Multiple Choice Questions

Blue

Reason — Blue light has a shorter wavelength, so it slows down more in glass and bends more towards the normal than red or yellow light. This means that the angle of refraction (∠𝑟) for blue light becomes smaller compared to red or yellow light. So the difference ∠𝑖 − ∠𝑟 becomes greatest for blue light.

A and R are true and R is the reason of A.

Explanation:

Assertion (A) is true: When light passes through a triangular prism, the angle of deviation first decreases with increasing angle of incidence, reaches a minimum, and then increases again. This means there are two angles of incidence that result in the same angle of deviation—one on either side of the minimum deviation point.

Reason (R) is also true: The principle of reversibility of light states that if the direction of a light ray is reversed, it retraces its original path. This principle explains why the same deviation occurs for two different angles of incidence because the path of light through the prism is symmetric.

Reason — Convex lens is converging lens and concave lens is diverging lens.

Option 1 Incorrect:
In this figure, the convex lens is shown causing divergence, which is not typical behavior for a convex lens.

Option 2 Correct:
In this figure, the concave lens is shown causing divergence, which aligns with its expected behavior.

Option 3 Incorrect:
In this figure, the parallel beam of light is incident obliquely on the lens, so it does not converge at the principal focus.

Option 4 Incorrect:
In this figure, the concave lens is shown causing convergence, which is incorrect as concave lenses diverge light.

There are two pulley systems with V.R. = 2 and two pulley system with V.R. = 3

Reason — The velocity ratio is always equal to the number of strands of the tackle (or number of sections of the strings)

Velocity Ratio (V.R.) = $\frac{\text{displacement of effort}}{\text{displacement of load}}$

In Figure 1:

Number of sections of the strings = 3

So, the effort must move 3 units of distance to raise the load by 1 unit.

Velocity ratio = $\frac{\text{displacement of effort}}{\text{displacement of load}}$

Velocity ratio = $\frac{3\text{d}}{\text{d}}=3$

In Figure 2:

Number of sections of the strings = 2

So, the effort must move 2 units of distance to raise the load by 1 unit.

Velocity ratio = $\frac{\text{displacement of effort}}{\text{displacement of load}}$

velocity ratio = $\frac{2\text{d}}{\text{d}}=2$

In Figure 3:

Number of sections of the strings = 3,

So, the effort must move 3 units of distance to raise the load by 1 unit.

Velocity ratio = $\frac{\text{displacement of effort}}{\text{displacement of load}}$

Velocity ratio $= \frac{3\text{d}}{\text{d}}=3$

In Figure 4:

Number of sections of the strings = 2,

So, the effort must move 2 units of distance to raise the load by 1 unit.

Velocity ratio = $\frac{\text{displacement of effort}}{\text{displacement of load}}$

Velocity ratio = $\frac{2\text{d}}{\text{d}}=2$

The magnitude of the moment of force is maximum in P and Q.

Reason

Option 1 Incorrect:
P & Q have same anticlockwise moment.

Option 2 Incorrect:
Maximum moment of force is for 90°. Here angle is not 90°.

Option 3 Correct:
Moment of force = force x perpendicular distance from pivot point.
For both P and Q, perpendicular distance from pivot point is maximum
Hence, the magnitude of the moment of force is maximum in P and Q.

Option 4 Incorrect:
R has anticlockwise moment which is taken positive.

9 cm

Reason — For a completely solid cone (of uniform density), the center of gravity (CG) lies at a height of one-fourth the height from the base.

Distance from apex = $\frac{3}{4}$ x Height

$\text{Distance from apex} = \frac{3}{4} \times \text{Height}$
So, for a cone of height 12 cm, $\text{CG} = \frac{3}{4} \times 12 = 9~\text{cm from the apex}$
This means that only the cone with CG at 9 cm from the apex behaves like a completely solid cone.

Force is acting at an angle of 60° with the displacement.

