Hello Friends
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 Current Affairs MCQs (Monday – Saturday)
Daily CSAT Quiz (Monday – Friday)
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
0 of 35 questions completed
Questions:
The following Test is based on the syllabus of 60 Days Plan-2025 for UPSC IAS Prelims 2025.
To view Solutions, follow these instructions:
You have already completed the test before. Hence you can not start it again.
Test is loading...
You must sign in or sign up to start the test.
You have to finish following test, to start this test:
0 of 35 questions answered correctly
Your time:
Time has elapsed
You have scored 0 points out of 0 points, (0)
| Average score |
|
| Your score |
|
| Pos. | Name | Entered on | Points | Result |
|---|---|---|---|---|
| Table is loading | ||||
| No data available | ||||
Consider the following statements regarding the systems of voting:
Which of the given above are demerits of the system of Proportional Representation?
Solution (d)
Statement Analysis:
Solution (d)
Statement Analysis:
Consider the following statements regarding the Leader of Opposition (LoP):
How many of the above statements is/are correct?
Solution (c)
Statement Analysis:
Currently, the Lok Sabha and Rajya Sabha have their own Leader of Opposition. Hence, Statement 3 is correct.
Solution (c)
Statement Analysis:
Currently, the Lok Sabha and Rajya Sabha have their own Leader of Opposition. Hence, Statement 3 is correct.
Consider the following statements regarding vacating of seats of Members of Parliament:
Select the answer using the code below:
Solution (d)
Statement Analysis:
The disqualifications cover a range of conditions, including defection as outlined in the Tenth Schedule of the Constitution. Hence, Statement 3 is correct.
Solution (d)
Statement Analysis:
The disqualifications cover a range of conditions, including defection as outlined in the Tenth Schedule of the Constitution. Hence, Statement 3 is correct.
Consider the following statements regarding the Special Powers of Rajya Sabha:
Select the answer using the code below:
Solution (a)
Statement Analysis:
The Special Powers of the Rajya Sabha are:
Under Article 312, Rajya Sabha can authorise the Parliament to create new All-India Services common to both the centre and states. Hence, Statement 3 is correct.
Solution (a)
Statement Analysis:
The Special Powers of the Rajya Sabha are:
Under Article 312, Rajya Sabha can authorise the Parliament to create new All-India Services common to both the centre and states. Hence, Statement 3 is correct.
Consider the following statements:
Statement I: Article 110 of the Constitution deals with the definition of Money Bills.
Statement II: The money bill’s defeat in the Lok Sabha leads to the resignation of the government.
Which one of the following is correct with respect to the above statements?
Solution (b)
Statement Analysis:
Solution (b)
Statement Analysis:
Consider the following statements regarding the duties and powers of the Prime Minister with respect to the President of India:
Select the answer using the code below:
Solution (d)
Statement Analysis:
If the President of India requires that the Prime Minister shall submit for the consideration of the Council of Ministers any matter on which a decision has been taken by a minister, but which has not been considered by the Council. Hence, Statement 3 is correct
Solution (d)
Statement Analysis:
If the President of India requires that the Prime Minister shall submit for the consideration of the Council of Ministers any matter on which a decision has been taken by a minister, but which has not been considered by the Council. Hence, Statement 3 is correct
Consider the following statements about the Departmentally Related Standing Committees (DRSCs):
Select the answer using the code below:
Solution (c)
Statement Analysis:
Solution (c)
Statement Analysis:
Consider the following statements regarding the ‘Special Mention’ in Parliament:
Which of the above given statements is/are correct?
Solution (c)
Statement Analysis:
A matter that is not a point of order or which cannot be raised during question hour, half-an-hour discussion, short duration discussion, calling attention notice, or under any rule of the House can be raised under the special mention. Hence, Statement 2 is correct.
Solution (c)
Statement Analysis:
A matter that is not a point of order or which cannot be raised during question hour, half-an-hour discussion, short duration discussion, calling attention notice, or under any rule of the House can be raised under the special mention. Hence, Statement 2 is correct.
