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1. Which one of the following forces is non-central and non-conservative

Which one of the following forces is non-central and non-conservative ?

Frictional force

Electric force

Gravitational force

Mechanical force

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Frictional force is non-central and non-conservative.

A central force is one that acts along the line connecting the two interacting bodies or towards a fixed point. Gravitational and electrostatic forces between point masses/charges are examples of central forces. Frictional force acts parallel to the surfaces in contact, opposing relative motion, and is not necessarily directed along a line connecting centers or towards a fixed point, making it non-central.
A conservative force is one for which the work done in moving an object between two points is independent of the path taken. Work done by a conservative force over a closed loop is zero. Electric and gravitational forces are conservative. Frictional force dissipates energy as heat; the work done by friction depends on the path taken and is always negative (it opposes motion), meaning it is a non-conservative force.

Mechanical force is a very general term and can encompass various specific forces, some of which might be conservative (like elastic spring force) or non-conservative (like applied force doing work against friction). Therefore, ‘Mechanical force’ itself is not specific enough to be definitively classified as non-central and non-conservative; its nature depends on the specific force being considered.

2. The focal length of the objective lens of a telescope is 50 cm. If the

The focal length of the objective lens of a telescope is 50 cm. If the magnification of the telescope is 25, then the focal length of the eye-piece is

12.5 cm

5 cm

2 cm

10 cm

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The focal length of the eye-piece is 2 cm.

For a refracting telescope used in normal adjustment (final image at infinity), the angular magnification (M) is given by the ratio of the focal length of the objective lens (f_o) to the focal length of the eye-piece lens (f_e): M = f_o / f_e.
Given f_o = 50 cm and M = 25.
We can rearrange the formula to solve for f_e: f_e = f_o / M.
Substituting the given values: f_e = 50 cm / 25 = 2 cm.

A telescope achieves magnification by using an objective lens with a long focal length and an eye-piece lens with a short focal length. The objective forms a real, inverted image of a distant object at its focal plane, and the eye-piece acts as a magnifying glass to view this intermediate image.

3. Light year is a unit of measurement of

Light year is a unit of measurement of

very large distances

time interval in years

amount of light received on earth in a year

mass of atoms

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Light year is a unit of measurement of very large distances.

A light-year is defined as the distance that light travels in vacuum in one Julian year (365.25 days). It is a unit of length used to express astronomical distances.

The speed of light in vacuum is approximately 3 x 10⁸ meters per second. One light-year is approximately equal to 9.461 x 10¹² kilometers or 5.879 x 10¹² miles. This unit is convenient for measuring the vast distances between stars and galaxies.

4. Consider the following statements about a solenoid: 1. The magnetic

Consider the following statements about a solenoid:

1. The magnetic field strength in a solenoid depends upon the number of turns per unit length in the solenoid
2. The magnetic field strength in a solenoid depends upon the current flowing in the wire of the solenoid
3. The magnetic field strength in a solenoid depends upon the diameter of the solenoid

Which of the statements given above are correct ?

1, 2 and 3

1 and 3 only

2 and 3 only

1 and 2 only

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Statements 1 and 2 are correct.

The magnetic field strength inside a long solenoid is given by the formula B ≈ μ₀ * n * I, where μ₀ is the permeability of free space, n is the number of turns per unit length (n = N/L), and I is the current flowing through the solenoid.
Statement 1 is correct as B is directly proportional to n (number of turns per unit length).
Statement 2 is correct as B is directly proportional to I (current).
Statement 3 is incorrect. For an ideal long solenoid, the magnetic field strength inside the solenoid (away from the ends) does not depend on its diameter. While the diameter might have minor effects in non-ideal cases (finite length solenoid, field near ends), the standard formula and theoretical treatment indicate no dependence on diameter for the uniform field inside a long solenoid.

The formula B = μ₀nI is an approximation that holds well for solenoids whose length is much greater than their diameter. In such cases, the magnetic field is strong, uniform inside (except near the ends), and zero outside.

5. Two metallic wires A and B are made using copper. The radius of wire A

Two metallic wires A and B are made using copper. The radius of wire A is r while its length is l. A dc voltage V is applied across the wire A, causing power dissipation, P. The radius of wire B is 2r and its length is 2l and the same dc voltage V is applied across it causing power dissipation, P₁. Which one of the following is the correct relationship between P and P₁?

P = 2P₁

P = P₁/2

P = 4P₁

P = P₁

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The correct relationship is P = P₁/2.

The resistance of a wire is given by R = ρ * (l / A), where ρ is resistivity, l is length, and A is the cross-sectional area (A = πr²). Power dissipated is P = V²/R.
For wire A: R_A = ρ * (l / (πr²)). Power P = V² / R_A = V² / [ρ * (l / (πr²))] = (V²πr²) / (ρl).
For wire B: radius is 2r, length is 2l. R_B = ρ * (2l / (π(2r)²)) = ρ * (2l / (4πr²)) = ρ * (l / (2πr²)).
Power P₁ = V² / R_B = V² / [ρ * (l / (2πr²))] = (2V²πr²) / (ρl).
Comparing P and P₁: P₁ = 2 * [(V²πr²) / (ρl)].
Since P = (V²πr²) / (ρl), we have P₁ = 2P. This relationship can be rewritten as P = P₁/2.

