If A's age is 12, then B's age = (4/3) × 12 = 16.

In the relation R, the pair (2,3) indicates that R(2) = 3.

The sum of the roots is -p, so 3 + 4 = -p, thus p = -7.

Modulus of resilience = (Yield strength²) / (2 * Shear modulus) = (400 MPa)² / (2 * 80 GPa) = 2 J/m³.

Let the numbers be x and y. x + y = 30 and x - y = 10. Solving these gives x = 20 and y = 10.

Shear rate = Shear stress / Viscosity = 10 Pa / 0.5 Pa.s = 20 s⁻¹.

The conjugate of a complex number a + bi is a - bi. Thus, the conjugate of 2 - 3i is 2 + 3i.

Multiplying z1 and z2: (1 + i)(2 - i) = 2 - i + 2i - 1 = 3 + i.

The efficiency of a Carnot cycle is given by the formula: efficiency = 1 - (T_c / T_h), where T_c is the absolute temperature of the cold reservoir and T_h is the absolute temperature of the hot reservoir.

The rate of a chemical reaction can be influenced by temperature, concentration of reactants, and the presence of catalysts.

Students who like only Mathematics = Total Mathematics - Both = 18 - 10 = 8.

According to the first law of thermodynamics, the change in internal energy (ΔU) is given by ΔU = Q - W. Here, Q = 100 J and W = 40 J, so ΔU = 100 J - 40 J = 60 J.

According to Ohm's Law (V = I * R), if voltage (V) is doubled and resistance (R) is constant, the current (I) must also double.

Resonance occurs when the driving frequency matches the natural frequency of the oscillator, leading to a significant increase in amplitude.

In dynamic equilibrium, the rates of the forward and reverse reactions are equal, but the concentrations of reactants and products may not be equal.

People who like at least one sport = (20 + 25 - 10) = 35. Therefore, people who like neither = 50 - 35 = 15.

People who like only bananas = Total bananas - Both = 25 - 10 = 15.

The frequency of a mass-spring system is given by f = (1/2π)√(k/m). If the spring constant (k) is doubled, the frequency increases by a factor of √2.

The oxidation state of the reducing agent decreases as it donates electrons.

The substance that is oxidized loses electrons during the redox reaction.

The equilibrium constant remains the same regardless of the concentrations of reactants or products, as it is only affected by temperature.

The maximum speed of an object in simple harmonic motion occurs at the equilibrium position, where the restoring force is zero and the kinetic energy is maximized.

People who like only chocolate = Total chocolate - Both = 120 - 50 = 70.

People who own only a car = Total car owners - Both = (60% of 100) - (20% of 100) = 60 - 20 = 40.

Impedance (Z) in an AC circuit is calculated using the formula Z = √(R^2 + X^2). Here, Z = √(4^2 + 3^2) = √(16 + 9) = √25 = 5 ohms.

According to Boyle's Law, if the volume of an ideal gas is halved while keeping the temperature constant, the pressure will double.

The word 'MATH' has 4 distinct letters. The number of arrangements is 4! = 24.

The number of ways to select 3 students from 10 is C(10, 3) = 10! / (3! * (10-3)!) = 120.

The number of arrangements of 4 different colored balls is 4! = 24.

The number of ways to distribute 5 different prizes to 3 students is 3^5 = 243.