Consider the following statements regarding the ‘Public Accounts Committee’:
How many of the above statements is/are correct?
Solution (a)
Statement Analysis:
Solution (a)
Statement Analysis:
Consider the following statements regarding the ‘Kitchen Cabinet’:
How many of the above statements is/are correct?
Solution (d)
Statement Analysis:
Solution (d)
Statement Analysis:
The Vice-President of India is elected by the members of an electoral college consisting of
Select the answer using the code below:
Solution (b)
Statement Analysis:
The Vice-President, like the president, is elected indirectly. The Vice-President of India is elected by an electoral college consisting of all the members of both houses of Parliament. This includes both Nominated members of Parliament and elected members of Parliament. Hence, option b is correct.
Solution (b)
Statement Analysis:
The Vice-President, like the president, is elected indirectly. The Vice-President of India is elected by an electoral college consisting of all the members of both houses of Parliament. This includes both Nominated members of Parliament and elected members of Parliament. Hence, option b is correct.
Consider the following statements regarding the Parliamentary Privileges of Parliament:
How many of the above statements is/are correct?
Solution (c)
Statement Analysis:
Solution (c)
Statement Analysis:
Consider the following statements regarding the functioning of the 17th Lok Sabha:
Which of the above given statements is/are correct?
Solution (a)
Statement Analysis:
The 17th Lok Sabha, which met from June 2019 to February 2024, conducted a noteworthy total of 274 sessions, lasting for 1,354 hours, and achieved a commendable work productivity rate of approximately 97%.
The functioning of the 17th Lok Sabha:
Solution (a)
Statement Analysis:
The 17th Lok Sabha, which met from June 2019 to February 2024, conducted a noteworthy total of 274 sessions, lasting for 1,354 hours, and achieved a commendable work productivity rate of approximately 97%.
The functioning of the 17th Lok Sabha:
Consider the following statements regarding the ‘Motion of Thanks’:
How many of the above statements is/are correct?
Solution (c)
Statement Analysis:
Solution (c)
Statement Analysis:
Consider the following statements regarding the Suspension of Members of Parliament:
Which of the above given statements is/are correct?
Solution (c)
Statement Analysis:
Rules of Procedure and Conduct of Business of Lok Sabha :
Rules of Procedure and Conduct of Business of Rajya Sabha:
The power to suspend is vested in the Speaker of the Lok Sabha and the Chairman of the Rajya Sabha. Hence, Statement 2 is correct.
Solution (c)
Statement Analysis:
Rules of Procedure and Conduct of Business of Lok Sabha :
Rules of Procedure and Conduct of Business of Rajya Sabha:
The power to suspend is vested in the Speaker of the Lok Sabha and the Chairman of the Rajya Sabha. Hence, Statement 2 is correct.
Consider the following statements regarding the ‘Ethics Committee’:
How many of the above statements is/are correct?
Solution (b)
Statement Analysis:
The Lok Sabha committee has 15 members while the Rajya Sabha committee has 10 members. Hence, Statement 3 is correct.
Solution (b)
Statement Analysis:
The Lok Sabha committee has 15 members while the Rajya Sabha committee has 10 members. Hence, Statement 3 is correct.
Consider the following statements with respect to ‘Parliamentary Forums’ in India:
How many of the statements above are correct?
Solution (a)
Explanation:
There is no obligation on these forums to submit an annual report to the President of India. Hence Statement 4 is incorrect.
Solution (a)
Explanation:
There is no obligation on these forums to submit an annual report to the President of India. Hence Statement 4 is incorrect.
With reference to the ‘Indian Parliamentary Group’, consider the following statements:
How many of the statements given above are correct?
Solution (b)
Explanation:
The Speaker of the Lok Sabha is the ex officio president of the Group. The Deputy Speaker of the Lok Sabha and the Deputy Chairman of the Rajya Sabha are the ex officio vice-presidents of the Group. The Secretary-General of the Lok Sabha acts as the ex officio Secretary-General of the Group. Hence Statement 3 is correct.
