UPSC NDA-2

21. What is the maximum number of electrons in the M-Shell ?

What is the maximum number of electrons in the M-Shell ?

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6
8
18
32
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Electron shells are denoted by letters K, L, M, N, … or by principal quantum numbers n = 1, 2, 3, 4, … The K-shell corresponds to n=1, the L-shell to n=2, the M-shell to n=3, and so on. The maximum number of electrons that can occupy a shell with principal quantum number ‘n’ is given by the formula $2n^2$. For the M-shell, n=3, so the maximum number of electrons is $2 \times (3)^2 = 2 \times 9 = 18$.
The formula for the maximum number of electrons in a shell with principal quantum number ‘n’ is $2n^2$.
K-shell (n=1): $2 \times 1^2 = 2$ electrons.
L-shell (n=2): $2 \times 2^2 = 8$ electrons.
M-shell (n=3): $2 \times 3^2 = 18$ electrons.
N-shell (n=4): $2 \times 4^2 = 32$ electrons.
While the formula $2n^2$ gives the maximum capacity of a shell, the actual filling of electrons follows the Aufbau principle, Hund’s rule, and the Pauli exclusion principle, which dictates the filling order based on subshells (s, p, d, f) and energy levels. The outermost shell cannot accommodate more than 8 electrons (octet rule, with some exceptions), and the second last shell cannot accommodate more than 18 electrons.

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22. Rutherford’s alpha-particle ($\alpha$) scattering experiment was respo

Rutherford’s alpha-particle ($\alpha$) scattering experiment was responsible for the discovery of which one of the following ?

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Electron
Proton
Atomic Nucleus
Neutron
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Rutherford’s alpha-particle scattering experiment, also known as the Gold Foil experiment, involved firing alpha particles at a thin sheet of gold foil. Most of the alpha particles passed straight through the foil, some were deflected at small angles, and a very small number were deflected at large angles or even bounced back. These observations led Rutherford to propose the existence of a small, dense, positively charged core at the center of the atom, which he called the nucleus. This experiment was a crucial step in understanding the structure of the atom, replacing Thomson’s plum pudding model.
The key finding was that the atom’s positive charge and most of its mass are concentrated in a tiny volume at the center, causing the rare but significant deflections of the positively charged alpha particles.
Electrons were discovered by J.J. Thomson using cathode ray tubes. Protons were later identified as the positively charged particles within the nucleus. Neutrons were discovered by James Chadwick in 1932, much later than Rutherford’s experiment (conducted in 1909-1911, model proposed in 1911).

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23. Three equal resistors are connected in parallel configuration in a clo

Three equal resistors are connected in parallel configuration in a closed electrical circuit. Then the total resistance in the circuit becomes

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one-third of the individual resistance.
two-third of the individual resistance.
equal to the individual resistance.
three times of the individual resistance.
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When resistors are connected in parallel, the total resistance is calculated using the formula for parallel resistances. If three equal resistors, each with resistance R, are connected in parallel, the reciprocal of the total resistance ($R_{total}$) is the sum of the reciprocals of the individual resistances: $1/R_{total} = 1/R + 1/R + 1/R = 3/R$. Therefore, $R_{total} = R/3$. The total resistance becomes one-third of the individual resistance.
For ‘n’ equal resistors each of resistance ‘R’ connected in parallel, the total resistance is $R_{total} = R/n$. In this case, n=3, so $R_{total} = R/3$.
In contrast, if the resistors were connected in series, the total resistance would be the sum of the individual resistances: $R_{total} = R + R + R = 3R$. Connecting resistors in parallel decreases the total resistance of the circuit, while connecting them in series increases it.

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24. A uniform motion of a car along a circular path experiences

A uniform motion of a car along a circular path experiences

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a change in speed due to a change in its direction of motion.
a change in velocity due to a change in its direction of motion.
a change in momentum due to no change in its direction of motion.
a constant momentum due to a change in its direction of motion.
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Uniform motion along a circular path means the object moves at a constant speed. However, velocity is a vector quantity, defined by both magnitude (speed) and direction. In circular motion, the direction of motion is constantly changing as the object moves along the curve. Since the direction of motion is changing, the velocity of the car is also continuously changing, even though its speed is constant.
Speed is the magnitude of velocity. In uniform circular motion, speed is constant. Velocity is a vector (speed + direction). The direction of motion is always tangent to the circular path and continuously changes. Therefore, velocity changes. Momentum is mass times velocity (p = mv). Since velocity changes, momentum also changes.
Since the velocity is changing, there is acceleration. This acceleration is called centripetal acceleration, and it is directed towards the center of the circle. It is responsible for changing the direction of the velocity vector. Uniform circular motion is an example of accelerated motion even though the speed is constant.

