1
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
2
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
$$\frac{\sigma_{1}+\sigma_{2}}{\sigma_{1} \sigma_{2}}$$
3
JEE Main 2022 (Online) 28th July Evening Shift
+4
-1

Given below are two statements :

Statement I : A uniform wire of resistance $$80 \,\Omega$$ is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be $$5 \,\Omega$$.

Statement II: Two resistances 2R and 3R are connected in parallel in a electric circuit. The value of thermal energy developed in 3R and 2R will be in the ratio $$3: 2$$.

In the light of the above statements, choose the most appropriate answer from the option given below

A
Both statement I and statement II are correct
B
Both statement I and statement II are incorrect
C
Statement I is correct but statement II is incorrect
D
Statement I is incorrect but statement II is correct
4
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1

A wire of resistance R1 is drawn out so that its length is increased by twice of its original length. The ratio of new resistance to original resistance is :

A
9 : 1
B
1 : 9
C
4 : 1
D
3 : 1
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