IASbaba Prelims 60 Days Plan, Rapid Revision Series (RaRe)
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The 60 Days Rapid Revision (RaRe) Series is IASbaba’s Flagship Initiative recommended by Toppers and loved by the aspirants’ community every year.
It is the most comprehensive program which will help you complete the syllabus, revise and practice tests on a daily basis. The Programme on a daily basis includes
Daily Prelims MCQs from Static (Monday – Saturday)
- Daily Static Quiz will cover all the topics of static subjects – Polity, History, Geography, Economics, Environment and Science and technology.
- 20 questions will be posted daily and these questions are framed from the topics mentioned in the schedule.
- It will ensure timely and streamlined revision of your static subjects.
Daily Current Affairs MCQs (Monday – Saturday)
- Daily 5 Current Affairs questions, based on sources like ‘The Hindu’, ‘Indian Express’ and ‘PIB’, would be published from Monday to Saturday according to the schedule.
Daily CSAT Quiz (Monday – Friday)
- CSAT has been an Achilles heel for many aspirants.
- Daily 5 CSAT Questions will be published.
Note – Daily Test of 20 static questions, 10 current affairs, and 5 CSAT questions. (35 Prelims Questions) in QUIZ FORMAT will be updated on a daily basis.
To Know More about 60 Days Rapid Revision (RaRe) Series – CLICK HERE
60 Day Rapid Revision (RaRe) Series Schedule – CLICK HERE
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The following Test is based on the syllabus of 60 Days Plan-2023 for UPSC IAS Prelims 2022.
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Question 1 of 35
1. Question
The spread in colours in a rainbow on sky is primarily due to?
Correct
Solution (b)
Rainbow is a natural spectrum. It is caused by dispersion (i.e., splitting of white light into seven constituent colors VIBGYOR) of sunlight by tiny droplets of water present in the atmosphere.
The most familiar example of dispersion is a rainbow, in which dispersion causes the spatial separation of a white light into components of different wavelengths (different colors).
Incorrect
Solution (b)
Rainbow is a natural spectrum. It is caused by dispersion (i.e., splitting of white light into seven constituent colors VIBGYOR) of sunlight by tiny droplets of water present in the atmosphere.
The most familiar example of dispersion is a rainbow, in which dispersion causes the spatial separation of a white light into components of different wavelengths (different colors).
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Question 2 of 35
2. Question
A hydrogen-inflated polythene balloon is released from the surface of the earth. As the balloon rises to an altitude up in the atmosphere, it will?
Correct
Solution (a)
The air pressure at high altitudes is less than at ground level, so, the balloon will expand until the pressure inside equals the pressure outside. Consequently, the size will increase and at some point, it will burst.
Incorrect
Solution (a)
The air pressure at high altitudes is less than at ground level, so, the balloon will expand until the pressure inside equals the pressure outside. Consequently, the size will increase and at some point, it will burst.
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Question 3 of 35
3. Question
Consider the following statements w.r.t ‘Incandescent Electric Bulb and Fluorescent Light Bulb’:
- An incandescent lamp generates light when electric current heats a tungsten filament wire so that it glows whereas fluorescent bulbs generate light by sending an electrical discharge through an ionized gas.
- The efficacy of incandescent bulbs is low while fluorescent is a very energy efficient light source.
- Argon, mercury vapor, strontium and calcium oxides are used in incandescent bulbs.
How many of the above statements are correct?
Correct
Solution (b)
Incandescent Electric Bulb and Fluorescent Light Bulb
- An incandescent lamp generates light when electric current heats a tungsten filament wire so that it glows, or incandesces.
- Fluorescent bulbs generate light by sending an electrical discharge through an ionized gas.
- Materials used in Fluorescent: Argon, mercury vapor, tungsten, barium, strontium and calcium oxides.
- Materials used in Incandescent: Argon, tungsten filament.
- The efficacy of incandescent bulbs is low which is a major disadvantage in terms of higher operating costs and more heat in the room.
- Fluorescent is a very energy efficient light source that enjoys low operating costs and contributes little heat to the room.
Incorrect
Solution (b)
Incandescent Electric Bulb and Fluorescent Light Bulb
- An incandescent lamp generates light when electric current heats a tungsten filament wire so that it glows, or incandesces.
- Fluorescent bulbs generate light by sending an electrical discharge through an ionized gas.
- Materials used in Fluorescent: Argon, mercury vapor, tungsten, barium, strontium and calcium oxides.
- Materials used in Incandescent: Argon, tungsten filament.
- The efficacy of incandescent bulbs is low which is a major disadvantage in terms of higher operating costs and more heat in the room.
- Fluorescent is a very energy efficient light source that enjoys low operating costs and contributes little heat to the room.
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Question 4 of 35
4. Question
Consider the following pairs:
- Heat- Celsius
- Sound- Decibel
- Electric Charge- Coulomb
- Electric Power- Watt
How many of the above pairs are correct?
Correct
Solution (c)
Heat is measured in terms of Joule (J) since it is energy. Celsius is used to measure temperature. All other options are correctly matched.
Incorrect
Solution (c)
Heat is measured in terms of Joule (J) since it is energy. Celsius is used to measure temperature. All other options are correctly matched.
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Question 5 of 35
5. Question
Consider the following:
- An electric motor is a rotating device that converts electrical energy to mechanical energy.
- A device that reverses the direction of flow of current through a circuit is called a commutator.
- A galvanometer is an instrument that can detect the presence of a current in a circuit.
How many of the above statements are correct?
Correct
Solution (c)
- An electric motor is a rotating device that converts electrical energy to mechanical energy. Electric motor is used as an important component in electric fans, refrigerators, mixers, washing machines, computers, MP3 players etc.
- A device that reverses the direction of flow of current through a circuit is called a commutator.
- A galvanometer is an instrument that can detect the presence of a current in a circuit.
Incorrect
Solution (c)
- An electric motor is a rotating device that converts electrical energy to mechanical energy. Electric motor is used as an important component in electric fans, refrigerators, mixers, washing machines, computers, MP3 players etc.
- A device that reverses the direction of flow of current through a circuit is called a commutator.
- A galvanometer is an instrument that can detect the presence of a current in a circuit.
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Question 6 of 35
6. Question
A person may bleed from the nose when at a great height above the sea level. With reference to this, which one of the following statements is correct?
Correct
Solution (b)
Atmospheric pressure decreases with increase in altitude.
As we go higher, the pressure within the blood vessels exceeds the external pressure. This causes the blood vessels to burst. Consequently, we suffer nose bleeding, ear bleeding etc.
Incorrect
Solution (b)
Atmospheric pressure decreases with increase in altitude.
As we go higher, the pressure within the blood vessels exceeds the external pressure. This causes the blood vessels to burst. Consequently, we suffer nose bleeding, ear bleeding etc.
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Question 7 of 35
7. Question
With reference to the Bose-Einstein Condensate, which of the following statement is incorrect?
