JEE Main 2025 (Online) 23rd January Evening Shift | Units & Measurements Question 9 | Physics

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 :

$6 \%$

$11.6 \%$

$4 \%$

$8.4 \%$

JEE Main 2025 (Online) 23rd January Evening Shift

MCQ (Single Correct Answer)

-1

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 :

(A)-(III), (B)-(II), (C)-(IV), (D)-(I)

$(\mathrm{A})-(\mathrm{I}),(\mathrm{B})-(\mathrm{IV}),(\mathrm{C})-(\mathrm{II}),(\mathrm{D})-(\mathrm{III})$

$(\mathrm{A})-(\mathrm{II}),(\mathrm{B})-(\mathrm{I}),(\mathrm{C})-(\mathrm{III}),(\mathrm{D})-(\mathrm{IV})$

(A)-(IV), (B)-(III), (C)-(I), (D)-(II)

JEE Main 2025 (Online) 23rd January Morning Shift

MCQ (Single Correct Answer)

-1

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

$\mathrm{L}$

$\mathrm{L}^3 \mathrm{~T}^{-2}$

$\mathrm{L}^2 \mathrm{~T}^{-2}$

$\mathrm{L}^2$

JEE Main 2025 (Online) 22nd January Evening Shift

MCQ (Single Correct Answer)

-1

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 $=(10.00 \pm 0.05) \mathrm{cm}]$