Magnetic field lines emerge from the north pole and enter the south pole of a bar magnet.

Adsorption is widely used in water purification processes to remove impurities.

Gas particles have the highest energy compared to solids and liquids, allowing them to move freely and occupy more space.

Particles in a solid have the least amount of energy compared to liquids, gases, and plasma.

In gases, particles move freely and are far apart compared to solids and liquids.

Integrating both sides, we get y = ∫(2x + 1)dx = x^2 + x + C.

Using an integrating factor, we find the solution is y = Ce^(2x) - 3/2.

This is a separable equation. Integrating gives y = Ce^(2x^3).

This is a separable equation. Integrating gives y = Cx.

This is a linear first-order equation. The solution is y = 5/2 + Ce^(-2x).

Using the integrating factor method, we find the solution y = (3/5) + Ce^(5x).

The characteristic equation is r^2 - 3r + 2 = 0, which factors to (r - 1)(r - 2) = 0. The general solution is y = C1e^(x) + C2e^(2x).

This is a first-order linear equation. The integrating factor method gives the solution y = 2 - Ce^(-6x).

This is a separable equation. Separating variables and integrating gives y = Cx.

Using an integrating factor e^(2x), we solve to get y = 3 - Ce^(-2x).

Using the integrating factor e^(∫(1/x)dx) = x, we solve to get y = x + C/x.

This is separable: dy/y = dx/x. Integrating gives ln|y| = ln|x| + C, thus y = Cx.

The Arrhenius equation relates the rate constant (k) to temperature (T) and activation energy (Ea).

Energy is defined as work done, which has the dimensional formula [M^1 L^2 T^-2].

Frequency is defined as the number of cycles per unit time, hence its dimensional formula is [T^-1].

Velocity is defined as displacement per unit time, hence its dimensional formula is [M^0 L^1 T^-1].

Lenz's Law states that the direction of induced current is such that it opposes the change in magnetic flux that produced it.

The force on a charged particle in a magnetic field is maximum when the angle between the velocity and the magnetic field is 90 degrees.

The force on a charged particle moving in a magnetic field is maximum when the angle between the velocity and the magnetic field is 90 degrees.

The force on a charged particle moving in a magnetic field is maximum when the particle moves perpendicular to the field.

Time period (T) = 1 / frequency (f) = 1 / 440 Hz ≈ 0.00227 s.

Time period (T) = 1 / frequency (f) = 1 / 440 Hz ≈ 0.00227 s.

According to the wave equation v = fλ, if frequency (f) is doubled and speed (v) remains constant, wavelength (λ) must halve.

The half-life of a first-order reaction is independent of the initial concentration and is directly proportional to the rate constant.

For a first-order reaction, the half-life is constant and is given by the formula t1/2 = 0.693/k.