UPSC NDA-2

1. An object of mass 2000 g possesses 100 J kinetic energy. The object mu

An object of mass 2000 g possesses 100 J kinetic energy. The object must be moving with a speed of

[amp_mcq option1=”10.0 m/s” option2=”11.1 m/s” option3=”11.2 m/s” option4=”12.1 m/s” correct=”option1″]

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The correct option is A. The kinetic energy (KE) of an object is given by the formula $\text{KE} = \frac{1}{2}mv^2$, where $m$ is the mass and $v$ is the speed. Given $\text{KE} = 100 \, \text{J}$ and $m = 2000 \, \text{g} = 2 \, \text{kg}$, we can solve for $v$.
Substitute the given values into the kinetic energy formula: $100 \, \text{J} = \frac{1}{2} \times (2 \, \text{kg}) \times v^2$. This simplifies to $100 = 1 \times v^2$, so $v^2 = 100$. Taking the square root of both sides gives $v = 10 \, \text{m/s}$ (since speed is a magnitude and must be non-negative).
It is important to ensure that all units are in the standard SI system before calculation. Mass is given in grams and must be converted to kilograms (1 kg = 1000 g). Energy is given in Joules, which is the standard SI unit.

2. A tennis ball is thrown in the vertically upward direction and the bal

A tennis ball is thrown in the vertically upward direction and the ball attains a maximum height of 20 m. The ball was thrown approximately with an upward velocity of

[amp_mcq option1=”8 m/s” option2=”12 m/s” option3=”16 m/s” option4=”20 m/s” correct=”option4″]

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The correct option is D. Using the kinematic equation $v^2 = u^2 + 2as$, where $v$ is the final velocity (0 m/s at max height), $u$ is the initial velocity, $a$ is the acceleration due to gravity (-g), and $s$ is the height (20 m).
At the maximum height of a vertically thrown object, its instantaneous velocity is zero. The acceleration acting on the object throughout its flight (ignoring air resistance) is the constant acceleration due to gravity, acting downwards. Taking the upward direction as positive, $a = -g$. Using $g \approx 10 \, \text{m/s}^2$ for approximation: $0^2 = u^2 + 2(-10)(20) \implies 0 = u^2 – 400 \implies u^2 = 400 \implies u = 20 \, \text{m/s}$. Using $g \approx 9.8 \, \text{m/s}^2$: $0^2 = u^2 + 2(-9.8)(20) \implies 0 = u^2 – 392 \implies u^2 = 392 \implies u \approx 19.8 \, \text{m/s}$. Both approximations are closest to 20 m/s among the given options.
This is a standard problem in projectile motion under constant acceleration (gravity). The time taken to reach the maximum height can be found using $v = u + at$. The total time of flight is twice the time to reach the maximum height (assuming it lands at the same level).

3. Which among the following is true for propagation of sound waves ?

Which among the following is true for propagation of sound waves ?

[amp_mcq option1=”Sound can travel in vacuum and it is a transverse wave in air.” option2=”Sound cannot travel in vacuum and it is a longitudinal wave in air.” option3=”Sound can travel in vacuum and it is a longitudinal wave in air.” option4=”Sound cannot travel in vacuum and it is a transverse wave in air.” correct=”option2″]

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The correct option is B. Sound waves are mechanical waves that require a medium to propagate and cannot travel through a vacuum. In air, sound waves are longitudinal waves, meaning the particles of the medium vibrate parallel to the direction of wave propagation.
Sound transmission involves the vibration of particles in a medium. In air, this vibration creates regions of compression and rarefaction that travel through the air as a wave. Because the particle displacement is along the direction of energy propagation, it is a longitudinal wave. Vacuum lacks the particles needed to transmit these vibrations, hence sound cannot travel in a vacuum.
Examples of longitudinal waves include sound waves in fluids and solids, and seismic P-waves. Examples of transverse waves include light waves, waves on the surface of water, and seismic S-waves (in solids). Transverse waves involve particle vibration perpendicular to the direction of wave propagation.

4. Reverberation is a phenomenon associated with a

Reverberation is a phenomenon associated with a

[amp_mcq option1=”multiple refraction of sound.” option2=”multiple reflection of sound.” option3=”single refraction of sound.” option4=”single reflection of sound.” correct=”option2″]

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The correct option is B. Reverberation is the persistence of sound in an enclosed space after the sound source has stopped, caused by multiple reflections of sound waves from surfaces within the space.
Reverberation is distinct from a single echo, which is a clearly discernible reflection. Reverberation occurs when reflected sound waves arrive at the listener in rapid succession, blending together and prolonging the original sound. It is a phenomenon resulting from numerous reflections.
Refraction of sound is the bending of sound waves as they pass from one medium to another or through a medium with varying properties (like temperature or density gradients). Single reflection is responsible for echoes or contributes to the overall sound experience in a space. Reverberation time is a key parameter in architectural acoustics, describing how long it takes for sound intensity to decay by 60 dB after the source stops.

