UPSC NDA-1 Archives

21. If the potential difference applied to an X-ray tube is doubled while

If the potential difference applied to an X-ray tube is doubled while keeping the separation between the filament and the target as same, what will happen to the cutoff wavelength?

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Will remain same

Will be doubled

Will be halved

Will be four times of the original wavelength

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The question asks what happens to the cutoff wavelength of X-rays produced in an X-ray tube if the potential difference is doubled while keeping the filament-target separation the same.

The production of X-rays in an X-ray tube involves accelerating electrons through a potential difference ($V$) and making them strike a target. The energy gained by an electron accelerated through potential $V$ is $eV$, where $e$ is the elementary charge. This energy is converted into electromagnetic radiation (X-rays) and heat. The minimum wavelength ($\lambda_{min}$) of the emitted X-rays, also known as the cutoff wavelength or Duane-Hunt limit, occurs when the entire energy of the electron is converted into a single X-ray photon. The energy of a photon is $hf = hc/\lambda$, where $h$ is Planck’s constant, $f$ is frequency, $c$ is the speed of light, and $\lambda$ is the wavelength.
According to the Duane-Hunt law: $eV = hc/\lambda_{min}$
This equation shows that the cutoff wavelength $\lambda_{min}$ is inversely proportional to the applied potential difference $V$: $\lambda_{min} \propto 1/V$.
If the potential difference is doubled, i.e., $V’ = 2V$, the new cutoff wavelength $\lambda’_{min}$ will be:
$\lambda’_{min} = \frac{hc}{e(2V)} = \frac{1}{2} \left(\frac{hc}{eV}\right) = \frac{1}{2} \lambda_{min}$
So, the cutoff wavelength will be halved. The separation between the filament and the target does not directly affect the cutoff wavelength, which is determined by the maximum energy of the electrons reaching the target, dictated by the potential difference.

The X-ray spectrum produced consists of a continuous spectrum (bremsstrahlung) with a minimum wavelength $\lambda_{min}$ and characteristic peaks at specific wavelengths. The cutoff wavelength depends only on the accelerating voltage, while the intensity and characteristic peaks also depend on the target material and the electron beam current.

22. A Kelvin thermometer and a Fahrenheit thermometer both give the same r

A Kelvin thermometer and a Fahrenheit thermometer both give the same reading for a certain sample. What would be the corresponding reading in a Celsius thermometer?

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574

301

273

232

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The question states that a Kelvin thermometer and a Fahrenheit thermometer give the same reading for a certain sample and asks for the corresponding reading in Celsius.

Let the reading on both the Kelvin and Fahrenheit scales be $x$.
The conversion formula from Celsius ($T_C$) to Kelvin ($T_K$) is $T_K = T_C + 273.15$. For many problems, 273 is used as an approximation, but using 273.15 gives a more precise answer.
The conversion formula from Celsius ($T_C$) to Fahrenheit ($T_F$) is $T_F = \frac{9}{5} T_C + 32$.
We are given $T_K = T_F = x$. So, we have two equations:
1) $x = T_C + 273.15$
2) $x = \frac{9}{5} T_C + 32$
Set the two expressions for $x$ equal to each other:
$T_C + 273.15 = \frac{9}{5} T_C + 32$
$273.15 – 32 = \frac{9}{5} T_C – T_C$
$241.15 = (\frac{9}{5} – 1) T_C$
$241.15 = (\frac{9-5}{5}) T_C$
$241.15 = \frac{4}{5} T_C$
$T_C = \frac{241.15 \times 5}{4} = \frac{1205.75}{4} = 301.4375$
The question asks for the reading in a Celsius thermometer. The calculated value is approximately 301.44. Among the given options, 301 is the closest value.

If we use the approximation $T_K = T_C + 273$, the calculation becomes:
$T_C + 273 = \frac{9}{5} T_C + 32$
$273 – 32 = \frac{4}{5} T_C$
$241 = \frac{4}{5} T_C$
$T_C = \frac{241 \times 5}{4} = \frac{1205}{4} = 301.25$
This value is also very close to 301. This confirms that 301 is the most likely intended answer, allowing for slight rounding or the use of an approximation in the original question setting.

23. Which one of the following is the correct relation between frequency $

Which one of the following is the correct relation between frequency $f$ and angular frequency $\omega$?

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$f = piomega$

$omega = 2pi f$

$f = 2omega/pi$

$f = 2piomega$

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The question asks for the correct relation between frequency ($f$) and angular frequency ($\omega$).

