New mode = 2 (as 4 is removed, 2 is the next most frequent).

Mode is the number that appears most frequently. Here, 4 appears 3 times.

Mode = 3 (most frequent value).

Removing 5 leaves 2, 3, 4, 4, 6. The new mode is 4.

Mode is the value that appears most frequently. Here, 5 appears 3 times.

Removing mode 6 leaves 3, 4, 4, 5, 7. New mode = 4.

Mode is the most frequent value. Here, 7 appears most frequently.

Removing mode 4 leaves {1, 2, 2, 3, 5}. New mode = 2.

Mode is the number that appears most frequently. Here, 3 appears 3 times.

RMS speed is inversely proportional to the square root of molar mass, so if M is doubled, v_rms decreases by sqrt(2).

The RMS speed is inversely proportional to the square root of the molar mass. If M is doubled, v_rms decreases by sqrt(2).

If the molar mass is halved, the RMS speed increases by a factor of sqrt(2) because RMS speed is inversely proportional to the square root of molar mass.

Mole fraction of solvent = 1 - mole fraction of solute = 1 - 0.2 = 0.8.

According to Raoult's Law, the vapor pressure of the solvent in the solution is 0.75 * 100 mmHg = 75 mmHg.

The mole fraction of the solute is 1 - X_solvent = 1 - 0.8 = 0.2.

The mole fraction of the solvent is 1 - X_solute = 1 - 0.2 = 0.8.

Angular momentum L = Iω = 10 kg m² * 5 rad/s = 50 kg m²/s.

Rotational kinetic energy is given by KE = 1/2 I ω² = 1/2 * 10 * 5² = 125 J.

Using τ = Iα, we have α = τ/I = 20 N·m / 10 kg·m² = 2 rad/s².

Rotational kinetic energy is given by KE = 1/2 I ω^2. If I is doubled and ω remains constant, KE also doubles.

Angular acceleration α = τ/I. If I is doubled and τ remains constant, α is halved.

Angular momentum L = Iω; if I is doubled and ω remains constant, L also doubles.

According to Newton's second law for rotation, τ = Iα, if I increases and τ is constant, α must decrease.

Damped frequency (ω_d) = ω_n√(1-ζ^2) = 5√(1-0.2^2) = 5√(0.96) ≈ 4.8 rad/s.

a_4 = 4^2 + 4 = 16 + 4 = 20.

When the object distance equals the focal length, the image is formed at infinity.

When the object is at the focal length, the image is formed at infinity.

Probability = Odds in favor / (Total odds) = 3 / (3 + 2) = 3/5 = 0.6.

Molarity = π / (RT) = 3.0 / (0.0821 * 298) = 0.12 M

Molarity = π / (RT) = 3.0 / (0.0821 * 298) = 0.12 M