Search Previous Year Questions

Calculation:

Given that light travels through carbon disulfide, its refractive index n_cs is greater than 1.

Using the formula n = c / v, we can write:

⇒ n_cs = Y / X

Since n_cs > 1:

⇒ Y / X > 1

⇒ Y > X

∴ The speed of light in carbon disulfide (X) is less than the speed of light in vacuum (Y).

The correct answer is: Option 1) X < Y

CONCEPT:

Right-hand thumb rule:

• According to this rule, if we imagine the linear wire conductor to be held in the grip of the right hand so that the thumb points in the direction of the current, then the curvature of the fingers around the conductor will represent the direction of the magnetic field lines.

EXPLANATION:

• If the current through a horizontal power line flows in the east to west direction, then the direction of the magnetic field at a point directly below it will be from north to south. Therefore option 2 is correct.

The correct answer is Copper.

Key Points

• The earliest historical evidence of the use of metal in Indian history is of Chalcolithic Age or Stone-Copper Age, which covered the period from 3500 to 1000 BC.
• It is the first element to be discovered in metallurgy.
• Copper and its alloys were also used to create copper-bronze images such as Buddhas or Hindu/Mahayana Buddhist deities.
• Later, Tin was mixed with copper and bronze appeared which was stronger metal than both tin and copper.

Additional Information

• Chalcolithic Age - 
• ​Chalcolithic means the use of copper and stone.
• The Chalcolithic period was a transition between the Stone Age and the Metal age.
• This was the period in which stone tools were losing their significance and, copper tools were finding grounds.
• The presence of painted pottery is a hallmark of the Chalcolithic period.

Calculation:

Using Snell's Law:

n₁ sinθ₁ = n₂ sinθ₂

⇒ Since n₂ > n₁, sinθ₂ < sinθ₁.

⇒ θ₂ < θ₁ (angle of refraction is smaller).

⇒ The light ray bends towards the normal.

Key Points

• The cause of refraction is a change in light speed and wherever the light speed changes most, the refraction is greatest.
• The speed is related to the optical density of a material that is related to the index of refraction of a material.
• Air is the least dense material (lowest index of refraction value) and water is the denser material (largest index of refraction value).
• Thus, it would be reasonable that the most refraction occurs for the transmission of light across an air-water boundary.
• Hence, the angle of refraction will be smaller than the angle of incidence.

Important Points

• Refraction:
• ​When a ray of light passes from one medium to another it suffers a change in direction at the boundary of two mediam is called refraction.
• The change in direction because the speed of light travels at different speeds in different mediums.
• The Refractive Index of a medium defines that it is denser or rarer.

​

Conclusion:

∴ The correct answer is Option 1: Bending towards the normal.

Explanation:

Verification of Given Equations:

1. s = ut + (1/2)at²: This is a standard equation of motion and is correct.

2. u = v - at: Rearranging the first equation of motion (v = u + at), we get u = v - at. This equation is correct.

3. u² - v² = 2as: Rearranging the third equation of motion (v² = u² + 2as), we get u² - v² = -2as. The negative sign is missing; hence, this equation is NOT correct.

4. Distance traveled during the n^th second = u + (1/2)a(2n - 1): This is a standard equation of motion and is correct.

∴ The incorrect equation is Option 3: u² - v² = 2as.

Concept Used:

Ammeter:

An ammeter is used to measure current in a circuit.

It is always connected in series with the circuit.

It has low resistance to ensure it does not alter the current flow.

Voltmeter:

A voltmeter is used to measure the voltage across a circuit component.

It is always connected in parallel to the component being measured.

It has high resistance to ensure minimal current flows through it.

∴ The incorrect statement is Statement 4.

Concept Used:

Conventional Energy Sources:

Derived from fossil fuels such as coal, petroleum, and natural gas.

Widely used but non-renewable and environmentally harmful.

Non-Conventional Energy Sources:

Renewable and environmentally friendly sources like solar energy, wind energy, tidal energy, geothermal energy, etc.

Tidal energy harnesses the movement of ocean tides to generate electricity.

Reasoning:

Petroleum, Natural Gas, and Coal are conventional sources of energy because they are derived from fossil fuels.

Tidal Energy is a non-conventional source of energy as it is renewable and does not rely on fossil fuels.

∴ The correct answer is Option 3: Tidal Energy.

Concept Used:

When resistors are connected in parallel, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances.

Formula:

1 / R_eq = 1 / R₁ + 1 / R₂ + 1 / R₃

Calculation:

Using the formula:

1 / R_eq = 1 / 1 + 1 / 1 + 1 / 1

⇒ 1 / R_eq = 1 + 1 + 1

⇒ 1 / R_eq = 3

⇒ R_eq = 1 / 3 Ω

∴ Equivalent Resistance, R_eq = 1 / 3 Ω

Concept:

Echo: An echo is the reflection of sound that arrives at the listener after a delay, caused by the sound wave bouncing off a surface.

Reflection of sound: When sound waves hit a hard surface, they bounce back, creating a reflected sound wave.

Conditions for echo formation:

The distance between the source and reflecting surface should be at least 17.2 meters (for sound velocity ~344 m/s).

The surface should be large and hard.

∴ he correct answer is Option 2: Reflection of sound waves.

Calculation:

Given:

Uniform speed ⇒ Velocity (v) is constant

Using the formula for acceleration:

a = dv/dt

⇒ Since v is constant, dv = 0

⇒ a = 0

∴ At uniform speed, acceleration is Zero.

The correct answer should be Option 3: Zero.