Detailed Solution:

The acceleration of a rocket is determined by the rate at which it ejects gases and the velocity of those gases.

1. Rocket Acceleration Equation: The acceleration of a rocket is given by:

   a = (vr * dm/dt) / m

   where:
   • a is the acceleration of the rocket,
   • vr is the relative speed of the ejected gases,
   • dm/dt is the rate of change of mass (rate of ejection of gases),
   • m is the current mass of the rocket.
2. Given Values: The problem gives:
   • vr = 11 km/s = 11,000 m/s,
   • dm/dt = 16 kg/s,
   • Initial Mass = 6000 kg.
3. Mass After One Minute: The mass of the rocket after one minute (60 seconds) is:

   m = 6000 kg - (16 kg/s × 60 s) = 6000 kg - 960 kg = 5040 kg

4. Acceleration Calculation: Now, substituting the values:

   a = (11,000 m/s × 16 kg/s) / 5040 kg

   a = 176,000 / 5040

   a = 34.92 m/s²

Therefore, the acceleration of the rocket one minute after the blast is 34.92 m/s².

Final Answer: 34.92 m/s²

Detailed Solution:

In an AC circuit with resistance and inductance, current depends on the total impedance of the circuit.

1. Impedance Calculation: The impedance (Z) in an AC circuit with resistance (R) and inductive reactance (XL) is calculated as:

   Z = √(R² + Xl²)

2. Given Values at 50 Hz: It is given that:
   • R = 30 Ω,
   • XL (at 50 Hz)= 20 Ω.
3. Inductive Reactance at 100 Hz: Inductive reactance is directly proportional to frequency:

   XL = 2πfL

   If frequency doubles from 50 Hz to 100 Hz, Inductive reactance doubles to 2*20 = 40 Ω

   • XL (at 100 Hz) = 40 Ω.
4. Impedance at 100 Hz: Calculate the new impedance:

   Z = √(30² + 40²) = √(900 + 1600) = √2500 = 50 Ω

5. Ohm's Law for AC Circuits: The current (I) is determined using Ohm's Law for AC circuits:

   I = V/Z

6. Current Calculation: Given that V = 200 V, the current will be:

   I = 200 V / 50 Ω = 4 A

Therefore, the current in the coil is 4 A.

Final Answer: 4 A

Detailed Solution:

The wavelengths in the hydrogen spectrum are calculated using the Rydberg formula.

1. Rydberg Formula: The Rydberg formula for wavelength is:

   1/λ = R(1/n1² - 1/n2²)

   where:
   • λ is the wavelength,
   • R is the Rydberg constant (1.097 × 10⁷ m⁻¹),
   • n1 and n2 are integers representing the lower and higher energy levels, respectively.
2. Paschen Series: For the Paschen series, n1 = 3.
3. Short Wavelength Limit: The short wavelength limit corresponds to the transition where n2 = ∞.
4. Substitution: Substitute n1 = 3 and n2 = ∞ in the formula:

   1/λ = 1.097 × 10⁷ m⁻¹ * (1/3² - 1/∞²)

   1/λ = 1.097 × 10⁷ m⁻¹ * (1/9 - 0)

   1/λ = 1.097 × 10⁷ m⁻¹/9

5. Simplification: Calculate the wavelength:

   λ = 9 / (1.097 × 10⁷ m⁻¹)

   λ = 8.20 × 10⁻⁷ m

Therefore, the short wavelength limit of the Paschen series is 8.20 × 10⁻⁷ m.

Final Answer: 8.20 × 10⁻⁷ m

Detailed Solution:

The solubility product (Ksp) is the equilibrium constant for the dissolution of a solid in water.

1. Dissociation of Ba(OH)2: The dissociation of Barium hydroxide in water is given by:

   Ba(OH)2 ⇌ Ba²⁺ + 2OH⁻

2. Ion Concentrations: If the solubility of Ba(OH)2 is S, then the concentrations of the ions will be:
   • [Ba²⁺] = S
   • [OH⁻] = 2S
3. Solubility Product Expression: The Ksp is given by:

   Ksp = [Ba²⁺] [OH⁻]²

4. Substitution and Calculation: Substitute the solubility values into the equation:

   Ksp = (S) * (2S)²

   Ksp = S * 4S² = 4S³

   Given that S = 1.73 × 10⁻¹⁴:

   Ksp = 4 * (1.73 × 10⁻¹⁴)³

5. Cube the Value of S :

   (1.73 × 10⁻¹⁴)³ = 5.18 × 10⁻⁴²

6. Multiply by 4 :

   Ksp = 4 * 5.18 × 10⁻⁴²

   Ksp = 20.7 × 10⁻⁴²

Therefore, the solubility product of Ba(OH)2 is 20.7 × 10⁻⁴².