Correct
Solution (d)
Statement 1 Statement 2 Statement 3 Statement 4 Correct Correct Correct Incorrect Scientists have always known about solids, liquids, and gases. Plasma was a new idea when it was identified by William Crookes in 1879. The Bose-Einstein condensate (BEC) was another state of matter. In 1920, Indian physicist Satyendra Nath Bose had done some calculations for a fifth state of matter. Building on his calculations, Albert Einstein predicted a new state of matter – the Bose-Einstein Condensate (BEC). In 2001, Eric A. Cornell, Wolfgang Ketterle and Carl E. Wieman of USA received the Nobel prize in physics for achieving “Bose-Einstein condensation”. The BEC is formed by cooling a gas of extremely low density, about one-hundred-thousandth the density of normal air, to super low temperatures. Plasmas are highly energized gases that have lost their electrons. Stars, including the Sun, are covered in plasma. Hydrogen (H) and helium (He) ions float around the Sun with their electrons moving freely. The BEC is all about atoms that are closer and less energetic than atoms in a solid. Incorrect
Solution (d)
Statement 1 Statement 2 Statement 3 Statement 4 Correct Correct Correct Incorrect Scientists have always known about solids, liquids, and gases. Plasma was a new idea when it was identified by William Crookes in 1879. The Bose-Einstein condensate (BEC) was another state of matter. In 1920, Indian physicist Satyendra Nath Bose had done some calculations for a fifth state of matter. Building on his calculations, Albert Einstein predicted a new state of matter – the Bose-Einstein Condensate (BEC). In 2001, Eric A. Cornell, Wolfgang Ketterle and Carl E. Wieman of USA received the Nobel prize in physics for achieving “Bose-Einstein condensation”. The BEC is formed by cooling a gas of extremely low density, about one-hundred-thousandth the density of normal air, to super low temperatures. Plasmas are highly energized gases that have lost their electrons. Stars, including the Sun, are covered in plasma. Hydrogen (H) and helium (He) ions float around the Sun with their electrons moving freely. The BEC is all about atoms that are closer and less energetic than atoms in a solid. -
Question 8 of 35
8. Question
The term ‘Tyndall effect’ is related to?
Correct
Solution (c)
Scattering of a beam of light is called the Tyndall effect after the name of the scientist who discovered this effect. Tyndall effect can also be observed when a fine beam of light enters a room through a small hole. This happens due to the scattering of light by the particles of dust and smoke in the air.
Incorrect
Solution (c)
Scattering of a beam of light is called the Tyndall effect after the name of the scientist who discovered this effect. Tyndall effect can also be observed when a fine beam of light enters a room through a small hole. This happens due to the scattering of light by the particles of dust and smoke in the air.
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Question 9 of 35
9. Question
‘The electromagnets are the magnets that are created when the electric current is passed through it’. Which of the following are based on electromagnetism?
- Microwaves
- Transformers
- Microphones
- Optical Instruments
Select the correct code:
Correct
Solution (d)
Electromagnet
- Electromagnet- device consisting of a core of magnetic material surrounded by a coil through which an electric current is passed to magnetize the core.
- The electromagnets are the magnets that are created when the electric current is passed through it. These electromagnets have immense applications in everyday life and every industry.
- The strength of the electromagnets can be altered by repeated variation in the amount of electric current that flows through them.
- Applications in:
- Electric Bells and Buzzers
- Loudspeakers
- Cranes in Lifting
- MRI machines
- Tape Recorders, Hard Disks etc.
- Microwaves
- Transformers
- Microphones
- Optical Instruments
- Pendrive etc.
Incorrect
Solution (d)
Electromagnet
- Electromagnet- device consisting of a core of magnetic material surrounded by a coil through which an electric current is passed to magnetize the core.
- The electromagnets are the magnets that are created when the electric current is passed through it. These electromagnets have immense applications in everyday life and every industry.
- The strength of the electromagnets can be altered by repeated variation in the amount of electric current that flows through them.
- Applications in:
- Electric Bells and Buzzers
- Loudspeakers
- Cranes in Lifting
- MRI machines
- Tape Recorders, Hard Disks etc.
- Microwaves
- Transformers
- Microphones
- Optical Instruments
- Pendrive etc.
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Question 10 of 35
10. Question
What do you understand by the term ‘Sonic boom’?
Correct
Solution (b)
When the speed of any object exceeds the speed of sound it is said to be travelling at supersonic speed. Bullets, jet aircrafts etc. often travel at supersonic speeds. When a sound, producing source moves with a speed higher than that of sound, it produces shock waves in air. These shock waves carry a large amount of energy. The air pressure variation associated with this type of shock waves produces a very sharp and loud sound called the “sonic boom”. The shock waves produced by a supersonic aircraft have enough energy to shatter window glass and even damage buildings.
Incorrect
Solution (b)
When the speed of any object exceeds the speed of sound it is said to be travelling at supersonic speed. Bullets, jet aircrafts etc. often travel at supersonic speeds. When a sound, producing source moves with a speed higher than that of sound, it produces shock waves in air. These shock waves carry a large amount of energy. The air pressure variation associated with this type of shock waves produces a very sharp and loud sound called the “sonic boom”. The shock waves produced by a supersonic aircraft have enough energy to shatter window glass and even damage buildings.
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Question 11 of 35
11. Question
Consider the following statements and identify the correct one/s:
- All conservation laws such as conservation of momentum, energy, etc. are considered to be fundamental laws.
- A conservation law can be easily proved.
- Law of conservation of momentum states that momentum can neither be created nor destroyed.
How many of the above statements are correct?
Correct
Solution (b)
Statement 1 Statement 2 Statement 3 Correct Incorrect Correct All conservation laws such as conservation of momentum, energy, angular momentum, charge etc. are considered to be fundamental laws in physics. These are based on observations and experiments. It is important to remember that a conservation law cannot be proved. It can be verified, or disproved, by experiments. An experiment whose result is in conformity with the law verifies or substantiates the law; it does not prove the law. On the other hand, a single experiment whose result goes against the law is enough to disprove it. Law of conservation of momentum states that: For two or more bodies in an isolated system acting upon each other, their total momentum remains constant unless an external force is applied. Therefore, momentum can neither be created nor destroyed. Incorrect
Solution (b)
Statement 1 Statement 2 Statement 3 Correct Incorrect Correct All conservation laws such as conservation of momentum, energy, angular momentum, charge etc. are considered to be fundamental laws in physics. These are based on observations and experiments. It is important to remember that a conservation law cannot be proved. It can be verified, or disproved, by experiments. An experiment whose result is in conformity with the law verifies or substantiates the law; it does not prove the law. On the other hand, a single experiment whose result goes against the law is enough to disprove it. Law of conservation of momentum states that: For two or more bodies in an isolated system acting upon each other, their total momentum remains constant unless an external force is applied. Therefore, momentum can neither be created nor destroyed. -
Question 12 of 35
12. Question
Consider the following w.r.t ddifferences between Alternating Current and Direct Current (AC and DC):
- Alternating current is the best way to transmit electricity over large distances.
