1
JEE Main 2023 (Online) 30th January Evening Shift
+4
-1
Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$

Assertion A: The nuclear density of nuclides ${ }_{5}^{10} \mathrm{~B},{ }_{3}^{6} \mathrm{Li},{ }_{26}^{56} \mathrm{Fe},{ }_{10}^{20} \mathrm{Ne}$ and ${ }_{83}^{209} \mathrm{Bi}$ can be arranged as $\rho_{\mathrm{Bi}}^{\mathrm{N}}>\rho_{\mathrm{Fe}}^{\mathrm{N}}>\rho_{\mathrm{Ne}}^{\mathrm{N}}>\rho_{\mathrm{B}}^{\mathrm{N}}>\rho_{\mathrm{Li}}^{\mathrm{N}}$

Reason R: The radius $R$ of nucleus is related to its mass number $A$ as $R=R_{0} A^{1 / 3}$, where $R_{0}$ is a constant.

In the light of the above statements, choose the correct answer from the options given below
A
${Both ~\mathbf{A}}$ and $\mathbf{R}$ are true and $\mathbf{R}$ is the correct explanation of $\mathbf{A}$
B
Both $\mathbf{A}$ and $\mathbf{R}$ are true but $\mathbf{R}$ is NOT the correct explanation of $\mathbf{A}$
C
$\mathbf{A}$ is false but $\mathbf{R}$ is true
D
$\mathbf{A}$ is true but $\mathbf{R}$ is false
2
JEE Main 2023 (Online) 30th January Evening Shift
+4
-1
A point source of $100 \mathrm{~W}$ emits light with $5 \%$ efficiency. At a distance of $5 \mathrm{~m}$ from the source, the intensity produced by the electric field component is:
A
$\frac{1}{40 \pi} \frac{W}{m^2}$
B
$\frac{1}{10 \pi} \frac{W}{m^2}$
C
$\frac{1}{20 \pi} \frac{W}{m^2}$
D
$\frac{1}{2 \pi} \frac{W}{m^2}$
3
JEE Main 2023 (Online) 30th January Evening Shift
+4
-1
Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$

Assertion A: Efficiency of a reversible heat engine will be highest at $-273^{\circ} \mathrm{C}$ temperature of cold reservoir.

Reason R: The efficiency of Carnot's engine depends not only on the temperature of the cold reservoir but it depends on the temperature of the hot reservoir too and is given as $\eta=\left(1-\frac{T_{2}}{T_{1}}\right)$

In the light of the above statements, choose the correct answer from the options given below
A
Both $\mathbf{A}$ and $\mathbf{R}$ are true and $\mathbf{R}$ is the correct explanation of $\mathbf{A}$
B
Both $\mathbf{A}$ and $\mathbf{R}$ are true but $\mathbf{R}$ is NOT the correct explanation of $\mathbf{A}$
C
A is false but $\mathbf{R}$ is true
D
A is true but $\mathbf{R}$ is false
4
JEE Main 2023 (Online) 30th January Evening Shift
+4
-1
A block of $\sqrt{3} \mathrm{~kg}$ is attached to a string whose other end is attached to the wall. An unknown force $\mathrm{F}$ is applied so that the string makes an angle of $30^{\circ}$ with the wall. The tension $\mathrm{T}$ is: (Given $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )

A
15 N
B
10 N
C
25 N
D
20 N
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