Solution (b)
Explanation:
The Speaker of the Lok Sabha is the ex officio president of the Group. The Deputy Speaker of the Lok Sabha and the Deputy Chairman of the Rajya Sabha are the ex officio vice-presidents of the Group. The Secretary-General of the Lok Sabha acts as the ex officio Secretary-General of the Group. Hence Statement 3 is correct.
Consider the following statements regarding the Indian Parliamentary Group (IPG):
How many of the above are the functions of the Indian Parliamentary Group?
Solution (b)
Explanation:
It is true that Parliamentary groups aim to study questions of public importance by arranging seminars and discussions among members of this group. The group organises seminars and symposia on parliamentary subjects of topical interest at national as well as international level. Hence Statement 3 is correct.
Solution (b)
Explanation:
It is true that Parliamentary groups aim to study questions of public importance by arranging seminars and discussions among members of this group. The group organises seminars and symposia on parliamentary subjects of topical interest at national as well as international level. Hence Statement 3 is correct.
With reference to legislative functioning in India, which of the following statements is correct with respect to ‘Quorum’?
Solution (d)
Explanation:
A provision regarding Quorum in State Legislature can be made by simple majority of the State Legislature. Hence Statement d is correct.
Solution (d)
Explanation:
A provision regarding Quorum in State Legislature can be made by simple majority of the State Legislature. Hence Statement d is correct.
With reference to Central Water Commission (CWC), consider the following statements:
How many of the above statements are correct?
Solution (a)
Context:
Explanation:
The National Water Academy, located in Pune, is responsible for training of central and state in-service engineers and it functions directly under the guidance of the Chairman. Hence, statement 3 is not correct.
Solution (a)
Context:
Explanation:
The National Water Academy, located in Pune, is responsible for training of central and state in-service engineers and it functions directly under the guidance of the Chairman. Hence, statement 3 is not correct.
With reference to International Energy Agency (IEA), consider the following statements:
How many of the above statements are correct?
Solution (d)
Context:
Explanation:
It is made up of 31 member countries, 13 association countries, and 5 accession countries. India joined this organization in 2017 as an Associate member. Some of the reports published by it include World Energy Outlook, World Energy Balances, Energy Technology Perspectives, World Energy Statistics. Hence, statement 3 is not correct.
Solution (d)
Context:
Explanation:
It is made up of 31 member countries, 13 association countries, and 5 accession countries. India joined this organization in 2017 as an Associate member. Some of the reports published by it include World Energy Outlook, World Energy Balances, Energy Technology Perspectives, World Energy Statistics. Hence, statement 3 is not correct.
Consider the following statements about Ningol Chakkouba Festival:
Which of the above statements is/are correct?
Solution (c)
Context:
Explanation:
Ningol means ‘married woman’ and Chakouba means ‘invitation for feast’; so the festival is the one where the married women are invited to their parents’ home for a feast. The main component of the festival is the visit of married sisters to their maternal homes for grand feast and joyous reunion followed by giving away the gifts. Hence, statement 2 is correct.
Solution (c)
Context:
Explanation:
Ningol means ‘married woman’ and Chakouba means ‘invitation for feast’; so the festival is the one where the married women are invited to their parents’ home for a feast. The main component of the festival is the visit of married sisters to their maternal homes for grand feast and joyous reunion followed by giving away the gifts. Hence, statement 2 is correct.
Consider the following statements about Yanadi tribe, seen in news recently:
Which of the above statements is/are correct?
Solution (b)
Context:
Explanation:
They have rich traditional health knowledge, including knowledge for everyday healthcare and specialized knowledge (e.g., snakebite cures). They harness the medicinal potential of plants for treating gastrointestinal disorders, respiratory ailments, skin conditions, and reproductive health issues. Hence, statement 2 is correct.
Solution (b)
Context:
Explanation:
They have rich traditional health knowledge, including knowledge for everyday healthcare and specialized knowledge (e.g., snakebite cures). They harness the medicinal potential of plants for treating gastrointestinal disorders, respiratory ailments, skin conditions, and reproductive health issues. Hence, statement 2 is correct.
Gobind Sagar Lake, one of the deepest man-made lakes in the world is located in?
