velocity ( v ) with time ( t ), v=\mathrm{At}^2+\frac{\mathrm{Bt}}{\mathrm{C}+\mathrm{t}}. The dimension of ABC is :
Options:
A) [M
0
L
1
T
−2
]
B) [M
0
L
2
T
−3
]
C) [M
0
L
2
T
−2
]
D) [M
0
L
1
T
−3
]
73
EasyJEE Mains2025
Match List - I with List - II. List - I List - II (A) Angular Impulse (I) M 0 L 2 T -2 (B) Latent Heat (II) M L 2 T -3 A -1 (C) Electrical resistivity (III) M L 2 T -1 (D) Electromotive force (IV) M L 3 T -3 A -2 Choose the correct answer from the options given below:
Options:
A) (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
B) (A)-(I), (B)-(III), (C)-(IV), (D)-(II)
C) (A)-(III), (B)-(I), (C)-(IV), (D)-(II)
D) (A)-(III), (B)-(I), (C)-(II), (D)-(IV)
74
EasyJEE Mains2025
For an experimental expression y=\frac{32.3 \times 1125}{27.4}, where all the digits are significant. Then to report the value of y we should write
Options:
A) y=1326.186
B) y=1326.2
C) y=1326.19
D) y=1330
75
MediumJEE Mains2025
The energy of a system is given as \mathrm{E}(\mathrm{t})=\alpha^3 \mathrm{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 \mathrm{~s}, maximum percentage error in the energy is :
Options:
A) 6 \%
B) 11.6 \%
C) 4 \%
D) 8.4 \%
76
EasyJEE Mains2025
Match List - I with List - II List - I List - II (A) Permeability of free space (I) \left[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-2}\right] (B) Magnetic field (II) \left[\mathrm{M} \mathrm{T}^{-2} \mathrm{~A}^{-1}\right] (C) Magnetic moment (III) \left[\mathrm{M} \mathrm{L} \mathrm{T}^{-2} \mathrm{~A}^{-2}\right] (D) Torsional constant (IV) \left[\mathrm{L}^2 \mathrm{~A}\right] Choose the correct answer from the options given below :
Options:
A) (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
B) (\mathrm{A})-(\mathrm{I}),(\mathrm{B})-(\mathrm{IV}),(\mathrm{C})-(\mathrm{II}),(\mathrm{D})-(\mathrm{III})
C) (\mathrm{A})-(\mathrm{II}),(\mathrm{B})-(\mathrm{I}),(\mathrm{C})-(\mathrm{III}),(\mathrm{D})-(\mathrm{IV})
D) (A)-(IV), (B)-(III), (C)-(I), (D)-(II)
77
EasyJEE Mains2025
The position of a particle moving on x-axis is given by x(t)=A \sin t+B \cos ^2 t+C t^2+D, where t is time. The dimension of \frac{A B C}{D} is
Options:
A) \mathrm{L}
B) \mathrm{L}^3 \mathrm{~T}^{-2}
C) \mathrm{L}^2 \mathrm{~T}^{-2}
D) \mathrm{L}^2
78
MediumJEE Mains2025
The maximum percentage error in the measurment of density of a wire is [Given, mass of wire =(0.60 \pm 0.003) \mathrm{g} radius of wire =(0.50 \pm 0.01) \mathrm{cm} length of wire =(10.00 \pm 0.05) \mathrm{cm}]
Options:
A) 7
B) 8
C) 5
D) 4
79
EasyJEE Mains2025
If B is magnetic field and \mu_0 is permeability of free space, then the dimensions of \left(B / \mu_0\right) is
Options:
A) \mathrm{MT}^{-2} \mathrm{~A}^{-1}
B) \mathrm{L}^{-1} \mathrm{~A}
C) \mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~A}^{-1}
D) \mathrm{LT}^{-2} \mathrm{~A}^{-1}
80
EasyJEE Mains2025
Given below are two statements : Statement I: In a vernier callipers, one vernier scale division is always smaller than one main scale division. Statement II : The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions. In the light of the above statements, choose the correct answer from the options given below.
Options:
A) Both Statement I and Statement II are false
B) Statement I is true but Statement II is false
C) Both Statement I and Statement II are true
D) Statement I is false but Statement II is true
81
EasyJEE Mains2024
The de-Broglie wavelength associated with a particle of mass m and energy E is h / \sqrt{2 m E}. The dimensional formula for Planck's constant is :
Options:
A) \left[\mathrm{M}^2 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]
B) \left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]
C) \left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]
D) \left[\mathrm{MLT}^{-2}\right]
82
EasyJEE Mains2024
The dimensional formula of latent heat is :
Options:
A) \left[\mathrm{M}^{\mathrm{0}} \mathrm{LT}^{-2}\right]
B) \left[\mathrm{MLT}^{-2}\right]
C) \left[\mathrm{M}^0 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]
D) \left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]
83
EasyJEE Mains2024
One main scale division of a vernier caliper is equal to \mathrm{m} units. If \mathrm{n}^{\text {th }} division of main scale coincides with (n+1)^{\text {th }} division of vernier scale, the least count of the vernier caliper is :
Options:
A) \frac{1}{(\mathrm{n}+1)}
B) \frac{m}{(n+1)}
C) \frac{n}{(n+1)}
D) \frac{\mathrm{m}}{\mathrm{n}(\mathrm{n}+1)}
84
EasyJEE Mains2024
If \epsilon_{\mathrm{o}} is the permittivity of free space and \mathrm{E} is the electric field, then \epsilon_{\mathrm{o}} \mathrm{E}^2 has the dimensions :
Options:
A) [\mathrm{M} \mathrm{L}^{-1} \mathrm{~T}^{-2}]
B) [\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-2}]
C) [\mathrm{M}^{\mathrm{0}} \mathrm{L}^{-2} \mathrm{TA}]
D) [\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^4 \mathrm{~A}^2]
85
MediumJEE Mains2024
There are 100 divisions on the circular scale of a screw gauge of pitch 1 \mathrm{~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 :
Options:
A) 4.65 mm
B) 4.60 mm
C) 4.55 mm
D) 3.35 mm
86
MediumJEE Mains2024
Least count of a vernier caliper is \frac{1}{20 \mathrm{~N}} \mathrm{~cm}. The value of one division on the main scale is 1 \mathrm{~mm}. Then the number of divisions of main scale that coincide with \mathrm{N} divisions of vernier scale is :
Options:
A) \left(\frac{2 \mathrm{~N}-1}{2 \mathrm{~N}}\right)
B) \left(\frac{2 \mathrm{~N}-1}{20 \mathrm{~N}}\right)
C) (2 \mathrm{~N}-1)
D) \left(\frac{2 \mathrm{~N}-1}{2}\right)
87
EasyJEE Mains2024
In an expression a \times 10^b :
Options:
A) a is order of magnitude for b \leq 5
B) b is order of magnitude for a \leq 5
C) b is order of magnitude for a \geq 5
D) b is order of magnitude for 5< a \leq 10
88
MediumJEE Mains2024
The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to 1 \mathrm{~mm}. The main scale reading is 2 \mathrm{~cm} and second division of vernier scale coincides with a division on main scale. If mass of the sphere is 8.635 \mathrm{g}, the density of the sphere is:
Options:
A) 2.2 \mathrm{~g} / \mathrm{cm}^3
B) 2.0 \mathrm{~g} / \mathrm{cm}^3
C) 1.7 \mathrm{~g} / \mathrm{cm}^3
D) 2.5 \mathrm{~g} / \mathrm{cm}^3
89
MediumJEE Mains2024
In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its 4^{\text {th }} division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 main scale divisions and zero error in the instrument is 0.04 \mathrm{~mm} then how many main scale divisions are there in 1 \mathrm{~cm} ?
Options:
A) 5
B) 40
C) 10
D) 20
90
MediumJEE Mains2024
In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division =49 \mathrm{~MSD} ; 20 divisions on main scale in each \mathrm{cm} For mark on paper \text { MSR }=8.45 \mathrm{~cm}, \mathrm{VC}=26 For mark on paper seen through slab \mathrm{MSR}=7.12 \mathrm{~cm}, \mathrm{VC}=41 For powder particle on the top surface of the glass slab \text { MSR }=4.05 \mathrm{~cm}, \mathrm{VC}=1 (MSR = Main Scale Reading, VC = Vernier Coincidence) Refractive index of the glass slab is :
Options:
A) 1.52
B) 1.35
C) 1.24
D) 1.42
91
MediumJEE Mains2024
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 measurement of mass. The percentage error in determining value of k is :
Options:
A) 5%
B) 3%
C) 1%
D) 4%
92
EasyJEE Mains2024
Match List I with List II LIST I LIST II A. Torque I. \left[M^1 L^1 T^{-2} A^{-2}\right] B. Magnetic field II. \left[L^2 A^1\right] C. Magnetic moment III. \left[M^1 T^{-2} A^{-1}\right] D. Permeability of free space IV. \left[M^1 L^2 T^{-2}\right] Choose the correct answer from the options given below:
Options:
A) A-I, B-III, C-II, D-IV
B) A-IV, B-II, C-III, D-I
C) A-III, B-I, C-II, D-IV
D) A-IV, B-III, C-II, D-I
93
EasyJEE Mains2024
While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is 1 \mathrm{~mm} and circular scale reading is equal to 42 divisions. Pitch of screw gauge is 1 \mathrm{~mm} and it has 100 divisions on circular scale. The diameter of the wire is \frac{x}{50} \mathrm{~mm}. The value of x is :
Options:
A) 42
B) 71
C) 21
D) 142
94
EasyJEE Mains2024
What is the dimensional formula of a b^{-1} in the equation \left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}, where letters have their usual meaning.
Options:
A) [\mathrm{M}^6 \mathrm{~L}^7 \mathrm{~T}^4]
B) [\mathrm{M}^{-1} \mathrm{~L}^5 \mathrm{~T}^3]
C) [\mathrm{M}^0 \mathrm{~L}^3 \mathrm{~T}^{-2}]
D) [\mathrm{ML}^2 \mathrm{~T}^{-2}]
95
EasyJEE Mains2024
A vernier callipers has 20 divisions on the vernier scale, which coincides with 19^{\text {th }} division on the main scale. The least count of the instrument is 0.1 \mathrm{~mm}. One main scale division is equal to ________ mm.
Options:
A) 5
B) 2
C) 1
D) 0.5
96
EasyJEE Mains2024
Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as 4.62 \mathrm{~s}, 4.632 \mathrm{~s}, 4.6 \mathrm{~s} and 4.64 \mathrm{~s}. The arithmetic mean of these readings in correct significant figure is :
Options:
A) 5 s
B) 4.6 s
C) 4.62 s
D) 4.623 s
97
EasyJEE Mains2024
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.