Reason — From the graph, when displacement d = 10 m, work done W = 50 J

Slope = $\frac{50\text{J}}{10\text{m}}$ = 5 Nm

$$\begin{aligned}\text{Slope of work displacement graph} = \text{F cos θ} \\[1em] \text{F cos θ} = 5 \text{ Nm} \\[1em] \text{cos θ} = \frac{5}{10} \\[1em] \text{cos θ} = 0.5 \\[1em] \text{cos θ} = \text{cos } 60° \\[1em] \text{θ} = 60°\end{aligned}$$

Z' > Z

Reason — Lubrication reduces friction at the axle of the pulley. This has three main effects:

1. Less effort (X') is needed to lift the same load (X' < X).
2. Since the machine now wastes less energy, the efficiency (Z') increases (Z' > Z).
3. Mechanical Advantage (Y'), which is Load/Effort, increases because the effort decreases while the load stays the same.

• Option (1): X’ > X Incorrect (It actually decreases)
• Option (2): Y’ < Y Incorrect (MA increases)
• Option (3): Z’ > Z Correct
• Option (4): Z’ = Z Incorrect (Efficiency increases)

Assertion is false, but the Reason is true.

Explanation :
Assertion (A) is false : An $i$ vs. $r$ graph is not a straight line because Snell's law relates the sine of the angle of incidence to the sine of the angle of refraction not the angles themselves.

Reason (R) is true : Snell's Law is the law of refraction, it tells us how light bends when it passes from one medium to another.

frequency

Reason

1. Speed in Vacuum → incorrect.
   All electromagnetic waves (radio, microwave, infrared, visible, UV, X-ray, gamma) travel at the same speed in a vacuum: So, speed of UV = speed of microwaves in vacuum
2. Speed in medium → incorrect.
   When electromagnetic waves enter a medium like glass or water, they slow down.
   UV rays have higher frequency than microwaves. Therefore, UV rays interacts more strongly with the medium hence, they slow down more.
3. frequency → correct.
   UV has a much higher frequency than microwaves.
   Frequency of UV = $10^{15}$ Hz
   Frequency of Microwaves = around $10^{9}$ - $10^{11}$ Hz
4. wavelength → incorrect.
   We know that,
   $\lambda = \frac{c}{f}$
   This means that a higher frequency corresponds to a shorter wavelength, while a lower frequency corresponds to a longer wavelength.

The length QR becomes less.

Reason — When Sumit’s grandmother lowers the volume, she’s reducing the wave’s amplitude, the maximum displacement from the mean position. In the diagram:

• P and R lie on the mean position (zero-displacement).
• Q marks the crest (maximum positive displacement).
• QR is the vertical distance from the equilibrium to the crest, which equals the amplitude. Reducing volume shrinks that vertical distance, so QR becomes smaller.

Only statement B is correct.

Explanation :

Given,
Mass (m) = 10 g
Heat supplied (Q) = 120 J
Temperature rise (ΔT) = 10 °C = 10 K

Statement A is incorrect:
Heat capacity of the sample (C) = $\frac{\text{Q}}{\text{ΔT}}$= $\frac{120 \text{J}} {10 \text{K}} = 12$ J/K
Here, numerical value is correct but unit of heat capacity is wrong in statement A.

Statement B is correct:
Specific heat capacity (c) = $\frac{\text{Q}}{\text{m.ΔT}}$ =$\frac{\text{120 J}}{\text{10g }\times\text {10 K}}$ = 1.2 J/g K

Both statements A and B are incorrect.

Explanation :

By resistance formula,
$\text{R} = \rho \cdot \frac{\text{L}}{\text{A}}$

Statement (A) is incorrect:
Given,
Resistivity of gold ρ_Au= 2.1 x 10^-8 ohm.m
Resistivity of platinum ρ_Pt= 10.5 x 10^-8 ohm.m

Let the cross-sectional area A be the same for both wires.

