Correct: Infrared (IR) region

Explanation: In the hydrogen spectrum, electron transitions that drop down to the $n=5$ energy level emit photons with very low energy and long wavelengths, placing the entire Pfund series firmly in the Infrared (IR) region of the electromagnetic spectrum.

Correct: Intensity of the image

Explanation: Cutting a lens horizontally reduces the total surface area available to gather light rays. While the focal length and radii of curvature remain exactly the same (meaning the image forms in the same place and size), fewer light rays converge to form the image, significantly reducing its intensity and making it dimmer.

Correct: Planck’s Constant

Explanation: Both angular momentum ($L = mvr$) and Planck’s Constant ($h$) share the derived unit of Joule-seconds ($text{J} cdot text{s}$), which breaks down into the fundamental SI base units of $text{kg} cdot text{m}^2 / text{s}$.

Correct: Equal to the potential on the surface

Explanation: The electric field ($E$) inside any hollow charged conductor is completely zero. Since the electric field is the negative gradient of the potential ($E = -Delta V / Delta r$), an electric field of zero means there is absolutely no change in potential ($Delta V = 0$). Therefore, the potential inside is constant and equals the potential at the surface.

Correct: $2.2text{ sec}$

Explanation: Using the basic kinematic formula $v = frac{d}{t}$, we rearrange to solve for time: $t = frac{d}{v}$. First, convert kilometers to meters: $0.75text{ km} = 750text{ m}$. Then, $t = frac{750}{340} approx 2.2text{ seconds}$.

Correct: Theory of Relativity

Explanation: Albert Einstein’s Special Theory of Relativity introduces the concept of relativistic mass. It posits that the measured mass of an object increases as its velocity approaches the speed of light, governed by the Lorentz factor.

Correct: $100text{ J}$

Explanation: The kinetic energy ($KE$) acquired by a charge ($q$) accelerating across a potential difference ($V$) is equal to the electrical work done on it. The formula is $KE = qV$. Substituting the values: $KE = 0.1text{ C} times 1000text{ V} = 100text{ Joules}$.

Correct: $2V$

Explanation: The speed of a wave traveling through a stretched string is determined by $v = sqrt{frac{T}{mu}}$, where $T$ is the tension. Because the speed is proportional to the square root of the tension ($sqrt{T}$), multiplying the tension by $4$ results in the speed multiplying by $sqrt{4}$, effectively doubling it to $2V$.

Correct: Frequency (via accelerating voltage)

Explanation: Penetrating power depends strictly on the kinetic energy of the individual X-ray photons. By Planck’s equation ($E = hf$), energy increases directly with frequency. Increasing intensity only increases the number of photons, not their individual penetrating strength.

Correct: Antineutron

Explanation: Every particle in the standard model has a corresponding antiparticle with the identical mass but reversed quantum numbers (such as baryon number). The exact antiparticle of the neutron is simply the antineutron.

Correct: Optical Fiber

Explanation: Optical fibers transmit data through light over long distances by trapping the light inside a glass core. Because the light strikes the boundary between the core and the cladding at an angle greater than the critical angle, it undergoes continuous total internal reflection without escaping.

Correct: Temperature

Explanation: Wien’s Displacement Law dictates that the wavelength corresponding to maximum emission intensity is inversely proportional to the absolute temperature ($lambda_{text{max}} T = text{constant}$). As an object heats up, its peak emission shifts toward shorter wavelengths, directly altering its perceived color.

Correct: Zero

Explanation: Due to the constant downward acceleration of gravity ($g$), the upward velocity of the ball steadily decreases. It momentarily halts completely at the exact apex of its flight before reversing direction to begin its descent. Thus, instantaneous velocity at the peak is zero.

Correct: $text{Ns}$

Explanation: Momentum ($p = mv$) has standard base units of $text{kg} cdot text{m/s}$. By Newton’s Second Law, an impulse ($F cdot Delta t$) causes a change in momentum. Therefore, Force $times$ Time yields Newton-seconds ($text{Ns}$), which is perfectly equivalent.

Correct: $2V$

Explanation: Relative velocity is calculated by vector subtraction: $v_{rel} = v_1 – v_2$. Since they move in opposite directions, one velocity is positive ($V$) and the other is negative ($-V$). Thus, $v_{rel} = V – (-V) = 2V$. They perceive each other as approaching at double the individual speed.

Correct: $3000text{ J}$

Explanation: Power is defined as energy over time ($P = frac{E}{t}$), meaning $E = P cdot t$. Time must be converted to standard SI units (seconds). $5text{ minutes} = 300text{ seconds}$. Thus, $E = 10text{ W} times 300text{ s} = 3000text{ Joules}$.

Correct: Both Transverse and EM waves

Explanation: Crests and troughs describe the highest and lowest points formed when oscillations occur perpendicular to the wave’s direction of travel. This defines all transverse waves. Because Electromagnetic (EM) waves are strictly transverse by nature, both answers are correct.

Correct: Zero

Explanation: The magnitude of a cross product is given by $|vec{A} times vec{B}| = AB sin(theta)$. Because a vector is perfectly parallel to itself, the enclosed angle $theta = 0^circ$. Since $sin(0^circ) = 0$, the entire cross product collapses entirely to the zero vector.

Correct: Zero

Explanation: Unlike electromagnetic radiation (which travels at $3 times 10^8 text{ m/s}$ in a vacuum), sound is a mechanical wave that absolutely requires a physical medium (particles) to transmit its vibrations. Because a vacuum is entirely void of particles, sound cannot travel through it.

Correct: $g/4$

Explanation: Newton’s law of universal gravitation dictates that $g = frac{GM}{r^2}$. At the Earth’s surface, $r = R_e$. At an altitude equal to the Earth’s radius ($h = R_e$), the total distance from the center of mass is $r = 2R_e$. Squaring this new distance yields $(2R_e)^2 = 4R_e^2$. Thus, the gravity becomes $frac{1}{4}$ of its surface value.