Q122 Jan 2025 · Shift 1MCQ
If $B$ is magnetic field and $\mu_0$ is permeability of free space, then the dimensions of $(B/\mu_0)$ is
- A$ML^2T^{-2}A^{-1}$
- B$MT^{-2}A^{-1}$
- C$LT^{-2}A^{-1}$
- D$L^{-1}A$
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JEE Main 2025 January Physics: Units, Measurements & Errors – Previous Year Questions
All 18 questions asked from Units, Measurements & Errors in JEE Main 2025 January Physics (22, 23, 24, 28 and 29 January, all shifts). This chapter is about 7.2% of the 250 Physics questions in the session: 14 single-correct (MCQ) and 4 numerical-value questions. Select an answer to attempt each question, and open “View solution” under it.
18questions
14MCQ
4numerical
7.2%of Physics paper
Topics asked in this chapter
- Dimensional Analysis – 10 questions
- Errors & Measuring Instruments – 8 questions
Dimensional Analysis
Q222 Jan 2025 · Shift 2MCQ
Which one of the following is the correct dimensional formula for the capacitance in F ? M, L, T and C stand for unit of mass, length, time and charge,
- A$[F]=[C^2M^{-1}L^{-2}T^2]$
- B$[F]=[CM^{-2}L^{-2}T^{-2}]$
- C$[F]=[CM^{-1}L^{-2}T^2]$
- D$[F]=[C^2M^{-2}L^2T^2]$
Q323 Jan 2025 · Shift 1MCQ
The electric flux is $\phi=\alpha\sigma+\beta\lambda$ where $\lambda$ and $\sigma$ are linear and surface charge density, respectively. $\left(\dfrac{\alpha}{\beta}\right)$ represents
- Acharge
- Bdisplacement
- Carea
- Delectric field
Q423 Jan 2025 · Shift 1MCQ
The position of a particle moving on $x$-axis is given by $x(t)=A\sin t+B\cos^2 t+Ct^2+D$, where $t$ is time. The dimension of $\dfrac{ABC}{D}$ is
- A$L^3T^{-2}$
- B$L^2$
- C$L^2T^{-2}$
- D$L$
Q523 Jan 2025 · Shift 2MCQ
Match List - I with List - II.
Choose the correct answer from the options given below :
| List - I | List - II | ||
| (A) | Permeability of free space | (I) | $[ML^2T^{-2}]$ |
| (B) | Magnetic field | (II) | $[MT^{-2}A^{-1}]$ |
| (C) | Magnetic moment | (III) | $[MLT^{-2}A^{-2}]$ |
| (D) | Torsional constant | (IV) | $[L^2A]$ |
Choose the correct answer from the options given below :
- A(A)-(IV), (B)-(III), (C)-(I), (D)-(II)
- B(A)-(III), (B)-(II), (C)-(IV), (D)-(I)
- C(A)-(II), (B)-(I), (C)-(III), (D)-(IV)
- D(A)-(I), (B)-(IV), (C)-(II), (D)-(III)
Q624 Jan 2025 · Shift 2MCQ
The energy $E$ and momentum $p$ of a moving body of mass $m$ are related by some equation. Given that $c$ represents the speed of light, identify the correct equation
- A$E^2=pc^2+m^2c^4$
- B$E^2=pc^2+m^2c^2$
- C$E^2=p^2c^2+m^2c^4$
- D$E^2=p^2c^2+m^2c^2$
Q728 Jan 2025 · Shift 2MCQ
Match List - I with List - II.