Options:
A) T^2=\frac{4 \pi^2 r}{G M^2}
B) T^2=4 \pi^2 r^3
C) T^2=\frac{4 \pi^2 r^3}{G M}
D) T^2=\frac{4 \pi^2 r^2}{G M}
98
EasyJEE Mains2024
The equation of stationary wave is : y=2 \mathrm{a} \sin \left(\frac{2 \pi \mathrm{nt}}{\lambda}\right) \cos \left(\frac{2 \pi x}{\lambda}\right) \text {. } Which of the following is NOT correct :
Options:
A) The dimensions of \mathrm{nt} is [L]
B) The dimensions of n is [\mathrm{LT}^{-1}]
C) The dimensions of x is [L]
D) The dimensions of n / \lambda is [T]
99
EasyJEE Mains2024
Match List - I with List - II . 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 Choose the correct answer from the options given below :
Options:
A) (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
B) (A)-(IV), (B)-(III), (C)-(I), (D)-(II)
C) (A)-(I), (B)-(II), (C)-(III), (D)-(IV)
D) (A)-(III), (B)-(IV), (C)-(II), (D)-(I)
100
EasyJEE Mains2024
10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is :
Options:
A) \frac{5}{11}
B) \frac{10}{11}
C) \frac{50}{11}
D) \frac{1}{2}
101
EasyJEE Mains2024
The dimensional formula of angular impulse is :
Options:
A) \left[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-2}\right]
B) \left[\mathrm{M} \mathrm{L}^{-2} \mathrm{~T}^{-1}\right]
C) \left[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-1}\right]
D) \left[\mathrm{M} \mathrm{L} \mathrm{T}^{-1}\right]
102
MediumJEE Mains2024
The radius (\mathrm{r}), length (l) and resistance (\mathrm{R}) of a metal wire was measured in the laboratory as \begin{aligned} & \mathrm{r}=(0.35 \pm 0.05) ~\mathrm{cm} \\\\ & \mathrm{R}=(100 \pm 10) ~\mathrm{ohm} \\\\ & l=(15 \pm 0.2)~ \mathrm{cm} \end{aligned} The percentage error in resistivity of the material of the wire is :
Options:
A) 37.3 \%
B) 25.6 \%
C) 35.6 \%
D) 39.9 \%
103
EasyJEE Mains2024
Consider two physical quantities A and B related to each other as E=\frac{B-x^2}{A t} where E, x and t have dimensions of energy, length and time respectively. The dimension of A B is
Options:
A) L^{-2} M^1 T^0
B) L^2 M^{-1} T^1
C) L^0 M^{-1} T^1
D) L^{-2} M^{-1} T^1
104
MediumJEE Mains2024
The measured value of the length of a simple pendulum is 20 \mathrm{~cm} with 2 \mathrm{~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 \mathrm{N} \%. The value of \mathrm{N} is:
Options:
A) 6
B) 5
C) 4
D) 8
105
EasyJEE Mains2024
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:
Options:
A) 0.144%
B) 0.2%
C) 0.1%
D) 0.3%
106
EasyJEE Mains2024
A force is represented by F=a x^2+b t^{\frac{1}{2}} where x= distance and t= time. The dimensions of b^2 / a are:
Options:
A) \left[\mathrm{ML}^2 \mathrm{~T}^{-3}\right]
B) \left[\mathrm{ML}^3 \mathrm{~T}^{-3}\right]
C) \left[M L T^{-2}\right]
D) \left[M L^{-1} T^{-1}\right]
107
EasyJEE Mains2024
If 50 Vernier divisions are equal to 49 main scale divisions of a traveling microscope and one smallest reading of main scale is 0.5 \mathrm{~mm}, the Vernier constant of traveling microscope is
Options:
A) 0.01 mm
B) 0.01 cm
C) 0.1 mm
D) 0.1 cm
108
EasyJEE Mains2024
If mass is written as m=k \mathrm{c}^{\mathrm{P}} G^{-1 / 2} h^{1 / 2} then the value of P will be : (Constants have their usual meaning with k a dimensionless constant)
Options:
A) 1/3
B) -1/3
C) 1/2
D) 2
109
EasyJEE Mains2024
Match List I with List II. List I List II (A) Coefficient of viscosity (I) \left[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-2}\right] (B) Surface tension (II) \left[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-1}\right] (C) Angular momentum (III) \left[\mathrm{M} \mathrm{L}^{-1} \mathrm{~T}^{-1}\right] (D) Rotational kinetic energy (IV) \left[\mathrm{M} \mathrm{L}^0 \mathrm{~T}^{-2}\right] Choose the correct answer from the options given below :
Options:
A) (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
B) (A)-(I), (B)-(II), (C)-(III), (D)-(IV)
C) (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
D) (A)-(III), (B)-(IV), (C)-(II), (D)-(I)
110
MediumJEE Mains2024
A physical quantity Q is found to depend on quantities a, b, c by the relation Q=\frac{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 :
Options:
A) 43%
B) 34%
C) 66%
D) 14%
111
EasyJEE Mains2024
The resistance R=\frac{V}{I} where \mathrm{V}=(200 \pm 5) \mathrm{V} and I=(20 \pm 0.2) \mathrm{A}, the percentage error in the measurement of \mathrm{R} is :
Options:
A) 5.5%
B) 3%
C) 7%
D) 3.5%
112
EasyJEE Mains2024
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading. Reason (R) : The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling. In the light of the above statements, choose the correct answer from the options given below :
Options:
A) Both (A) and (R) are correct and (R) is the correct explanation of (A)
B) Both (A) and (R) are correct 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
113
EasyJEE Mains2024
Given below are two statements : 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 :
Options:
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
114
EasyJEE Mains2023
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 :
Options:
A) \frac{1}{2}, 0, \frac{1}{2}
B) 1,1,0
C) 1,-1,0
D) \frac{1}{2}, \frac{1}{2}, 0
115
MediumJEE Mains2023
In the equation \left[X+\frac{a}{Y^{2}}\right][Y-b]=\mathrm{R} T, X is pressure, Y is volume, \mathrm{R} is universal gas constant and T is temperature. The physical quantity equivalent to the ratio \frac{a}{b} is:
Options:
A) Impulse
B) Energy
C) Pressure gradient
D) Coefficient of viscosity
116
EasyJEE Mains2023
A body of mass (5 \pm 0.5) ~\mathrm{kg} is moving with a velocity of (20 \pm 0.4) ~\mathrm{m} / \mathrm{s}. Its kinetic energy will be
Options:
A) (1000 \pm 140) ~\mathrm{J}
B) (500 \pm 0.14) ~\mathrm{J}
C) (1000 \pm 0.14) ~\mathrm{J}
D) (500 \pm 140) ~\mathrm{J}
117
EasyJEE Mains2023
Match List I with List II LIST I LIST II A. Spring constant I. \mathrm{[T^{-1}]} B. Angular speed II. \mathrm{[MT^{-2}]} C. Angular momentum III. \mathrm{[ML^2]} D. Moment of inertia IV. \mathrm{[ML^2T^{-1}]} Choose the correct answer from the options given below:
Options:
A) A-IV, B-I, C-III, D-II
B) A-II, B-III, C-I, D-IV
C) A-II, B-I, C-IV, D-III
D) A-I, B-III, C-II, D-IV
118
MediumJEE Mains2023
If force (F), velocity (V) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be :
Options:
A) \mathrm{FV}^{-2} \mathrm{~T}^{2}
B) \mathrm{FV}^{4} \mathrm{~T}^{-6}
C) \mathrm{F}^{2} \mathrm{~V}^{-2} \mathrm{~T}^{6}
D) \mathrm{FV}^{-4} \mathrm{~T}^{-2}
119
EasyJEE Mains2023
Given below are two statements : Statements I : Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances. Statements II : \mathrm{Au} < \mathrm{Parsec} (\mathrm{Pc}) < \mathrm{ly} In the light of the above statements, choose the most appropriate answer from the options given below:
Options:
A) Both Statements I and Statements II are incorrect.
B) Both Statements I and Statements II are correct,
C) Statements I is incorrect but Statements II is correct.
D) Statements I is correct but Statements II is incorrect.
120
MediumJEE Mains2023
In an experiment with vernier callipers of least count 0.1 \mathrm{~mm}, when two jaws are joined together the zero of vernier scale lies right to the zero of the main scale and 6th division of vernier scale coincides with the main scale division. While measuring the diameter of a spherical bob, the zero of vernier scale lies in between 3.2 \mathrm{~cm} and 3.3 \mathrm{~cm} marks, and 4th division of vernier scale coincides with the main scale division. The diameter of bob is measured as
Options:
A) 3 .18 \mathrm{~cm}
B) 3.22 \mathrm{~cm}
C) 3.26 \mathrm{~cm}
D) 3.25 \mathrm{~cm}
121
EasyJEE Mains2023
A physical quantity P is given as P = {{{a^2}{b^3}} \over {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
Options:
A) 12%
B) 13%
C) 16%
D) 14%
122
EasyJEE Mains2023
Match List I with List II LIST I LIST II A. Torque I. \mathrm{ML^{-2}T^{-2}} B. Stress II. \mathrm{ML^2T^{-2}} C. Pressure gradient III. \mathrm{ML^{-1}T^{-1}} D. Coefficient of viscosity IV. \mathrm{ML^{-1}T^{-2}} Choose the correct answer from the options given below:
Options:
A) A-II, B-I, C-IV, D-III
B) A-II, B-IV, C-I, D-III
C) A-IV, B-II, C-III, D-I
D) A-III, B-IV, C-I, D-II
123
EasyJEE Mains2023
Dimension of \frac{1}{\mu_{0} \in_{0}} should be equal to
Options:
A) \mathrm{T}^{2} / \mathrm{L}^{2}
B) \mathrm{T} / \mathrm{L}
C) \mathrm{L}^{2} / \mathrm{T}^{2}
D) \mathrm{L} / \mathrm{T}
124
EasyJEE Mains2023
A cylindrical wire of mass (0.4 \pm 0.01) \mathrm{g} has length (8 \pm 0.04) \mathrm{cm} and radius (6 \pm 0.03) \mathrm{mm}. The maximum error in its density will be:
Options:
A) 1%
B) 5%
C) 4%
D) 3.5%
125
MediumJEE Mains2023
Two resistances are given as \mathrm{R}_{1}=(10 \pm 0.5) \Omega and \mathrm{R}_{2}=(15 \pm 0.5) \Omega. The percentage error in the measurement of equivalent resistance when they are connected in parallel is -
Options:
A) 2.33
B) 5.33
C) 4.33
D) 6.33
126
MediumJEE Mains2023
If the velocity of light \mathrm{c}, universal gravitational constant \mathrm{G} and Planck's constant \mathrm{h} are chosen as fundamental quantities. The dimensions of mass in the new system is :
Options:
A) \left[\mathrm{h}^{1} \mathrm{c}^{1} \mathrm{G}^{-1}\right]
B) \left[\mathrm{h}^{-1 / 2} \mathrm{c}^{1 / 2} \mathrm{G}^{1 / 2}\right]
C) \left[\mathrm{h}^{1 / 2} \mathrm{c}^{1 / 2} \mathrm{G}^{-1 / 2}\right]
D) \left[\mathrm{h}^{1 / 2} \mathrm{c}^{-1 / 2} \mathrm{G}^{1}\right]
127
EasyJEE Mains2023
Match List I with List II LIST I LIST II A. Angular momentum I. \left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right] B. Torque II. \left[\mathrm{ML}^{-2} \mathrm{~T}^{-2}\right] C. Stress III \left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right] D. Pressure gradient IV. \left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right] Choose the correct answer from the options given below:
Options:
A) A - I, B - IV, C - III, D - II
B) A - III, B - I, C - IV, D - II
C) A - IV, B - II, C - I, D - III
D) A - II, B - III, C - IV, D - I
128
EasyJEE Mains2023
Match List I with List II : List I List II A. Torque I. \mathrm{kg} \mathrm{m}^{-1} \mathrm{~s}^{-2} B. Energy density II. \mathrm{kg} \,\mathrm{ms}^{-1} C. Pressure gradient III. \mathrm{kg}\, \mathrm{m}^{-2} \mathrm{~s}^{-2} D. Impulse IV. \mathrm{kg} \,\mathrm{m}^{2} \mathrm{~s}^{-2} Choose the correct answer from the options given below:
Options:
A) A-IV, B-I, C-III, D-II
B) A-IV, B-I, C-II, D-III
C) A-I, B-IV, C-III, D-II
D) A-IV, B-III, C-I, D-II
129
EasyJEE Mains2023
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 - {t \over B}} \right)^2} = {a^2}. The dimensions of t is given as [\mathrm{T^{-1}]}.