Solution (c)
Context:
Explanation:
Gobind Sagar Lake is a manmade reservoir located in the Una and Bilaspur districts of Himachal Pradesh. It is named in honour of Guru Gobind Singh, the tenth Sikh Guru. Its source is the Bhakra Dam on the Sutlej River. Gobind Sagar reservoir is 90 k.m. long and encompasses an area of approximately 170 sq. km. The maximum and mean depths of the reservoir are 163.07 m and 55 m, respectively, making it one of the deepest man-made lakes in the world. Hence, option c is the correct answer.
Solution (c)
Context:
Explanation:
Gobind Sagar Lake is a manmade reservoir located in the Una and Bilaspur districts of Himachal Pradesh. It is named in honour of Guru Gobind Singh, the tenth Sikh Guru. Its source is the Bhakra Dam on the Sutlej River. Gobind Sagar reservoir is 90 k.m. long and encompasses an area of approximately 170 sq. km. The maximum and mean depths of the reservoir are 163.07 m and 55 m, respectively, making it one of the deepest man-made lakes in the world. Hence, option c is the correct answer.
Recently, ‘Mount Lewotobi Laki-Laki volcano’ which erupted for the second time in a week is located in?
Solution (d)
Context:
Explanation:
Solution (d)
Context:
Explanation:
With reference to Visible Emission Line Coronagraph (VELC), consider the following statements:
Which of the above statements are correct?
Solution (d)
Context:
Explanation:
It will observe the solar corona, which is the tenuous, outermost layer of the solar atmosphere. It can image the solar corona down to 1.05 times the solar radius, which is the closest any such payload has imaged. It will analyze the coronal temperature, plasma velocity, density, etc. It will also study Coronal Mass Ejections (CMEs) and the solar wind. Hence, statement 3 is correct.
Solution (d)
Context:
Explanation:
It will observe the solar corona, which is the tenuous, outermost layer of the solar atmosphere. It can image the solar corona down to 1.05 times the solar radius, which is the closest any such payload has imaged. It will analyze the coronal temperature, plasma velocity, density, etc. It will also study Coronal Mass Ejections (CMEs) and the solar wind. Hence, statement 3 is correct.
Consider the following statements about ‘Minuteman III’ seen in news recently:
Which of the above statements are correct?
Solution (d)
Context:
Explanation:
Solution (d)
Context:
Explanation:
Consider the following statements about Proba-3 Mission, which was seen in news recently:
Which of the above statements is/are correct?
Solution (b)
Context:
Explanation:
The core objective of the mission is to create an artificial eclipse by precisely coordinating two independent satellites. This capability will enable scientists to observe the Sun’s corona, a region typically obscured by the intense brightness of the Sun. Hence, statement 2 is correct.
Solution (b)
Context:
Explanation:
The core objective of the mission is to create an artificial eclipse by precisely coordinating two independent satellites. This capability will enable scientists to observe the Sun’s corona, a region typically obscured by the intense brightness of the Sun. Hence, statement 2 is correct.
With reference to Common Cat Snake, consider the following statements:
Which of the above statements is/are correct?
Solution (a)
Context:
Explanation:
In India, it is found all over the country, excluding north-east states after Sikkim; it is also, not found in Indian islands. It can be found in almost all kinds of forests and wide ranges of elevations. It is a medium-sized snake that is usually found in the 70-100 cm range. It comes in the category of least concern under IUCN Red list. Hence, statement 2 is not correct.
Solution (a)
Context:
Explanation:
In India, it is found all over the country, excluding north-east states after Sikkim; it is also, not found in Indian islands. It can be found in almost all kinds of forests and wide ranges of elevations. It is a medium-sized snake that is usually found in the 70-100 cm range. It comes in the category of least concern under IUCN Red list. Hence, statement 2 is not correct.
Passage – 1
Pointing out that tax evasion is enabling billionaires to enjoy effective tax rates equivalent to 0% to 0.5% of their wealth, the European Union Tax Observatory in its ‘Global Tax Evasion Report 2024’ has called for a global minimum tax on billionaires equal to 2% of their wealth.