Resistance of gold:

$$\begin{aligned}R_{Au}=ρ_{Au} \frac{l_{Au}}{A} \\[1em] R_{Au}=2.1\times10^{-8} \times\frac{1}{A} \\[1em] R_{Au}= \frac{2.1\times10^{-8}}{A} \\[1em]\end{aligned}$$

Resistance of platinum:

$$\begin{aligned}R_{Pt}=ρ_{Pt} \frac{l_{Pt}}{A} \\[1em] R_{Pt}=10.5\times10^{-8} \times\frac{5}{A} \\[1em] R_{Pt}= \frac{52.5\times10^{-8}}{A} \\[1em] R_{Au} \not = R_{Pt}\end{aligned}$$

Statement (B) is incorrect:
Let the length of both wires are same.
Resistance of gold:

$$\begin{aligned}R_{Au}=ρ_{Au} \frac{l}{A_{Au}} \\[1em] R_{Au}=2.1\times10^{-8} \times\frac{l}{π\times 1^2 } \\[1em] R_{Au}= \frac{2.1\times10^{-8}\times l}{π} \\[1em]\end{aligned}$$

Resistance of platinum:

$$\begin{aligned}R_{Pt}=ρ_{Pt} \frac{l}{A_{Pt}} \\[1em] R_{Pt}=10.5\times10^{-8} \times\frac{l}{π\times 5^2 } \\[1em] R_{Au}= \frac{10.5\times10^{-8}\times l}{25π} \\[1em] R_{Au} \not = R_{Pt}\end{aligned}$$

Both Assertion and Reason are true, but Reason is not the correct explanation of the Assertion

Explanation :
Assertion (A) is true : A switch can be used to open and close a circuit, regardless of whether it's connected to the live or neutral wire. However, for safety reasons, the switch should be connected to the live wire.
Reason (R) is true : It is true that the neutral wire is at zero potential, but this does not justify its use for a switch. The function of a switch is to break the live wire, thereby completely disconnecting the circuit from the power source.

A and C are connected to the positive terminal of the battery.

Reason — Clock rule : if current at the face of the loop is clockwise, so it behaves as south pole, while current at the face of the loop is anticlockwise, so it behaves as north pole.
"When points A and C are connected to the positive terminal, the second end of the first electromagnet becomes the south pole because the current at that end flows in clockwise direction. Similarly, the first end of the second electromagnet becomes the north pole since the current there is anticlockwise. Due to these opposite polarities at the facing ends, the electromagnets attract each other."

Both C & D

Reason — A balanced nuclear equation must conserve:

• Mass number (top value) — total nucleons (protons + neutrons)
• Atomic number (bottom value) — total protons

Equation A
LHS: Mass number= q-1
Atomic number = p-5
RHS: mass number= (q-5 + 4) = q-1
Atomic number= (p-3 + 2) = p-1
so this equation is not balanced.

Equation B
LHS: Mass number= q-4
Atomic number = p-4
RHS: mass number= (q-4 + 0) = q-4
Atomic number= p-5 + (-1) = p-6
so this equation is not balanced.

Equation C
LHS: Mass number= q-1
Atomic number = p-5
RHS: mass number= (q-5 + 4) = q-1
Atomic number= (p-7 + 2) = p-5
so this equation is balanced.

Equation D
LHS: Mass number= q-4
Atomic number= p-7
RHS: Mass number= q-4 + 0 = q-4
Atomic number= p-5 + 2(-1) = p-7
so this equation is balanced.

L – Q, M – R, N – P

Reason — The frequency of a tuning fork is inversely proportional to the square of the length of its prongs i.e., $f \propto \frac{1}{l^2}$
So, tunning fork L has highest frequency, N has lowest frequency and M has medium frequency

Frequency is inversely proportional to the length of the air column i.e., $f \propto \frac{1}{l}$
So, air column Q has highest frequency, P has lowest frequency and R has medium frequency

Highest frequency tuning fork (L) should match with the highest frequency air column (Q).
So, L-Q combination will resonate.

Medium frequency tuning fork (M) should match with the medium frequency air column (R).
So, M-R combination will resonate.

Lowest frequency tuning fork (N) should match with the lowest frequency air column (P).
So, N-P combination will resonate.

1:1:1

Reason — For each metal, the heat supplied is $Q$ and the temperature rise is $\Delta T$, so

$Q = m c , ΔT ; ⟹ ; m c = \frac{Q}{ΔT}.$

Because both $Q$ and $ΔT$ are identical for A, B and C, the product $m c$ i.e., the thermal (heat) capacity, is the same for all three metals. Hence their thermal capacities are in the ratio $1:1:1$.