Options:
A) \mathrm{A=[L^{-1}T^{-1}],B=[LT^{-1}]}
B) \mathrm{A=[L^{-1}T^{-1}],B=[LT]}
C) \mathrm{A=[LT],B=[L^{-1}T^{-1}]}
D) \mathrm{A=[L^{-1}T],B=[LT^{-1}]}
130
EasyJEE Mains2023
Match List I with List II : List I (Physical Quantity) List II (Dimensional Formula) A. Pressure gradient I. \left[\mathrm{M}^{\circ} \mathrm{L}^{2} \mathrm{~T}^{-2}\right] B. Energy density II. \left[\mathrm{M}^{1} \mathrm{L}^{-1} \mathrm{~T}^{-2}\right] C. Electric Field III. \left[\mathrm{M}^{1} \mathrm{L}^{-2} \mathrm{~T}^{-2}\right] D. Latent heat IV. \left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right] Choose the correct answer from the options given below:
Options:
A) A-III, B-II, C-IV, D-I
B) A-III, B-II, C-I, D-IV
C) A-II, B-III, C-IV, D-I
D) A-II, B-III, C-I, D-IV
131
EasyJEE Mains2023
Match List I with List II List I List II A. Young's Modulus (Y) I. \mathrm{[ML^{-1}T^{-1}]} B. Co-efficient of Viscosity (\eta) II. \mathrm{[ML^2T^{-1}]} C. Planck's Constant (h) III. \mathrm{[ML^{-1}T^{-2}]} D. Work function (\varphi ) IV. \mathrm{[ML^2T^{-2}]} Choose the correct answer from the options given below :
Options:
A) A-II, B-III, C-IV, D-I
B) A-I, B-II, C-III, D-IV
C) A-I, B-III, C-IV, D-II
D) A-III, B-I, C-II, D-IV
132
EasyJEE Mains2023
Match List I with List II List-I List-II A. Planck's constant (h) I. \mathrm{[{M^1}\,{L^2}\,{T^{ - 2}}]} B. Stopping potential (Vs) II. \mathrm{[{M^1}\,{L^1}\,{T^{ - 1}}]} C. Work function (\phi) III. \mathrm{[{M^1}\,{L^2}\,{T^{ - 1}}]} D. Momentum (p) IV. \mathrm{[{M^1}\,{L^2}\,{T^{ - 3}}\,{A^{ - 1}}]} Choose the correct answer from the options given below :
Options:
A) A-I, B-III, C-IV, D-II
B) A-III, B-IV, C-I, D-II
C) A-II, B-IV, C-III, D-I
D) A-III, B-I, C-II, D-IV
133
EasyJEE Mains2022
Match List I with List II. List I List II A. Torque I. Nms^{ - 1} B. Stress II. J kg^{ - 1} C. Latent Heat III. Nm D. Power IV. Nm^{ - 2} Choose the correct answer from the options given below :
Options:
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
134
EasyJEE Mains2022
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 \rho and radius of the drop is r, then \mathrm{T}=\mathrm{K} \sqrt{\rho \mathrm{r}^{3} / \mathrm{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.
Options:
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
135
EasyJEE Mains2022
A travelling microscope has 20 divisions per \mathrm{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?
Options:
A) 0.001 cm
B) 0.002 mm
C) 0.002 cm
D) 0.005 cm
136
EasyJEE Mains2022
In an experiment to find out the diameter of wire using screw gauge, the following observations were noted : (A) Screw moves 0.5 \mathrm{~mm} on main scale in one complete rotation (B) Total divisions on circular scale =50 (C) Main scale reading is 2.5 \mathrm{~mm} (D) 45^{\text {th }} division of circular scale is in the pitch line (E) Instrument has 0.03 mm negative error Then the diameter of wire is :
Options:
A) 2.92 mm
B) 2.54 mm
C) 2.98 mm
D) 3.45 mm
137
MediumJEE Mains2022
Consider the efficiency of carnot's engine is given by \eta=\frac{\alpha \beta}{\sin \theta} \log_e \frac{\beta x}{k T}, 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 :
Options:
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.
138
EasyJEE Mains2022
The dimensions of \left(\frac{\mathrm{B}^{2}}{\mu_{0}}\right) will be : (if \mu_{0} : permeability of free space and B : magnetic field)
Options:
A) \left[\mathrm{M}\, \mathrm{L}^2 \,\mathrm{T}^{-2}\right]
B) \left[\mathrm{M} \,\mathrm{L} \,\mathrm{T}^{-2}\right]
C) \left[\mathrm{M} \,\mathrm{L}^{-1} \,\mathrm{~T}^{-2}\right]
D) \left[\mathrm{M} \,\mathrm{L}^{2} \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]
139
MediumJEE Mains2022
An expression of energy density is given by u=\frac{\alpha}{\beta} \sin \left(\frac{\alpha x}{k t}\right), where \alpha, \beta are constants, x is displacement, k is Boltzmann constant and t is the temperature. The dimensions of \beta will be :
Options:
A) \left[\mathrm{ML}^{2} \mathrm{~T}^{-2} \theta^{-1}\right]
B) \left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{-2}\right]
C) \left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}\right]
D) \left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{0}\right]
140
MediumJEE Mains2022
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 :
Options:
A) 15%
B) 25%
C) 75%
D) 5%
141
MediumJEE Mains2022
In a Vernier Calipers, 10 divisions of Vernier scale is equal to the 9 divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and 4^{\text {th }} Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to 1 \mathrm{~mm}. While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between 30 and 31 divisions of main scale reading and 6^{\text {th }} Vernier scale division exactly coincides with the main scale reading. The diameter of the spherical body will be :
Options:
A) 3.02 cm
B) 3.06 cm
C) 3.10 cm
D) 3.20 cm
142
EasyJEE Mains2022
A screw gauge of pitch 0.5 \mathrm{~mm} is used to measure the diameter of uniform wire of length 6.8 \mathrm{~cm}, the main scale reading is 1.5 \mathrm{~mm} and circular scale reading is 7 . The calculated curved surface area of wire to appropriate significant figures is : [Screw gauge has 50 divisions on its circular scale]
Options:
A) 6.8 cm
2
B) 3.4 cm
2
C) 3.9 cm
2
D) 2.4 cm
2
143
EasyJEE Mains2022
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 will be :
Options:
A) 2
B) 4
C) 6
D) 8
144
MediumJEE Mains2022
If momentum [P], area [\mathrm{A}] and time [\mathrm{T}] are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is :
Options:
A) \left[\mathrm{P} \,\mathrm{A}^{-1} \mathrm{~T}^{0}\right]
B) \left[\mathrm{P} \,\mathrm{A}\mathrm{~T}^{-1}\right]
C) \left[\mathrm{P}\,\mathrm{A}^{-1} \mathrm{~T}\right]
D) \left[\mathrm{P} \,\mathrm{A}^{-1} \mathrm{~T}^{-1}\right]
145
MediumJEE Mains2022
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 :
Options:
A) {2 \over {n + 1}} mm
B) {5 \over {n + 1}} mm
C) {1 \over {2n}} mm
D) {1 \over {5n}} mm
146
MediumJEE Mains2022
Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as {v_2} = {n \over {{m^2}}}{v_1} and {a_2} = {{{a_1}} \over {mn}} respectively. Here m and n are constants. The relations for distance and time in two systems respectively are :
Options:
A) {{{n^3}} \over {{m^3}}}{L_1} = {L_2} and {{{n^2}} \over m}{T_1} = {T_2}
B) {L_1} = {{{n^4}} \over {{m^2}}}{L_2} and {T_1} = {{{n^2}} \over m}{T_2}
C) {L_1} = {{{n^2}} \over m}{L_2} and {T_1} = {{{n^4}} \over {{m^2}}}{T_2}
D) {{{n^2}} \over m}{L_1} = {L_2} and {{{n^4}} \over {{m^2}}}{T_1} = {T_2}
147
EasyJEE Mains2022
The SI unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be :
Options:
A) [ML
-1
T
-1
]
B) [ML
-1
T
-2
]
C) [ML
2
T
-1
]
D) [M
-1
L
3
T
0
]
148
EasyJEE Mains2022
A silver wire has a 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 :
Options:
A) 4%
B) 3%
C) 6%
D) 7%
149
EasyJEE Mains2022
The dimension of mutual inductance is :
Options:
A) [M{L^2}{T^{ - 2}}{A^{ - 1}}]
B) [M{L^2}{T^{ - 3}}{A^{ - 1}}]
C) [M{L^2}{T^{ - 2}}{A^{ - 2}}]
D) [M{L^2}{T^{ - 3}}{A^{ - 2}}]
150
MediumJEE Mains2022
An expression for a dimensionless quantity P is given by P = {\alpha \over \beta }{\log _e}\left( {{{kt} \over {\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 :
Options:
A) [M
0
L
-1
T
0
]
B) [M L
0
T
-2
]
C) [M L T
-2
]
D) [M L
2
T
-2
]
151
EasyJEE Mains2022
If Z = {{{A^2}{B^3}} \over {{C^4}}}, then the relative error in Z will be :
Options:
A) {{\Delta A} \over A} + {{\Delta B} \over B} + {{\Delta C} \over C}
B) {{2\Delta A} \over A} + {{3\Delta B} \over B} - {{4\Delta C} \over C}
C) {{2\Delta A} \over A} + {{3\Delta B} \over B} + {{4\Delta C} \over C}
D) {{\Delta A} \over A} + {{\Delta B} \over B} - {{\Delta C} \over C}
152
EasyJEE Mains2022
Identify the pair of physical quantities that have same dimensions:
Options:
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
153
EasyJEE Mains2022
Identify the pair of physical quantities which have different dimensions:
Options:
A) Wave number and Rydberg's constant
B) Stress and Coefficient of elasticity
C) Coercivity and Magnetisation
D) Specific heat capacity and Latent heat
154
MediumJEE Mains2021
A student determined Young's Modulus of elasticity using the formula Y = {{Mg{L^3}} \over {4b{d^3}\delta }}. The value of g is taken to be 9.8 m/s 2 , without any significant error, his observation are as following. 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 (\delta ) 0.01 mm 5 mm Then the fractional error in the measurement of Y is :
Options:
A) 0.0083
B) 0.0155
C) 0.155
D) 0.083
155
MediumJEE Mains2021
If velocity [V], time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will be :
Options:
A) [FT
-1
V
-1
]
B) [FTV
-1
]
C) [FT
2
V]
D) [FVT
-1
]
156
EasyJEE Mains2021
Match List - I with List - II. List - I List - II (a) Torque (i) MLT^{ - 1} (b) Impulse (ii) MT^{ - 2} (c) Tension (iii) ML^{ 2}T^{ - 2} (d) Surface Tension (iv) MLT^{ - 2} Choose the most appropriate answer from the option given below :
Options:
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)
157
EasyJEE Mains2021
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, \in = permittivity, E = electric field, J = current density, L = length.
Options:
A) v = {{\pi p{a^4}} \over {8\eta L}}
B) h = {{2s\cos \theta } \over {\rho rg}}
C) J = \in {{\partial E} \over {\partial t}}
D) W = \Gamma \theta
158
EasyJEE Mains2021
Match List - I with List - II. 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) \eta (coefficient of viscocity) (iv) kg\,{m^{ - 1}}{s^{ - 2}} Choose the most appropriate answer from the options given below :
Options:
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)
159
EasyJEE Mains2021
If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density :
Options:
A) [FL
-4
T
2
]
B) [FL
-3
T
2
]
C) [FL
-5
T
2
]
D) [FL
-3
T
3
]
160
EasyJEE Mains2021
Which of the following is not a dimensionless quantity?
