Class 11 • Physics

Units , Dimensions and Error Analysis

Chapter-1

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Medium

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

Options:

A) 3.43

B) 7.60

C) 3.35

D) 6.76

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

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]

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

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

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

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

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

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}

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}

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)

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}

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

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

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

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

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

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.

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

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

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}

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]

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

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}

MediumCOMEDK2023

A tentative explanation of observations without assuming that it is true is called

Options:

A) hypothesis

B) physical laws

C) theory

D) model

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.

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

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 \pm$0.1%

B) \pm1% and \pm$0.2%

C) \pm1% and \pm$1%

D) \pm0.1% and \pm$1%

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

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

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

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−1T−2] II. [ML2T−2] III. [ML0T−2] IV. [ML−1T−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

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

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

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

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

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

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

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

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}

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

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 \%

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]

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

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

EasyJEE Mains2025

Match List - I with List - II. List - I List - II (A) Mass density (I) [ML2T−3] (B) Impulse (II) [MLT−1] (C) Power (III) [ML2T0] (D) Moment of inertia (IV) [ML−3T0] 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)

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

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

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)

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

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

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

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}

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)

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 L3 T-2 (D) Gravitational Constant (IV) M L2 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)

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

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) [M0L1T−2]

B) [M0L2T−3]

C) [M0L2T−2]

D) [M0L1T−3]

EasyJEE Mains2025

Match List - I with List - II. List - I List - II (A) Angular Impulse (I) M0 L2 T-2 (B) Latent Heat (II) M L2 T-3 A-1 (C) Electrical resistivity (III) M L2 T-1 (D) Electromotive force (IV) M L3 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)

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

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 \%

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)

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

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

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}

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

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]

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]

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)}

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]

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

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)

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

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

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

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

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%

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

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

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}]

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

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

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}

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]

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)

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}

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]

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 \%

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

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

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%

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]

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

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

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)

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%

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%

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

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

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

100

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

101

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}

102

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

103

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}

104

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.

105

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}

106

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%

107

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

108

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}

109

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%

110

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

111

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]

112

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

113

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

114

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}]}

115

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

116

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

117

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

118

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

119

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

120

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

121

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

122

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 $\alpha is same as that of \beta$.

123

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]

124

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]

125

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%

126

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

127

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 cm2

B) 3.4 cm2

C) 3.9 cm2

D) 2.4 cm2

128

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

129

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]

130

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

131

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}

132

EasyJEE Mains2022

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

Options:

A) [ML$-1T-$1]

B) [ML$-1T-$2]

C) [ML2T$-$1]

D) [M$-$1L3T0]

133

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%

134

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}}]

135

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) [M0 L$-$1 T0]

B) [M L0 T$-$2]

C) [M L T$-$2]

D) [M L2 T$-$2]

136

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}

137

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

138

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

139

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/s2, without any significant error, his observation are as following. PhysicalQuantity Least count of theEquipment usedfor 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

140

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) [FT2 V]

D) [FVT$-$1]

141

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)

142

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

143

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)

144

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$-$4T2]

B) [FL$-$3T2]

C) [FL$-$5T2]

D) [FL$-$3T3]

145

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

146

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

147

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)

148

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

149

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 20th 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

150

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 = EL2M$-5G-$2 are :

Options:

A) [M0 L1 T0]

B) [M$-1 L-$1 T2]

C) [M1 L1 T$-$2]

D) [M0 L0 T0]

151

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 $\pm$2

B) 4 and $\pm$3

C) {{16} \over 3} and \pm {3 \over 2}

D) 8 and $\pm$ 2

152

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.

153

EasyJEE Mains2021

The force is given in terms of time t and displacement x by the equation F = A cos Bx + C sin DtThe 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}}]

154

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}]

155

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

156

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%

157

EasyJEE Mains2021

One main scale division of a vernier callipers is 'a' cm and nth 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)}}

158

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}}]

159

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}}]

160

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}}]

161

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)

162

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 72nd 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

163

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}]

164

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

165

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

166

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

167

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%

168

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

169

MediumJEE Mains2020

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

Options:

A) MLT–3K–1

B) MLT–2K–2

C) MLT–2K

D) MLT–3K

170

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) ML0T–3

C) M2L0T–1

D) ML2T–2

171

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

172

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) [P2AT–2]

B) \left[ {{P^{{1 \over 2}}}A{T^{ - 1}}} \right]

C) \left[ {P{A^{{1 \over 2}}}{T^{ - 1}}} \right]

D) [PA–1T–2]

173

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–1V0

B) FA2V–1

C) FA2V–2

D) FA2V–3

174

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 7th 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 4th 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

175

MediumJEE Mains2020

For the four sets of three measured physical quantities as given below. Which of the following options is correct ? (i) A1 = 24.36, B1 = 0.0724, C1 = 256.2 (ii) A2 = 24.44, B2 = 16.082, C2 = 240.2 (iii) A3 = 25.2, B3 = 19.2812, C3 = 236.183 (iv) A4 = 25, B4 = 236.191, C4 = 19.5

Options:

A) A1 + B1 + C1 = A2 + B2 + C2 = A3 + B3 + C3 = A4 + B4 + C4

B) A4 + B4 + C4 $ < A1 + B1 + C1 < A3 + B3 + C3 < $ A2 + B2 + C2

C) A4 + B4 + C4 $ < $ A1 + B1 + C1 = A2 + B2 + C2 = A3 + B3 + C3

D) A4 + B4 + C4 $ > A3 + B3 + C3 = A2 + B2 + C2 > $ A1 + B1 + C1

176

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

177

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

178

MediumJEE Mains2020

The dimension of stopping potential V0 in photoelectric effect in units of Planck's constant 'h', speed of light 'c' and Gravitational constant 'G' and ampere A is :

Options:

A) h1/3 G2/3 c1/3 A–1

B) h0 c5 G-1 A-1

C) h2/3 c5/3 G1/3 A–1

D) h2 G3/2 c1/3 A–1

179

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) ML2T–2

B) MLT–2

C) ML-1T–2

D) ML2T–1

180

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}}}}

181

MediumJEE Mains2019

In the formula X = 5YZ2 , X and Z have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y in SI units?

