Step 1: Identify the variables.

• Initial mass of the rocket (m₀) = 6000 kg.
• Rate of mass ejection (ṁ) = 16 kg/s.
• Relative speed of ejected gases (v_r) = 11 km/s = 11000 m/s.
• Time (t) = 1 minute = 60 seconds.

Step 2: Calculate the mass of the rocket after 1 minute. The mass decreases at a constant rate:

m = m₀ - (ṁ ⋅ t).

Substitute the values:

m = 6000 - (16 ⋅ 60) = 6000 - 960 = 5040 kg.

Step 3: Use the rocket equation to find acceleration. The acceleration of the rocket is given by:

a = (ṁ ⋅ v_r) / m.

Substitute the known values:

a = (16 ⋅ 11000) / 5040.

Simplify:

a = 176000 / 5040 = 34.92 m/s².

Thus, the acceleration of the rocket after 1 minute is 34.92 m/s².

According to the problem, the inductive reactance at 50 Hz is:

X_L = 20 Ω.

The inductive reactance X_L is given by:

X_L = 2πfL.

Substitute f = 50 Hz and X_L = 20 Ω:

2π × 50 × L = 20.

Simplify:

L = 20 / (2π × 50) = 1 / (5π) H.

If the frequency is increased to 100 Hz, the new inductive reactance is:

X_L = 2πfL.

Substitute f = 100 Hz and L = 1 / (5π) H:

X_L = 2π × 100 × (1 / (5π)) = 40 Ω.

The impedance Z of the circuit is given by:

Z = √(R² + X_L²).

Substitute R = 30 Ω and X_L = 40 Ω:

Z = √(30² + 40²) = √(900 + 1600) = √2500.

Simplify:

Z = 50 Ω.

The current I is calculated using Ohm's Law:

I = V / Z.

Substitute V = 200 V and Z = 50 Ω:

I = 200 / 50 = 4 A.

Thus, the current flowing through the coil is:

I = 4 A.

Step 1: Recall the formula for the Paschen series.

The wavelength λ of a spectral line in the Paschen series is given by:

1/λ = R (1/3² - 1/n²), n = 4, 5, 6, ...

where:

• R is the Rydberg constant (1.097 × 10⁷ m^-1),
• n is the principal quantum number (n > 3).

Step 2: Calculate the wavelength for the first member (n = 4).

For n = 4:

1/λ₁ = R (1/3² - 1/4²).

Simplify:

1/λ₁ = R (1/9 - 1/16).

Find the common denominator:

1/λ₁ = R ⋅ (16 - 9) / 144 = R ⋅ 7 / 144.

Given R = 1.097 × 10⁷ m^-1, calculate:

1/λ₁ = 1.097 × 10⁷ ⋅ 7 / 144.

Simplify:

1/λ₁ ≈ 5.33 × 10⁵ m^-1.

Convert to λ₁:

λ₁ = 1 / (5.33 × 10⁵) ≈ 18800 Å.

Step 3: Calculate the short wavelength limit (n = ∞).

For n = ∞, the formula becomes:

1/λ_min = R (1/3²).

Substitute R = 1.097 × 10⁷ m^-1:

1/λ_min = 1.097 × 10⁷ ⋅ 1/9.

Simplify:

1/λ_min = (1.097 × 10⁷) / 9 ≈ 1.22 × 10⁶ m^-1.

Convert to λ_min:

λ_min = 1 / (1.22 × 10⁶) ≈ 8.225 × 10^-7 m.

Convert to angstroms:

λ_min = 8225 Å.

Thus, the short wavelength limit of the Paschen series is 8225 Å.

The solubility product (K_sp) of Ba(OH)₂ can be calculated using its solubility (S).

Step 1: Dissociation of Ba(OH)₂.

Ba(OH)₂ dissociates in water as:

Ba(OH)₂ → Ba²⁺ + 2OH^-.

Let the solubility of Ba(OH)₂ be S. Then, the concentrations of the ions at equilibrium are:

• [Ba²⁺] = S,
• [OH^-] = 2S.

Step 2: Solubility product expression.

The solubility product (K_sp) is given by:

K_sp = [Ba²⁺] ⋅ [OH^-]².

Substitute the concentrations:

K_sp = S ⋅ (2S)².

Simplify:

K_sp = S ⋅ 4S² = 4S³.

Step 3: Calculate K_sp.

Substitute S = 1.73 × 10^-14:

K_sp = 4 ⋅ (1.73 × 10^-14)³.

Calculate (1.73)³:

1.73³ ≈ 5.17.

Calculate (10^-14)³:

(10^-14)³ = 10^-42.

Substitute into the equation:

K_sp = 4 ⋅ 5.17 ⋅ 10^-42.

Simplify:

K_sp = 20.7 × 10^-42.

Thus, the solubility product is:

K_sp = 20.7 × 10^-42.

Ferromagnetism refers to the property of certain materials to form permanent magnets or be attracted to magnets. Among the given options:

• Zinc (Zn): It is a diamagnetic material and does not exhibit ferromagnetic properties.
• Copper (Cu): Copper is also diamagnetic, showing no ferromagnetic behavior.
• Manganese (Mn): Manganese is paramagnetic in its pure state but not ferromagnetic.
• Chromium (Cr): Chromium is typically antiferromagnetic at room temperature, but certain alloys can exhibit ferromagnetic behavior.

The correct answer as ferromagnetic is Chromium, particularly in specific alloyed forms.

Step 1: Understanding the composition of Fe₃O₄:

Fe₃O₄ is a mixed oxide composed of FeO and Fe₂O₃. In this structure:

• FeO contains iron with an oxidation state of +2.
• Fe₂O₃ contains iron with an oxidation state of +3.

Step 2: Calculating the average oxidation state:

The formula for Fe₃O₄ contains 3 atoms of iron, where:

Oxidation states: 1 (Fe⁺²) + 2 (Fe⁺³).

The total oxidation number for all iron atoms is:

(+2) + 2(+3) = +8.

The average oxidation state of iron is:

+8 / 3.

Thus, the oxidation state of Fe in Fe₃O₄ is +8/3.

Step 1: Recall the formula for Celsius to Fahrenheit conversion.

The conversion formula is given by:

F = (9/5 × C) + 32.

Step 2: Substitute the given value of C = 72.

F = (9/5 × 72) + 32.

Step 3: Perform the calculation.

First, calculate (9/5) × 72:

(9/5) × 72 = 129.6.

Add 32 to this result:

F = 129.6 + 32 = 161.6.

Thus, 72 °C = 161.6 °F.

Menstrual blood typically does not clot because of the presence of fibrinolysins. These enzymes are responsible for breaking down fibrin, which is essential for clot formation. As a result:

• The blood remains in a fluid state.
• This prevents clot formation within the uterine lining during menstruation.

This mechanism ensures that the menstrual blood flows smoothly without forming clots under normal physiological conditions.

The mitral valve, located between the left atrium and the left ventricle of the heart, is also called the bicuspid valve. It is named so because it has two cusps (leaflets).

• The mitral valve ensures one-way blood flow from the left atrium to the left ventricle, preventing backflow.
• It works in coordination with other valves in the heart, like the tricuspid valve, which is present on the right side.

Thus, the correct answer is bicuspid valve.