UPSC NDA-2

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

Which one of the following statements is not correct?

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Pitch of a sound is its characteristic by which we can generally differentiate between a male voice and a female voice.
The loudness of sound is related to its frequency.
A musical sound has certain well-defined frequencies which are generally harmonics of a fundamental frequency.
The timbre of a particular musical sound is related to the waveform of the sound wave.
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The loudness of sound is primarily related to the intensity of the sound wave, which is proportional to the square of its amplitude. Frequency, on the other hand, determines the pitch of the sound. A higher frequency corresponds to a higher pitch, while a larger amplitude corresponds to a louder sound. Therefore, the statement that the loudness of sound is related to its frequency is incorrect.
Loudness relates to amplitude (intensity), while pitch relates to frequency. Timbre relates to waveform (harmonics).
Statement A is correct: Pitch helps differentiate voices; female voices typically have higher fundamental frequencies (and thus higher pitch) than male voices. Statement C is correct: Musical sounds are typically periodic and composed of a fundamental frequency and its harmonic overtones. Statement D is correct: Timbre, or quality, is determined by the combination and relative intensity of overtones present in addition to the fundamental frequency, which shapes the waveform and allows us to distinguish between different instruments or voices.

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32. Which one of the following statements is correct?

Which one of the following statements is correct?

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The speed of sound waves in a medium depends upon the elastic property of the medium but not on inertia property.
The speed of sound waves in a medium depends upon the inertia property of the medium but not on elastic property.
The speed of sound waves in a medium depends neither on its elastic property nor on its inertia property.
The speed of sound waves in a medium depends both on elastic and inertia properties of the medium.
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The speed of sound waves in a medium is determined by the medium’s properties related to elasticity and inertia. Sound waves are mechanical waves, meaning they propagate through a medium by causing particles of the medium to oscillate. The elastic property (like Bulk modulus or Young’s modulus) determines how easily the medium restores its shape or volume after being deformed by the wave. The inertia property (density) determines how much resistance the medium offers to changes in motion. The speed of sound increases with increasing elasticity and decreases with increasing density. Therefore, the speed of sound depends on both properties.
Speed of mechanical waves depends on the elastic modulus and density of the medium. Higher elasticity allows faster propagation of disturbances. Higher density provides more inertia, resisting quick motion.
The formula for the speed of sound in a fluid is $v = \sqrt{B/\rho}$, where B is the Bulk modulus and $\rho$ is the density. For a solid rod, $v = \sqrt{Y/\rho}$, where Y is Young’s modulus. These formulas explicitly show dependence on both an elastic property and density.

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33. If we plot a graph between volume V and inverse of pressure P (i.e., 1

If we plot a graph between volume V and inverse of pressure P (i.e., 1/P) for an ideal gas at constant temperature T, the curve so obtained is:

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straight line
circle
parabola
hyperbola
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A graph between volume V and inverse of pressure (1/P) for an ideal gas at constant temperature T is a straight line.
According to the Ideal Gas Law, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. For a fixed amount of gas (n is constant) at a constant temperature (T is constant), the product nRT is a constant. Let’s call this constant C. So, PV = C (This is Boyle’s Law). We want to plot V against 1/P. Rearranging the equation, we get V = C * (1/P). If we let Y = V and X = 1/P, the equation becomes Y = CX. This is the equation of a straight line passing through the origin with slope C (which is equal to nRT).
Plotting V versus P directly would yield a hyperbola (PV = C). A parabola is typically associated with quadratic relationships, and a circle with relationships involving the sum of squares.

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34. Which one of the following four particles, whose displacement x and ac

Which one of the following four particles, whose displacement x and acceleration a, are related as follows, is executing simple harmonic motion?

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a = +3x
a = +3x²
a = -3
a = -3x
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The particle executing simple harmonic motion is the one where acceleration ‘a’ and displacement ‘x’ are related as a = -3x.
Simple Harmonic Motion (SHM) is defined by a linear restoring force proportional to the displacement from the equilibrium position and directed towards it. According to Newton’s second law (F = ma), this implies that the acceleration is also proportional to the displacement and directed towards the equilibrium position. The general form of the acceleration-displacement relationship for SHM is a = -ω²x, where ω² is a positive constant (related to the system’s properties like mass and stiffness). Option D, a = -3x, fits this form with ω² = 3 (or ω = √3).
Option A, a = +3x, represents unstable equilibrium where the acceleration is away from the origin. Option B, a = +3x², is a non-linear relationship. Option C, a = -3, represents motion under constant acceleration, which is not SHM.

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35. A particle is executing simple harmonic motion. Which one of the follo

A particle is executing simple harmonic motion. Which one of the following statements about the acceleration of the oscillating particle is true ?

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It is always in the opposite direction to velocity
It is proportional to the frequency of oscillation
It is minimum when the speed is maximum
It decreases as the potential energy increases
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In simple harmonic motion, the acceleration of the oscillating particle is minimum when the speed is maximum.
Simple Harmonic Motion (SHM) is characterized by an acceleration that is directly proportional to the displacement from the equilibrium position and is always directed towards the equilibrium position (a = -ω²x, where x is displacement and ω is angular frequency). The equilibrium position is where the displacement x = 0. At this point, the restoring force and acceleration are zero, representing the minimum magnitude of acceleration. In SHM, the speed of the particle is maximum at the equilibrium position (x=0) and zero at the extreme positions (maximum |x|). Thus, acceleration (minimum at x=0) is minimum when speed (maximum at x=0) is maximum.
Option A is incorrect; acceleration is in the opposite direction to velocity only when the object is slowing down (moving away from equilibrium). When moving towards equilibrium, velocity and acceleration are in the same direction. Option B is incorrect; acceleration is proportional to the *square* of the angular frequency (ω²), not frequency directly, though frequency is proportional to ω. Option D is incorrect; potential energy is maximum at the extreme positions where |x| is maximum, and acceleration magnitude |a| = ω²|x| is also maximum there. So, as potential energy increases, acceleration magnitude increases, not decreases.