A < C < D < B

Reason

$$\begin{aligned}\text{R} = \rho \frac{l}{A} \\[1em] \text{R} = \rho\frac{l}{\pi r^2} \\[1em] \text{R}=\rho\frac{4l}{\pi d^2} \\[1em]\end{aligned}$$

Here, $\rho$ is specific resistance , l is length of conductor, d is diameter of conductor.

Conductor A:

$$\begin{aligned}R_A = \frac{\rho\times 4l}{\pi (2d)^2} \\[1em] R_A = \frac{\rho l}{\pi d^2}\end{aligned}$$

Conductor B:

$$\begin{aligned}R_B = \frac{\rho\times 4\times 3l}{\pi d^2} \\[1em] R_B = \frac{12\rho l}{\pi d^2}\end{aligned}$$

Conductor C:

$$\begin{aligned}R_C = \frac{\rho\times 4\times 2l}{\pi (2d^2)} \\[1em] R_C = \frac{2\rho l}{\pi d^2}\end{aligned}$$

Conductor D:

$$\begin{aligned}R_D = \frac{\rho\times 4\times l}{\pi d^2} \\[1em] R_D = \frac{4\rho l}{\pi d^2}\end{aligned}$$

so, A < C < D < B

A is false, but R is true.

Explanation :
Assertion (A) is false: to hear reflected sound.

$$\begin{aligned}\text{Minimum distance (d)}= \frac{\text{vt}}{2}\\[1em] = \frac{330 \times 0.1}{2} \\[1em] = 16.5\text{ m}\\[1em]\end{aligned}$$

Minimum distance (d) = 16.5 m
2d = x + y
So x + y ≥ 33 m, to hear the reflected sound.

Reason (R) is true: For humans to distinctly hear reflected sound must reach the ears at least 0.1 second after the original sound.

Current starts flowing through AC wire concealed in the adjacent wall.

Reason — When the AC is switched on, electric current flows through the concealed wires, generating a magnetic field around them. This magnetic field interacts with the magnetic compass, causing the needle to deflect. Air movement or vibrations don’t affect magnetic fields, so they wouldn’t cause the needle to move.

Substance A will experience a smaller temperature change than substance B.

Reason — Specific heat capacity tells us how much heat is needed to raise the temperature of a substance. A higher specific heat means the substance absorbs more heat without a big temperature rise. So, with the same heat energy and mass, Substance A (with higher specific heat) will heat up less than Substance B.

I, II and III

Reason

Conclusion I Correct: When light enters a denser medium from a rarer medium, it bends towards the normal due to refraction. In a prism, this causes the light to bend toward the base.

Conclusion II Correct:
Refraction occurs both at the entry and exit surfaces of the prism.
→ At the first surface (entry from air into glass), it bends towards the normal—because it's entering a denser medium.
→ At the second surface (exit from glass into air), it bends away from the normal—because it's emerging into a rarer medium.

Conclusion III. Correct:
The emergent ray deviates from the original path, forming an angle with the incident ray. This angle is called the angle of deviation.

conclusion IV Incorrect:
At the second surface (glass to air), light moves from denser to rarer medium, so it bends away from the normal. Hence, the angle of refraction is greater than the angle of incidence.

Reason — In circular motion, the velocity of an object is always tangential to the point on its path. In the figure, the ball is moving clockwise within the ring, and upon lifting the ring, the ball moves toward the right, making option 3 the correct choice.

A is true, but R is false.

Explanation :
Assertion (A) is true: During sunset (or sunrise), sunlight has to pass through a greater thickness of Earth’s atmosphere. Shorter wavelengths like blue and violet scatter more and get removed from the direct path. The longer wavelength red light dominates, giving the sky its reddish hue.
Reason (R) is false: Actually, red light scatters the least. According to Rayleigh scattering, the scattering is inversely proportional to the fourth power of wavelength. So shorter wavelengths scatter much more than longer ones—this is why the sky looks blue during midday.

A is false, but R is true.

Explanation :
Work is given by $$\begin{aligned}\vec{W} = \vec{F} \cdot \vec{S} \\[1em] W = F S \cos\theta\end{aligned}$$ so the reason is correct.

