Work done (W) = nRT ln(Vf/Vi). Here, nRT = PVi = 100 kPa * 1 m³ = 100 kJ. W = 100 kJ * ln(2) ≈ 69.3 kJ.

The work done in an isothermal expansion is W = nRT ln(Vf/Vi). Assuming 1 mole of gas, W = 1 * 8.31 * 300 * ln(2) ≈ 600 J.

Using the formula v_rms = sqrt((3RT)/M), we can rearrange to find T = (v_rms^2 * M) / (3R). Substituting v_rms = 500 m/s and M = 0.02 kg/mol gives T = 500 K.

In an adiabatic compression, the temperature of the gas increases due to work done on it.

Using Boyle's Law, P1V1 = P2V2, we find P2 = P1 * (V1/V2) = 1 atm * (4 L / 1 L) = 4 atm.

Profit Margin = ((Revenue - Cost) / Revenue) * 100 = ((600 - 500) / 600) * 100 = 16.67%.

Each family will receive ₹1,20,000 / 8 = ₹15,000.

Fraction = ₹50,000 / ₹2,00,000 = 1/4.

Amount reserved for administrative costs = 10% of ₹5,00,000 = ₹50,000.

To find the number of people who play only football, we subtract those who play both from those who play football: 12 - 5 = 7.

To find the number of friends who play only football, we subtract those who play both from those who play football: 12 - 5 = 7.

The number of friends who like only football is calculated as: Only Football = Total Football - Both = 5 - 2 = 3.

B is the youngest as A is older than B and C is younger than D.

Total cost = Average cost per person × Number of people = 20 × 5 = $100.

Let the initial number of students be x. The work done is inversely proportional to the number of days. Setting up the equation gives x = 10.

Let the number of students be n. Total height = 150n. After one leaves, total height = 148(n - 1). Setting the equations gives 150n - 148(n - 1) = height of student.

Total score = 75 * 10 = 750. New total = 750 - 90 = 660. New average = 660 / 9 = 73.33.

The mode is 2, as it appears four times in the data set.

The mode is 50, which appears 3 times in the scores.

Amount spent on awareness programs = 25% of ₹3,00,000 = 0.25 * 3,00,000 = ₹75,000.

Upper limit = Measured value + Error = 180 + 1 = 181 cm

Height = Rate × Time = 300 m/min × 10 min = 3000 m

Time = Height / Rate = 1500 m / 300 m/min = 5 minutes

Distance = Speed * Time = 240 km/h * (45/60) h = 180 km.

Volume of a hemisphere = (2/3)πr³ = (2/3)π(3)³ = (2/3)π(27) = 18π cm³.

For a hollow cylinder, the electric field at a point outside is E = λ/(2πε₀r) using Gauss's law.

The electric field inside a hollow charged sphere is zero due to symmetry.

Inside a hollow charged sphere, the electric field is zero due to symmetry.

The electric field inside a hollow charged sphere is zero due to symmetry.

For a hollow sphere, I = (2/3)mr^2. Using energy conservation, the translational kinetic energy is 2/3 of the potential energy at the top.