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36. How is the kinetic energy of a moving object affected if the net work

How is the kinetic energy of a moving object affected if the net work done on it is positive ?

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Decreases
Increases
Remains constant
Becomes zero
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If the net work done on a moving object is positive, its kinetic energy increases.
This is directly explained by the Work-Energy Theorem, which states that the net work (W_net) done on an object by external forces is equal to the change in its kinetic energy (ΔKE): W_net = ΔKE = KE_final – KE_initial. If W_net is positive, then ΔKE must be positive, meaning KE_final > KE_initial. Therefore, the kinetic energy increases.
Conversely, if the net work done is negative, the kinetic energy decreases. If the net work done is zero, the kinetic energy remains constant (although the velocity vector might change direction, the speed and thus KE remain the same).

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37. Along a streamline flow of fluid

Along a streamline flow of fluid

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the velocity of all fluid particles at a given instant is constant
the speed of a fluid particle remains constant
the velocity of all fluid particles crossing a given position is constant
the velocity of a fluid particle remains constant
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Along a streamline flow of fluid, the velocity of all fluid particles crossing a given position is constant.
Streamline flow is a characteristic of steady flow. In steady flow, the velocity of the fluid at any fixed point in space does not change over time. Therefore, any fluid particle that passes through a particular point will have the same velocity as any other particle that passes through that same point at a different time. Streamlines are the paths followed by fluid particles in steady flow.
Option A is incorrect because the velocity can vary from one streamline to another at a given instant. Option B is incorrect because the speed of a particle can change along a streamline if the cross-sectional area of the flow changes (e.g., in a converging or diverging pipe, based on the continuity equation). Option D is incorrect because the velocity of a specific fluid particle changes as it moves along a streamline, unless the flow is uniform (velocity is the same everywhere). Option C accurately describes a key property of steady flow: the velocity field is constant with respect to time.

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38. Fluoride toothpaste is sometimes recommended because fluoride

Fluoride toothpaste is sometimes recommended because fluoride

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prevents plaque formation
hardens the enamel of the tooth
kills pathogenic bacteria
prevents tooth ache
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Fluoride toothpaste is sometimes recommended because fluoride hardens the enamel of the tooth.
Fluoride works by strengthening the tooth enamel through a process called remineralization. When fluoride is present in the mouth, it is incorporated into the crystalline structure of the enamel, forming fluorapatite. Fluorapatite is more resistant to acid dissolution than hydroxyapatite, the original mineral in enamel. This increased resistance helps protect teeth from decay caused by acids produced by bacteria in plaque, effectively hardening the enamel and making it more resilient to cavities.
While fluoride can have some antibacterial effects at higher concentrations, its primary mechanism for preventing cavities in toothpaste is by enhancing enamel remineralization and increasing its acid resistance. Brushing action and other ingredients help remove plaque, but fluoride itself doesn’t primarily prevent plaque formation. It helps prevent tooth decay, which is a common cause of toothache, but it is not a direct pain reliever.

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39. A plant having yellow leaves with dead spots has the deficiency of

A plant having yellow leaves with dead spots has the deficiency of

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Potassium
Magnesium
Nitrate
Phosphate
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A plant having yellow leaves with dead spots likely has a deficiency of Potassium.
Potassium (K) is a mobile nutrient in plants. Deficiency symptoms typically appear first in older leaves because the plant translocates potassium to younger, growing tissues. Common symptoms of potassium deficiency include chlorosis (yellowing) along the margins and tips of older leaves, which progresses inwards. As the deficiency worsens, these yellow areas often develop into necrotic spots (dead tissue), giving the appearance of scorched or brown margins and tips.
Magnesium (Mg) deficiency also causes chlorosis but typically results in interveinal chlorosis (yellowing between the veins while the veins remain green). Nitrate (Nitrogen) deficiency causes general yellowing of the entire leaf, starting with older leaves. Phosphate (Phosphorus) deficiency can cause stunted growth and sometimes purplish discoloration, especially on stems and the undersides of leaves, but not typically yellowing with marginal necrosis.

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40. A horse and a donkey can breed to produce mule which is an infertile a

A horse and a donkey can breed to produce mule which is an infertile animal. The infertility is because horse and donkey belong to different

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class
order
species
genus
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Mules are infertile because horses and donkeys belong to different species.
A species is generally defined as a group of organisms that can interbreed and produce fertile offspring. While horses (Equus caballus) and donkeys (Equus asinus) can interbreed to produce a mule (or a hinny), their offspring are almost always sterile. This sterility arises because horses and donkeys have different numbers of chromosomes (horses have 64, donkeys have 62). The mule inherits 63 chromosomes, which cannot pair properly during meiosis, preventing the formation of viable gametes (sperm or eggs), thus leading to infertility.
Horses and donkeys belong to the same genus, Equus, which indicates a relatively recent common ancestor compared to differences at the order or class level. The ability to produce hybrid offspring, even if infertile, is common between closely related species within the same genus.

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