Options:
A) Relative magnetic permeability (\mu
r
)
B) Power factor
C) Permeability of free space (\mu
0
)
D) Quality factor
161
EasyJEE Mains2021
If E and H represents the intensity of electric field and magnetising field respectively, then the unit of E/H will be :
Options:
A) ohm
B) mho
C) joule
D) newton
162
EasyJEE Mains2021
Match List - I with List - II Choose the most appropriate answer from the options given below :
Options:
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)
163
EasyJEE Mains2021
If the length of the pendulum in pendulum clock increases by 0.1%, then the error in time per day is :
Options:
A) 86.4 s
B) 4.32 s
C) 43.2 s
D) 8.64 s
164
EasyJEE Mains2021
In a Screw Gauge, 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 20 th division of the circular scale coincides with reference line. Calculate the true reading.
Options:
A) 5.00 mm
B) 5.25 mm
C) 5.15 mm
D) 5.20 mm
165
EasyJEE Mains2021
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 :
Options:
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
]
166
MediumJEE Mains2021
A physical quantity 'y' is represented by the formula y = {m^2}{r^{ - 4}}{g^x}{l^{ - {3 \over 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.
Options:
A) 5 and \pm2
B) 4 and \pm3
C) {{16} \over 3} and \pm {3 \over 2}
D) 8 and \pm 2
167
EasyJEE Mains2021
Assertion A : If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is 5 mm and there are 50 total divisions on circular scale, then least count is 0.001 cm. Reason R : Least Count = {{Pitch} \over {Total\,divisions\,on\,circular\,scale}} In the light of the above statements, choose the most appropriate answer from the options given below :
Options:
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.
168
EasyJEE Mains2021
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} \over B} is :
Options:
A) [{M^0}L{T^{ - 1}}]
B) [M{L^2}{T^{ - 3}}]
C) [{M^1}{L^1}{T^{ - 2}}]
D) [{M^2}{L^2}{T^{ - 3}}]
169
MediumJEE Mains2021
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 :
Options:
A) [{t^{ - 1}}{v^1}{l^{ - 2}}]
B) [{t^1}{v^2}{l^{ - 1}}]
C) [{t^{ - 2}}{v^{ - 1}}{l^1}]
D) [{t^{ - 1}}{v^{ - 2}}{l^1}]
170
EasyJEE Mains2021
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)
Options:
A) 8.58 cm
B) 8.54 cm
C) 8.56 cm
D) 8.36 cm
171
MediumJEE Mains2021
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 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?
Options:
A) 0.14%
B) 9%
C) 1.4%
D) 0.9%
172
EasyJEE Mains2021
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 :
Options:
A) {{10a} \over n}
B) {{10na} \over {(n - 1)}}
C) \left( {{{n - 1} \over {10n}}} \right)a
D) {{10a} \over {(n - 1)}}
173
EasyJEE Mains2021
If 'C' and 'V' represent capacity and voltage respectively then what are the dimensions of \lambda where C/V = \lambda ?
Options:
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}}]
174
EasyJEE Mains2021
In a typical combustion engine the workdone by a gas molecule is given by W = {\alpha ^2}\beta {e^{{{ - \beta {x^2}} \over {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 :
Options:
A) [{M^0}L{T^0}]
B) [ML{T^{ - 1}}]
C) [ML{T^{ - 2}}]
D) [{M^2}L{T^{ - 2}}]
175
MediumJEE Mains2021
If e is the electronic charge, c is the speed of light in free space and h is Planck's constant, the quantity {1 \over {4\pi {\varepsilon _0}}}{{|e{|^2}} \over {hc}} has dimensions of :
Options:
A) [ML{T^{ - 1}}]
B) [ML{T^0}]
C) [{M^0}{L^0}{T^0}]
D) [L{C^{ - 1}}]
176
EasyJEE Mains2021
Match List - I with List - II : List I List II (a) h (Planck's constant) (i) [ML{T^{ - 1}}] (b) E (kinetic energy) (ii) [M{L^2}{T^{ - 1}}] (c) V (electric potential) (iii) [M{L^2}{T^{ - 2}}] (d) P (linear momentum) (iv) [M{L^2}{I^{ - 1}}{T^{ - 3}}] Choose the correct answer from the options given below :
Options:
A) (a) \to (ii), (b) \to (iii), (c) \to (iv), (d) \to (i)
B) (a) \to (i), (b) \to (ii), (c) \to (iv), (d) \to (iii)
C) (a) \to (iii), (b) \to (ii), (c) \to (iv), (d) \to (i)
D) (a) \to (iii), (b) \to (iv), (c) \to (ii), (d) \to (i)
177
EasyJEE Mains2021
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 72 nd division on circular scale coincides with the reference line. The radius of the wire is :
Options:
A) 1.80 mm
B) 0.90 mm
C) 0.82 mm
D) 1.64 mm
178
MediumJEE Mains2021
The work done by a gas molecule in an isolated system is given by, W = \alpha {\beta ^2}{e^{ - {{{x^2}} \over {\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 :
Options:
A) [{M^0}L{T^0}]
B) [M{L^2}{T^{ - 2}}]
C) [ML{T^{ - 2}}]
D) [{M^2}L{T^2}]
179
MediumJEE Mains2020
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 :
Options:
A) (5.54 \pm 0.07) mm
B) (5.5375 \pm 0.0740) mm
C) (5.5375 \pm 0.0739) mm
D) (5.538 \pm 0.074) mm
180
MediumJEE Mains2020
A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of 0.5mm is noticed on the pitch scale. The nature of zero error involved and the least count of the screw gauge, are respectively :
Options:
A) Positive, 0.1 mm
B) Positive, 0.1 \mu m
C) Positive, 10 \mu m
D) Negative, 2 \mu m
181
MediumJEE Mains2020
The quantities x = {1 \over {\sqrt {{\mu _0}{\varepsilon _0}} }}, y = {E \over B} and z = {l \over {CR}} are defined where C-capacitance, R-Resistance, l-length, E-Electric field, B-magnetic field and {{\varepsilon _0}}, {{\mu _0}}, - free space permittivity and permeability respectively. Then :
Options:
A) Only y and z have the same dimension
B) x, y and z have the same dimension
C) Only x and y have the same dimension
D) Only x and z have the same dimension
182
MediumJEE Mains2020
A physical quantity z depends on four observables a, b, c and d, as z = {{{a^2}{b^{{2 \over 3}}}} \over {\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 :
Options:
A) 13.5 %
B) 14.5%
C) 16.5%
D) 12.25%
183
MediumJEE Mains2020
A quantity x is given by \left( {{{IF{v^2}} \over {W{L^4}}}} \right) in terms of moment of inertia I, force F, velocity v, work W and Length L. The dimensional formula for x is same as that of :
Options:
A) Coefficient of viscosity
B) Force constant
C) Energy density
D) Planck's constant
184
MediumJEE Mains2020
Dimensional formula for thermal conductivity is (here K denotes the temperature):
Options:
A) MLT
–3
K
–1
B) MLT
–2
K
–2
C) MLT
–2
K
D) MLT
–3
K
185
MediumJEE Mains2020
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 :
Options:
A) MLT
–2
B) ML
0
T
–3
C) M
2
L
0
T
–1
D) ML
2
T
–2
186
MediumJEE Mains2020
Using screw gauge of pitch 0.1 cm and 50 divisions on its circular scale, the thickness of an object is measured. It should correctly be recorded as
Options:
A) 2.123 cm
B) 2.124 cm
C) 2.125 cm
D) 2.121 cm
187
MediumJEE Mains2020
If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is
Options:
A) [P
2
AT
–2
]
B) \left[ {{P^{{1 \over 2}}}A{T^{ - 1}}} \right]
C) \left[ {P{A^{{1 \over 2}}}{T^{ - 1}}} \right]
D) [PA
–1
T
–2
]
188
MediumJEE Mains2020
The least count of the main scale of a vernier callipers is 1 mm. Its vernier scale is divided into 10 divisions and coincide with 9 divisions of the main scale. When jaws are touching each other, the 7 th division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale between 3.1 cm and 3.2 cm and 4 th VSD coincides with a main scale division. The length of the cylinder is : (VSD is vernier scale division)
Options:
A) 3.21 cm
B) 2.99 cm
C) 3.07 cm
D) 3.2 cm
189
MediumJEE Mains2020
If speed V, area A and force F are chosen as fundamental units, then the dimension of Young’s modulus will be
Options:
A) FA
–1
V
0
B) FA
2
V
–1
C) FA
2
V
–2
D) FA
2
V
–3
190
MediumJEE Mains2020
For the four sets of three measured physical quantities as given below. Which of the following options is correct ? (i) A 1 = 24.36, B 1 = 0.0724, C 1 = 256.2 (ii) A 2 = 24.44, B 2 = 16.082, C 2 = 240.2 (iii) A 3 = 25.2, B 3 = 19.2812, C 3 = 236.183 (iv) A 4 = 25, B 4 = 236.191, C 4 = 19.5
Options:
A) A
1
+ B
1
+ C
1
= A
2
+ B
2
+ C
2
= A
3
+ B
3
+ C
3
= A
4
+ B
4
+ C
4
B) A
4
+ B
4
+ C
4
< A
1
+ B
1
+ C
1
< A
3
+ B
3
+ C
3
< A
2
+ B
2
+ C
2
C) A
4
+ B
4
+ C
4
< A
1
+ B
1
+ C
1
= A
2
+ B
2
+ C
2
= A
3
+ B
3
+ C
3
D) A
4
+ B
4
+ C
4
> A
3
+ B
3
+ C
3
= A
2
+ B
2
+ C
2
>
A
1
+ B
1
+ C
1
191
MediumJEE Mains2020
If the screw on a screw-gauge is given six rotations, it moves by 3 mm on the main scale. If there are 50 divisions on the circular scale the least count of the screw gauge is :
Options:
A) 0.001 mm
B) 0.01 cm
C) 0.02 mm
D) 0.001 cm
192
MediumJEE Mains2020
A quantity f is given by f = \sqrt {{{h{c^5}} \over G}} where c is speed of light, G universal gravitational constant and h is the Planck's constant. Dimension of f is that of :
Options:
A) Energy
B) Momentum
C) Area
D) Volume
193
MediumJEE Mains2020
The dimension of stopping potential V 0 in photoelectric effect in units of Planck's constant 'h', speed of light 'c' and Gravitational constant 'G' and ampere A is :
Options:
A) h
1/3
G
2/3
c
1/3
A
–1
B) h
0
c
5
G
-1
A
-1
C) h
2/3
c
5/3
G
1/3
A
–1
D) h
2
G
3/2
c
1/3
A
–1
194
MediumJEE Mains2020
The dimension of {{{B^2}} \over {2{\mu _0}}}, where B is magnetic field and {{\mu _0}} is the magnetic permeability of vacuum, is :
Options:
A) ML
2
T
–2
B) MLT
–2
C) ML
-1
T
–2
D) ML
2
T
–1
195
MediumJEE Mains2019
Which of the following combinations has the dimension of electrical resistance ( \in 0 is the permittivity of vacuum and \mu 0 is the permeability of vacuum)?
Options:
A) \sqrt {{{{ \in _0}} \over {{\mu _0}}}}
B) {{{{ \in _0}} \over {{\mu _0}}}}
C) \sqrt {{{{\mu _0}} \over {{ \in _0}}}}
D) {{{{\mu _0}} \over {{ \in _0}}}}
196
MediumJEE Mains2019
In 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?