Options:

A) [M–3L–2T8A4]

B) [M–2L–2T6A3]

C) [M–1L–2T4A2]

D) [M–2L0 T–4A–2]

182

MediumJEE Mains2019

The area of a square is 5.29 cm2. The area of 7 such squares taking into account the significant figures is :-

Options:

A) 37.0 cm2

B) 37 cm2

C) 37.030 cm2

D) 37.03 cm2

183

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/m3

B) 0.10 kg/m3

C) 0.31 kg/m3

D) 0.07 kg/m3

184

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%

185

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) S1/2I1/2h0

B) S3/2I1/2h0

C) S1/2I1/2h-1

D) S1/2I3/2h-1

186

MediumJEE Mains2019

In SI units, the dimensions of $\sqrt {{{{ \in _0}} \over {{\mu _0}}}} $ is :

Options:

A) A–1 TML3

B) A2T3M–1L–2

C) AT–3ML3/2

D) AT2M–1L–1

187

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) [LT2]

188

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

189

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$-$2A2F2

B) V$-4A-$2F

C) V$-$4A2F

D) V$-2A2F-$2

190

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) M2L2T$-$2

B) M2LT$-$4

C) MLT$-$4

D) M0L2LT$-$4

191

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 cm3

B) 4264 $ \pm $ 81 cm3

C) 4300 $ \pm $ 80 cm3

D) 4260 $ \pm $ 80 cm3

192

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

193

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

194

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}}}}

195

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 %

196

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

197

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%

198

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%

199

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 c3

B) G2 $\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}}}}

200

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

201

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

202

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}}} b2 c3 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%

203

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 C2 h]

C) [M] = [T$-1 C-2 h-$1]

D) [M] = [T C$-$2 h]

204

MediumJEE Mains2017

The following observations were taken for determining surface tension T of water by capillary method: diameter of capillary, D = 1.25 $\times 10-2 m rise of water, h = 1.45 \times 10-2m Using g = 9.80 m/s2 and the simplified relation T = {{rhg} \over 2} \times {10^3}N/m$, the possible error in surface tension is closest to :

Options:

A) 10 %

B) 0.15 %

C) 1.5 %

D) 2.4 %

205

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 L3 T3 I

C) M$-1 L-$3 T3 I2

D) M$-1 L-$3 T3 I

206

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 45th 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 25th division coincides with the main scale line?

Options:

A) 0.70 mm

B) 0.50 mm

C) 0.75 mm

D) 0.80 mm

207

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

208

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.

209

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]

210

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 %

211

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

212

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

213

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

214

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

215

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

216

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

217

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

218

MediumJEE Mains2008

The dimension of magnetic field in M, L, T and C (coulomb) is given as

Options:

A) MLT-1C-1

B) MT2C-2

C) MT-1C-1

D) MT-2C-1

219

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

220

MediumJEE Mains2004

Which one of the following represents the correct dimensions of the coefficient of viscosity?

Options:

A) ML-1T-1

B) MLT-1

C) ML-1T-2

D) ML-2T-2

221

MediumJEE Mains2003

Dimensions of ${1 \over {{\mu _0}{\varepsilon _0}}}$, where symbols have their usual meaning, are

Options:

A) [ L-1T ]

B) [ L-2T2 ]

C) [ L2T-2 ]

D) [ LT-1 ]

222

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}}

223

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

224

EasyJEE 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__________%

Options:

225

MediumJEE 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= _________ .

Options:

226

MediumJEE 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 _______ .

Options:

227

EasyJEE 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}

Options:

228

EasyJEE Mains2023

In a screw gauge, there are 100 divisions on the circular scale and the main scale moves by $0.5 \mathrm{~mm} on a complete rotation of the circular scale. The zero of circular scale lies 6 divisions below the line of graduation when two studs are brought in contact with each other. When a wire is placed between the studs, 4 linear scale divisions are clearly visible while 46^{\text {th }} division the circular scale coincide with the reference line. The diameter of the wire is ______________ \times 10^{-2} \mathrm{~mm}$.

Options:

229

MediumJEE 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 ___________.

Options:

230

MediumJEE 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.

Options:

231

EasyJEE 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.

Options:

232

EasyJEE 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 ____________.

Options:

233

EasyJEE 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.

Options:

234

EasyJEE 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.

Options:

235

EasyJEE 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 _______________%.

Options:

236

MediumJEE 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 8th 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.

Options:

237

MediumJEE 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 ..............%

Options:

238

HardJEE 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.

Options:

239

MediumJEE Mains2021

Three students S1, S2 and S3 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. StudentNo. Length ofPendulum (cm) No. ofoscillations (n) Total time forn oscillations Timeperiod (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 E1, E2 and E3 are the percentage errors in 'g' for students 1, 2 and 3 respectively, then the minimum percentage error is obtained by student no. ______________.

Options:

240

EasyJEE 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 __________.

Options:

241

EasyJEE 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 _________.

Options:

242

MediumJEE 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_______.

Options:

243

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) A2 $-$ B2C2

B) {{\left( {A - C} \right)} \over D}

C) {A \over B} - C

D) {C \over {BD}} - {{A{D^2}} \over C}

243

Total Questions

106

Easy

136

Medium

Hard

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