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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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Consider the following regarding amendments to the Constitution:
How many of the above statements are correct?
Solution (a)
Statement 1 | Statement 2 | Statement 3 |
Correct | Incorrect | Incorrect |
It is important to remember that all amendments to the Constitution are initiated only in the Parliament. Besides the special majority in the Parliament no outside agency, like a constitution commission or a separate body, is required for amending the Constitution. | There are many articles in the Constitution, which mention that these articles can be amended by a simple law of the Parliament. For example, article 2 and 3. For amending the remaining parts of the Constitution, provision has been made in Article 368 of the Constitution.
Thus, all provisions related to amendment are not contained in article 368. |
Under article 368, there are two methods of amending the Constitution and they apply to two different sets of articles of the Constitution. One method is that amendment can be made by special majority of the two houses of the Parliament. The other method is more difficult: it requires special majority of the Parliament and consent of half of the State legislatures. After the passage in the Parliament and in some cases, in State legislatures, no referendum is required for ratification of the amendment. |
Solution (a)
Statement 1 | Statement 2 | Statement 3 |
Correct | Incorrect | Incorrect |
It is important to remember that all amendments to the Constitution are initiated only in the Parliament. Besides the special majority in the Parliament no outside agency, like a constitution commission or a separate body, is required for amending the Constitution. | There are many articles in the Constitution, which mention that these articles can be amended by a simple law of the Parliament. For example, article 2 and 3. For amending the remaining parts of the Constitution, provision has been made in Article 368 of the Constitution.
Thus, all provisions related to amendment are not contained in article 368. |
Under article 368, there are two methods of amending the Constitution and they apply to two different sets of articles of the Constitution. One method is that amendment can be made by special majority of the two houses of the Parliament. The other method is more difficult: it requires special majority of the Parliament and consent of half of the State legislatures. After the passage in the Parliament and in some cases, in State legislatures, no referendum is required for ratification of the amendment. |
Consider the following statements and identify the correct one/s:
Select the answer:
Solution (a)
Statement 1 | Statement 2 |
Correct | Incorrect |
Till date, there have been 106 amendments of the Constitution of India since it was first enacted in 1950. Given the relatively difficult method of amending the Constitution, the number of amendments appears quite high.
|
Years 1970-1990 saw the highest number of constitutional amendment as given above. |
Solution (a)
Statement 1 | Statement 2 |
Correct | Incorrect |
Till date, there have been 106 amendments of the Constitution of India since it was first enacted in 1950. Given the relatively difficult method of amending the Constitution, the number of amendments appears quite high.
|
Years 1970-1990 saw the highest number of constitutional amendment as given above. |
Consider the following statements regarding 42nd Constitutional Amendment Act:
How many of the above statements are correct?
Solution (b)
Statement 1 | Statement 2 | Statement 3 |
Correct | Correct | Incorrect |
One of the most significant amendments to the Indian Constitution is the 42nd Amendment Act of 1976 enacted by the Indian National Congress, led by Indira Gandhi.
This Act is also known as the ‘Mini Constitution’ because of the large number of revisions it made to the Constitution of India. |
The 42nd amendment was particularly seen as a wide-ranging amendment affecting large parts of the Constitution. This amendment made changes to the Preamble, to the seventh schedule of the Constitution and to 53 articles of the Constitution. | The amendment was also an attempt to override the ruling of the Supreme Court given in the Kesavananda case. Even the duration of the Lok Sabha was extended from five to six years. Fundamental duties were included in the Constitution by this amendment act. The 42nd amendment also put restrictions on the review powers of the Judiciary. |
Solution (b)
Statement 1 | Statement 2 | Statement 3 |
Correct | Correct | Incorrect |
One of the most significant amendments to the Indian Constitution is the 42nd Amendment Act of 1976 enacted by the Indian National Congress, led by Indira Gandhi.