- The frequency of alternating current is 50Hz or 60Hz depending upon the country whereas the frequency of direct current is zero.
- The magnitude of alternating current varies with time whereas the magnitude of D.C current does not vary with time.
How many of the above statements are correct?
Correct
Solution (c)
Electricity flows in two ways: in an alternating current (AC) or in a direct current (DC).
- Electricity is nothing but the movement of electrons through a conductor
- In DC, the electrons flow steadily in a single direction, or forward.
- In AC, electrons keep switching directions.
- Alternating current is the best way to transmit electricity over large distances. D.C current does not travel safely over a long distance because D.C current loses much energy as compared to A.C.
- The frequency of alternating current is 50Hz or 60Hz depending upon the country. The frequency of direct current is zero.
- The magnitude of alternating current varies with time. The magnitude of D.C current does not vary with time.
- C current is produced mainly by Generators. D.C current is produced from battery or cell etc.
- In A.C current power factor always lies between 0 to 1. In D.C current power factor always remains 1.
- AC is used in homes, industries, etc. DC is used in refrigerators, TV, etc.
Incorrect
Solution (c)
Electricity flows in two ways: in an alternating current (AC) or in a direct current (DC).
- Electricity is nothing but the movement of electrons through a conductor
- In DC, the electrons flow steadily in a single direction, or forward.
- In AC, electrons keep switching directions.
- Alternating current is the best way to transmit electricity over large distances. D.C current does not travel safely over a long distance because D.C current loses much energy as compared to A.C.
- The frequency of alternating current is 50Hz or 60Hz depending upon the country. The frequency of direct current is zero.
- The magnitude of alternating current varies with time. The magnitude of D.C current does not vary with time.
- C current is produced mainly by Generators. D.C current is produced from battery or cell etc.
- In A.C current power factor always lies between 0 to 1. In D.C current power factor always remains 1.
- AC is used in homes, industries, etc. DC is used in refrigerators, TV, etc.
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Question 13 of 35
13. Question
Consider the following w.r.t ‘Refractive Index’:
- The refractive index is dimensionless.
- The value of the refractive index for a given pair of media depends upon the speed of light in the two media.
- Higher the refractive index, the higher the optical density and faster is the speed of light.
How many of the above statements are correct?
Correct
Solution (b)
Refractive Index
Refractive Index, also called index of refraction, measure of the bending of a ray of light when passing from one medium into another. The refractive index can be linked to an important physical quantity, the relative speed of propagation of light in different media.
It turns out that light propagates with different speeds in different media.
- Light travels the fastest in vacuum with the highest speed of 3×10^8 m s–1.
- In air, the speed of light is only marginally less, compared to that in vacuum.
- It reduces considerably in glass or water.
- The value of the refractive index for a given pair of media depends upon the speed of light in the two media.
- The refractive index is dimensionless.
- The refractive index, represented by symbol n, is the velocity of light in vacuum divided by the velocity of light in a medium.
- Formula: n=c/v
- n is the refractive index
- c is the velocity of light in a vacuum (3 × 10^8 m/s)
- v is the velocity of light in a substance
- Higher the refractive index, the higher the optical density and slower is the speed of light.
Incorrect
Solution (b)
Refractive Index
Refractive Index, also called index of refraction, measure of the bending of a ray of light when passing from one medium into another. The refractive index can be linked to an important physical quantity, the relative speed of propagation of light in different media.
It turns out that light propagates with different speeds in different media.
- Light travels the fastest in vacuum with the highest speed of 3×10^8 m s–1.
- In air, the speed of light is only marginally less, compared to that in vacuum.
- It reduces considerably in glass or water.
- The value of the refractive index for a given pair of media depends upon the speed of light in the two media.
- The refractive index is dimensionless.
- The refractive index, represented by symbol n, is the velocity of light in vacuum divided by the velocity of light in a medium.
- Formula: n=c/v
- n is the refractive index
- c is the velocity of light in a vacuum (3 × 10^8 m/s)
- v is the velocity of light in a substance
- Higher the refractive index, the higher the optical density and slower is the speed of light.
-
Question 14 of 35
14. Question
Consider the following statements and identify the incorrect one/s:
- Magnetic field is a quantity that has both direction and magnitude.
- If two field-lines are found to cross each other then it indicates the relative strength of the magnetic field.
Select the answer:
Correct
Solution (b)
Statement 1 Statement 2 Correct Incorrect Magnetic field is a quantity that has both direction and magnitude. The direction of the magnetic field is taken to be the direction in which a north pole of the compass needle moves inside it. Therefore, it is taken by convention that the field lines emerge from north pole and merge at the south pole. No two field-lines are found to cross each other. If they did, it would mean that at the point of intersection, the compass needle would point towards two directions, which is not possible. The relative strength of the magnetic field is shown by the degree of closeness of the field lines. Incorrect
Solution (b)
Statement 1 Statement 2 Correct Incorrect Magnetic field is a quantity that has both direction and magnitude. The direction of the magnetic field is taken to be the direction in which a north pole of the compass needle moves inside it. Therefore, it is taken by convention that the field lines emerge from north pole and merge at the south pole. No two field-lines are found to cross each other. If they did, it would mean that at the point of intersection, the compass needle would point towards two directions, which is not possible. The relative strength of the magnetic field is shown by the degree of closeness of the field lines. -
Question 15 of 35
15. Question
Consider the following statements with respect to Pole star:
- It is aligned with the Earth’s axis of rotation.
- It’s the only star that doesn’t appear to move.
- The star known as Polaris is the present North Star, which has been earth’s pole star since its birth.
How many of the above statements are correct?
Correct
Solution (b)
Statement 1 Statement 2 Statement 3 Correct Correct Incorrect What makes the Pole Star special is the fact that it points us to geographic north. The Pole Star is aligned with the Earth’s axis of rotation. So, when we observe in its direction, we’re looking in the direction of north. From our perspective on Earth, every star in the sky pivots around the Pole Star, causing them to rise and set. Because of its position over the North Pole, it’s the only star that doesn’t appear to move. At present, the star known as Polaris is the North Star. However, Polaris has not always been the North Star and will not always be the North Star. (Note: Read about Milankovic cycle for better understanding) Incorrect
Solution (b)
Statement 1 Statement 2 Statement 3 Correct Correct Incorrect What makes the Pole Star special is the fact that it points us to geographic north. The Pole Star is aligned with the Earth’s axis of rotation. So, when we observe in its direction, we’re looking in the direction of north. From our perspective on Earth, every star in the sky pivots around the Pole Star, causing them to rise and set. Because of its position over the North Pole, it’s the only star that doesn’t appear to move. At present, the star known as Polaris is the North Star. However, Polaris has not always been the North Star and will not always be the North Star. (Note: Read about Milankovic cycle for better understanding) -
Question 16 of 35
16. Question
Consider the following statements:
- Light year is the distance travelled by light in one year.