Frequency ($f$) represents the number of cycles or revolutions per unit of time (usually per second), measured in Hertz (Hz).
Angular frequency ($\omega$) represents the rate of rotation or oscillation in terms of angle per unit of time (usually radians per second), measured in rad/s.
One complete cycle or revolution corresponds to an angle of $2\pi$ radians. If $f$ cycles occur per second, then the total angle covered per second is $f \times (2\pi)$ radians.
Therefore, the angular frequency $\omega$ is related to the frequency $f$ by the equation:
$\omega = 2\pi f$

Angular frequency is commonly used in physics and engineering, particularly when dealing with circular motion, oscillations (like simple harmonic motion), and waves. It simplifies many equations compared to using frequency directly, especially in the context of derivatives and integrals involving sinusoidal functions. The unit of angular frequency is radians per second (rad/s), whereas the unit of frequency is Hertz (Hz) or cycles per second.

24. Suppose a rod is given a negative charge by rubbing it with wool. Whic

Suppose a rod is given a negative charge by rubbing it with wool. Which one of the following statements is correct in this case ?

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The positive charges are transferred from rod to wool

The positive charges are transferred from wool to rod

The negative charges are transferred from rod to wool

The negative charges are transferred from wool to rod

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The question describes a rod being given a negative charge by rubbing it with wool and asks about the charge transfer process.

When two different materials are rubbed together, electrons can be transferred from one material to the other due to differences in their electron affinities. This process is called charging by friction or triboelectric effect. If the rod gains a negative charge, it means it has received negative charge carriers, which are electrons. Since positive charges (protons) are fixed within the nucleus of atoms in the solid material, they are generally not transferred during rubbing. Therefore, the negative charge acquired by the rod must come from the wool.
– If the rod becomes negatively charged, it has *gained* electrons.
– These electrons must have come from the wool.
So, negative charges (electrons) are transferred from the wool to the rod. The wool loses electrons and becomes positively charged.

The triboelectric series lists materials in order of their tendency to gain or lose electrons when rubbed. Materials higher on the list tend to lose electrons and become positively charged, while materials lower on the list tend to gain electrons and become negatively charged. Wool is typically higher than many common materials like plastic or ebonite (used for rods), indicating it tends to lose electrons to these materials when rubbed.

25. Which one of the following States does NOT have the Headquarters of an

Which one of the following States does NOT have the Headquarters of any Railway Zone ?

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Jharkhand

Chhattisgarh

Odisha

Bihar

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The question asks which state among the given options does not have the headquarters of any Railway Zone.

Let’s check the locations of Railway Zone Headquarters among the given states:
A) **Jharkhand:** Does not host the headquarters of any Zonal Railway. Ranchi is a divisional headquarters.
B) **Chhattisgarh:** Bilaspur is the headquarters of the South East Central Railway (SECR).
C) **Odisha:** Bhubaneswar is the headquarters of the East Coast Railway (ECoR).
D) **Bihar:** Hajipur is the headquarters of the East Central Railway (ECR).
Thus, Jharkhand is the state that does not have the headquarters of any Railway Zone among the options provided.

As of the latest information, Indian Railways is divided into 18 zones, each headed by a General Manager. The headquarters are spread across various cities and states in India. The states in the options that have Zonal HQs are Chhattisgarh (Bilaspur), Odisha (Bhubaneswar), and Bihar (Hajipur).

26. Which of the following regions is/are NOT known for cotton-textile ind

Which of the following regions is/are NOT known for cotton-textile industry ?
1. Mumbai – Pune region
2. Madurai – Coimbatore region
3. Dhanbad – Jamshedpur region
4. Indore – Ujjain region
Select the correct answer using the code given below :

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1 and 3

2 and 3

1, 2 and 4

3 only

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The question asks which region(s) among the given options are *not* known for the cotton-textile industry.

1. **Mumbai – Pune region:** Mumbai has historically been a major center for the cotton textile industry in India (“Manchester of India”). The surrounding region, including Pune, is also associated with this industry.
2. **Madurai – Coimbatore region:** This region in Tamil Nadu is a very prominent textile hub, particularly for cotton textiles, and Coimbatore is often referred to as the “Manchester of South India”.
3. **Dhanbad – Jamshedpur region:** Located in Jharkhand, this region is the heart of India’s coal mining and heavy industries, particularly known for iron and steel production (Jamshedpur hosts the Tata Steel plant). It is not known for cotton textiles.
4. **Indore – Ujjain region:** Situated in Madhya Pradesh, this region is part of the cotton-growing belt and has established cotton textile mills.
Therefore, the Dhanbad – Jamshedpur region is the one not primarily associated with the cotton-textile industry.

The location of the cotton textile industry is influenced by factors such as proximity to raw materials (cotton growing areas), market, transport facilities, labor availability, and capital. Historically, port cities like Mumbai gained prominence due to import of machinery and export of finished goods. Interior locations developed based on proximity to raw cotton production.

27. Which of the following are the major coral reef areas of India ? 1. Gu

Which of the following are the major coral reef areas of India ?
1. Gulf of Kachchh
2. Gulf of Mannar
3. Lakshadweep
4. Andaman and Nicobar Islands
Select the correct answer using the code given below :

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1 and 3 only

2 and 4 only

1, 2 and 3 only

1, 2, 3 and 4

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The question asks to identify the major coral reef areas of India from the given options.