Choose the correct answer from the options given below :
| List - I | List - II | ||
| (A) | Angular Impulse | (I) | $[M^0L^2T^{-2}]$ |
| (B) | Latent Heat | (II) | $[ML^2T^{-3}A^{-1}]$ |
| (C) | Electrical resistivity | (III) | $[ML^2T^{-1}]$ |
| (D) | Electromotive force | (IV) | $[ML^3T^{-3}A^{-2}]$ |
Choose the correct answer from the options given below :
- A(A)-(III), (B)-(I), (C)-(II), (D)-(IV)
- B(A)-(II), (B)-(I), (C)-(IV), (D)-(III)
- C(A)-(III), (B)-(I), (C)-(IV), (D)-(II)
- D(A)-(I), (B)-(III), (C)-(IV), (D)-(II)
Q829 Jan 2025 · Shift 1MCQ
The pair of physical quantities not having same dimensions is :
- APressure and Young's modulus
- BSurface tension and impulse
- CAngular momentum and Planck's constant
- DTorque and energy
Q929 Jan 2025 · Shift 1MCQ
The expression given below shows the variation of velocity ($v$) with time ($t$), $v=At^2+\dfrac{Bt}{C+t}$. The dimension of ABC is :
- A$[M^0L^2T^{-2}]$
- B$[M^0L^1T^{-3}]$
- C$[M^0L^2T^{-3}]$
- D$[M^0L^1T^{-2}]$
Q1029 Jan 2025 · Shift 2MCQ
Match List - I with List - II.
Choose the correct answer from the options given below :
| List - I | List - II | ||
| (A) | Young's Modulus | (I) | $ML^{-1}T^{-1}$ |
| (B) | Torque | (II) | $ML^{-1}T^{-2}$ |
| (C) | Coefficient of Viscosity | (III) | $M^{-1}L^3T^{-2}$ |
| (D) | Gravitational Constant | (IV) | $ML^2T^{-2}$ |
Choose the correct answer from the options given below :
- A(A)-(II), (B)-(IV), (C)-(I), (D)-(III)
- B(A)-(II), (B)-(I), (C)-(IV), (D)-(III)
- C(A)-(IV), (B)-(II), (C)-(III), (D)-(I)
- D(A)-(I), (B)-(III), (C)-(II), (D)-(IV)
Errors & Measuring Instruments
Q1122 Jan 2025 · Shift 1MCQ
Given below are two statements :
Statement I : In 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.
Statement I : In 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.
- AStatement I is false but Statement II is true
- BStatement I is true but Statement II is false
- CBoth Statement I and Statement II are false
- DBoth Statement I and Statement II are true
Q1222 Jan 2025 · Shift 2MCQ
The maximum percentage error in the measurement of density of a wire is [Given, mass of wire $=(0.60\pm0.003)$ g, radius of wire $=(0.50\pm0.01)$ cm, length of wire $=(10.00\pm0.05)$ cm]
- A5
- B8
- C4
- D7
Q1323 Jan 2025 · Shift 2MCQ
The energy of a system is given as $E(t)=\alpha^2e^{-\beta t}$, 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 $t=5$ s, maximum percentage error in the energy is :
- A8.4%
- B11.6%
- C6%
- D4%
Q1424 Jan 2025 · Shift 1MCQ
For an experimental expression $y=\dfrac{32.3\times1125}{27.4}$, where all the digits are significant. Then to report the value of $y$ we should write
- A$y=1326.2$
- B$y=1330$
- C$y=1326.186$
- D$y=1326.19$
Q1524 Jan 2025 · Shift 1Numerical
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 $\times10^{-3}$ mm.
Q1628 Jan 2025 · Shift 1Numerical
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 $\dfrac{x}{100}$ where $x$ is .
Q1728 Jan 2025 · Shift 1Numerical
In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of $[M^aL^bT^c]$. If $b=3$, the value of $c$ is .
Q1829 Jan 2025 · Shift 2Numerical
A physical quantity $Q$ is related to four observables $a,b,c,d$ as follows : $Q=\dfrac{ab^4}{cd}$ where, $a=(60\pm3)\,$Pa; $b=(20\pm0.1)\,$m; $c=(40\pm0.2)\,\mathrm{Nsm^{-2}}$ and $d=(50\pm0.1)\,$m, then the percentage error in $Q$ is $\dfrac{x}{1000}$, where $x=$ .