A = ρ * (L / R) = 3 x 10^-6 * (4 / 12) = 1 mm².

Resistance R is proportional to length; if length doubles, resistance also doubles to 24 Ω.

R = R0(1 + α(T - T0)) = 5(1 + 0.004(100 - 20)) = 6.4 Ω.

Resistance is directly proportional to resistivity; hence, wire B with higher resistivity will have higher resistance.

Resistance R = ρ(L/A). For wire A, R_A = ρ(2L/(A/2)) = 4ρ(L/A) = 4R_B.

Resistivity ρ = R * (A / L) = 3 * (2 x 10^-6 / 10) = 1.5 x 10^-6 Ω·m.

The extension of the wire can be calculated using the formula: extension = (F * L) / (A * Y).

The elongation ΔL of a wire is given by ΔL = (F * L) / (A * Y), where Y is Young's modulus.

The elongation ΔL of a wire is given by ΔL = FL / (AE), where E is Young's modulus.

Stress = Force / Area. Halving the diameter increases the area by a factor of 1/4, thus stress quadruples.

Elongation is inversely proportional to the area. Halving the diameter reduces the area to a quarter, thus elongation quadruples.

Stress (σ) = Force (F) / Area (A). Halving the diameter increases the area by a factor of 4, thus stress quadruples.

Elongation is inversely proportional to the area. Doubling the diameter increases the area by a factor of 4, thus elongation becomes L/4.

Elongation (ΔL) = (F * L) / (A * Y), where A is the cross-sectional area and Y is Young's modulus.

Since A has a Dog, B does not have a Cat or Fish, C has a Bird, and D has a Rabbit, E must have a Fish.

E plays the violin as D does not play the guitar or piano.

Since A and C cannot sit next to each other, E must be sitting between B and D.

D plays the flute as per the given conditions.

Since A does not play Cricket or Football, and B plays Tennis, C plays Basketball, and D does not play Badminton, E must play Badminton.

Since A does not play Cricket or Football, and B plays Tennis, C plays Basketball, and D does not play Badminton, E must play Badminton.

D must play tennis as A, B, C, and E have already been assigned sports.

D is E's spouse as A and B are married and C is D's sibling.

D is E's spouse as A and B are married and C is D's sibling.

E is a pilot as the professions of A, B, C, and D are already assigned.

D is the odd one out as he is only friends with B.

E is sitting next to D as D is opposite E.

D must be the doctor since A cannot be the doctor or artist, and B is a lawyer.

E must be the artist as A cannot be a doctor or artist, B is a lawyer, C is an engineer, and D is not a teacher.

Since A is not a doctor or engineer, and B is a teacher, C cannot be a lawyer or artist, leaving E as the lawyer.

Since D is younger than E and A is older than B, D must be the youngest.