Physics

Step 1: Identify the type of inhibition.
Because remains unchanged while increases, this is *competitive inhibition*. For competitive inhibition: Step 2: Substitute the values.
Step 3: Solve for .
Step 4: Conclusion.
The inhibition constant is 3.0 mM.

Step 1: Determine number of half-lives.
Half-life = 300 days Time elapsed = 900 days Step 2: Apply decay formula.
Remaining mass = Step 3: Convert to mg.
Step 4: Conclusion.
Mass remaining = 125.0 mg.

Step 1: Effect of dielectric on electric field.
A dielectric reduces the effective electric field inside the capacitor: , where . Thus, .
Step 2: Effect of dielectric on capacitance.
Capacitance increases by a factor : So .
Step 3: Evaluate options.
Only option (B) correctly states both effects: reduced electric field and increased capacitance.
Step 4: Conclusion.
Thus, and .

Step 1: Recall assumptions of kinetic theory.
Ideal gas molecules are treated as point masses → negligible volume. They are always in continuous random motion and collisions are perfectly elastic. Intermolecular forces are assumed negligible.
Step 2: Evaluate statements.
(A) Correct — volume is negligible compared to container volume.
(B) Incorrect — they do possess kinetic energy proportional to temperature.
(C) Correct — random motion is a fundamental assumption.
(D) Correct — attractive forces are negligible for ideal behaviour.
Step 3: Conclusion.
Thus, (A), (C), and (D) are correct assumptions.

Step 1: Use elastic collision formulas.
For elastic collision between masses and ( ): Velocity of lighter mass Y after collision is:
When : , .
Step 2: Substitute approximations.
.
Step 3: Use momentum substitution relation.
Under the given simplification, the effective relative velocity simplifies to . This matches option (C).

Step 1: Apply dimensional analysis.
Given: . Since has dimension [L] and is a length constant, must also have dimension [L].
Step 2: Determine the dimension of .
. Therefore, .
Step 3: Conclusion.
Hence, the dimension of is .

Step 1: Understanding the electric field between conducting plates.
For two infinite conducting plates with opposite charge densities and , the electric field between them is given by: This is the field produced by one plate. Since both plates contribute to the electric field, the total electric field between them is twice this value. Hence, the total electric field is: Step 2: Conclusion.
The value of is 2.

Step 1: Understanding the problem.
The wire is bent into the shape of a square loop. If the resistance of the wire is 40 and we need to find the resistance between two diagonally opposite corners, we need to divide the total resistance by the number of resistances in the path between the corners.
Step 2: Calculation.
Since the wire is bent into a square, there are 4 equal segments, each contributing to the total resistance. The resistance between any two diagonally opposite corners is the sum of the two segments along the diagonal, which is half of the total resistance. Therefore, the resistance between two diagonally opposite corners is: Step 3: Conclusion.
The resistance between any two diagonally opposite corners is 20 .

Step 1: Understanding semiconductor behavior.
In intrinsic semiconductors, the number of free electrons is equal to the number of holes. An intrinsic semiconductor becomes an n-type semiconductor when a trivalent element is added, creating additional free electrons. The I-V characteristics of a p-n diode are non-linear, not straight. In reverse bias, the current in a p-n diode is carried by the minority carriers.
Step 2: Analyzing the options.
(A) In intrinsic semiconductors, the number of electrons is equal to the number of holes at any temperature: True — This is a characteristic of intrinsic semiconductors.
(B) An intrinsic semiconductor changes to an n-type semiconductor upon addition of a trivalent element: Incorrect — A trivalent element (which creates holes) would make the semiconductor p-type, not n-type.
(C) The shape of the I-V characteristics of a p-n diode is a straight line: Incorrect — The I-V characteristics of a p-n diode are non-linear and exponential, not linear.
(D) In the reverse bias condition, the current in a p-n diode is due to the minority carriers: Correct — In reverse bias, the current is due to the minority carriers in a p-n junction.
Step 3: Conclusion.
The correct answer is (D) In the reverse bias condition, the current in a p-n diode is due to the minority carriers.

Step 1: Understanding electromagnetic waves.
Electromagnetic waves, such as light, radio waves, and X-rays, can propagate through a vacuum without requiring a material medium. They carry both energy and momentum, and they are transverse in nature, meaning the oscillations are perpendicular to the direction of wave propagation.
Step 2: Analyzing the options.
(A) carry energy: Correct — Electromagnetic waves carry energy.
(B) carry momentum: Correct — Electromagnetic waves carry momentum, which can be transferred to objects they interact with.
(C) are transverse in nature while travelling in vacuum: Correct — Electromagnetic waves are transverse in nature.
(D) do not need a material medium to travel: Correct — Unlike sound waves, electromagnetic waves can travel through a vacuum.
Step 3: Conclusion.
The correct answer is (D) do not need a material medium to travel, as electromagnetic waves can propagate through space without needing a medium.

Step 1: Understanding kinetic theory.
The kinetic theory of gases states that the average kinetic energy of gas molecules depends only on the temperature of the gas, regardless of the type of molecule. This means that for a diatomic molecule, its average energy depends only on temperature.
Step 2: Analyzing the options.
(A) mass of each atom and the temperature: Incorrect — The average energy depends only on temperature, not on the mass of individual atoms.
(B) mass of each atom and the bond length: Incorrect — These factors do not directly influence the average energy.
(C) mass of each atom, bond length, and temperature: Incorrect — Only temperature affects the average energy.
(D) temperature only: Correct — The average energy of a molecule in an ideal gas depends only on temperature.
Step 3: Conclusion.
The correct answer is (D) temperature only, as the average energy is directly related to temperature.

Step 1: Identify circuit connections.
The 6 and 3 resistors are connected in parallel. This parallel combination is in series with a 6 and a 2 resistor. Battery voltage = 30 V.
Step 2: Calculate equivalent resistance of parallel branch.
Step 3: Calculate total circuit resistance.
Step 4: Find total current from the battery.
Step 5: Voltage drop across parallel branch.
Step 6: Current through the 3 resistor.
In parallel combination, same voltage across each resistor: Step 7: Power dissipated across 3 .
**(Recheck)**: small correction — if actual equivalent gives 12 W, not 15 W. Step 8: Conclusion.

Step 1: Recall the definition of acceleration.
Acceleration is the rate of change of velocity with respect to time. Positive acceleration means velocity increases with time.
Step 2: Analyze the given graphs.
(A) shows position increasing linearly — constant velocity (zero acceleration).
(B) shows position constant — object at rest (zero velocity, zero acceleration).
(C) shows velocity increasing linearly with time — constant positive acceleration.
(D) shows velocity constant — no acceleration.
Step 3: Conclusion.
Hence, the correct graph representing positive acceleration is (C).

Step 1: Relationship between potential and velocity.
Thus, increasing increases . Step 2: Magnetic radius formula.
Hence, radius increases. Step 3: Time period of circular motion.
Independent of or ; thus, no change. Step 4: Work by magnetic field.
The magnetic force does no work because it is perpendicular to motion. Step 5: Conclusion.
Hence, (A) and (B) are correct.