- The distance of the Sun from the Earth is around 8 light minutes.
Which of the statement/s given above is/are correct?
Correct
Solution (c)
Statement 1 Statement 2 Correct Correct Large distances in space are expressed in another unit known as light year. It is the distance travelled by light in one year. One light-year equals 5,878,625,370,000 miles i.e. 9.5 trillion km. The speed of light is about 300,000 km per second. Thus, the distance of the Sun from the Earth may be said to be about 8 light minutes. The distance of Alpha Centauri is about 4.3 light years. Incorrect
Solution (c)
Statement 1 Statement 2 Correct Correct Large distances in space are expressed in another unit known as light year. It is the distance travelled by light in one year. One light-year equals 5,878,625,370,000 miles i.e. 9.5 trillion km. The speed of light is about 300,000 km per second. Thus, the distance of the Sun from the Earth may be said to be about 8 light minutes. The distance of Alpha Centauri is about 4.3 light years. -
Question 17 of 35
17. Question
Consider the following statements with reference to ‘Microwave Oven’ and identify the correct statement/s:
- Its basic principle is to generate microwave radiation of appropriate frequency in the working space of the oven.
- One should use metal containers and not porcelain vessels in a microwave oven to avoid dangers from accumulated electric charges.
Which of the statement/s given above is/are correct?
Correct
Solution (a)
Statement 1 Statement 2 Correct Incorrect The basic principle of a microwave oven is to generate microwave radiation of appropriate frequency in the working space of the oven where we keep food. This way energy is not wasted in heating up the vessel. In the conventional heating method, the vessel on the burner gets heated first, and then the food inside gets heated because of transfer of energy from the vessel. In the microwave oven, energy is directly delivered to water molecules which is shared by the entire food. One should use porcelain vessels and not metal containers in a microwave oven because of the danger of getting a shock from accumulated electric charges. Metals may also melt from heating. The porcelain container remains unaffected and cool, because its large molecules vibrate and rotate with much smaller frequencies, and thus cannot absorb microwaves. Hence, they do not get heated up. Incorrect
Solution (a)
Statement 1 Statement 2 Correct Incorrect The basic principle of a microwave oven is to generate microwave radiation of appropriate frequency in the working space of the oven where we keep food. This way energy is not wasted in heating up the vessel. In the conventional heating method, the vessel on the burner gets heated first, and then the food inside gets heated because of transfer of energy from the vessel. In the microwave oven, energy is directly delivered to water molecules which is shared by the entire food. One should use porcelain vessels and not metal containers in a microwave oven because of the danger of getting a shock from accumulated electric charges. Metals may also melt from heating. The porcelain container remains unaffected and cool, because its large molecules vibrate and rotate with much smaller frequencies, and thus cannot absorb microwaves. Hence, they do not get heated up. -
Question 18 of 35
18. Question
Consider the following pairs with reference to link between technology and associated principle:
Technology Scientific principle(s)
- Steam engine – Laws of thermodynamics
- Aeroplane – Bernoulli’s principle
- Optical fibres – Magnetic confinement of plasma
- Tokamak – Photoelectric effect
Select the correct match:
Correct
Solution (a)
Statement 1 Statement 2 Statement 3 Statement 4 Correct Correct Incorrect Incorrect The Second Law of Thermodynamics state that heat flows spontaneously only from hotter to colder bodies. This implies that a steam engine can do work only with a drop in temperature. The steam that enters a steam turbine is hotter than the steam that exits it. Bernoulli’s Principle states that faster moving air has low air pressure and slower moving air has high air pressure. Air pressure is the amount of pressure, or “push”, air particles exert. It is this principle that helps us understand how airplanes produce lift (or the ability to get into the air). Optical fibres rely on total internal reflection for their operation. An optical fibre is a thin rod of high-quality glass. Light/infrared getting in at one end undergoes repeated total internal reflection and emerges at the other end. Notice that light refracts towards the normal as it enters the optical fibre. A tokamak is a machine that confines a plasma using magnetic fields in a donut shape that scientists call a torus. Fusion energy scientists believe that tokamaks are the leading plasma confinement concept for future fusion power plants. Tokamaks are helping in attaining nuclear fusion reactors. Incorrect
Solution (a)
Statement 1 Statement 2 Statement 3 Statement 4 Correct Correct Incorrect Incorrect The Second Law of Thermodynamics state that heat flows spontaneously only from hotter to colder bodies. This implies that a steam engine can do work only with a drop in temperature. The steam that enters a steam turbine is hotter than the steam that exits it. Bernoulli’s Principle states that faster moving air has low air pressure and slower moving air has high air pressure. Air pressure is the amount of pressure, or “push”, air particles exert. It is this principle that helps us understand how airplanes produce lift (or the ability to get into the air). Optical fibres rely on total internal reflection for their operation. An optical fibre is a thin rod of high-quality glass. Light/infrared getting in at one end undergoes repeated total internal reflection and emerges at the other end. Notice that light refracts towards the normal as it enters the optical fibre. A tokamak is a machine that confines a plasma using magnetic fields in a donut shape that scientists call a torus. Fusion energy scientists believe that tokamaks are the leading plasma confinement concept for future fusion power plants. Tokamaks are helping in attaining nuclear fusion reactors. -
Question 19 of 35
19. Question
With reference to major scientific contributions by Indians, consider the following pairs:
- N. Saha – Quantum statistics
- N. Bose – Thermal ionisation
- Chandrasekhar – Structure and evolution of stars
How many of the pairs given above is/are correct?
Correct
Solution (a)
Statement 1 Statement 2 Statement 3 Incorrect Incorrect Correct Meghnad Saha (1893–1956) was an Indian physicist who did much of his work in the last decades of British colonial rule. In the 1920s he made important contributions to the theory of thermal ionization and its application to stellar spectra. Satyendra Nath Bose was an Indian mathematician and physicist specialising in theoretical physics. He is best known for his work on quantum mechanics in the early 1920s, in developing the foundation for Bose statistics and the theory of the Bose condensate. Subrahmanyan Chandrasekhar was an Indian-American astrophysicist who spent his professional life in the United States. He shared the 1983 Nobel Prize for Physics with William A. Fowler for “…theoretical studies of the physical processes of importance to the structure and evolution of the stars“. Incorrect
Solution (a)
Statement 1 Statement 2 Statement 3 Incorrect Incorrect Correct Meghnad Saha (1893–1956) was an Indian physicist who did much of his work in the last decades of British colonial rule. In the 1920s he made important contributions to the theory of thermal ionization and its application to stellar spectra. Satyendra Nath Bose was an Indian mathematician and physicist specialising in theoretical physics. He is best known for his work on quantum mechanics in the early 1920s, in developing the foundation for Bose statistics and the theory of the Bose condensate. Subrahmanyan Chandrasekhar was an Indian-American astrophysicist who spent his professional life in the United States. He shared the 1983 Nobel Prize for Physics with William A. Fowler for “…theoretical studies of the physical processes of importance to the structure and evolution of the stars“. -
Question 20 of 35
20. Question
People with hearing loss may need a hearing aid. This hearing aid consists of which of the following components?