Final Answer: 20.7 × 10⁻⁴²

Detailed Solution:

Ferromagnetism is a phenomenon where a material exhibits strong magnetic properties due to the alignment of magnetic moments.

1. Ferromagnetism Definition: Ferromagnetic materials have a strong attraction to magnets and can be magnetized easily. This happens when the magnetic domains of the material align.
2. Chromium:
   • Chromium primarily exhibits antiferromagnetic properties at low temperatures but can exhibit ferromagnetic behavior under specific conditions.
   • It also shows a range of magnetic behaviors depending on factors such as temperature.
3. Other Options:
   • Zinc is diamagnetic, with no magnetic properties as the atoms lack unpaired electrons
   • Copper is diamagnetic and displays very weak magnetic effects.
   • Manganese is paramagnetic, with unpaired electrons in the atom which weakly respond to magnetic fields.
4. Ferromagnetic Materials: Common examples of ferromagnetic materials include iron, cobalt, and nickel.

Therefore, among the given options, Chromium can show ferromagnetic behaviour.

Final Answer: Chromium

Detailed Solution:

Fe3O4 is a mixed oxide containing iron in two different oxidation states, and thus its average oxidation state can be found.

1. Composition of Fe3O4:
   • Fe3O4 is a mixed oxide of iron, containing both Fe²⁺ and Fe³⁺ ions.
   • It is not a pure compound with a single oxidation state for iron, it can also be written as FeO.Fe₂O₃
2. Total Negative Charge: The total negative charge of oxygen in Fe3O4 is:

   -2 (per O) * 4 = -8

3. Balancing the Charges: To balance the overall charge of the compound, the total positive charge of Fe ions must be +8.
4. Oxidation states of Fe: Considering there are 3 Fe atoms, we can express its average oxidation state as:

   2x + 1y = 8, where x is the Fe²⁺ and y is the Fe³⁺ number of atoms

   Since Fe₃O₄ is FeO.Fe₂O₃ we have one Fe²⁺ and two Fe³⁺ ions:

   1 * (+2) + 2 *(+3) = +8

5. Average Oxidation State: The average oxidation state of Fe is:

   (2 + 3 + 3) / 3 = 8/3

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

Final Answer: 8/3

Detailed Solution:

The conversion between Celsius and Fahrenheit scales is a common calculation.

1. Conversion Formula: The formula to convert Celsius to Fahrenheit is:

   °F = (9/5 × °C) + 32

2. Substitute Celsius Value: Given °C = 72:

   °F = (9/5 × 72) + 32

3. Calculation: Solving the equation:

   °F = (129.6) + 32

   °F = 161.6°F

Therefore, 72°C is equal to 161.6°F.

Final Answer: 161.6°F

Detailed Solution:

Menstrual blood differs from other blood due to the presence of components that prevent clotting.

1. Fibrinolysins:
   • Fibrinolysins are enzymes that break down fibrin, which is the main protein involved in blood clotting.
   • In menstrual fluid, fibrinolysis prevents clots by dissolving the fibrin, allowing the blood to flow more freely and not coagulate.
2. Other Options:
   • Fibrinogen is a protein involved in blood clot formation and does not prevent clotting.
   • Thromboplastin is a protein that initiates the coagulation cascade, which encourages clotting.
   • Prothrombin is a precursor to thrombin, another clotting factor, and does not prevent clot formation.

Therefore, menstrual blood does not clot due to the presence of fibrinolysins.

Final Answer: Fibrinolysins

Detailed Solution:

The heart has four valves that regulate blood flow.

1. Mitral Valve: The mitral valve, also called the left atrioventricular valve, is located between the left atrium and the left ventricle.
2. Bicuspid Valve: The mitral valve is also known as the bicuspid valve because it has two flaps (or cusps).
3. Other Options:
   • The tricuspid valve is located between the right atrium and right ventricle and has three flaps (or cusps).
   • The pulmonary valve is located between the right ventricle and the pulmonary artery.
   • The aortic valve is located between the left ventricle and the aorta.

Therefore, the mitral valve is also known as the bicuspid valve.

Final Answer: Bicuspid valve