The resistance of wire B is half the resistance of wire A (R_B = (ρl / (2πr²)) compared to R_A = (ρl / (πr²))). Since power is inversely proportional to resistance for a constant voltage (P = V²/R), lower resistance leads to higher power dissipation. Therefore, wire B dissipates more power than wire A when the same voltage is applied.

6. The following 3 (three) items consist of two statements, Statement I a

The following 3 (three) items consist of two statements, Statement I and Statement II. Examine these two statements carefully and select the correct answer using the code given below :
Statement I : Abul Fazl shaped, represented and arti-culated the ideas associated with the reign of Akbar
Statement II : The qualities of Abul Fazl impressed Akbar who found the former suitable as an adviser and spokesperson for his policies

Code :

Both the statements are indivi-dually true and Statement II is the correct explanation of Statement I

Both the statements are indivi-dually true and Statement II is NOT the correct explanation of Statement I

Statement I is true but Statement II is false

Statement I is false but Statement II is true

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Both statements are individually true, and Statement II is the correct explanation of Statement I.

Statement I is true because Abul Fazl, as Akbar’s court historian and confidante, played a crucial role in articulating and documenting Akbar’s philosophical and administrative ideas, particularly his concept of Sulh-i-Kul (universal peace) and divine sovereignty (Farr-i-Izadi). His works, like Akbarnama and Ain-i-Akbari, are primary sources for understanding Akbar’s reign and thoughts. Statement II is also true. Akbar was highly impressed by Abul Fazl’s intellectual capabilities, writing skills, and administrative acumen, leading him to rely on Abul Fazl as a principal advisor and the official chronicler and spokesperson for his policies and reign.

Statement II provides the reason why Statement I is true. Abul Fazl was able to shape, represent, and articulate Akbar’s ideas precisely because Akbar recognized his qualities and appointed him to positions of trust and influence, making him the official interpreter and promoter of the emperor’s vision.

7. Who among the following historians have described the Quit India movem

Who among the following historians have described the Quit India movement as a ‘spontaneous revolution’ ?

Gordon Johnson

David Arnold

F G Hutchins

Peter Robb

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The historian F G Hutchins is known for describing the Quit India Movement as a ‘spontaneous revolution’.

Hutchins argued that the movement was not centrally planned by the Congress leadership but rather arose spontaneously from the popular frustration and discontent following the arrest of major leaders and the failure of the Cripps Mission.

While many historians acknowledge the widespread and spontaneous nature of the popular resistance during the Quit India Movement, interpretations vary regarding the extent of prior planning or the role of different political groups. However, F.G. Hutchins is specifically associated with the term “spontaneous revolution” in this context.

8. Which of the following is/are environmental effects of Rotation of the

Which of the following is/are environmental effects of Rotation of the Earth ?

1. Daily or diurnal rhythm in day-light and air temperature
2. Flow path of both air and water are turned consistently in a side-ward direction
3. The movement of the tides

Select the correct answer using the code given below :

1 and 2 only

1 and 3 only

1, 2 and 3

3 only

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The rotation of the Earth on its axis has several significant environmental effects. These include:
1. Creating the cycle of day and night, leading to diurnal variations in sunlight and thus air temperature (daily rhythm).
2. Causing the Coriolis effect, which deflects moving objects (like air and water currents) to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. This influences wind patterns, ocean currents, and even the flow of rivers over long distances.
The movement of tides is primarily caused by the gravitational pull of the Moon and the Sun. While Earth’s rotation influences the timing and frequency of tides experienced at a particular location, the tidal bulges themselves are a result of gravitational forces, not Earth’s rotation directly causing the water movement as its primary effect in this context.

– Rotation causes day-night cycles (diurnal rhythm).
– Rotation causes the Coriolis effect, deflecting air and water flows.
– Tides are primarily caused by gravitational forces from the Moon and Sun.

The Coriolis effect is a fundamental concept in meteorology and oceanography, explaining large-scale weather patterns like cyclones and the direction of ocean currents. The interaction of Earth’s rotation with tidal forces contributes to phenomena like tidal currents and the timing of high/low tides, but the fundamental cause of the tidal bulge is gravity.

10. River Sarda drains in the Northern Plains of Uttar Pradesh. Before ent

River Sarda drains in the Northern Plains of Uttar Pradesh. Before entering in the Plains, Sarda is known as

Saraswati

Bhagirathi

Kali

Pindar

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The Sarda River is also known as the Mahakali River or Kali Ganga in its upper reaches. It originates in the Pithoragarh district of Uttarakhand, India, and flows along the border between Nepal and India. Before it descends into the plains near Banbasa, it is predominantly referred to as the Kali River. In the plains of Uttar Pradesh, it takes the name Sarda or Sharda.

– The Sarda River serves as a border river between India and Nepal.
– Its upper course is known as Kali or Mahakali River.
– It enters the Indian plains in Uttarakhand and flows through Uttar Pradesh.

The Kali River meets the Gori Ganga River at Jauljibi, and further downstream, it meets the Sarayu River at Pancheshwar. It is a major tributary of the Ghaghara River, which eventually joins the Ganga River.