- Amplifier
- Microphone
- Speaker
Select the answer:
Correct
Solution (d)
Statement 1 Statement 2 Statement 3 Correct Correct Correct The hearing aid receives sound through a microphone. The microphone converts the sound waves to electrical signals. These electrical signals are amplified by an amplifier. The amplified electrical signals are given to a speaker of the hearing aid. The speaker converts the amplified electrical signal to sound and sends to the ear for clear hearing. Incorrect
Solution (d)
Statement 1 Statement 2 Statement 3 Correct Correct Correct The hearing aid receives sound through a microphone. The microphone converts the sound waves to electrical signals. These electrical signals are amplified by an amplifier. The amplified electrical signals are given to a speaker of the hearing aid. The speaker converts the amplified electrical signal to sound and sends to the ear for clear hearing. -
Question 21 of 35
21. Question
Consider the following statements regarding the Production Linked Incentive Scheme (PLI):
- It aims to scale up domestic manufacturing capability, accompanied by higher import substitution and employment generation.
- It is currently active in three key sectors – mobile manufacturing, manufacturing of medical devices, and automobiles and auto components.
- It provides financial rewards to domestic and foreign companies for manufacturing in India, based on a percentage of their revenue over up to five years.
How many of the above statements are correct?
Correct
Solution (b)
- The Production Linked Incentive Scheme (PLI) aims to scale up domestic manufacturing capability, accompanied by higher import substitution and employment generation. Hence statement 1 is correct.
- It is currently active in 14 key sectors – mobile manufacturing, manufacturing of medical devices, automobiles and auto components, pharmaceuticals, drugs, specialty steel, telecom & networking products, electronic products, white goods (ACs and LEDs), food products, textile products, solar PV modules, advanced chemistry cell (ACC) battery, and drones and drone components. Hence statement 2 is incorrect.
- It provides financial rewards to domestic and foreign companies for manufacturing in India, based on a percentage of their revenue over up to five years. Hence statement 3 is correct.
Incorrect
Solution (b)
- The Production Linked Incentive Scheme (PLI) aims to scale up domestic manufacturing capability, accompanied by higher import substitution and employment generation. Hence statement 1 is correct.
- It is currently active in 14 key sectors – mobile manufacturing, manufacturing of medical devices, automobiles and auto components, pharmaceuticals, drugs, specialty steel, telecom & networking products, electronic products, white goods (ACs and LEDs), food products, textile products, solar PV modules, advanced chemistry cell (ACC) battery, and drones and drone components. Hence statement 2 is incorrect.
- It provides financial rewards to domestic and foreign companies for manufacturing in India, based on a percentage of their revenue over up to five years. Hence statement 3 is correct.
-
Question 22 of 35
22. Question
Consider the following statements regarding the Mahakaleshwar Temple:
- It is situated beside the Rudra Sagar Lake in Uttar Pradesh.
- It is a Hindu temple dedicated to Shiva and is one of the twelve Jyotirlingams.
- Its idol is Dakshina Mukhi, facing south, unlike all the other Jyotirlingas.
How many of the above statements are correct?
Correct
Solution (b)
- The Mahakaleshwar Temple is situated beside the Rudra Sagar Lake in Madhya Pradesh. Hence statement 1 is incorrect.
- The temple complex comes with a spacious courtyard that is adorned with the finest sculptures that are believed to be influenced by the Chalukya, Maratha, and Bhumija styles of structural design.
- It is a Hindu temple dedicated to Shiva and is one of the twelve Jyotirlingams. Hence statement 2 is correct.
- The images of Ganesh, Parvati, and Karttikeya are installed in the west, north, and east of the sanctum sanctorum.
- Its idol is Dakshina Mukhi, facing south, unlike all the other Jyotirlingas. Hence statement 3 is correct.
- The temple also houses a tank constructed in the Sarvatobhadra style.
Incorrect
Solution (b)
- The Mahakaleshwar Temple is situated beside the Rudra Sagar Lake in Madhya Pradesh. Hence statement 1 is incorrect.
- The temple complex comes with a spacious courtyard that is adorned with the finest sculptures that are believed to be influenced by the Chalukya, Maratha, and Bhumija styles of structural design.
- It is a Hindu temple dedicated to Shiva and is one of the twelve Jyotirlingams. Hence statement 2 is correct.
- The images of Ganesh, Parvati, and Karttikeya are installed in the west, north, and east of the sanctum sanctorum.
- Its idol is Dakshina Mukhi, facing south, unlike all the other Jyotirlingas. Hence statement 3 is correct.
- The temple also houses a tank constructed in the Sarvatobhadra style.
-
Question 23 of 35
23. Question
Consider the following statements regarding the Pravasi Bharatiya Diwas:
- It is celebrated on January 9 to mark the contribution and achievements of the overseas Indian community to the development of India.
- It is the flagship event of the Ministry of Tourism.
Choose the correct code:
Correct
Solution (a)
- The Pravasi Bharatiya Diwas is celebrated on January 9 to mark the contribution and achievements of the overseas Indian community to the development of India. Hence statement 1 is correct.
- It commemorates the return of Mahatma Gandhi, the greatest Pravasi, from South Africa to India in 1915, who led India’s freedom struggle and changed the lives of Indians forever.
- It was first celebrated in 2003. It was an annual event earlier, but in 2015, the government revised its format to celebrate PBD once every two years.
- It is the flagship event of the Ministry of External Affairs. Hence statement 2 is incorrect.
- It has become a platform to connect the Indian diaspora with their roots and encourage their continued engagement with India’s progress.
- It is held in different cities, to showcase the diversity and progress of different regions of Toa. To date, 17 conventions have been held. The last Pravasi Bharatiya Divas was celebrated in the Indore of Madhya Pradesh in 2023.
Incorrect
Solution (a)
- The Pravasi Bharatiya Diwas is celebrated on January 9 to mark the contribution and achievements of the overseas Indian community to the development of India. Hence statement 1 is correct.
- It commemorates the return of Mahatma Gandhi, the greatest Pravasi, from South Africa to India in 1915, who led India’s freedom struggle and changed the lives of Indians forever.
- It was first celebrated in 2003. It was an annual event earlier, but in 2015, the government revised its format to celebrate PBD once every two years.
- It is the flagship event of the Ministry of External Affairs. Hence statement 2 is incorrect.
- It has become a platform to connect the Indian diaspora with their roots and encourage their continued engagement with India’s progress.
