1
JEE Main 2023 (Online) 30th January Morning Shift
+4
-1 Electric field in a certain region is given by $$\overrightarrow{\mathrm{E}}=\left(\frac{\mathrm{A}}{x^{2}} \hat{i}+\frac{\mathrm{B}}{y^{3}} \hat{j}\right) \text {. The } \mathrm{SI} \text { unit of } \mathrm{A} \text { and } \mathrm{B}$$ are :

A
$$\mathrm{Nm}^{2} \mathrm{C} ; \mathrm{Nm}^{3} \mathrm{C}$$
B
$$\mathrm{Nm}^{3} \mathrm{C}^{-1} ; \mathrm{Nm}^{2} \mathrm{C}^{-1}$$
C
$$\mathrm{Nm}^{3} \mathrm{C} ; \mathrm{Nm}^{2} \mathrm{C}$$
D
$$\mathrm{Nm}^{2} \mathrm{C}^{-1} ; \mathrm{Nm}^{3} \mathrm{C}^{-1}$$
2
JEE Main 2023 (Online) 30th January Morning Shift
+4
-1 Two isolated metallic solid spheres of radii $$\mathrm{R}$$ and $$2 \mathrm{R}$$ are charged such that both have same charge density $$\sigma$$. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is $$\sigma^{\prime}$$. The ratio $$\frac{\sigma^{\prime}}{\sigma}$$ is :

A
$$\frac{5}{3}$$
B
$$\frac{5}{6}$$
C
$$\frac{9}{4}$$
D
$$\frac{4}{3}$$
3
JEE Main 2023 (Online) 29th January Evening Shift
+4
-1 A point charge $$2\times10^{-2}~\mathrm{C}$$ is moved from P to S in a uniform electric field of $$30~\mathrm{NC^{-1}}$$ directed along positive x-axis. If coordinates of P and S are (1, 2, 0) m and (0, 0, 0) m respectively, the work done by electric field will be

A
600 mJ
B
$$-1200$$ mJ
C
1200 mJ
D
$$-600$$ mJ
4
JEE Main 2023 (Online) 29th January Morning Shift
+4
-1

In a cuboid of dimension $$2 \mathrm{~L} \times 2 \mathrm{~L} \times \mathrm{L}$$, a charge $$q$$ is placed at the center of the surface '$$\mathrm{S}$$' having area of $$4 \mathrm{~L}^{2}$$. The flux through the opposite surface to '$$\mathrm{S}$$' is given by

A
$$\frac{q}{2 \epsilon_{0}}$$
B
$$\frac{q}{3 \epsilon_{0}}$$
C
$$\frac{q}{12 \epsilon_{0}}$$
D
$$\frac{q}{6 \in_{0}}$$
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