UPSC NDA-2

41. Two forces, one of 3 newton and another of 4 newton are applied on a s

Two forces, one of 3 newton and another of 4 newton are applied on a standard 1 kg body, placed on a horizontal and frictionless surface, simultaneously along the x-axis and the y-axis, respectively, as shown below:
The magnitude of the resultant acceleration is:

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7 m/s²
1 m/s²
5 m/s²
√7 m/s²
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UPSC NDA-2 – 2015
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The correct option is C, 5 m/s².
Two forces are applied simultaneously and are perpendicular to each other (along the x and y axes). The resultant force is the vector sum of these forces. Since they are perpendicular, the magnitude of the resultant force (F_resultant) is found using the Pythagorean theorem: F_resultant = $\sqrt{F_x^2 + F_y^2}$. Given F_x = 3 N and F_y = 4 N, F_resultant = $\sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$ N. According to Newton’s second law of motion, the acceleration (a) of an object is directly proportional to the net force (F) acting on it and inversely proportional to its mass (m) (a = F/m). For a 1 kg body with a resultant force of 5 N, the magnitude of the acceleration is a = 5 N / 1 kg = 5 m/s².
The direction of the resultant force (and thus acceleration) would be at an angle to the x-axis, given by θ = atan(Fy/Fx) = atan(4/3). However, the question only asks for the magnitude of the acceleration. This problem illustrates how to find the resultant of perpendicular forces and apply Newton’s second law.

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42. To weld metals together, high temperature is required. Such a high tem

To weld metals together, high temperature is required. Such a high temperature is obtained by burning:

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Acetylene in oxygen
LPG in oxygen
Methane in oxygen
Acetylene in nitrogen
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The correct option is A, Acetylene in oxygen.
Welding requires a high-temperature flame to melt and fuse metals. The combustion of acetylene (C₂H₂) with oxygen (O₂) produces an oxy-acetylene flame, which can reach temperatures of around 3500 °C, making it suitable for welding. Other fuel gases like LPG and methane produce lower temperatures when burned with oxygen. Burning acetylene in nitrogen would not sustain combustion as nitrogen is inert and would not provide the necessary oxidant.
Oxy-acetylene welding is a common process used for welding, cutting, and heating metals. The high temperature is achieved by using pure oxygen as the oxidant instead of air, which contains about 78% nitrogen and would limit the flame temperature. Different ratios of acetylene to oxygen can produce oxidizing, neutral, or carburizing flames, used for various applications.

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43. Which one of the following statements is not correct?

Which one of the following statements is not correct?

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Temperatures decrease from the equator to poles
Temperatures in equatorial regions change substantially from January to July
Large land masses located in the subarctic and arctic zones develop centres of extremely low temperatures in winter
Highlands are always colder than surrounding low lands
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Statement B is not correct. Temperatures in equatorial regions exhibit very little seasonal variation because the sun’s rays are always close to vertical throughout the year. Seasonal temperature changes are much more pronounced at higher latitudes due to the varying angle of sunlight and length of day/night.
This question tests knowledge of geographical factors influencing temperature distribution and variation across the globe.
Statement A is correct; average temperatures generally decrease with increasing latitude. Statement C is correct; large landmasses in high latitudes experience extreme cold winters due to continentality and long periods without sunlight. Statement D is correct; temperature generally decreases with increasing altitude due to the atmospheric lapse rate.

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44. Conservation of momentum in a collision between particles can be under

Conservation of momentum in a collision between particles can be understood on the basis of:

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Newton's first law of motion
Newton's second law of motion only
Both Newton's second law of motion and Newton's third law of motion
Conservation of energy
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Conservation of momentum for a system of particles is a direct consequence of Newton’s laws of motion. Specifically, when particles collide, the forces they exert on each other are internal forces within the system. Newton’s third law states that these forces are equal in magnitude and opposite in direction (action-reaction). Applying Newton’s second law (F = dp/dt) to each particle and summing over the system shows that the net internal force is zero, meaning the total momentum (sum of momenta of all particles) remains constant in the absence of external forces. Thus, conservation of momentum stems from both Newton’s second and third laws.
Conservation of momentum for a system relies on the principle of action-reaction (Newton’s third law) and the relationship between force and change in momentum (Newton’s second law).
Newton’s first law describes inertia. Conservation of energy is a separate fundamental principle, although in elastic collisions, both momentum and kinetic energy are conserved. In inelastic collisions, only momentum is conserved (assuming no external forces).

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45. Which of the following statements regarding heavy water are correct?

Which of the following statements regarding heavy water are correct?

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  • 1. It is extensively used as a moderator in nuclear reactors
  • 2. It cannot be used in exchange reaction to study reaction mechanism
  • 3. Viscosity of heavy water is relatively smaller than that of ordinary water
  • 4. The dielectric constant of heavy water is smaller than that of ordinary water

Select the correct answer using the code given below:

1 and 2
2 and 3
3 and 4
1 and 4
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UPSC NDA-2 – 2015
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Statement 1 is correct: Heavy water (D₂O) is an excellent moderator in nuclear reactors because deuterium has a low neutron absorption cross-section and can effectively slow down fast neutrons to thermal energies. Statement 2 is incorrect: Heavy water and deuterated compounds are commonly used in isotopic exchange reactions to study reaction mechanisms and kinetics. Statement 3 is incorrect: The viscosity of heavy water is slightly higher than that of ordinary water at typical temperatures. Statement 4 is correct: The dielectric constant of heavy water is slightly smaller than that of ordinary water.
This question tests specific properties of heavy water compared to ordinary water.
Heavy water is chemically similar to ordinary water but has different physical properties due to the heavier deuterium isotope replacing hydrogen. It is essential for some types of nuclear reactors (like CANDU reactors) that use unenriched uranium fuel.