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25. Work is said to be one Joule when a force of

Work is said to be one Joule when a force of

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4 N moves an object by 25 cm.
2 N moves an object by 1 m.
1 N moves an object by 1 cm.
1 N moves an object by 50 cm.
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Work done by a force is defined as the product of the force applied and the displacement of the object in the direction of the force. The SI unit of work is the Joule (J). One Joule of work is done when a force of one Newton (N) moves an object by one meter (m) in the direction of the force.
The formula for work (W) is W = F × d, where F is the force and d is the displacement in the direction of the force. 1 Joule = 1 Newton × 1 meter. We need to check which option results in W = 1 J.
Option A: F = 4 N, d = 25 cm = 0.25 m. W = 4 N × 0.25 m = 1 N·m = 1 J.
Option B: F = 2 N, d = 1 m. W = 2 N × 1 m = 2 J.
Option C: F = 1 N, d = 1 cm = 0.01 m. W = 1 N × 0.01 m = 0.01 J.
Option D: F = 1 N, d = 50 cm = 0.5 m. W = 1 N × 0.5 m = 0.5 J.
Work is a scalar quantity. If the force and displacement are not in the same direction, the work done is calculated as W = Fd cos(θ), where θ is the angle between the force and displacement vectors. In the context of this question, it is implied that the force and displacement are in the same direction.

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26. Fundamental laws of physics require

Fundamental laws of physics require

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conservation of energy and non-conservation of charge.
conservation of charge and non-conservation of linear momentum.
conservation of charge and non-conservation of energy.
conservation of energy, momentum and charge.
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Fundamental laws of physics are based on core principles, including several conservation laws. Energy, linear momentum, angular momentum, and electric charge are quantities that are conserved in isolated systems according to fundamental physical principles.
Conservation means that the total amount of the quantity remains constant over time within a closed system, even though it may be transformed or transferred between different forms or parts of the system. These conservation laws are derived from symmetries in nature and are cornerstones of physics.
Conservation of energy (first law of thermodynamics) states that energy cannot be created or destroyed, only transformed. Conservation of momentum (linear and angular) arises from Newton’s laws and implies that the total momentum of a system remains constant in the absence of external forces or torques. Conservation of charge states that the net electric charge of an isolated system remains constant.

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27. Weight and mass of an object are defined with Newton’s laws of motion.

Weight and mass of an object are defined with Newton’s laws of motion. Which among the following is true ?

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Weight is a constant of proportionality.
Mass is a constant of proportionality.
Mass is not a constant of proportionality.
Weight is a universal constant.
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Newton’s second law of motion states that the acceleration (a) of an object is directly proportional to the net force (F) acting on it and inversely proportional to its mass (m). Mathematically, F = ma. In this equation, mass (m) is the constant of proportionality relating the force to the acceleration it produces.
Mass is an intrinsic property of an object that measures its inertia (resistance to change in motion) and its gravitational pull. Weight (W) is the force exerted on an object due to gravity (W = mg), where g is the acceleration due to gravity.
Mass is a fundamental constant of proportionality in Newton’s second law and is a universal property of the object. Weight is a force and is not a universal constant; it varies depending on the strength of the gravitational field (value of g).

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28. Buoyancy is a/an

Buoyancy is a/an

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upward pressure
downward pressure
downward force
upward force
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Buoyancy is the upward force exerted by a fluid (liquid or gas) on an object immersed in it. This force opposes the weight of the object, which acts downwards.
According to Archimedes’ principle, the buoyant force is equal to the weight of the fluid displaced by the object. It is caused by the pressure difference between the bottom and top surfaces of the object due to the weight of the fluid column above them.
Pressure is force per unit area. While buoyancy arises from pressure differences, buoyancy itself is defined as a force. Forces have direction, and the buoyant force always acts upwards.

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29. Which one of the following viruses used to be responsible for highly i

Which one of the following viruses used to be responsible for highly infectious disease Smallpox ?

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Adenovirus
Variola virus
Aichi virus
Coxsackie virus
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Smallpox was a devastating infectious disease caused by the Variola virus. It was eradicated globally by 1980 due to a successful vaccination campaign led by the World Health Organization.
The Variola virus is a member of the Orthopoxvirus genus, which also includes vaccinia virus and monkeypox virus. Smallpox caused a characteristic rash, fever, and often led to severe scarring or death.
Adenoviruses cause various illnesses, primarily respiratory infections. Aichi virus is an enterovirus linked to gastroenteritis. Coxsackie viruses are also enteroviruses known for causing hand, foot, and mouth disease, and other conditions.

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30. Different varieties of the same gene are called

Different varieties of the same gene are called

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Genotypes
Sib pairs
Alleles
Isomers
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Alleles are different versions or forms of the same gene. They arise through mutations and are located at the same position (locus) on homologous chromosomes.
For example, the gene for flower color might have two alleles: one for purple flowers and one for white flowers. These different alleles determine the variation in traits observed within a population.
Genotype refers to the genetic makeup of an organism, i.e., the combination of alleles it possesses for a particular trait or set of traits. Sib pairs are simply siblings. Isomers are chemical compounds with the same molecular formula but different structural formulas.

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