This Act is also known as the ‘Mini Constitution’ because of the large number of revisions it made to the Constitution of India. |
The 42nd amendment was particularly seen as a wide-ranging amendment affecting large parts of the Constitution. This amendment made changes to the Preamble, to the seventh schedule of the Constitution and to 53 articles of the Constitution. | The amendment was also an attempt to override the ruling of the Supreme Court given in the Kesavananda case. Even the duration of the Lok Sabha was extended from five to six years. Fundamental duties were included in the Constitution by this amendment act. The 42nd amendment also put restrictions on the review powers of the Judiciary. |
One thing that has had a long lasting effect on the evolution of the Indian Constitution is the theory of the basic structure of the Constitution. The Judiciary advanced this theory in the famous case of:
Solution (d)
Statement 1 | Statement 2 | Statement 3 | Statement 4 |
Incorrect | Incorrect | Incorrect | Correct |
Golaknath v. State Of Punjab or simply the Golaknath case, was a 1967 Indian Supreme Court case, in which the Court ruled that Parliament could not curtail any of the Fundamental Rights in the Constitution. The Supreme Court, by thin majority of 6:5, held that a constitutional amendment under Article 368 of the Constitution was an ordinary ‘law’ within the meaning of Article 13(3) of the Constitution. | Minerva Mills Ltd. and Ors. v. Union Of India is a landmark decision of the Supreme Court of India that applied and evolved the basic structure doctrine of the Constitution of India. In the Minerva Mills case, the Supreme Court provided key clarifications on the interpretation of the basic structure doctrine. The court ruled that the power of the parliament to amend the constitution is limited by the constitution. | India became a contracting party to the Ramsar Convention in 1981 and has been implementing conservation programmes for wetlands, mangroves, and coral reefs. | Kesavananda Bharati Sripadagalvaru v. State of Kerala, also known as the Kesavananda Bharati judgement, is a landmark decision of the Supreme Court of India that outlined the basic structure doctrine of the Indian Constitution. The case is also known as the Fundamental Rights Case. The court asserted its right to strike down amendments to the constitution that were in violation of the fundamental architecture of the constitution. |
Solution (d)
Statement 1 | Statement 2 | Statement 3 | Statement 4 |
Incorrect | Incorrect | Incorrect | Correct |
Golaknath v. State Of Punjab or simply the Golaknath case, was a 1967 Indian Supreme Court case, in which the Court ruled that Parliament could not curtail any of the Fundamental Rights in the Constitution. The Supreme Court, by thin majority of 6:5, held that a constitutional amendment under Article 368 of the Constitution was an ordinary ‘law’ within the meaning of Article 13(3) of the Constitution. | Minerva Mills Ltd. and Ors. v. Union Of India is a landmark decision of the Supreme Court of India that applied and evolved the basic structure doctrine of the Constitution of India. In the Minerva Mills case, the Supreme Court provided key clarifications on the interpretation of the basic structure doctrine. The court ruled that the power of the parliament to amend the constitution is limited by the constitution. | India became a contracting party to the Ramsar Convention in 1981 and has been implementing conservation programmes for wetlands, mangroves, and coral reefs. | Kesavananda Bharati Sripadagalvaru v. State of Kerala, also known as the Kesavananda Bharati judgement, is a landmark decision of the Supreme Court of India that outlined the basic structure doctrine of the Indian Constitution. The case is also known as the Fundamental Rights Case. The court asserted its right to strike down amendments to the constitution that were in violation of the fundamental architecture of the constitution. |
Consider the following statements with reference to Basic Structure Doctrine:
Select the answer:
Solution (a)
Statement 1 | Statement 2 |
Correct | Incorrect |
Kesavananda Bharati ruling has contributed to the evolution of the Constitution in the following ways – It has set specific limits to the Parliament’s power to amend the Constitution. It says that no amendment can violate the basic structure of the Constitution. It places the Judiciary as the final authority in deciding if an amendment violates basic structure and what constitutes the basic structure. | The doctrine of basic structure though is not exactly defined but all interpretations of the Constitution and all institutions in the country have accepted the theory of basic structure. The theory of basic structure is itself an example of a living constitution. There is no mention of this theory in the Constitution. It has emerged from judicial interpretation. Thus, Judiciary and its interpretation have practically amended Constitution without a formal amendment. |
Solution (a)
Statement 1 | Statement 2 |
Correct | Incorrect |
Kesavananda Bharati ruling has contributed to the evolution of the Constitution in the following ways – It has set specific limits to the Parliament’s power to amend the Constitution. It says that no amendment can violate the basic structure of the Constitution. It places the Judiciary as the final authority in deciding if an amendment violates basic structure and what constitutes the basic structure. | The doctrine of basic structure though is not exactly defined but all interpretations of the Constitution and all institutions in the country have accepted the theory of basic structure. The theory of basic structure is itself an example of a living constitution. There is no mention of this theory in the Constitution. It has emerged from judicial interpretation. Thus, Judiciary and its interpretation have practically amended Constitution without a formal amendment. |
Consider the following statements regarding electoral college of Vice-President:
Which of the statements given above is/are correct?
