IASbaba's Flagship Course: Integrated Learning Programme (ILP) - 2024 Read Details
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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
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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.
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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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The spread in colours in a rainbow on sky is primarily due to?
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).
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).
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?
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.
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.
Consider the following statements w.r.t ‘Incandescent Electric Bulb and Fluorescent Light Bulb’:
How many of the above statements are correct?
Solution (b)
Incandescent Electric Bulb and Fluorescent Light Bulb
Solution (b)
Incandescent Electric Bulb and Fluorescent Light Bulb
Consider the following pairs:
How many of the above pairs are 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.
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.
Consider the following:
How many of the above statements are correct?
Solution (c)
Solution (c)
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?
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.
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.
With reference to the Bose-Einstein Condensate, which of the following statement is 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. |
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. |
The term ‘Tyndall effect’ is related to?
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.
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.
‘The electromagnets are the magnets that are created when the electric current is passed through it’. Which of the following are based on electromagnetism?
Select the correct code:
Solution (d)
Electromagnet
Solution (d)
Electromagnet
What do you understand by the term ‘Sonic boom’?
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.
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.
Consider the following statements and identify the correct one/s:
How many of the above statements are 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. |
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. |
Consider the following w.r.t ddifferences between Alternating Current and Direct Current (AC and DC):
How many of the above statements are correct?
Solution (c)
Electricity flows in two ways: in an alternating current (AC) or in a direct current (DC).
Solution (c)
Electricity flows in two ways: in an alternating current (AC) or in a direct current (DC).
Consider the following w.r.t ‘Refractive Index’:
How many of the above statements are 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.
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.
Consider the following statements and identify the incorrect one/s:
Select the answer:
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. |
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. |
Consider the following statements with respect to Pole star:
How many of the above statements are 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) |
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) |
Consider the following statements:
Which of the statement/s given above is/are 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. |
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. |
Consider the following statements with reference to ‘Microwave Oven’ and identify the correct statement/s:
Which of the statement/s given above is/are 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. |
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. |
Consider the following pairs with reference to link between technology and associated principle:
Technology Scientific principle(s)
Select the correct match:
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. |
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. |
With reference to major scientific contributions by Indians, consider the following pairs:
How many of the pairs given above is/are 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“. |
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“. |
People with hearing loss may need a hearing aid. This hearing aid consists of which of the following components?
Select the answer:
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. |
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. |
Consider the following statements regarding the Production Linked Incentive Scheme (PLI):
How many of the above statements are correct?
Solution (b)
Solution (b)
Consider the following statements regarding the Mahakaleshwar Temple:
How many of the above statements are correct?
Solution (b)
Solution (b)
Consider the following statements regarding the Pravasi Bharatiya Diwas:
Choose the correct code:
Solution (a)
Solution (a)
Consider the following statements about the Scheme for Residential Education for Students in High Schools in Targeted Areas (SHRESHTA):
Choose the correct code:
Solution (c)
Solution (c)
Consider the following statements regarding the International Classification of Diseases:
How many of the above statements are correct?
Solution (c)
Solution (c)
Consider the following statements regarding the MCG-01-24-014:
Choose the correct code:
Solution (c)
Solution (c)
Consider the following statements regarding Kavaratti Island:
Choose the correct code:
Solution (c)
Solution (c)
Consider the following statements:
Choose the correct code:
Solution (a)
Solution (a)
Consider the following statements about Elasmobranch:
How many of the above statements are correct?
Solution (b)
Solution (b)
How many different words can be formed from the letters of the word EDUCATION so
that vowels are always together?
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.
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.
Consider the following statements regarding Sky Dew:
Choose the correct code:
Solution (c)
Solution (c)
How many odd numbers with distinct digits can be created using the digits 1, 2, 3, 4, 5 and 6?
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
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
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?
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).
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).
How many zeroes are there at the end of the product 1*2*3*——*19*20?
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.
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.
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?
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 > 40
Consequently, 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
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 > 40
Consequently, 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