Options:
A) [M
–3
L
–2
T
8
A
4
]
B) [M
–2
L
–2
T
6
A
3
]
C) [M
–1
L
–2
T
4
A
2
]
D) [M
–2
L
0
T
–4
A
–2
]
197
MediumJEE Mains2019
The area of a square is 5.29 cm 2 . The area of 7 such squares taking into account the significant figures is :-
Options:
A) 37.0 cm
2
B) 37 cm
2
C) 37.030 cm
2
D) 37.03 cm
2
198
MediumJEE Mains2019
In the density measurement of a cube, the mass and edge length are measured as (10.00 ± 0.10) kg and (0.10 ± 0.01) m, respectively. The error in the measurement of density is :
Options:
A) 0.01 kg/m
3
B) 0.10 kg/m
3
C) 0.31 kg/m
3
D) 0.07 kg/m
3
199
MediumJEE Mains2019
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 :-
Options:
A) S
1/2
I
1/2
h
0
B) S
3/2
I
1/2
h
0
C) S
1/2
I
1/2
h
-1
D) S
1/2
I
3/2
h
-1
200
MediumJEE Mains2019
In a simple pendulum experiment for determination of acceleration due to gravity (g), time taken for 20 oscillations is measured by using a watch of 1 second least count. The mean value of time taken comes out to be 30 s. The length of pendulum is measured by using a meter scale of least count 1 mm and the value obtained is 55.0 cm. The percentage error in the determination of g is close to :-
Options:
A) 0.2%
B) 3.5%
C) 0.7%
D) 6.8%
201
MediumJEE Mains2019
In SI units, the dimensions of \sqrt {{{{ \in _0}} \over {{\mu _0}}}} is :
Options:
A) A
–1
TML
3
B) A
2
T
3
M
–1
L
–2
C) AT
–3
ML
3/2
D) AT
2
M
–1
L
–1
202
MediumJEE Mains2019
Let \ell , r, C and V represent inductance, resistance, capacitance and voltage, respectively. The dimension of {\ell \over {rCV}} in SI units will be :
Options:
A) [A
–1
]
B) [LTA]
C) [LA
–2
]
D) [LT
2
]
203
MediumJEE Mains2019
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 :
Options:
A) 500
B) 100
C) 200
D) 50
204
MediumJEE Mains2019
If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young,s modulus will be:
Options:
A) V
-2
A
2
F
2
B) V
-4
A
-2
F
C) V
-4
A
2
F
D) V
-2
A
2
F
-2
205
MediumJEE Mains2019
The force of interaction between two atoms is given by F = \alpha \beta exp \left( { - {{{x^2}} \over {\alpha kt}}} \right); where x is the distance, k is the Boltzmann constant and T is temperature and \alpha and \beta are two constants. The dimension of \beta is :
Options:
A) M
2
L
2
T
-2
B) M
2
LT
-4
C) MLT
-4
D) M
0
L
2
LT
-4
206
MediumJEE Mains2019
The diameter and height of a cylinder are measured by a meter scale to be 12.6 \pm 0.1 cm and 34.2 \pm 0.1 cm, respectively. What will be the value of its volume in appropriate significant figures ?
Options:
A) 4264.4 \pm 81.0 cm
3
B) 4264 \pm 81 cm
3
C) 4300 \pm 80 cm
3
D) 4260 \pm 80 cm
3
207
MediumJEE Mains2019
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 is 50 g, the numerical value of density of the material is -
Options:
A) 40
B) 640
C) 16
D) 410
208
MediumJEE Mains2019
The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies 3 divisions below the mean line. The readings of the main scale and the circular scale, for a thin sheet, are 5.5 mm and 48 respectively, the thickness of this sheet is :
Options:
A) 5.755 mm
B) 5.950 mm
C) 5.725 mm
D) 5.740 mm
209
MediumJEE Mains2019
Expression for time in terms of G(universal gravitional constant), h (Planck constant) and c (speed of light) is proportional to :
Options:
A) \sqrt {{{h{c^5}} \over G}}
B) \sqrt {{{{c^3}} \over {Gh}}}
C) \sqrt {{{Gh} \over {{c^5}}}}
D) \sqrt {{{Gh} \over {{c^3}}}}
210
MediumJEE Mains2019
A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume remains unchanged is :
Options:
A) 2.0 %
B) 2.5 %
C) 1.0 %
D) 0.5 %
211
MediumJEE Mains2018
The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5% respectively in the measurement of a physical quantity A = {{{P^3}{Q^2}} \over {\sqrt R S}}. The maximum percentage error in the value of A will be :
Options:
A) 6.0%
B) 7.5%
C) 8.5%
D) 6.5%
212
MediumJEE Mains2018
The relative uncertainly in the period of a satellite orbiting around the earth is 10 -2 . If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is :
Options:
A) 10
-2
B) 2 \times 10
-2
C) 3 \times 10
-2
D) 6 \times 10
-2
213
MediumJEE Mains2018
The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is:
Options:
A) 6%
B) 2.5%
C) 3.5%
D) 4.5%
214
MediumJEE Mains2018
The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants G, h and c. Which of the following correctly gives the Planck length ?
Options:
A) G \hbar
2
c
3
B) G
2
\hbar c
C) {G^{{\raise0.5ex\hbox{\scriptstyle 1}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{\scriptstyle 2}}}}{\hbar ^2}c
D) {\left( {{{G\hbar } \over {{c^3}}}} \right)^{{\raise0.5ex\hbox{\scriptstyle 1}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{\scriptstyle 2}}}}
215
MediumJEE Mains2018
The relative error in the determination of the surface area of sphere is \alpha . Then the relative error in the determination of its volume is :
Options:
A) {3 \over 2}\alpha
B) {2 \over 3}\alpha
C) {5 \over 2}\alpha
D) \alpha
216
MediumJEE Mains2018
In a screw gauge, 5 complete rotations of the screw cause it to move a linear distance of 0.25 cm. There are 100 circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of 4 main scale divisions and 30 circular scale divisions. Assuming negligible zero error, the thickness of the wire is :
Options:
A) 0.4300 cm
B) 0.2150 cm
C) 0.3150 cm
D) 0.0430 cm
217
MediumJEE Mains2017
A physical quantity P is described by the relation P = a^{{\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}} b 2 c 3 d -4 If the relative errors in the measurement of a, b, c and d respectively, are 2%, 1%, 3% and 5%, then the relative error in P will be :
Options:
A) 8%
B) 12%
C) 32%
D) 25%
218
MediumJEE Mains2017
Time (T), velocity (C) and angular momentum (h) are chosen as fundamentalquantities instead of mass, length and time. In terms of these, the dimensions of mass would be :
Options:
A) [M] = [T
-1
C
-2
h]
B) [M] = [T
-1
C
2
h]
C) [M] = [T
-1
C
-2
h
-1
]
D) [M] = [T C
-2
h]
219
MediumJEE Mains2017
The following observations were taken for determining surface tension T of water by capillary method: diameter of capillary, D = 1.25 \times 10 -2 m rise of water, h = 1.45 \times 10 -2 m Using g = 9.80 m/s 2 and the simplified relation T = {{rhg} \over 2} \times {10^3}N/m, the possible error in surface tension is closest to :
Options:
A) 10 %
B) 0.15 %
C) 1.5 %
D) 2.4 %
220
MediumJEE Mains2016
In the following ‘I’ refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity :
Options:
A) ML
-3
T
-3
I2
B) M
-1
L
3
T
3
I
C) M
-1
L
-3
T
3
I
2
D) M
-1
L
-3
T
3
I
221
MediumJEE Mains2016
A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be :
Options:
A) 92 \pm 1.8 s
B) 92 \pm 3 s
C) 92 \pm 2 s
D) 92 \pm 5.0 s
222
MediumJEE Mains2016
A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the 45 th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the 25 th division coincides with the main scale line?
Options:
A) 0.70 mm
B) 0.50 mm
C) 0.75 mm
D) 0.80 mm
223
MediumJEE Mains2014
A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?
Options:
A) A screw gauge having 100 divisions in the circular scale and pitch as 1 mm.
B) A screw gauge having 50 divisions in the circular scale and pitch as 1 mm.
C) A meter scale.
D) A vernier calliper where the 10 divisions in vernier scale matches with 9 division in main scale and main scale has 10 divisions in 1 cm.
224
MediumJEE Mains2013
Let [{\varepsilon _0}] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then:
Options:
A) {\varepsilon _0} = \left[ {{M^{ - 1}}{L^{ - 3}}{T^2}A} \right]
B) {\varepsilon _0} = \left[ {{M^{ - 1}}{L^{ - 3}}{T^4}{A^2}} \right]
C) {\varepsilon _0} = \left[ {{M^1}{L^2}{T^1}{A^2}} \right]
D) {\varepsilon _0} = \left[ {{M^1}{L^2}{T^1}A} \right]
225
MediumJEE Mains2012
Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is
Options:
A) 6 %
B) zero
C) 1 %
D) 3 %
226
MediumJEE Mains2012
A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading: 58.5 degree Vernier scale reading : 09 divisions Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data
Options:
A) 58.59 degree
B) 58.77 degree
C) 58.65 degree
D) 59 degree
227
MediumJEE Mains2011
A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading : 0 mm Circular scale reading : 52 divisions Given that 1 mm on main scale corresponds to 100 divisions of the circular scale. The diameter of wire from the above date is:
Options:
A) 0.052 cm
B) 0.026 cm
C) 0.005 cm
D) 0.52 cm
228
MediumJEE Mains2010
The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 \times 10 –3 are
Options:
A) 5, 1, 2
B) 5, 1, 5
C) 5, 5, 2
D) 4, 4, 2
229
MediumJEE Mains2009
In an experiment the angles are required to be measured using an instrument, 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a degree(=0.5^\circ ), then the least count of the instrument is:
Options:
A) one minute
B) half minute
C) one degree
D) half degree
230
MediumJEE Mains2008
A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 ms −1 . The magnitude of its momentum is recorded as
Options:
A) 17.6 kg ms
-1
B) 17.565 kg ms
-1
C) 17.56 kg ms
-1
D) 17.57 kg ms
-1
231
MediumJEE Mains2008
Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of − 0.03 mm while measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is
Options:
A) 3.32 mm
B) 3.73 mm
C) 3.67 mm
D) 3.38 mm
232
MediumJEE Mains2008
An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distances are measured by
Options:
A) a vernier scale provided on the microscope
B) a standard laboratory scale
C) a meter scale provided on the microscope
D) a screw gauge provided on the microscope
233
MediumJEE Mains2008
The dimension of magnetic field in M, L, T and C (coulomb) is given as
Options:
A) MLT
-1
C
-1
B) MT
2
C
-2
C) MT
-1
C
-1
D) MT
-2
C
-1
234
MediumJEE Mains2005
Out of the following pair, which one does NOT have identical dimensions is
Options:
A) angular momentum and Planck's constant
B) impulse and momentum
C) moment of inertia and moment of a force
D) work and torque
235
MediumJEE Mains2004
Which one of the following represents the correct dimensions of the coefficient of viscosity?
Options:
A) ML
-1
T
-1
B) MLT
-1
C) ML
-1
T
-2
D) ML
-2
T
-2
236
MediumJEE Mains2003
Dimensions of {1 \over {{\mu _0}{\varepsilon _0}}}, where symbols have their usual meaning, are
Options:
A) [ L
-1
T ]
B) [ L
-2
T
2
]
C) [ L
2
T
-2
]
D) [ LT
-1
]
237
MediumJEE Mains2003
The physical quantities not having same dimensions are
Options:
A) torque and work
B) momentum and Planck's constant
C) stress and Young's modulus
D) speed and {\left( {{\mu _0}{\varepsilon _0}} \right)^{ - 1/2}}
238
MediumJEE Mains2002
Identify the pair whose dimensions are equal
Options:
A) torque and work
B) stress and energy
C) force and stress
D) force and work
239
EasyInteger TypeJEE Mains2025
A physical quantity C is related to four other quantities \mathrm{p}, \mathrm{q}, \mathrm{r} and s as follows C=\frac{p q^2}{r^3 \sqrt{s}} The percentage errors in the measurement of \mathrm{p}, \mathrm{q}, \mathrm{r} and s are 1 \%, 2 \%, 3 \% and 2 \%, respectively. The percentage error in the measurement of C will be__________%
Answer: Enter a numeric value
240
MediumInteger TypeJEE Mains2025
\text { A physical quantity } Q \text { is related to four observables } a, b, c, d \text { as follows : } Q = \frac{ab^4}{cd} where, \mathrm{a}=(60 \pm 3) \mathrm{Pa} ; \mathrm{b}=(20 \pm 0.1) \mathrm{m} ; \mathrm{c}=(40 \pm 0.2) \mathrm{Nsm}^{-2} and \mathrm{d}=(50 \pm 0.1) \mathrm{m}, then the percentage error in Q is \frac{x}{1000}, where x= _________ .