Solution (a)
Statement 1 | Statement 2 |
Correct | Incorrect |
Electoral college of Vice-President consists of both elected and nominated members of the Parliament (in the case of President, only elected members). | Electoral college of Vice-President does not include the members of the state legislative assemblies or Council (in the case of President, the elected members of the state legislative assemblies are included). |
Note:
Solution (a)
Statement 1 | Statement 2 |
Correct | Incorrect |
Electoral college of Vice-President consists of both elected and nominated members of the Parliament (in the case of President, only elected members). | Electoral college of Vice-President does not include the members of the state legislative assemblies or Council (in the case of President, the elected members of the state legislative assemblies are included). |
Note:
Which of the following are discretionary Powers of the President?
How many of the above statements are correct?
Solution (c)
Discretionary Powers of the President:
In such a situation, the President has to use his own discretion in judging who really may have the support of the majority or who can actually form and run the government.
Solution (c)
Discretionary Powers of the President:
In such a situation, the President has to use his own discretion in judging who really may have the support of the majority or who can actually form and run the government.
Consider the following statements and identify the correct statement/s:
Select the answer:
Solution (c)
Statement 1 | Statement 2 |
Correct | Correct |
Article 74 (1): There shall be a Council of Ministers with the Prime Minister at the head to aid and advise the President who shall in the exercise of his functions, act in accordance with such advice. Provided that the President may require the Council of Ministers to reconsider such advice, and the President shall act in accordance with the advice tendered after such reconsideration. | The word shall indicates that the advice is binding on the President. In view of the controversy about the scope of the President’s powers, a specific mention was made in the Constitution by an amendment that the advice of the Council of Ministers will be binding on the President. By another amendment made later, it was decided that the President can ask the Council of Ministers to reconsider its advice but, has to accept the reconsidered advice of the Council of Ministers. |
Solution (c)
Statement 1 | Statement 2 |
Correct | Correct |
Article 74 (1): There shall be a Council of Ministers with the Prime Minister at the head to aid and advise the President who shall in the exercise of his functions, act in accordance with such advice. Provided that the President may require the Council of Ministers to reconsider such advice, and the President shall act in accordance with the advice tendered after such reconsideration. | The word shall indicates that the advice is binding on the President. In view of the controversy about the scope of the President’s powers, a specific mention was made in the Constitution by an amendment that the advice of the Council of Ministers will be binding on the President. By another amendment made later, it was decided that the President can ask the Council of Ministers to reconsider its advice but, has to accept the reconsidered advice of the Council of Ministers. |
Jawaharlal Nehru described which post as ‘the Linchpin of Government’?
