1
JEE Main 2023 (Online) 30th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The charge flowing in a conductor changes with time as $$\mathrm{Q}(\mathrm{t})=\alpha \mathrm{t}-\beta \mathrm{t}^{2}+\gamma \mathrm{t}^{3}$$. Where $$\alpha, \beta$$ and $$\gamma$$ are constants. Minimum value of current is :

A
$$\beta-\frac{\alpha^{2}}{3 \gamma}$$
B
$$\alpha-\frac{3 \beta^{2}}{\gamma}$$
C
$$\alpha-\frac{\beta^{2}}{3 \gamma}$$
D
$$\alpha-\frac{\gamma^{2}}{3 \beta}$$
2
JEE Main 2023 (Online) 30th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Heat is given to an ideal gas in an isothermal process.

A. Internal energy of the gas will decrease.

B. Internal energy of the gas will increase.

C. Internal energy of the gas will not change.

D. The gas will do positive work.

E. The gas will do negative work.

Choose the correct answer from the options given below :

A
B and D only
B
C and E only
C
A and E only
D
C and D only
3
JEE Main 2023 (Online) 30th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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
$$\mathrm{Nm}^{2} \mathrm{C}^{-1} ; \mathrm{Nm}^{3} \mathrm{C}^{-1}$$
4
JEE Main 2023 (Online) 30th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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
$$\frac{4}{3}$$
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