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46. Which one of the following describes the Lithosphere?

Which one of the following describes the Lithosphere?

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Upper and lower mantle
Crust and upper mantle
Crust and core
Mantle and core
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The Lithosphere is defined as the rigid outer part of the Earth, consisting of the crust and the uppermost part of the mantle. It is situated above the asthenosphere, which is a more ductile layer of the upper mantle.
Understanding the layered structure of the Earth (Crust, Mantle, Core) and the physical properties of these layers (Lithosphere, Asthenosphere, Mesosphere, etc.) is key.
The lithosphere is broken into tectonic plates that move over the asthenosphere. The thickness of the lithosphere varies, being thinner under oceanic crust and thicker under continental crust.

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47. The resistance of a wire of length / and area of cross-section a is x

The resistance of a wire of length / and area of cross-section a is x ohm. If the wire is stretched to double its length, its resistance would become:

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2x ohm
0.5 x ohm
4x ohm
6x ohm
This question was previously asked in
UPSC NDA-2 – 2015
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The resistance (R) of a wire is given by R = ρ * (l/a), where ρ is resistivity, l is length, and a is cross-sectional area. If the wire is stretched to double its length (l’ = 2l), its volume (V = a * l) remains constant. So, a’ * l’ = a * l => a’ * (2l) = a * l => a’ = a/2. The new resistance is R’ = ρ * (l’/a’) = ρ * (2l / (a/2)) = ρ * (4l/a) = 4 * (ρ * l/a) = 4x.
When a wire is stretched, its length increases, and its cross-sectional area decreases while its volume remains constant. This significantly increases its resistance.
The resistance is directly proportional to length and inversely proportional to cross-sectional area. Stretching the wire affects both parameters simultaneously.

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48. Carbon and energy requirements of autotrophic organisms are fulfilled

Carbon and energy requirements of autotrophic organisms are fulfilled by:

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Photosynthesis
Gluconeogenesis
Glycogenesis
External sources
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Autotrophic organisms, such as plants and some bacteria, synthesize their own organic compounds for energy and carbon requirements. The primary process by which most autotrophs achieve this is photosynthesis, using light energy to convert carbon dioxide and water into glucose (a carbohydrate) and oxygen.
Autotrophs obtain their carbon and energy through processes like photosynthesis or chemosynthesis.
Gluconeogenesis and Glycogenesis are metabolic pathways primarily occurring in heterotrophic organisms (like animals) or for storage/synthesis within the organism, not the means by which autotrophs *initially* acquire carbon and energy from external inorganic sources. External sources are what heterotrophs consume.

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49. Which of the following are the properties of an electron? 1. Electron

Which of the following are the properties of an electron?
1. Electron is a constituent of cathode ray
2. Electron is a negatively charged particle
3. The mass of the electron is equal to the mass of the proton
4. Electron is deflected by the electric field but not by magnetic field
Select the correct answer using the code given below:

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1 and 2 only
1, 2 and 3
3 and 4
1 and 4
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UPSC NDA-2 – 2015
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Statement 1 is correct: Cathode rays are streams of electrons. Statement 2 is correct: Electrons are negatively charged fundamental particles. Statement 3 is incorrect: The mass of an electron is significantly smaller (about 1/1836) than the mass of a proton. Statement 4 is incorrect: Electrons, being charged particles, are deflected by both electric fields and magnetic fields.
This question tests basic properties of electrons, a fundamental particle in physics and chemistry.
Electrons are leptons and are one of the constituents of atoms, orbiting the nucleus. Their charge is approximately -1.602 x 10⁻¹⁹ Coulombs.

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50. Which one of the following is the correct sequence about various level

Which one of the following is the correct sequence about various levels of organization of Biosphere?

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Ecosystem—Biosphere — Community — Population
Population — Organism — Eco system — Biosphere
Organism — Community — Population — Biosphere
Organism — Population — Eco system — Biosphere
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UPSC NDA-2 – 2015
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The correct sequence of organization in the biosphere, from smallest to largest functional level typically starts with individual organisms, then populations of the same species, communities of different species interacting, ecosystems where the community interacts with its environment, and finally the biosphere encompassing all ecosystems. Option D, Organism — Population — Eco system — Biosphere, follows this logical progression, although it skips the ‘Community’ level, which is often included between Population and Ecosystem. Among the given options, it presents the most accurate relative ordering.
Understanding the hierarchical levels of organization in ecology, from individual organisms to the entire biosphere, is fundamental.
The typical hierarchy is Organism -> Population -> Community -> Ecosystem -> Biome -> Biosphere. An ecosystem includes both the living (biotic community) and non-living (abiotic) components of an area.

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