- It is held in different cities, to showcase the diversity and progress of different regions of Toa. To date, 17 conventions have been held. The last Pravasi Bharatiya Divas was celebrated in the Indore of Madhya Pradesh in 2023.
-
Question 24 of 35
24. Question
Consider the following statements about the Scheme for Residential Education for Students in High Schools in Targeted Areas (SHRESHTA):
- It aims to provide access to the best private residential schools for meritorious students from Scheduled Caste (SC) communities.
- It is implemented by the Department of Social Justice and Empowerment, Ministry of Social Justice & Empowerment.
Choose the correct code:
Correct
Solution (c)
- The Scheme for Residential Education for Students in High Schools in Targeted Areas (SHRESHTA) aims to provide access to the best private residential schools for meritorious students from Scheduled Caste (SC) communities. Hence statement 1 is correct.
- It will provide scholarships to meritorious students from SC communities to study in private and NGO-run residential schools for Classes 9-12.
- It is implemented by the Department of Social Justice and Empowerment, Ministry of Social Justice & Empowerment. Hence statement 2 is correct.
- The core objectives of the scheme are to enhance the reach of the development initiatives of the government and fill in the gap in service-deprived SC dominant areas in the education sector.
- The scheme will collaborate with voluntary organisations to provide an environment that can help create conditions for socio-economic upliftment and the overall development of the SC communities.
- Students whose annual parental income is less than Rs 2,50,000 and who belong to SC communities are eligible to participate in this scheme.
- Only those candidates who have passed or are appearing in Class VIII/X in the given academic session can apply for admission to Class IX/XI.
Incorrect
Solution (c)
- The Scheme for Residential Education for Students in High Schools in Targeted Areas (SHRESHTA) aims to provide access to the best private residential schools for meritorious students from Scheduled Caste (SC) communities. Hence statement 1 is correct.
- It will provide scholarships to meritorious students from SC communities to study in private and NGO-run residential schools for Classes 9-12.
- It is implemented by the Department of Social Justice and Empowerment, Ministry of Social Justice & Empowerment. Hence statement 2 is correct.
- The core objectives of the scheme are to enhance the reach of the development initiatives of the government and fill in the gap in service-deprived SC dominant areas in the education sector.
- The scheme will collaborate with voluntary organisations to provide an environment that can help create conditions for socio-economic upliftment and the overall development of the SC communities.
- Students whose annual parental income is less than Rs 2,50,000 and who belong to SC communities are eligible to participate in this scheme.
- Only those candidates who have passed or are appearing in Class VIII/X in the given academic session can apply for admission to Class IX/XI.
-
Question 25 of 35
25. Question
Consider the following statements regarding the International Classification of Diseases:
- It is developed by the World Health Organization (WHO) to classify diseases internationally.
- It facilitates the collection and dissemination of data on various diseases and mortality.
- In India, the Central Bureau of Health Intelligence (CBHI) under the Ministry of Health and Family Welfare serves as its collaborator.
How many of the above statements are correct?
Correct
Solution (c)
- The International Classification of Diseases (ICD) is developed by the World Health Organization (WHO) to classify diseases internationally. Hence statement 1 is correct.
- The global data on diseases currently available is mainly based on healthcare practices to be diagnosed through modern biomedicine.
- It serves a broad range of uses globally and provides critical knowledge on the extent, causes, and consequences of human disease and death worldwide via data that is reported and coded with the ICD.
- Clinical terms coded with ICD are the main basis for health recording and statistics on disease in primary, secondary, and tertiary care, as well as on cause of death certificates.
- It facilitates the collection and dissemination of data on various diseases and mortality. Hence statement 2 is correct.
- These data and statistics support payment systems, service planning, administration of quality and safety, and health services research.
- Diagnostic guidance linked to categories of ICD also standardizes data collection and enables large-scale research.
- The classification of data and terminology relating to diseases based on Ayush systems such as Ayurveda, Siddha, Unani, etc. is not yet included in the WHO ICD series.
- In India, the Central Bureau of Health Intelligence (CBHI) under the Ministry of Health and Family Welfare serves as its collaborator. Hence statement 3 is correct.
Incorrect
Solution (c)
- The International Classification of Diseases (ICD) is developed by the World Health Organization (WHO) to classify diseases internationally. Hence statement 1 is correct.
- The global data on diseases currently available is mainly based on healthcare practices to be diagnosed through modern biomedicine.
- It serves a broad range of uses globally and provides critical knowledge on the extent, causes, and consequences of human disease and death worldwide via data that is reported and coded with the ICD.
- Clinical terms coded with ICD are the main basis for health recording and statistics on disease in primary, secondary, and tertiary care, as well as on cause of death certificates.
- It facilitates the collection and dissemination of data on various diseases and mortality. Hence statement 2 is correct.
- These data and statistics support payment systems, service planning, administration of quality and safety, and health services research.
- Diagnostic guidance linked to categories of ICD also standardizes data collection and enables large-scale research.
- The classification of data and terminology relating to diseases based on Ayush systems such as Ayurveda, Siddha, Unani, etc. is not yet included in the WHO ICD series.
- In India, the Central Bureau of Health Intelligence (CBHI) under the Ministry of Health and Family Welfare serves as its collaborator. Hence statement 3 is correct.
-
Question 26 of 35
26. Question
Consider the following statements regarding the MCG-01-24-014:
- It is a galaxy situated approximately 275 million light-years away from Earth in the constellation of Hydra.
- It falls under the category of Type-2 Seyfert galaxies.
Choose the correct code:
Correct
Solution (c)
- The MCG-01-24-014 is a galaxy situated approximately 275 million light-years away from Earth in the constellation of Hydra. Hence statement 1 is correct.
- It boasts a well-defined structure and an extremely energetic core classified as an active galactic nucleus (AGN).
- It falls under the category of Type-2 Seyfert galaxies. Hence statement 2 is correct.
- Seyfert galaxies are any of a class of galaxies known to have active nuclei. They are one of the most common types of active galaxies, sharing the stage with the more distant and luminous quasars.
Incorrect
Solution (c)
- The MCG-01-24-014 is a galaxy situated approximately 275 million light-years away from Earth in the constellation of Hydra. Hence statement 1 is correct.
- It boasts a well-defined structure and an extremely energetic core classified as an active galactic nucleus (AGN).
- It falls under the category of Type-2 Seyfert galaxies. Hence statement 2 is correct.
- Seyfert galaxies are any of a class of galaxies known to have active nuclei. They are one of the most common types of active galaxies, sharing the stage with the more distant and luminous quasars.
-
Question 27 of 35
27. Question
Consider the following statements regarding Kavaratti Island:
- It is located between Agatti Island on the west and Andrott Island on the east.
- It has been selected as one of the hundred Indian cities to be developed as a smart city under the flagship Smart Cities Mission.
Choose the correct code:
Correct
Solution (c)
- Kavaratti Island is located between Agatti Island on the west and Andrott Island on the east. Hence statement 1 is correct.
