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Resonance in a series R-L-C circuit occurs when the inductive reactance ($X_L$ ) is equal to the capacitive reactance ($X_C$ ). At this frequency, the circuit's impedance is at its minimum and is equal to the resistance (R), and the current is at its maximum.

A bimetallic strip is made of two metals with different coefficients of linear expansion. When heated, the metal with the higher linear expansivity expands more than the other. This unequal expansion causes the strip to bend, with the more expansive metal on the outside of the curve. This principle is used in thermostats and thermometers

This is the definition of inertia, which is the property of a body to resist changes in its state of motion. It is the basis for Newton's first law of motion. A more massive body has more inertia

1. Identify the velocity equation: v=10+2t2

2. Recall relationship between velocity and acceleration: Acceleration (a) is the first derivative of velocity with respect to time ( $a=\frac{dv}{dt}$ )

3. Differentiate the velocity equation:

1. $a=\frac{d}{dt}(10+2t^2)$
2. a=0+2×2t
3. a=4t

4. Substitute the given time (t=5 s):

1. $a=4×5=20 ms^{-1}$
2. $\therefore a=20ms^{-1}$

1. General wave equation: For a wave moving in the positive x-direction is y=Asin(kx−ωt), where A is amplitude, k is wave number, and ω is angular frequency.

2. Extract given values:

1. Amplitude (A) = 0.15 m
2. Frequency (f) = 550 Hz
3. Wavelength (λ) = 0.01 m

1. Calculate wave speed (v):
2. v=fλ=550 Hz×0.01 m=5.5 m/s

3. Calculate angular frequency (ω):

1. ω=2πf=2π×550=1100π rad/s

4. Calculate wave number (k):

1. k=$\frac{2π}{λ}=\frac{2π}{0.01}=200π rad/m$

5. Substitute values into the general equation:

1. y=0.15sin(200πx−1100πt)

6. Factor out 200π to match option A's format (y=Asin[k(x−vt)], where k=200π and v=5.5):

1. y=0.15sin[200π(x−(1100π/200π)t)]
2. y=0.15sin[200π(x−5.5t)]

Hypermetropia is a sight defect where the person can see distant objects clearly but cannot focus on near objects. The normal near point is 25 cm, but for a hypermetropic person, it is farther away. To correct this, a converging (convex) lens is needed to help the eye focus the light from a near object onto the retina. The lens should form a virtual image of the object at the person's near point (50 cm). Using the lens formula, $1/f = 1/u + 1/v$ , with $u = 25$ cm (desired near point) and $v = -50$ cm (virtual image at the person's near point), we have $1/f = 1/25 + 1/(-50) = 2/50 - 1/50 = 1/50$ . So, the focal length f = 50 cm = 0.5 m. The power of the lens (P) is the reciprocal of the focal length in meters: P = 1/f = 1/0.5 = +2.0 D.

"The frictional force is independent of the area of the surfaces in contact." is True.

1. Sliding friction does not depend on the contact area under normal conditions.
2. Even if one surface is larger, the frictional force remains the same.

"The frictional force depends on the nature of the surfaces in contact." is True

1. Friction is affected by how rough or smooth the surfaces are.
2. Example: Rubber on concrete vs. metal on ice.

"The frictional force depends on the speed of sliding." is False

1. Under most everyday conditions, sliding friction remains constant regardless of speed.
2. Speed only affects friction in special cases (e.g., very high speeds or fluid-lubricated surfaces).

"The frictional force is directly proportional to the normal reaction." is True

1. This is based on the standard friction equation:
2. Friction = μ × Normal Force

The Correct Combination:

1. Statements I, II, and IV are true
2. Correct Option: A. I, II and IV

The relationship between wave velocity (V), frequency (f), and wavelength ($\lambda$ ) is given by the formula $V = f\lambda$ . To find the wavelength, we rearrange the formula to $\lambda = V/f$ . Substituting the given values, $\lambda = 340 m/s / 200 Hz = 1.7$ m.

The horizontal component of a force ($F_x$ ) is found by multiplying the magnitude of the force ($F$ ) by the cosine of the angle ($\theta$ ) it makes with the horizontal. The formula is $F_x = F \cos(\theta)$. Substituting the values, $F_x = 40 \cos(60^\circ) = 40 \times 0.5 = 20$ N.

A DC motor works by a force exerted on a current-carrying coil in a magnetic field. To ensure the motor continues to rotate in one direction, the direction of the current in the coil must be reversed every half rotation. The commutator is a device that performs this function, reversing the current and ensuring that the torque always acts in the same direction, leading to continuous rotation.

Isotopes of an element are atoms that have the same number of protons (atomic number) but a different number of neutrons. Because they have the same number of protons, they belong to the same chemical element. The difference in the number of neutrons results in different mass numbers. For example, Carbon-12 and Carbon-14 are isotopes of carbon, both having 6 protons, but Carbon-12 has 6 neutrons while Carbon-14 has 8 neutrons.

A vector quantity is a physical quantity that has both magnitude and direction. Momentum is a vector quantity, as it is the product of mass (a scalar) and velocity (a vector), and it has a direction. Speed, mass, and work are all scalar quantities, having only magnitude.

For resistors connected in parallel, the reciprocal of the total effective resistance ($R_T$) is the sum of the reciprocals of the individual resistances. The formula is $1/R_T = 1/R_1 + 1/R_2 + 1/R_3$ . Substituting the given values, we get $1/R_T = 1/2 + 1/3 + 1/6$ . Finding a common denominator, we get $1/R_T = 3/6 + 2/6 + 1/6 = 6/6 = 1$ . Therefore, $R_T = 1$ Ω.

Rectification is the process of converting alternating current (AC), which periodically reverses direction, into direct current (DC), which flows only in one direction. This is typically done using semiconductor diodes, which allow current to flow in one direction only

According to the pressure law (also known as Gay-Lussac's law), for a fixed mass of gas at constant volume, the pressure is directly proportional to its absolute temperature. As the temperature of the gas increases, the kinetic energy of the gas molecules increases. This results in the molecules hitting the walls of the container with greater force and more frequently, leading to an increase in the pressure

The electric potential difference (or voltage) between two points is defined as the work done per unit positive charge in moving the charge from one point to the other. It is measured in Volts (V), which is equivalent to Joules per Coulomb (J/C)

Conduction is the main mode of heat transfer in solids. It occurs through the vibration of particles and the transfer of kinetic energy from one particle to another. Convection, on the other hand, involves the movement of fluid (liquid or gas) particles, and radiation is the transfer of heat through electromagnetic waves.

The critical angle is the angle of incidence in the denser medium for which the angle of refraction in the less dense medium is 90°. When the angle of incidence exceeds the critical angle, the light ray is no longer refracted, but is instead totally internally reflected into the denser medium.

The energy stored in a capacitor (E) is given by the formula $E = \frac{1}{2}CV^2$ , where $ is the capacitance and $V$ is the potential difference. The capacitance of a parallel plate capacitor is given by $C = \frac{\epsilon A}{d}$ , which is constant if the area (A) and separation ($d$) are constant. If the potential difference (V) is doubled, the new potential difference is 2V. The new energy stored will be $E_{new} = \frac{1}{2}C(2V)^2 = \frac{1}{2}C(4V^2) = 4(\frac{1}{2}CV^2) = 4E$ . Therefore, the energy stored is quadrupled.

A solar panel, or photovoltaic (PV) cell, works on the principle of the photoelectric effect. It converts light energy (from the sun) directly into electrical energy. The photons from the sunlight hit the semiconductor material in the panel, knocking electrons free to create an electric current.