This would both address evasion and “generate nearly $250 billion from less than 3,000 individuals,” the report stated. The report justified the proposal by noting that while the number of taxpayers affected by it would be miniscule, the tax rate for them (2%) “Would still be very modest” given that the wealth of billionaires has grown at 7% a year annually on average since 1995 (net of inflation). Assessing the impact of international efforts made so far to curb tax evasion, the report highlighted the success of one measure — the automatic exchange of bank information — in reducing offshore tax evasion by a factor of three over the past 10 years. The report observed that before this measure came into effect, “households owned the equivalent of 10% of world GDP in financial wealth in tax havens globally, the bulk of which was undeclared to tax authorities and belonged to high-net-worth individuals.
Q.31) Which of the following statements best reflects the most logical and rational implication conveyed by the above passage?
Solution (a)
Statement Analysis:
Option (a) is correct: The passage mentions the Global Tax Evasion Report 2024 which calls for taxing billionaires globally. This would help in checking tax evasion. The passage says that “This would both address evasion and “generate nearly $250 billion from less than 3,000 individuals”. This implies that the amount raised by taxing billionaires would be substantial. Hence, option (a) is correct.
Option (b) is not correct: The passage mentions tax evasion as the reason why billionaires enjoy lower tax. However, there is no mention of inadequate policy implementation or corrupt bureaucracy as a reason for lower tax rates for billionaires. Hence, option (b) is not correct.
Option (c) is not correct: The central theme of the passage is to check tax evasion by billionaires by offering lower tax rates. This would help in the collection of $250 billion from billionaires. The tax havens are mentioned in the context of the places having stored undeclared income. Scrutinizing them to check tax evasion can be one of the logical suggestions, however, the same is not mentioned in the passage. Hence, option (c) is not correct.
Option (d) is not correct: The passage mentions the need for taxing the wealth of rich individuals and that their undeclared money is stashed in tax havens. There is no direct connection established between tax havens thriving due to the undeclared money of billionaires being stored there. Moreover, tax havens are not the main focus of the passage. Hence, option (d) is not correct.
Solution (a)
Statement Analysis:
Option (a) is correct: The passage mentions the Global Tax Evasion Report 2024 which calls for taxing billionaires globally. This would help in checking tax evasion. The passage says that “This would both address evasion and “generate nearly $250 billion from less than 3,000 individuals”. This implies that the amount raised by taxing billionaires would be substantial. Hence, option (a) is correct.
Option (b) is not correct: The passage mentions tax evasion as the reason why billionaires enjoy lower tax. However, there is no mention of inadequate policy implementation or corrupt bureaucracy as a reason for lower tax rates for billionaires. Hence, option (b) is not correct.
Option (c) is not correct: The central theme of the passage is to check tax evasion by billionaires by offering lower tax rates. This would help in the collection of $250 billion from billionaires. The tax havens are mentioned in the context of the places having stored undeclared income. Scrutinizing them to check tax evasion can be one of the logical suggestions, however, the same is not mentioned in the passage. Hence, option (c) is not correct.
Option (d) is not correct: The passage mentions the need for taxing the wealth of rich individuals and that their undeclared money is stashed in tax havens. There is no direct connection established between tax havens thriving due to the undeclared money of billionaires being stored there. Moreover, tax havens are not the main focus of the passage. Hence, option (d) is not correct.
Passage – 2
Microalgae, which form the base of the food chain in the ocean and capture carbon dioxide from the atmosphere, appear to rely on a unique strategy to cope with global warming, according to a new study. The findings are published in the journal Nature Microbiology. As climate change reduces the availability of nutrients in the sea, marine microalgae or eukaryotic phytoplankton fire up a protein called rhodopsin. It is related to the protein in the human eye responsible for vision in dim light. This light-responsive protein is helping the microalgae flourish with the help of sunlight in place of traditional chlorophyll. Microbial rhodopsins, per the study, are proposed to be major light capturers in the ocean. Estimates suggested they may absorb as much light as chlorophyll-based photosynthesis in the sea, which also captures light to generate energy and food. However, their biological role in these organisms was unclear before the study. “Global warming is increasing drought on land and the same thing happens in the ocean: The warmer the surface water gets, the lower are the nutrients in these surface water layers,” Thomas Mock, professor of marine microbiology in University of East Anglia’s School of Environmental Sciences and the study’s author, said in a statement.