But zero work doesn't always mean zero displacement. For example, when force is perpendicular to displacement (like carrying a bag horizontally). Here, the angle between force and displacement is 90° so work done $$\begin{aligned}|\vec{W}| = |\vec{F}||\vec{S}| \cos 90°= 0 \\[1em]\end{aligned}$$ work is still zero, even though displacement exists. Therefore, the reason is correct, but the assertion is not.

inversely proportional to its length but directly proportional to the square root of the tension of the wire.

Reason— The frequency f of a stretched string is given by:

$\text{f} = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$

Where:

• L is the length of the string,
• T is the tension,
• $\mu$ is the linear mass density

Therefore, frequency of a stretched string is inversely proportional to its length but directly proportional to the square root of the tension of the wire.

Bend towards the normal.

Reason— Given:

• First medium: Refractive index n₁ = 1.33
• Second medium: Refractive index n₂ = 1.5
  Since n₂ > n₁ the second medium is optically denser.

When light travels obliquely from a rarer medium to a denser medium, it bends towards the normal.

Both A and R are true, and R is the correct explanation of A.

Explanation :
Assertion (A) is true: Most cameras use a convex lens, and when an object is placed beyond the centre of curvature (i.e., farther than 2F), the image formed is: Real, Inverted, Diminished and can be captured on a screen.

Reason (R) is true: The image formed is real, can be taken on a screen, and is diminished in size. That matches the properties of the image formed by a convex lens when the object is placed beyond 2F. So the Reason is also true.

high specific latent heat of fusion of ice.

Reason— Ice requires a large amount of heat energy to change from solid to liquid without a change in temperature. This is because it has a high specific latent heat of fusion—about 336 J/g. In high-altitude glaciers, even when temperatures rise slightly, the ice melts slowly and steadily over time, ensuring a continuous supply of water to rivers throughout the year.

$I_1 = I_2 = I_3$

Reason— In a series connection, the same current flows through each component, regardless of their resistances. This happens because there is only one path for the current.
∴ Current I is the same across all resistors, So $I_1 = I_2 = I_3$

2:3:6

Reason— A loop corresponds to half a wavelength, let length of string be $l$.

• Pattern P has 3 loops, so P has $l = \frac{3λ_1}{2} ⇒ λ_1= \frac{2l}{3}$
• Pattern Q has 2 loops, so Q has $l = \frac{2λ_2}{2} ⇒ λ_2=l$
• Pattern R has 1 loops, so R has $l = \frac{λ_3}{2} ⇒ λ_3=2l$

ratio $λ_1 : λ_2 : λ_3=\frac{2l}{3}:l:2l$ ⇒ $λ_1 : λ_2 : λ_3=2:3:6$

Only the P.E of the molecules increases, but the K.E remains the same.

Reason— When a substance changes from a solid to a liquid, the heat energy absorbed is used to overcome the intermolecular forces holding the solid particles together, thus increasing the potential energy (P.E.) of the molecules. However, the kinetic energy (K.E.), which relates to the vibrational motion of the molecules, does not change significantly during this phase change. The added energy goes entirely into breaking the bonds between the molecules, not into increasing their speed of vibration.

Both A and R are correct, but R is not the correct explanation of A

Explanation :
Assertion (A) is true: According to Oersted’s experiment and Ampere’s law, passing an electric current through a conductor generates concentric circular magnetic field lines around it.

Reason (R) is true: According to Faraday’s law of electromagnetic induction, A changing magnetic flux through a coil induces an electromotive force, hence a current.

Reason (R) describes electromagnetic induction (how a changing magnetic field induces current in a coil). Assertion (A) describes the generation of a magnetic field by a steady current. These are two distinct phenomenon, one is about field creation, the other about induced currents, so the Reason (R) does not explain the Assertion (A).

(c)

proton

electron

alpha particle

Reason — Charge on particles :

• Electron = - 1.6 X 10^-19 C
• proton = + 1.6 X 10^-19 C
• neutron = no charge
• alpha particle = + 3.2 X 10^-19 C