Answer: Enter a numeric value
241
MediumInteger TypeJEE Mains2025
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 _______ .
Answer: Enter a numeric value
242
EasyInteger TypeJEE Mains2025
The least count of a screw guage is 0.01 mm . If the pitch is increased by 75 \% and number of divisions on the circular scale is reduced by 50 \%, the new least count will be ________ \times 10^{-3} \mathrm{~mm}
Answer: Enter a numeric value
243
EasyInteger TypeJEE Mains2023
In a screw gauge, there are 100 divisions on the circular scale and the main scale moves by 0.5 \mathrm{~mm} on a complete rotation of the circular scale. The zero of circular scale lies 6 divisions below the line of graduation when two studs are brought in contact with each other. When a wire is placed between the studs, 4 linear scale divisions are clearly visible while 46^{\text {th }} division the circular scale coincide with the reference line. The diameter of the wire is ______________ \times 10^{-2} \mathrm{~mm}.
Answer: Enter a numeric value
244
MediumInteger TypeJEE Mains2022
In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of 0.5 \mathrm{~s} is measured from time of 100 oscillation with a watch of 1 \mathrm{~s} resolution. If measured value of length is 10 \mathrm{~cm} known to 1 \mathrm{~mm} accuracy, The accuracy in the determination of \mathrm{g} is found to be x \%. The value of x is ___________.
Answer: Enter a numeric value
245
MediumInteger TypeJEE Mains2022
The one division of main scale of Vernier callipers reads 1 \mathrm{~mm} and 10 divisions of Vernier scale is equal to the 9 divisions on main scale. When the two jaws of the instrument touch each other, the zero of the Vernier lies to the right of zero of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the zero of the Vernier scale lies in between 4.1 \mathrm{~cm} and 4.2 \mathrm{~cm} and 6^{\text {th }} Vernier division coincides scale division. The diameter of the bob will be ____________ \times 10 -2 cm.
Answer: Enter a numeric value
246
EasyInteger TypeJEE Mains2022
The Vernier constant of Vernier callipers is 0.1 mm and it has zero error of (-0.05) cm. While measuring diameter of a sphere, the main scale reading is 1.7 cm and coinciding vernier division is 5. The corrected diameter will be _________ \times 10 -2 cm.
Answer: Enter a numeric value
247
EasyInteger TypeJEE Mains2022
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 {x \over {121}}\% . The value of x is ____________.
Answer: Enter a numeric value
248
EasyInteger TypeJEE Mains2022
A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in 1 cm on main scale and 50 Vernier scale divisions are equal to 49 main scale divisions, then least count of the travelling microscope is __________ \times 10 -6 m.
Answer: Enter a numeric value
249
EasyInteger TypeJEE Mains2022
In a vernier callipers, each cm on the main scale is divided into 20 equal parts. If tenth vernier scale division coincides with nineth main scale division. Then the value of vernier constant will be _________ \times 10 -2 mm.
Answer: Enter a numeric value
250
EasyInteger TypeJEE Mains2022
For z = {a^2}{x^3}{y^{{1 \over 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 _______________%.
Answer: Enter a numeric value
251
MediumInteger TypeJEE Mains2021
The diameter of a spherical bob is measured using a vernier callipers. 9 divisions of the main scale, in the vernier callipers, are equal to 10 divisions of vernier scale. One main scale division is 1 mm. The main scale reading is 10 mm and 8 th division of vernier scale was found to coincide exactly with one of the main scale division. If the given vernier callipers has positive zero error of 0.04 cm, then the radius of the bob is ___________ \times 10 -2 cm.
Answer: Enter a numeric value
252
MediumInteger TypeJEE Mains2021
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 ..............%
Answer: Enter a numeric value
253
HardInteger TypeJEE Mains2021
Student A and student B used two screw gauges of equal pitch and 100 equal circular divisions to measure the radius of a given wire. The actual value of the radius of the wire is 0.322 cm. The absolute value of the difference between the final circular scale readings observed by the students A and B is ______________. [Figure shows position of reference 'O' when jaws of screw gauge are closed] Given pitch = 0.1 cm.
Answer: Enter a numeric value
254
MediumInteger TypeJEE Mains2021
Three students S 1 , S 2 and S 3 perform an experiment for determining the acceleration due to gravity (g) using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table. Student No. Length of Pendulum (cm) No. of oscillations (n) Total time for n oscillations Time period (s) 1 64.0 8 128.0 16.0 2 64.0 4 64.0 16.0 3 20.0 4 36.0 9.0 (Least count of length = 0.1 cm and Least count for time = 0.1 s) If E 1 , E 2 and E 3 are the percentage errors in 'g' for students 1, 2 and 3 respectively, then the minimum percentage error is obtained by student no. ______________.
Answer: Enter a numeric value
255
EasyInteger TypeJEE Mains2021
The radius of a sphere is measured to be (7.50 \pm 0.85) cm. Suppose the percentage error in its volume is x. The value of x, to the nearest x, is __________.
Answer: Enter a numeric value
256
EasyInteger TypeJEE Mains2021
The resistance R = {V \over I}, where V = (50 \pm 2)V and I = (20 \pm 0.2)A. The percentage error in R is 'x'%. The value of 'x' to the nearest integer is _________.
Answer: Enter a numeric value
257
MediumInteger TypeJEE Mains2020
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( {{x \over {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_______.
Answer: Enter a numeric value
258
MediumJEE Mains2016
A, B, C and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation AD = C ln (BD) holds true. Then which of the combination is not a meaningful quantity ?
Options:
A) A
2
- B
2
C
2
B) {{\left( {A - C} \right)} \over D}
C) {A \over B} - C
D) {C \over {BD}} - {{A{D^2}} \over C}
259
MediumJEE Advanced2007
Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II . Match the physical quantities in Column I with the units in Column II . Column I (A) GM e M s , G \to universal gravitational constant, M e \to mass of the earth, M s \to mass of the Sun (B) {{3RT} \over M}, R \to universal gas constant, T \to absolute temperature, M \to molar mass (C) {{{F^2}} \over {{q^2}{B^2}}} , F \to force, q \to charge, B \to magnetic field (D) {{G{M_e}} \over {{R_e}}}, G \to universal gravitational constant, M e \to mass of the earth, R e \to radius of the earth Column II (p) (volt) (coulomb) (metre) (q) (kilogram) (metre) 3 (second) −2 (r) (meter) 2 (second) −2 (s) (farad) (volt) 2 (kg) −1
Options:
A) A \to (p) & (q), B \to (r) & (s), C \to (r) & (s), D \to (r) & (s)
B) A \to (p), B \to (r) & (s), C \to (r) & (s), D \to (r) & (s)
C) A \to (p) & (q), B \to (r) & (s), C \to (r) & (s), D \to (r)
D) A \to (p) & (q), B \to (r), C \to (r) & (s), D \to (r) & (s)
260
MediumJEE Advanced2025
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 :
Options:
A) [M
0
L
0
T
0
I
0
K
0
]
B) [M
0
L
0
T
0
I
0
K
−1
]
C) [M
1
L
2
T
−2
I
−1
K
−1
]
D) [M
1
L
2
T
−4
I
−1
K
−1
]
261
EasyJEE Advanced2025
Figure 1 shows the configuration of main scale and Vernier scale before measurement. Fig. 2 shows the configuration corresponding to the measurement of diameter D of a tube. The measured value of D is:
Options:
A) 0.12 cm
B) 0.11 cm
C) 0.13 cm
D) 0.14 cm
262
MediumJEE Advanced2024
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 :
Options:
A) (2 n,-n,-n,-n)
B) (n,-n,-2 n,-n)
C) (n,-n,-n,-2 n)
D) (2 n,-n,-2 n,-2 n)
263
MediumJEE Advanced2023
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?
Options:
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
264
MediumJEE Advanced2022
Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is 0.5 \mathrm{~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. Measurement condition Main scale reading Circular scale reading Two arms of gauge touching each other without wire 0 division 4 divisions Attempt-1: With wire 4 divisions 20 divisions Attempt-2: With wire 4 divisions 16 divisions What are the diameter and cross-sectional area of the wire measured using the screw gauge?
Options:
A) 2.22 \pm 0.02 \mathrm{~mm}, \pi(1.23 \pm 0.02) \mathrm{mm}^{2}
B) 2.22 \pm 0.01 \mathrm{~mm}, \pi(1.23 \pm 0.01) \mathrm{mm}^{2}
C) 2.14 \pm 0.02 \mathrm{~mm}, \pi(1.14 \pm 0.02) \mathrm{mm}^{2}
D) 2.14 \pm 0.01 \mathrm{~mm}, \pi(1.14 \pm 0.01) \mathrm{mm}^{2}
265
MediumJEE Advanced2021
The smallest division on the main scale of a Vernier calipers is 0.1 cm. Ten divisions of the Vernier scale correspond to nine divisions of the main scale. The figure below on the left shows the reading of this calipers with no gap between its two jaws. The figure on the right shows the reading with a solid sphere held between the jaws. The correct diameter of the sphere is
Options:
A) 3.07 cm
B) 3.11 cm
C) 3.15 cm
D) 3.17 cm
266
MediumJEE Advanced2018
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 $z \pm \Delta z = {{x \pm \Delta x} \over {y \pm \Delta y}} = {x \over y}\left( {1 \pm {{\Delta x} \over x}} \right){\left( {1 \pm {{\Delta y} \over y}} \right)^{ - 1}}. The series expansion for {\left( {1 \pm {{\Delta y} \over y}} \right)^{ - 1}}, to first power in \Delta y/y. is 1 \pm \left( {\Delta y/y} \right). The relative errors in independent variables are always added. So the error in z will be \Delta z = z\left( {{{\Delta x} \over x} + {{\Delta y} \over y}} \right). The above derivation makes the assumption that \Delta x/x < < 1, \Delta y/y < < 1. Therefore, the higher powers of these quantities are neglected. Consider the ratio r = {{\left( {1 - a} \right)} \over {1 + a}} to be determined by measuring a dimensionless quantity a. If the error in the measurement of a is \Delta a\left( {\Delta a/a < < 1.} \right. then what is the error \Delta r in determining r$?
