Problem: Out of five resistances of resistance R ohm each, 3 are connected in parallel and are joined to the rest 2 in series. Find the resultant resistance.

Solution:
To solve this problem, we need to use the formula for the equivalent resistance of resistors in parallel and in series.

Step 1: Calculate the equivalent resistance of the 3 resistors in parallel.

When resistors are connected in parallel, their equivalent resistance can be calculated using the formula:

1/Rp = 1/R1 + 1/R2 + 1/R3

where Rp is the equivalent resistance, and R1, R2, and R3 are the resistances of the individual resistors.

In this case, we have three resistors of resistance R ohm each, so we can substitute R for each of the individual resistances:

1/Rp = 1/R + 1/R + 1/R
1/Rp = 3/R
Rp = R/3

Therefore, the equivalent resistance of the 3 resistors in parallel is R/3 ohm.

Step 2: Calculate the equivalent resistance of the 2 resistors in series.

When resistors are connected in series, their equivalent resistance can be calculated using the formula:

Rs = R1 + R2

where Rs is the equivalent resistance, and R1 and R2 are the resistances of the individual resistors.

In this case, we have two resistors of resistance R ohm each, so we can substitute R for each of the individual resistances:

Rs = R + R
Rs = 2R

Therefore, the equivalent resistance of the 2 resistors in series is 2R ohm.

Step 3: Calculate the resultant resistance.

Now that we have the equivalent resistance of the resistors in parallel and in series, we can calculate the overall equivalent resistance of the circuit by adding them together:

Rtotal = Rp + Rs
Rtotal = R/3 + 2R
Rtotal = 7R/3

Therefore, the resultant resistance is 7/3R ohm.

Answer: The correct answer is (b) 7/3R.