India has four major coral reef regions:
1. **Gulf of Kachchh:** Located on the west coast.
2. **Gulf of Mannar:** Located on the southeast coast, between India and Sri Lanka.
3. **Lakshadweep Islands:** An archipelago of coral islands in the Arabian Sea.
4. **Andaman and Nicobar Islands:** Located in the Bay of Bengal, known for extensive fringing and barrier reefs.
All four options provided are indeed major coral reef areas in India.

Coral reefs are diverse underwater ecosystems held together by calcium carbonate structures secreted by corals. They are found in warm, shallow, clear, sunny, and agitated waters. These ecosystems are among the most biologically diverse on Earth, providing habitat for a vast array of marine life and protecting coastlines from erosion. Threats to coral reefs include climate change (coral bleaching), pollution, unsustainable fishing practices, and habitat destruction.

28. Match List I with List II and select the correct answer using the code

Match List I with List II and select the correct answer using the code given below the Lists :

List I (Place)	List II (Mineral)
A. Lakwa	1. Copper
B. Malanjkhand	2. Petroleum
C. Kalakot	3. Zinc
D. Zawar	4. Coal

Code :

	A	B	C	D
(a)	3	4	1	2
(b)	3	1	4	2
(c)	2	1	4	3
(d)	2	4	1	3

(a)

(b)

(c)

(d)

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The correct matching code is A-2, B-1, C-4, D-3. This corresponds to option (d) in the provided code table.

This question tests knowledge of important mineral locations in India.

– Lakwa is an oil field located in Assam, known for petroleum extraction (Match A-2).
– Malanjkhand is a well-known region in Madhya Pradesh famous for its large copper reserves and mining operations (Match B-1).
– Kalakot is a location in the Jammu region of Jammu and Kashmir, historically known for its coal deposits and mining (Match C-4).
– Zawar is a historic mining area near Udaipur in Rajasthan, renowned for its zinc and lead mines, active since ancient times (Match D-3).
Thus, the correct match is A-2, B-1, C-4, D-3, which corresponds to option (d) in the question’s code table.

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29. Which one of the following was NOT a feature of the Subsidiary Allianc

Which one of the following was NOT a feature of the Subsidiary Alliance of Lord Wellesley ?

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The British were responsible for protecting the ally from any external threats

All internal threats were to be handled by the ally alone, with no help from the British

The ally was to provide resources for maintaining a British armed contingent stationed in its territory

The ally could not enter into any agreement with other rulers without the permission of the British

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The statement that all internal threats were to be handled by the ally alone, with no help from the British, was NOT a feature of the Subsidiary Alliance system.

The Subsidiary Alliance was a treaty system implemented by the British East India Company, primarily by Lord Wellesley, to bring Indian states under their control. Under this system, the Indian ruler had to accept British paramountcy and adhere to certain terms in exchange for protection.

A key provision of the Subsidiary Alliance was that the British promised to protect the allied state from *both* external aggression and internal rebellion. This provision for British assistance against internal threats was a crucial aspect that allowed the British to intervene in the internal affairs of the allied state and gradually undermine the ruler’s authority and control over his own subjects and army. Options A, C, and D correctly describe features of the Subsidiary Alliance: the British guaranteed protection from external threats (A), the ally had to pay for the British contingent (C), and the ally could not enter into treaties without British permission (D).

30. Which one of the following was NOT a cause of the Revolt of 1857 ?

Which one of the following was NOT a cause of the Revolt of 1857 ?

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The rumour that the British had mixed the bone dust of cows and pigs into the flour being sold in the market

The prophecy that British rule would come to an end on the centenary of the Battle of Plassey on 23rd June, 1857

Popular discontent with British rule

The prophecy that the end of British rule would lead to the end of the Kali Yuga and the return of Ram Rajya

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The prophecy that the end of British rule would lead to the end of the Kali Yuga and the return of Ram Rajya was NOT a known cause of the Revolt of 1857.

The Revolt of 1857 had multiple causes, including political grievances, economic exploitation, social and religious factors, and military issues. Rumours, prophecies, and popular discontent played a significant role in igniting and spreading the rebellion.

Options A, B, and C are all widely recognized causes or contributing factors to the Revolt of 1857. The rumour about greased cartridges and contaminated flour (A) was a major immediate trigger, playing on religious fears. The belief tied to the centenary of the Battle of Plassey (B) reflects the anti-British sentiment and anticipation of the end of their rule. Popular discontent (C) was a pervasive underlying cause stemming from decades of British policies. While the revolt had religious dimensions and rebels often fought for the restoration of traditional rule (like the Mughal Emperor or Maratha Peshwa), the specific prophecy regarding Kali Yuga and Ram Rajya (D) is not typically listed among the established major causes or motivating factors of the revolt in historical accounts.