Options:
A) {{\Delta a} \over {{{\left( {1 + a} \right)}^2}}}
B) {{2\Delta a} \over {{{\left( {1 + a} \right)}^2}}}
C) {{2\Delta a} \over {\left( {1 - {a^2}} \right)}}
D) {{2a\Delta a} \over {\left( {1 - {a^2}} \right)}}
267
MediumJEE Advanced2018
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 $z \pm \Delta z = {{x \pm \Delta x} \over {y \pm \Delta y}} = {x \over y}\left( {1 \pm {{\Delta x} \over x}} \right){\left( {1 \pm {{\Delta y} \over y}} \right)^{ - 1}}. The series expansion for {\left( {1 \pm {{\Delta y} \over y}} \right)^{ - 1}}, to first power in \Delta y/y. is 1 \pm \left( {\Delta y/y} \right). The relative errors in independent variables are always added. So the error in z will be \Delta z = z\left( {{{\Delta x} \over x} + {{\Delta y} \over y}} \right). The above derivation makes the assumption that \Delta x/x < < 1, \Delta y/y < < 1. Therefore, the higher powers of these quantities are neglected. In an experiment the initial number of radioactive nuclei is 3000. It is found that 1000 \pm 40 nuclei decayed in the first 1.0s. For \left| x \right| < < 1. \ln \left( {1 + x} \right) = x up to first power in x. The error \Delta \lambda , in the determination of the decay constant \lambda , in {s^{ - 1}},$ is
Options:
A) 0.04
B) 0.03
C) 0.02
D) 0.01
268
MediumJEE Advanced2017
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 = 10m{s^{ - 2}} and the velocity of sound is 300 m{s^{ - 1}}. Then the fractional error in the measurement, \delta L/L, is closest to
Options:
A) 0.2\%
B) 1\%
C) 3%
D) 5%
269
MediumJEE Advanced2016
There are two Vernier calipers both of which have 1 cm divided into 10 equal divisions on the main scale. The Vernier scale of one of the calipers (C 1 ) has 10 equal divisions that correspond to 9 main scale divisions. The Vernier scale of the other caliper (C 2 ) has 10 equal divisions that correspond to 11 main scale divisions. The readings of the two calipers are shown in the figure. The measured values (in cm) by calipers C 1 and C 2 respectively, are
Options:
A) 2.85 and 2.82
B) 2.87 and 2.83
C) 2.87 and 2.86
D) 2.87 and 2.87
270
MediumJEE Advanced2013
Match List I with List II and select the correct answer using the codes given below the lists: List I P. Boltzmann Constant Q. Coefficient of viscosity R. Plank Constant S. Thermal conductivity List II 1. [ML 2 T -1 ] 2. [ML -1 T -1 ] 3. [MLT -3 K -1 ] 4. [ML 2 T -2 K -1 ]
Options:
A) \eqalign{
& P\,\,\,\,Q\,\,\,\,R\,\,\,\,S \cr
& 3\,\,\,\,\,\,1\,\,\,\,\,2\,\,\,\,\,4 \cr}
B) \eqalign{
& P\,\,\,\,Q\,\,\,\,R\,\,\,\,S \cr
& 3\,\,\,\,\,\,2\,\,\,\,\,1\,\,\,\,\,4 \cr}
C) \eqalign{
& P\,\,\,\,Q\,\,\,\,R\,\,\,\,S \cr
& 4\,\,\,\,\,\,2\,\,\,\,\,1\,\,\,\,\,3 \cr}
D) \eqalign{
& P\,\,\,\,Q\,\,\,\,R\,\,\,\,S \cr
& 4\,\,\,\,\,\,1\,\,\,\,\,2\,\,\,\,\,3 \cr}
271
MediumJEE Advanced2013
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
Options:
A) 5.112 cm
B) 5.124 cm
C) 5.136 cm
D) 5.148 cm
272
MediumJEE Advanced2012
In the determination of Young's modulus \left( {Y = {{4MLg} \over {\pi l{d^2}}}} \right) by using Searle's method, a wire of length L = 2 m and diameter d = 0.5 mm is used. For a load M = 2.5 kg, an extension l = 0.25 mm in the length of the wire is observed. Quantities d and l are measured using a screw gauge and a micrometer, respectively. They have the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to the maximum probable error of the Y measurement
Options:
A) due to the errors in the measurements of d and l are the same.
B) due to the error in the measurement of d is twice that due to the error in the measurement of l.
C) due to the error in the measurement of l is twice that due to the error in the measurement of d.
D) due to the error in the measurement of d is four times that due to the error in the measurement of l.
273
MediumJEE Advanced2011
A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing fixed positive ions surrounded by free electrons can be treated as neutral plasma. Let 'N' be the number density of free electrons, each of mass 'm'. When the electrons are subjected to an electric field, they are displaced relatively away from the heavy positive ions. If the electric field becomes zero, the electrons begin to oscillate about the positive ions with a natural angular frequency '{\omega _p}' which is called the plasma frequency. To sustain the oscillations, a time varying electric field needs to be applied that has an angular frequency \omega , where a part of the energy is absorbed and a part of it is reflected. As \omega approaches {\omega _p} all the free electrons are set to resonance together and all the energy is reflected. This is the explanation of high reflectivity of metals. Taking the electronic charge as 'e' and the permittivity as '{\varepsilon _0}'. Use dimensional analysis to determine the correct expression for {\omega _p}.
Options:
A) \sqrt {{{Ne} \over {m{\varepsilon _0}}}}
B) \sqrt {{{m{\varepsilon _0}} \over {Ne}}}
C) \sqrt {{{N{e^2}} \over {m{\varepsilon _0}}}}
D) \sqrt {{{m{\varepsilon _0}} \over {N{e^2}}}}
274
MediumJEE Advanced2011
The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2 %, the relative percentage error in the density is
Options:
A) 0.9 %
B) 2.4 %
C) 3.1 %
D) 4.2 %
275
MediumJEE Advanced2010
A vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers, the least count is
Options:
A) 0.02 mm
B) 0.05 mm
C) 0.1 mm
D) 0.2 mm
276
MediumJEE Advanced2008
Student I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a simple pendulum. They use different length of the pendulum and/or record time for different number of oscillations. The observations area shown in the table. Least count for length = 0.1 cm Least count for time = 0.1 s Student Length of the pendulum (cm) No. of oscillations (n) Total time for(n) oscillations (s) Time periods (s) I 64.0 8 128.0 16.0 II 64.0 4 64.0 16.0 III 20.0 4 36.0 9.0 If E I , E II and E III are the percentage errors in g, i.e., \left(\frac{\triangle g}g\times100\right) for students I, II and III, respectively,then
Options:
A) E
I
= 0
B) E
I
is minimum
C) E
I
= E
II
D) E
II
is maximum
277
MediumJEE Advanced2007
A student performs an experiment to determine the Young's modulus of a wire, exactly 2 m long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be 0.8 mm with an uncertainty of \pm0.05\;\mathrm{mm} at a load of exactly 1.0 kg. The student also measures the diameter of the wire to be 0.4 mm with an uncertainty of \pm0.01\;\mathrm{mm}. Take g = 9.8 m/s 2 (exact). The Young's modulus obtained from the reading is
Options:
A) \left(2.0\;\pm\;0.3\right)\times10^{11}\;\mathrm N/\mathrm m^2
B) \left(2.0\;\pm\;0.2\right)\times10^{11}\;\mathrm N/\mathrm m^2
C) \left(2.0\;\pm\;0.1\right)\times10^{11}\;\mathrm N/\mathrm m^2
D) \left(2.0\;\pm\;0.05\right)\times10^{11}\;\mathrm N/\mathrm m^2
278
MediumJEE Advanced2006
In a screw gauge, the zero of main scale coincides with the fifth division of circular scale in figure (i).The circular division of screw gauge is 50. It moves 0.5 mm on main scale in one rotation.The diameter of the ball in figure (ii) is
Options:
A) 2.25 mm
B) 2.20 mm
C) 1.20 mm
D) 1.25 mm
279
MediumJEE Advanced2006
A student performs an experiment for determination of g\left(=\frac{4 \pi^2 l}{\mathrm{~T}^2}\right), l=1 m, and he commits an error of \Delta l. For T , he takes the time of n oscillations with the stop watch of least count \Delta \mathrm{T} and he commits a human error of 0.1 s . For which of the following data, the measurement of g will be most accurate?
Options:
A) \begin{array}{l}\triangle\mathcal l\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\triangle\mathrm T\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm n\\5\;\mathrm{mm}\;\;\;\;\;\;\;\;\;\;\;\;0.2\;\sec\;\;\;\;\;\;\;\;\;\;\;\;10\end{array}
B) \begin{array}{l}\triangle\mathcal l\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\triangle\mathrm T\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm n\\5\;\mathrm{mm}\;\;\;\;\;\;\;\;\;\;\;\;0.2\;\sec\;\;\;\;\;\;\;\;\;\;\;\;20\end{array}
C) \begin{array}{l}\triangle\mathcal l\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\triangle\mathrm T\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm n\\5\;\mathrm{mm}\;\;\;\;\;\;\;\;\;\;\;\;0.1\;\sec\;\;\;\;\;\;\;\;\;\;\;\;10\end{array}
D) \begin{array}{l}\triangle\mathcal l\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\triangle\mathrm T\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm n\\1\;\mathrm{mm}\;\;\;\;\;\;\;\;\;\;\;\;0.1\;\sec\;\;\;\;\;\;\;\;\;\;\;\;50\end{array}
280
MediumJEE Advanced2005
Which of the following set have different dimensions?
Options:
A) Pressure, Young's modulus, Stress
B) EMF, Potential difference, Electric potential
C) Heat, Work done, Energy
D) Dipole moment, Electric flux, Electric field
281
MediumJEE Advanced2005
The side of a cube is measured by vernier callipers (10 divisions of a vernier scale coincide with 9 divisions of main scale, where 1 division of main scale is 1 mm). The main scale reads 10 mm and first division of vernier scale coincides with the main scale; Mass of the cube is 2.736 g. Find the density of the cube in appropriate significant figures.
Options:
A) 5\times10^3
B) 7\times10^4
C) 2.66\times10^3
D) 3.45\times10^3
282
MediumJEE Advanced2004
Pressure depends on distance as, P = {\alpha \over \beta }\exp \left( { - {{\alpha z} \over {k\theta }}} \right), where \alpha , \beta are constants, z in distance, k is Boltzman's constant and \theta is temperature. The dimention of \beta are
Options:
A) [M
0
L
0
T
0
]
B) [M
-1
L
-1
T
-1
]
C) [M
0
L
2
T
0
]
D) [M
-1
L
1
T
2
]
283
MediumJEE Advanced2004
A wire of length l = 6 \pm 0.06 cm and r = 0.5 \pm 0.005 cm and mass m = 0.3 \pm 0.003 gm. Maximum percentage error in density is
Options:
A) 4
B) 2
C) 1
D) 6.8
284
MediumJEE Advanced2003
A cube has a side of length 1.2 ✕ 10 -2 m. Calculate its volume.
Options:
A) 1.7 ✕ 10
-6
m
3
B) 1.73 ✕ 10
-6
m
3
C) 1.70 ✕ 10
-6
m
3
D) 1.732 ✕ 10
-6
m
3
285
MediumJEE Advanced2001
A quantity X is given by {\varepsilon _0}L{{\Delta V} \over {\Delta t}} where {\varepsilon _0} is the permittivity of the free space, L is a length, {\Delta V} is a potential difference and {\Delta t} is a time interval. The dimentional formula for X is the same as that of
Options:
A) resistance
B) charge
C) voltage
D) current
286
MediumJEE Advanced2000
The dimension of \left( {{1 \over 2}} \right){\varepsilon _0}{E^2} ( {\varepsilon _0} : permittivity of free space, E electric field )
Options:
A) MLT
-1
B) ML
2
T
-2
C) ML
-1
T
-2
D) ML
2
T
-1
287
EasyJEE Advanced2025
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 cm 3 with correct significant figures:
Options:
A) 3.2 \times 10^{-5}
B) 32.0 \times 10^{-6}
C) 3.0 \times 10^{-5}
D) 3 \times 10^{-5}
288
MediumJEE Advanced2021
A physical quantity \overrightarrow S is defined as \overrightarrow S = (\overrightarrow E \times \overrightarrow B )/{\mu _0}, where \overrightarrow E is electric field, \overrightarrow B is magnetic field and \mu 0 is the permeability of free space. The dimensions of \overrightarrow S are the same as the dimensions of which of the following quantity(ies)?