Q.32) Which one of the following statements best reflects the crux of the passage?
Solution (c)
Statement Analysis:
Option (a) is not correct: According to the passage, the protein rhodopsin is responsible for vision in humans and microalgae use it in place of chlorophyll to survive in the oceans. The same phenomenon is not taking place in both ecosystems, even though the same biochemical is used. It can be assumed that the biochemical rhodopsin is being utilised by humans and microalgae differently and hence as far as the information in the passage is concerned, it is not the ‘same’ phenomenon that is occurring on land and water. Even if it was, we could not have generalized it based on just one example. Hence, option (a) is not correct.
Option (b) is not correct: The passage mentions the adaptation of the microalgae to the changing environment and how it has adapted to the effects of global warming. The passage does not talk about climate mitigation, or whether biochemical like rhodopsin may prove helpful in such a cause.
Option (c) is correct: Consider the line, “As climate change reduces the availability of nutrients in the sea, marine microalgae or eukaryotic phytoplankton fire up a protein called rhodopsin”. This implies that microalgae are adopting to changing external environment. It is further mentioned in the passage, “Estimates suggested they may absorb as much light as chlorophyll-based photosynthesis in the sea, which also captures light to generate energy and food”. These lines imply that rhodopsin replaces chlorophyll in microalgae to facilitate food production. This way, the passage revolves around the theme of adaptability to changing external conditions. Hence, option (c) is correct.
Option (d) is not correct: The passage revolves around the theme of adaptability by taking the case of microalgae and discussing the process of their survival in the absence of chlorophyll. The passage does not mention the effects of adaptability on productivity. The passage only narrates how adaptability can help in survival in a changing environment. Hence, option (d) is not correct.
Solution (c)
Statement Analysis:
Option (a) is not correct: According to the passage, the protein rhodopsin is responsible for vision in humans and microalgae use it in place of chlorophyll to survive in the oceans. The same phenomenon is not taking place in both ecosystems, even though the same biochemical is used. It can be assumed that the biochemical rhodopsin is being utilised by humans and microalgae differently and hence as far as the information in the passage is concerned, it is not the ‘same’ phenomenon that is occurring on land and water. Even if it was, we could not have generalized it based on just one example. Hence, option (a) is not correct.
Option (b) is not correct: The passage mentions the adaptation of the microalgae to the changing environment and how it has adapted to the effects of global warming. The passage does not talk about climate mitigation, or whether biochemical like rhodopsin may prove helpful in such a cause.
Option (c) is correct: Consider the line, “As climate change reduces the availability of nutrients in the sea, marine microalgae or eukaryotic phytoplankton fire up a protein called rhodopsin”. This implies that microalgae are adopting to changing external environment. It is further mentioned in the passage, “Estimates suggested they may absorb as much light as chlorophyll-based photosynthesis in the sea, which also captures light to generate energy and food”. These lines imply that rhodopsin replaces chlorophyll in microalgae to facilitate food production. This way, the passage revolves around the theme of adaptability to changing external conditions. Hence, option (c) is correct.
Option (d) is not correct: The passage revolves around the theme of adaptability by taking the case of microalgae and discussing the process of their survival in the absence of chlorophyll. The passage does not mention the effects of adaptability on productivity. The passage only narrates how adaptability can help in survival in a changing environment. Hence, option (d) is not correct.
In Anil’s store, there are 20 flashlights, two fifths of which are defective. For a marriage party decoration, his servant Ram randomly chose three flashlights to place them in the hall. What is the probability that the hall will be lighted?
Solution (d)
Explanation:
Total number of flashlights = 20
Number of defective flashlight = 20 × (2/5) = 8
Number of working flashlights = 20 – 8 = 12
Three flashlights can be selected from 20 flashlights in 20C3 ways.
