1
JEE Main 2023 (Online) 24th January Morning Shift
+4
-1 As shown in the figure, a network of resistors is connected to a battery of 24V with an internal resistance of 3 $$\Omega$$. The currents through the resistors R$$_4$$ and R$$_5$$ are I$$_4$$ and I$$_5$$ respectively. The values of I$$_4$$ and I$$_5$$ are : A
$$\mathrm{I_4=\frac{8}{5}A}$$ and $$\mathrm{I_5=\frac{2}{5}A}$$
B
$$\mathrm{I_4=\frac{6}{5}A}$$ and $$\mathrm{I_5=\frac{24}{5}A}$$
C
$$\mathrm{I_4=\frac{2}{5}A}$$ and $$\mathrm{I_5=\frac{8}{5}A}$$
D
$$\mathrm{I_4=\frac{24}{5}A}$$ and $$\mathrm{I_5=\frac{6}{5}A}$$
2
JEE Main 2022 (Online) 29th July Evening Shift
+4
-1 Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Alloys such as constantan and manganin are used in making standard resistance coils.

Reason R: Constantan and manganin have very small value of temperature coefficient of resistance.

In the light of the above statements, choose the correct answer from the options given below.

A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is NOT the correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.
3
JEE Main 2022 (Online) 29th July Evening Shift
+4
-1 A $$1 \mathrm{~m}$$ long wire is broken into two unequal parts $$\mathrm{X}$$ and $$\mathrm{Y}$$. The $$\mathrm{X}$$ part of the wire is streched into another wire W. Length of $$W$$ is twice the length of $$X$$ and the resistance of $$\mathrm{W}$$ is twice that of $$\mathrm{Y}$$. Find the ratio of length of $$\mathrm{X}$$ and $$\mathrm{Y}$$.

A
1 : 4
B
1 : 2
C
4 : 1
D
2 : 1
4
JEE Main 2022 (Online) 29th July Morning Shift
+4
-1 Two metallic wires of identical dimensions are connected in series. If $$\sigma_{1}$$ and $$\sigma_{2}$$ are the conductivities of the these wires respectively, the effective conductivity of the combination is :

A
$$\frac{\sigma_{1} \sigma_{2}}{\sigma_{1}+\sigma_{2}}$$
B
$$\frac{2 \sigma_{1} \sigma_{2}}{\sigma_{1}+\sigma_{2}}$$
C
$$\frac{\sigma_{1}+\sigma_{2}}{2 \sigma_{1} \sigma_{2}}$$
D
$$\frac{\sigma_{1}+\sigma_{2}}{\sigma_{1} \sigma_{2}}$$
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