Solution (d)
Statement 1 | Statement 2 | Statement 3 | Statement 4 |
Incorrect | Incorrect | Incorrect | Correct |
The president of India is the head of state of the Republic of India. The president is the nominal head of the executive, as well as the commander-in-chief of the Indian Armed Forces. The office of president was created when India became a republic on 26 January 1950, when its constitution came into force. The president is indirectly elected by an electoral college comprising both houses of the Parliament of India and the legislative assemblies of each of India’s states and territories. | The Vice-President of India is the second highest constitutional office in the country. He serves for a five-year term. The only provision in the Constitution is with regard to the Vice-President’s function as the Chairperson of the Council of States, which is performed, during the period of such vacancy, by the Deputy Chairperson of the Rajya Sabha, or any other member of the Rajya Sabha authorised by the President of India. The VP may resign his office by submitting his resignation to the President of India. | The speaker of the Lok Sabha is the presiding officer and the highest authority of the Lok Sabha, the lower house of the Parliament of India. The speaker is elected generally in the first meeting of the Lok Sabha following general elections. Serving for a term of five years, the speaker chosen from sitting members of the Lok Sabha. | The Prime Minister acts as a link between the Council of Ministers on the one hand and the President as well as the Parliament on the other. It is this role of the Prime Minister which led Pt. Nehru to describe him as ‘the linchpin of Government’. It is also the constitutional obligation of the Prime Minister to communicate to the President all decisions of the Council of Ministers relating to the administration of the affairs of the Union and proposals for legislation. |
Solution (d)
Statement 1 | Statement 2 | Statement 3 | Statement 4 |
Incorrect | Incorrect | Incorrect | Correct |
The president of India is the head of state of the Republic of India. The president is the nominal head of the executive, as well as the commander-in-chief of the Indian Armed Forces. The office of president was created when India became a republic on 26 January 1950, when its constitution came into force. The president is indirectly elected by an electoral college comprising both houses of the Parliament of India and the legislative assemblies of each of India’s states and territories. | The Vice-President of India is the second highest constitutional office in the country. He serves for a five-year term. The only provision in the Constitution is with regard to the Vice-President’s function as the Chairperson of the Council of States, which is performed, during the period of such vacancy, by the Deputy Chairperson of the Rajya Sabha, or any other member of the Rajya Sabha authorised by the President of India. The VP may resign his office by submitting his resignation to the President of India. | The speaker of the Lok Sabha is the presiding officer and the highest authority of the Lok Sabha, the lower house of the Parliament of India. The speaker is elected generally in the first meeting of the Lok Sabha following general elections. Serving for a term of five years, the speaker chosen from sitting members of the Lok Sabha. | The Prime Minister acts as a link between the Council of Ministers on the one hand and the President as well as the Parliament on the other. It is this role of the Prime Minister which led Pt. Nehru to describe him as ‘the linchpin of Government’. It is also the constitutional obligation of the Prime Minister to communicate to the President all decisions of the Council of Ministers relating to the administration of the affairs of the Union and proposals for legislation. |
Which of the following are part of the ‘Basic Structure’ of the Indian Constitution?
Select the correct answer using the code given below:
Solution (d)
Statement 1 | Statement 2 | Statement 3 | Statement 4 |
Correct | Correct | Correct | Correct |
Articles 32 and 226. | Effective access to justice. | The Parliamentary system of government. | Freedom and dignity of the individual. |
Solution (d)
Statement 1 | Statement 2 | Statement 3 | Statement 4 |
Correct | Correct | Correct | Correct |
Articles 32 and 226. | Effective access to justice. | The Parliamentary system of government. | Freedom and dignity of the individual. |
With reference to the Constitutional Amendment Bill, consider the following statements:
How many of the above statements are correct?
Solution (b)
Statement 1 | Statement 2 | Statement 3 | Statement 4 |
Correct | Incorrect | Correct | Incorrect |
The constitutional amendment bill must be passed in each House by a special majority, that is, a majority of the total membership of the House and a majority of two-thirds of the members of the House present and voting. | The Constitutional Amendment bill does not require prior permission of the President of India. | Article 368 in Part XX of the Constitution deals with the powers of Parliament to amend the Constitution and its procedure. It states that the Parliament may, in exercise of its constituent power, amend by way of addition, variation or repeal any provision of the Constitution in accordance with the procedure laid down for the purpose. | The Constitutional Amendment bill can be introduced either by a minister or by a private member. |
Solution (b)
Statement 1 | Statement 2 | Statement 3 | Statement 4 |
Correct | Incorrect | Correct | Incorrect |
The constitutional amendment bill must be passed in each House by a special majority, that is, a majority of the total membership of the House and a majority of two-thirds of the members of the House present and voting. | The Constitutional Amendment bill does not require prior permission of the President of India. | Article 368 in Part XX of the Constitution deals with the powers of Parliament to amend the Constitution and its procedure. It states that the Parliament may, in exercise of its constituent power, amend by way of addition, variation or repeal any provision of the Constitution in accordance with the procedure laid down for the purpose. | The Constitutional Amendment bill can be introduced either by a minister or by a private member. |
Which of the following form the part of basic structure of the Constitution?