Number of ways of drawing 3 flashlights from 8 defective flashlights is 8C3.
So, the probability that all the three flashlights are defective = 8C3/20C3 = [8!/{3!(8 – 3)!}] / [20!/{3!(20 – 3)!}] = 14/285
The probability that at least one flash light is good = 1 – Probability that no flashlight is good = 1– (14/285) = 271/285
Hence, option (d) is the right answer.
Solution (d)
Explanation:
Total number of flashlights = 20
Number of defective flashlight = 20 × (2/5) = 8
Number of working flashlights = 20 – 8 = 12
Three flashlights can be selected from 20 flashlights in 20C3 ways.
Number of ways of drawing 3 flashlights from 8 defective flashlights is 8C3.
So, the probability that all the three flashlights are defective = 8C3/20C3 = [8!/{3!(8 – 3)!}] / [20!/{3!(20 – 3)!}] = 14/285
The probability that at least one flash light is good = 1 – Probability that no flashlight is good = 1– (14/285) = 271/285
Hence, option (d) is the right answer.
Anuja has some toys with her. She has 8 times as many one-rupee toys as three-rupee toys. She also has some five-rupee toys too. The total amount invested by her in these toys together is Rs.200. If the number of three-rupee toys is more than 10, then which of the following can be concluded?
Solution (c)
Explanation:
Let o, t, f denote the number of toys of one rupee, three rupees and five rupees respectively. Then according to the question,
o + 3t + 5f= 200 (i)
o =St (ii)
From equations (i) and (ii), we get:
(8t + 3t) + 5f= 200
Or 11 t + 5f= 200
Clearly, t must be a multiple of 5.
Number of three-rupee toys is more than 10. So, t > 10.
Thus, values oft can be 15, 20, …..
But t= 20 is not possible as 11 x (20) = 220 >200
Thus t= 15, o=8t=8×15= 120
f = (200 – 11t)/5 = (200 – 11 x 15)/5 = 7
Thus, there are 15 + 7 + 120 = 142 toys in all.
Hence, option (c) is the right answer.
Solution (c)
Explanation:
Let o, t, f denote the number of toys of one rupee, three rupees and five rupees respectively. Then according to the question,
o + 3t + 5f= 200 (i)
o =St (ii)
From equations (i) and (ii), we get:
(8t + 3t) + 5f= 200
Or 11 t + 5f= 200
Clearly, t must be a multiple of 5.
Number of three-rupee toys is more than 10. So, t > 10.
Thus, values oft can be 15, 20, …..
But t= 20 is not possible as 11 x (20) = 220 >200
Thus t= 15, o=8t=8×15= 120
f = (200 – 11t)/5 = (200 – 11 x 15)/5 = 7
Thus, there are 15 + 7 + 120 = 142 toys in all.
Hence, option (c) is the right answer.
The average of six numbers is a. The average of the numbers occurring at even places and odd places are b and c respectively. Which of the following statements is true?
Solution (b)
Explanation:
Average of 6 numbers = a
Thus, the sum of six numbers = 6a………………(i)
Now, out of 6 numbers there are 3 numbers at even positions and 3 at odd positions.
Average of numbers occurring at even places = b.
So, sum of numbers at even positions = 3b…………(ii)
Similarly, average of numbers occurring at odd places = c So, sum of numbers at odd positions = 3c. ………….(iii)
From (i), (ii) and (iii), we get:
6a = 3b + 3c
Thus, 2a = (b + c)
Hence, option (b) is the right answer.
Solution (b)
Explanation:
Average of 6 numbers = a
Thus, the sum of six numbers = 6a………………(i)
Now, out of 6 numbers there are 3 numbers at even positions and 3 at odd positions.
Average of numbers occurring at even places = b.
So, sum of numbers at even positions = 3b…………(ii)
Similarly, average of numbers occurring at odd places = c So, sum of numbers at odd positions = 3c. ………….(iii)
From (i), (ii) and (iii), we get:
6a = 3b + 3c
Thus, 2a = (b + c)
Hence, option (b) is the right answer.
All the Best
IASbaba