5. Nuclear energy is generated by

Nuclear energy is generated by

[amp_mcq option1=”nuclear fission and its expression was proposed by Einstein.” option2=”nuclear fission and its expression was proposed by Rutherford.” option3=”nuclear fusion and its expression was proposed by Bohr.” option4=”nuclear fusion and its expression was proposed by Heisenberg.” correct=”option1″]

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The correct option is A. Nuclear energy is typically generated through nuclear fission in power plants, and the fundamental principle linking mass and energy, which is the basis of energy release in both fission and fusion, is expressed by Einstein’s famous equation E=mc².
Nuclear power plants primarily utilize nuclear fission of heavy elements like Uranium or Plutonium to produce energy. While nuclear fusion is the source of energy in stars and a potential future energy source on Earth, current commercial nuclear power is based on fission. The relationship between the mass deficit and the energy released in nuclear reactions is described by Albert Einstein’s mass-energy equivalence principle, E=mc².
Nuclear fission is a nuclear reaction in which a heavy nucleus splits into lighter nuclei, releasing a large amount of energy. Nuclear fusion is a reaction in which light nuclei combine to form a heavier nucleus, also releasing energy. Rutherford is known for the discovery of the nucleus and the planetary model of the atom (later refined). Bohr developed a model of the atom explaining atomic spectra. Heisenberg is one of the pioneers of quantum mechanics, known for the uncertainty principle.

6. Spherical mirror formula relating an object distance ‘u’, image distan

Spherical mirror formula relating an object distance ‘u’, image distance ‘v’ and focal length of mirror ‘f’ may be applied to a plane mirror when

[amp_mcq option1=”focal length goes to infinity.” option2=”focal length goes to zero.” option3=”image distance goes to zero.” option4=”image distance goes to infinity.” correct=”option1″]

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The correct answer is A) focal length goes to infinity.
A plane mirror can be considered a spherical mirror with an infinitely large radius of curvature. Since the focal length of a spherical mirror is half its radius of curvature (f = R/2), the focal length of a plane mirror is also infinite.
The spherical mirror formula is 1/u + 1/v = 1/f. If f goes to infinity, then 1/f goes to zero. The formula becomes 1/u + 1/v = 0, which implies v = -u. This relationship (image distance is the negative of object distance, indicating a virtual image at the same distance behind the mirror as the object is in front) is consistent with the properties of a plane mirror.

7. Which one of the following hormones is responsible for the development

Which one of the following hormones is responsible for the development of female sexual characters ?

[amp_mcq option1=”Prolactin” option2=”Estrogen” option3=”Oxytocin” option4=”Progesterone” correct=”option2″]

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The correct answer is B) Estrogen.
Estrogen is the primary female sex hormone responsible for the development and maintenance of secondary sexual characteristics in females, such as breast development, widening of the hips, and maturation of the reproductive organs.
Prolactin is involved in milk production. Oxytocin is involved in uterine contractions during childbirth and milk let-down. Progesterone is mainly involved in preparing the uterus for pregnancy and maintaining pregnancy.

8. Intestinal bacteria are main source of which one of the following vita

Intestinal bacteria are main source of which one of the following vitamins ?

[amp_mcq option1=”Vitamin E” option2=”Vitamin C” option3=”Vitamin B₁₂” option4=”Vitamin A” correct=”option3″]

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The correct answer is C) Vitamin B₁₂.
Bacteria residing in the large intestine (colon) of humans are known to synthesize several vitamins, including Vitamin K and various B vitamins, particularly Vitamin B₁₂ (cobalamin).
While intestinal bacteria produce B₁₂, its absorption primarily occurs in the ileum (part of the small intestine) and requires intrinsic factor produced by the stomach. Dietary intake is the main source of Vitamin B₁₂ for humans, as the bacterial production in the colon might not be sufficient or readily absorbable. However, among the options provided, B₁₂ is the vitamin most notably associated with production by intestinal bacteria.

9. What is the total number of chambers in the stomach of domestic animal

What is the total number of chambers in the stomach of domestic animals like cattle, buffalo, goat and sheep ?

[amp_mcq option1=”Four” option2=”Two” option3=”One” option4=”Three” correct=”option1″]

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The correct answer is A) Four.
Domestic animals like cattle, buffalo, goat, and sheep are ruminants. Ruminants possess a unique digestive system featuring a four-chambered stomach.
The four chambers are the rumen, reticulum, omasum, and abomasum. The rumen is the largest chamber where microbial fermentation of plant material occurs. The abomasum is the true glandular stomach, similar to that of monogastric animals.

10. Power of a lens of focal length 25 cm is

Power of a lens of focal length 25 cm is

[amp_mcq option1=”+2-5 Dioptre” option2=”+3 Dioptre” option3=”+4 Dioptre” option4=”+5 Dioptre” correct=”option3″]

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The correct answer is C) +4 Dioptre.
The power of a lens (P) is defined as the reciprocal of its focal length (f), when the focal length is expressed in meters. The formula is P = 1/f.
Given focal length f = 25 cm. Convert this to meters: 25 cm = 0.25 m.
Power P = 1 / 0.25 m = 1 / (1/4) m = 4 Dioptre (D).
A positive power indicates a converging (convex) lens.
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