Options:
A) {{Energy} \over {Ch\arg e \times Current}}
B) {{Force} \over {Length \times Time}}
C) {{Energy} \over {Volume}}
D) {{Power} \over {Area}}
289
MediumJEE Advanced2020
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
Options:
A) \alpha + p = 2\beta
B) p + q - r = \beta
C) p - q + r = \alpha
D) p + q + r = \beta
290
MediumJEE Advanced2019
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?
Options:
A) The dimension of force is [L]
-3
B) The dimension of power is [L]
-5
C) The dimension of energy is [L]
-2
D) The dimension of linear momentum is [L]
-1
291
MediumJEE Advanced2016
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 {{{7\left( {R - r} \right)} \over {5g}}} . The values of R and r are measured to be (60 \pm 1) mm and (10 \pm 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?
Options:
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 %
292
MediumJEE Advanced2016
A length-scale (l) 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 I is(are) dimensionally correct?
Options:
A) l = \sqrt {\left( {{{n{q^2}} \over {\varepsilon {k_b}T}}} \right)}
B) l = \sqrt {\left( {{{\varepsilon {k_b}T} \over {n{q^2}}}} \right)}
C) l = \sqrt {\left( {{{{q^2}} \over {\varepsilon {n^{2/3}}{k_B}T}}} \right)}
D) l = \sqrt {\left( {{{{q^2}} \over {\varepsilon {n^{1/3}}{k_B}T}}} \right)}
293
MediumJEE Advanced2015
Consider a Vernier callipers in which each 1 cm on the main scale is divided into 8 equal divisions and a screw gauge with 100 divisions on its circular scale. In the Vernier callipers, 5 divisions of the Vernier scale coincide with 4 divisions on the main scale and in the screw gauge, one complete rotation of the circular scale moves it by two divisions on the linear scale. Then:
Options:
A) If the pitch of the screw gauge is twice the least count of the Vernier callipers, the least count of the
screw gauge is 0.01 mm.
B) If the pitch of the screw gauge is twice the least count of the Vernier callipers, the least count of the
screw gauge is 0.005 mm.
C) If the least count of the linear scale of the screw gauge is twice the least count of the Vernier callipers,
the least count of the screw gauge is 0.01 mm.
D) If the least count of the linear scale of the screw gauge is twice the least count of the Vernier callipers,
the least count of the screw gauge is 0.005 mm.
294
MediumJEE Advanced2015
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)
Options:
A) M \propto \sqrt c
B) M \propto \sqrt G
C) L \propto \sqrt h
D) L \propto \sqrt G
295
MediumJEE Advanced2010
A student uses a simple pendulum of exactly 1m length to determine g, the acceleration due to gravity. He uses a stop watch with the least count of 1 sec for this and records 40 seconds for 20 oscillations. For this observation, which of the following statement(s) is (are) true?
Options:
A) Error ΔT in measuring T, the time period, is 0.05 seconds
B) Error ΔT in measuring T, the time period, is 1 second
C) Percentage error in the determination of g is 5%
D) Percentage error in the determination of g is 2.5%
296
MediumJEE AdvancedIIT-JEE 1998
Let [{\mathrm\varepsilon}_\mathrm o] denote the dimentional formula of the permittivity of the vacuum, and [\mu_o] that of the permeability of the vacuum.If M = mass, L = length, T = time and I = electric current,
Options:
A) \left[{\mathrm\varepsilon}_\mathrm o\right]\;=\;\mathrm M^{-1}\mathrm L^{-3}\mathrm T^2\;\mathrm I
B) \left[{\mathrm\varepsilon}_\mathrm o\right]\;=\;\mathrm M^{-1}\mathrm L^{-3}\mathrm T^4\mathrm I^2
C) \left[{\mathrm\mu}_\mathrm o\right]\;=\;\mathrm{MLT}^{-2}\mathrm I^{-2}
D) \left[{\mathrm\mu}_\mathrm o\right]\;=\;\mathrm{ML}^2\mathrm T^{-1}\;\mathrm I
297
MediumJEE AdvancedIIT-JEE 1998
The SI unit of inductance, the henry can be written as
Options:
A) weber/ampere
B) volt-sec/amp
C) Joule/(ampere)
2
D) ohm-second
298
MediumJEE AdvancedIIT-JEE 1995 Screening
The pairs of physical quantities that have the same dimensions is (are):
Options:
A) Reynolds number and coefficient of friction
B) Curie and frequency of a light wave
C) Latent heat and gravitational potential
D) Planck's constant and torque
299
MediumJEE AdvancedIIT-JEE 1986
The dimensions of the quantities in one ( or more ) of the following pairs are the same. Identify the pair(s)
Options:
A) Torque and Work
B) Angular momentum and Work
C) Energy and Young's modulus
D) Light year and Wavelength
300
EasyInteger TypeJEE Advanced2024
The dimensions of a cone are measured using a scale with a least count of 2 \mathrm{~mm}. The diameter of the base and the height are both measured to be 20.0 \mathrm{~cm}. The maximum percentage error in the determination of the volume is _______.
Answer: Enter a numeric value
301
MediumInteger TypeJEE Advanced2023
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 \mathrm{~cm} and the distance of its real image from the lens is 20 \pm 0.2 \mathrm{~cm}. The error in the determination of focal length of the lens is n \%. The value of n is ______.
Answer: Enter a numeric value
302
MediumInteger TypeJEE Advanced2022
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 \epsilon_{0} is the permittivity of vacuum. In terms of these physical constants, the dimension of the magnetic field is [B]=[e]^{\alpha}\left[m_{e}\right]^{\beta}[h]^{\gamma}[k]^{\delta}. The value of \alpha+\beta+\gamma+\delta is _______.
Answer: Enter a numeric value
303
MediumInteger TypeJEE Advanced2019
An optical bench has 1.5 m long scale having four equal divisions in each cm. While measuring the focal length of a convex lens, the lens is kept at 75 cm mark of the scale and the object pin is kept at 45 cm mark. The image of the object pin on the other side of the lens overlaps with image pin that is kept at 135 cm mark. In this experiment, the percentage error in the measurement of the focal length of the lens is ..............
Answer: Enter a numeric value
304
MediumInteger TypeJEE Advanced2018
A steel wire of diameter 0.5 mm and Young's modulus 2 \times {10^{11}}\,\,N{m^{ - 2}} carries a load of mass M. The length of the wire with the load is 1.0 m.A vernier scale with 10 divisions is attached to the end of this wire. Next to the steel wire is a reference wire to which a main scale, of least count 1.0 mm , is attached. The 10 divisions of the vernier scale correspond to 9 divisions of the main scale. Initially, the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is increased by 1.2 kg, the vernier scale division which coincides with a main scale division is _____________. Take g = 10\,m\,{s^{ - 2}}. and \pi = 3.2.
Answer: Enter a numeric value
305
MediumInteger TypeJEE Advanced2015
The energy of a system as a function of time t is given as E(t) = {A^2}\exp \left( { - \alpha t} \right), 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
Answer: Enter a numeric value
306
MediumInteger TypeJEE Advanced2014
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
Answer: Enter a numeric value
307
MediumInteger TypeJEE Advanced2014
During Searle's experiment, zero of the Vernier scale lies between 3.20 \times 10 -2 m and 3.25 \times 10 -2 m of the main scale. The 20 th division of the Vernier scale exactly coincides with one of the main scale divisions. When an additional load of 2 kg is applied to the wire, the zero of the Vernier scale still lies between 3.20 \times 10 -2 m and 3.25 \times 10 -2 m of the main scale but now the 45 th division of Vernier scale coincides with one of the main scale divisions. The length of the thin metallic wire is 2 m and its cross-sectional area is 8 \times 10 -7 m 2 . The least count of the Vernier scale is 1.0 \times 10 -5 m. The maximum percentage error in the Young's modulus of the wire is
Answer: Enter a numeric value
308
MediumInteger TypeJEE Advanced2005
The side of a cube is measured by vernier callipers (10 divisions of a vernier scale coincide with 9 divisions of main scale, where 1 division of main scale is 1 mm). The main scale reads 10 mm and first division of vernier scale coincides with the main scale. Mass of the cube is 2.736 g. Find the density of the cube in appropriate significant figures.
Answer: Enter a numeric value
309
MediumInteger TypeJEE Advanced2004
A screw gauge having 100 equal divisions and a pitch of length 1 mm is used to measure the diameter of a wire of length 5.6 cm. The main scale reading is 1mm and 47 th circular division coincides with the main scale. Find the curved surface area of wire in cm 2 to appropriate significant figures. ( use \pi = {{22} \over 7} )
Answer: Enter a numeric value
310
MediumInteger TypeJEE Advanced2004
In Searle's experiment, which is used to find Young's Modulus of elasticity, the diameter of experimental wire is D = 0.05 cm ( measured by a scale of least count 0.001 cm ) and length is L = 110 cm ( measured by a scale of least count 0.1 cm ). A weight of 50 N causes an extension of X = 0.125 cm (measured by a micrometer of least count 0.001 cm ). Find maximum possible error in the value of Young's modulus. Screw gauge and and meter scale are free from error.
Answer: Enter a numeric value
311
MediumInteger TypeJEE Advanced2003
If n th divisions of the main scale coincide with (n+1) th divisions of vernier scale. Given one main scale division is equal to 'a' units. Find the least count of the vernier.
Answer: Enter a numeric value
312
MediumInteger TypeJEE AdvancedIIT-JEE 1990
Column - I gives the three physical quantities. Select the appropriate units for the choices given in Column - II. Some of the physical quantities may have more than one choice correct: Column I Column II Capacitance (i) ohm-second Inductance (ii) coulomb 2 - joule -1 Magnetic Induction (iii) coulomb (volt) -1 (iv) newton (amp-meter) -1 (v) volt-second (ampere) -1
Answer: Enter a numeric value
313
MediumInteger TypeJEE AdvancedIIT-JEE 1983
Match the physical quantities given in column I with dimension expressed in terms of mass (M), length (L), time (T), and charge (Q) given in column II and write the correct answer against the matched quantity in a tabular form in your answer book. Column I Column II Angular Momentum ML 2 T -2 Latent heat ML 2 Q -2 Torque ML 2 T -1 Capacitance ML 3 T -1 Q -2 Inductance M -1 L -2 T 2 Q 2 Resistivity L 2 T -2
Answer: Enter a numeric value
314
MediumInteger TypeJEE AdvancedIIT-JEE 1982
Write the dimensions of the followings in terms of mass, time, length and charge (i) magnetic flux (ii) rigidity modulus
Answer: Enter a numeric value
315
MediumInteger TypeJEE AdvancedIIT-JEE 1981
A gas bubble, from an explosion under water, oscillates with a period T proportional to p a d b E c . Where 'P' is the static pressure, 'd' is the density of water and 'E' is the total energy of the explosion. Find the value of a, b and c.
Answer: Enter a numeric value
316
MediumInteger TypeJEE AdvancedIIT-JEE 1980
Give the MKS units for each of the following quantities. (i) Young's modulus (ii) Magnetic Induction (iii) Power of a lens
Answer: Enter a numeric value
317
MediumInteger TypeJEE AdvancedIIT-JEE 1997
The equation of state for real gas is given by \left( {P + {a \over {{V^2}}}} \right)\left( {V - b} \right) = RT. The dimention of the constant a is ___________.
Answer: Enter a numeric value
318
MediumInteger TypeJEE AdvancedIIT-JEE 1988
In the formula X = 3YZ 2 , X and Z have dimensions of capacitance and magnetic induction respectively. The dimensions of Y in MKSQ system are _____________
Answer: Enter a numeric value
319
MediumInteger TypeJEE AdvancedIIT-JEE 1985
Plank' constant has dimension __________.
Answer: Enter a numeric value
319
Total Questions
109
Easy
209
Medium
1
Hard
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