- It is the capital of Lakshadweep (the smallest Union Territory of India) and its most developed island.
- It lies 360 km off the coast of the State of Kerala.
- It is located in the centre of the Lakshadweep archipelago.
- It has been selected as one of the hundred Indian cities to be developed as a smart city under the flagship Smart Cities Mission. Hence statement 2 is correct.
- There is a shallow lagoon on the western side of the island, and coconut palms grow on the northern side.
- The island is home to 12 atolls, five submerged banks, and three coral reefs.
- It is noted for the carved wooden pillars and roofs of its mosques and the carved stones of its graveyards.
Incorrect
Solution (c)
- Kavaratti Island is located between Agatti Island on the west and Andrott Island on the east. Hence statement 1 is correct.
- It is the capital of Lakshadweep (the smallest Union Territory of India) and its most developed island.
- It lies 360 km off the coast of the State of Kerala.
- It is located in the centre of the Lakshadweep archipelago.
- It has been selected as one of the hundred Indian cities to be developed as a smart city under the flagship Smart Cities Mission. Hence statement 2 is correct.
- There is a shallow lagoon on the western side of the island, and coconut palms grow on the northern side.
- The island is home to 12 atolls, five submerged banks, and three coral reefs.
- It is noted for the carved wooden pillars and roofs of its mosques and the carved stones of its graveyards.
-
Question 28 of 35
28. Question
Consider the following statements:
- Chandubi Festival is organised every year along the Chandubi Lake in the state of Assam.
- Chandubi Lake is a saline lake that was created during a massive earthquake in the year 1897.
Choose the correct code:
Correct
Solution (a)
- Chandubi Festival is organised every year along the Chandubi Lake in the state of Assam. Hence statement 1 is correct.
- The main attractions of the Chandubi festival are the local folk culture, ethnic cuisine, local handloom and dresses, boating, etc.
- The major aim of the Chandubi Festival is to promote eco-tourism in this biodiversity hotspot of Assam.
- Chandubi Lake is a freshwater lake that was created during a massive earthquake in the year 1897. Hence statement 2 is incorrect.
- The name Chandubi is derived from two words where Chand means five and Dubi means sinking in Khasi language.
- It was turned into an economically viable water body that would sustain different communities living around the lake.
Incorrect
Solution (a)
- Chandubi Festival is organised every year along the Chandubi Lake in the state of Assam. Hence statement 1 is correct.
- The main attractions of the Chandubi festival are the local folk culture, ethnic cuisine, local handloom and dresses, boating, etc.
- The major aim of the Chandubi Festival is to promote eco-tourism in this biodiversity hotspot of Assam.
- Chandubi Lake is a freshwater lake that was created during a massive earthquake in the year 1897. Hence statement 2 is incorrect.
- The name Chandubi is derived from two words where Chand means five and Dubi means sinking in Khasi language.
- It was turned into an economically viable water body that would sustain different communities living around the lake.
-
Question 29 of 35
29. Question
Consider the following statements about Elasmobranch:
- It refers to the sharks, rays, and skates.
- They have a skeleton made of bone.
- They have large livers full of oil to provide buoyancy.
How many of the above statements are correct?
Correct
Solution (b)
- Elasmobranch refers to the sharks, rays, and skates. Hence statement 1 is correct.
- They have five to seven-gill openings on each side.
- Spiracles aid in breathing.
- They have a skeleton made of cartilage, rather than bone. Hence statement 2 is incorrect.
- They have several rows of teeth which are continually replaced.
- Their skin is made of tiny, hard, tooth-like placoid scales called denticles.
- These are renowned for their highly tuned senses, which make them incredibly successful in their environment.
- They don’t have swim bladders, but instead, their large livers are full of oil to provide buoyancy. Hence statement 3 is correct.
- They reproduce sexually with internal fertilization and either bear live young or lay eggs.
Incorrect
Solution (b)
- Elasmobranch refers to the sharks, rays, and skates. Hence statement 1 is correct.
- They have five to seven-gill openings on each side.
- Spiracles aid in breathing.
- They have a skeleton made of cartilage, rather than bone. Hence statement 2 is incorrect.
- They have several rows of teeth which are continually replaced.
- Their skin is made of tiny, hard, tooth-like placoid scales called denticles.
- These are renowned for their highly tuned senses, which make them incredibly successful in their environment.
- They don’t have swim bladders, but instead, their large livers are full of oil to provide buoyancy. Hence statement 3 is correct.
- They reproduce sexually with internal fertilization and either bear live young or lay eggs.
-
Question 30 of 35
30. Question
How many different words can be formed from the letters of the word EDUCATION so
that vowels are always together?
Correct
Solution (b)
The vowels in the order presented are: E, U, A, I, O or perhaps better sorted as: A, E, I, O, U Think of the vowels as one block, and have some other letter (say X) representing that block. We go from the word EDUCATION to X,D,C,T,N
The initial 9 letter word drops to 9-5 = 4 letters after we kick out the vowels. Then introducing letter X brings the count up to 5 letters.
Anywhere you see an X, replace it with some permutation of A,E,I,O,U.
There are 5! = 5*4*3*2*1 = 120 ways to arrange X,D,C,T,N
And there are 5! = 120 ways to arrange the five vowels.
Overall, there are (5!)*(5!) = 120*120 = 14400 different arrangements such that the vowels stick together.
Incorrect
Solution (b)
The vowels in the order presented are: E, U, A, I, O or perhaps better sorted as: A, E, I, O, U Think of the vowels as one block, and have some other letter (say X) representing that block. We go from the word EDUCATION to X,D,C,T,N
The initial 9 letter word drops to 9-5 = 4 letters after we kick out the vowels. Then introducing letter X brings the count up to 5 letters.
Anywhere you see an X, replace it with some permutation of A,E,I,O,U.
There are 5! = 5*4*3*2*1 = 120 ways to arrange X,D,C,T,N
And there are 5! = 120 ways to arrange the five vowels.
Overall, there are (5!)*(5!) = 120*120 = 14400 different arrangements such that the vowels stick together.
-
Question 31 of 35
31. Question
Consider the following statements regarding Sky Dew:
- It is a high-altitude observation balloon that acts as a detection radar blip for small unmanned aircraft and cruise missiles.
- It has been jointly developed by Israel Defense and US company TCOM.
Choose the correct code:
Correct
Solution (c)
- Sky Dew is a high-altitude observation balloon that acts as a detection radar blip for small unmanned aircraft and cruise missiles. Hence statement 1 is correct.
- It is one of the largest aerial threat warning systems in the world.
- It has been jointly developed by Israel Defense and US company TCOM. Hence statement 2 is correct.
- The project was entirely funded by the U.S. Department of Defence. The Israel Air Force was handed over the Sky Dew in 2022.
- The system comprises a blimp capable of flying at high altitudes with radar and detection systems to scan a wide range in any direction.
- The radar on the balloon is capable of observing at 250 km and tracking multiple targets, including low-altitude ones and those in valleys. It can carry 7,000 pounds and has an operational altitude of 10,000 feet.
Incorrect
Solution (c)
- Sky Dew is a high-altitude observation balloon that acts as a detection radar blip for small unmanned aircraft and cruise missiles. Hence statement 1 is correct.
- It is one of the largest aerial threat warning systems in the world.
- It has been jointly developed by Israel Defense and US company TCOM. Hence statement 2 is correct.
- The project was entirely funded by the U.S. Department of Defence. The Israel Air Force was handed over the Sky Dew in 2022.
- The system comprises a blimp capable of flying at high altitudes with radar and detection systems to scan a wide range in any direction.
- The radar on the balloon is capable of observing at 250 km and tracking multiple targets, including low-altitude ones and those in valleys. It can carry 7,000 pounds and has an operational altitude of 10,000 feet.
-
Question 32 of 35
32. Question
How many odd numbers with distinct digits can be created using the digits 1, 2, 3, 4, 5 and 6?
Correct
Solution (c)
=> Single digit numbers: 1, 3 or 5: Three numbers
=> Two–digit numbers: Units digit = 1, 3 or 5. For the tens’ digit, there are 5 choices {anything apart from what went into the units digit}. So, there will be 3 × 5 = 15 such numbers.
=> Three–digit numbers: Units digit = 1, 3 or 5. For the tens’ digit, there are 5 choices {anything apart from what went into the units digit}. For the 100s’ digit, there are 4 choices {anything apart from what went into the units digit or tens digit}. So, there will be 3 * 5 * 4 = 60 such numbers.
=> 4–digit numbers: There will be 3 * 5 * 4 * 3 = 180 numbers.
=> 5–digit numbers: There will be 3 * 5 * 4 * 3 * 2 = 360 numbers.
=> 6–digit numbers: There will be 3 * 5 * 4 * 3 * 2 * 1 = 360 numbers.Total number of numbers = 360 + 360 + 180 + 60 + 15 + 3 = 978
Incorrect
Solution (c)
=> Single digit numbers: 1, 3 or 5: Three numbers
=> Two–digit numbers: Units digit = 1, 3 or 5. For the tens’ digit, there are 5 choices {anything apart from what went into the units digit}. So, there will be 3 × 5 = 15 such numbers.
=> Three–digit numbers: Units digit = 1, 3 or 5. For the tens’ digit, there are 5 choices {anything apart from what went into the units digit}. For the 100s’ digit, there are 4 choices {anything apart from what went into the units digit or tens digit}. So, there will be 3 * 5 * 4 = 60 such numbers.
=> 4–digit numbers: There will be 3 * 5 * 4 * 3 = 180 numbers.
=> 5–digit numbers: There will be 3 * 5 * 4 * 3 * 2 = 360 numbers.
=> 6–digit numbers: There will be 3 * 5 * 4 * 3 * 2 * 1 = 360 numbers.Total number of numbers = 360 + 360 + 180 + 60 + 15 + 3 = 978
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Question 33 of 35
33. Question
256 players participate in a chess tournament. Two players play a match. Matches are played on a knock-out basis, wherein loser in a match is eliminated from the tournament. All the matches produce a winner. How many matches have to be played to determine the winner of the tournament?
Correct
Solution (b)
For two players, we need one match.
The first round, having 256 players will need 256/2 = 128 matches.
Now there are 128 players left. To ensure that all players play a match, we need 128/2 = 64 matches
Continuing in the same way Total number of matches = 128+64+ 32+ 16+8+4+2+1= 255
OR
In 1 match 1 player is eliminated For tournament to conclude there should be only 1 winner and hence 255 players need to lose. Hence we need 255 matches to eliminate 255 players. Hence option (b).
Incorrect
Solution (b)
For two players, we need one match.
The first round, having 256 players will need 256/2 = 128 matches.
Now there are 128 players left. To ensure that all players play a match, we need 128/2 = 64 matches
Continuing in the same way Total number of matches = 128+64+ 32+ 16+8+4+2+1= 255
OR
In 1 match 1 player is eliminated For tournament to conclude there should be only 1 winner and hence 255 players need to lose. Hence we need 255 matches to eliminate 255 players. Hence option (b).
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Question 34 of 35
34. Question
How many zeroes are there at the end of the product 1*2*3*——*19*20?
Correct
Solution (d)
Zero is there when we have 2 x 5. This creates 10 and as many pairs of 2 x 5 are there we will have same number of zeros at the end.
Now, there are 10 twos in the series as there are 10 even numbers from 1 to 20. So, we need to check the number of fives. We have fives at 5, 10 (5 x 2), 15 (5 x 3) and 20 (5 x 2 x 2). So, the number of zeros at the end will be 4.
Incorrect
Solution (d)
Zero is there when we have 2 x 5. This creates 10 and as many pairs of 2 x 5 are there we will have same number of zeros at the end.
Now, there are 10 twos in the series as there are 10 even numbers from 1 to 20. So, we need to check the number of fives. We have fives at 5, 10 (5 x 2), 15 (5 x 3) and 20 (5 x 2 x 2). So, the number of zeros at the end will be 4.
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Question 35 of 35
35. Question
Consider a class of 40 students whose average weight is 40 kg. m new students join this class whose average weight is n kg. If it is known that m + n = 50, what is the maximum possible average weight of the class now?
Correct
Solution (b)
If the overall average weight has to increase after the new people are added, the average weight of the new entrants has to be higher than 40.
So, n > 40Consequently, m has to be < 10 (as n + m = 50)
Working with the “differences” approach, we know that the total additional weight added by “m” students would be (n – 40) each, above the already existing average of 40.m(n – 40) is the total extra additional weight added, which is shared amongst 40 + m students.
So, m * (n−40)/(m+40) has to be maximum for the overall average to be maximum.
At this point, use the trial and error approach (or else, go with the answer options) to arrive at the answer
The maximum average occurs when m = 5, and n = 45
And the average is 40 + (45 – 40) * 5/45 = 40 + 5/9 = 40.56 kgsIncorrect
Solution (b)
If the overall average weight has to increase after the new people are added, the average weight of the new entrants has to be higher than 40.
So, n > 40Consequently, m has to be < 10 (as n + m = 50)
Working with the “differences” approach, we know that the total additional weight added by “m” students would be (n – 40) each, above the already existing average of 40.m(n – 40) is the total extra additional weight added, which is shared amongst 40 + m students.
So, m * (n−40)/(m+40) has to be maximum for the overall average to be maximum.
At this point, use the trial and error approach (or else, go with the answer options) to arrive at the answer
The maximum average occurs when m = 5, and n = 45
And the average is 40 + (45 – 40) * 5/45 = 40 + 5/9 = 40.56 kgs
All the Best
IASbaba