Select the correct answer using the code given below:
Solution (d)
Statement 1 | Statement 2 | Statement 3 | Statement 4 |
Correct | Correct | Correct | Correct |
Welfare state (socio-economic justice) | Secular character of the Constitution | Judicial review | Effective access to justice |
Some of the features of the Constitution termed as “basic” are listed below:
Solution (d)
Statement 1 | Statement 2 | Statement 3 | Statement 4 |
Correct | Correct | Correct | Correct |
Welfare state (socio-economic justice) | Secular character of the Constitution | Judicial review | Effective access to justice |
Some of the features of the Constitution termed as “basic” are listed below:
Which of the following statements is/are correct about the First Amendment Act, 1951?
How many of the above statements are correct?
Solution (b)
Statement 1 | Statement 2 | Statement 3 |
Correct | Incorrect | Correct |
It added the Ninth Schedule to protect the land reform and other laws included in it from the judicial review. | Added three more grounds of restrictions on the freedom of speech and expression, viz., public order, friendly relations with foreign states and incitement to an offence. Also, made the restrictions ‘reasonable’ and thus, justiciable in nature. | It empowered the state to make special provisions for the advancement of the socially and economically backward classes. |
Solution (b)
Statement 1 | Statement 2 | Statement 3 |
Correct | Incorrect | Correct |
It added the Ninth Schedule to protect the land reform and other laws included in it from the judicial review. | Added three more grounds of restrictions on the freedom of speech and expression, viz., public order, friendly relations with foreign states and incitement to an offence. Also, made the restrictions ‘reasonable’ and thus, justiciable in nature. | It empowered the state to make special provisions for the advancement of the socially and economically backward classes. |
In which of the following case, the Supreme Court adhered to the doctrine of the ‘basic structure’ and also further clarified that it would apply to constitutional amendments enacted after April 24, 1973?
Solution (c)
In Waman Rao vs Union of India case, 1981, the Supreme Court adhered to the doctrine of the ‘basic structure’ and also further clarified that it would apply to constitutional amendments enacted after April 24, 1973.
Solution (c)
In Waman Rao vs Union of India case, 1981, the Supreme Court adhered to the doctrine of the ‘basic structure’ and also further clarified that it would apply to constitutional amendments enacted after April 24, 1973.
Consider the following statements:
How many of the above statements are correct?
Solution (b)
Statement 1 | Statement 2 | Statement 3 |
Correct | Correct | Incorrect |
Change in the name of a state does not require a Constitutional Amendment. | Inclusion of a language in the 8th Schedule requires a Constitutional Amendment. | Change in the name of a language included in the 8th Schedule requires a Constitutional Amendment.
When the name of Oriya language, included in the 8th Schedule, was changed to Odia, the 96th Constitutional Amendment act, 2011 was passed by the Parliament. |
Solution (b)
Statement 1 | Statement 2 | Statement 3 |
Correct | Correct | Incorrect |
Change in the name of a state does not require a Constitutional Amendment. | Inclusion of a language in the 8th Schedule requires a Constitutional Amendment. | Change in the name of a language included in the 8th Schedule requires a Constitutional Amendment.
When the name of Oriya language, included in the 8th Schedule, was changed to Odia, the 96th Constitutional Amendment act, 2011 was passed by the Parliament. |
Consider the following statements and identify the correct statement/s:
Select the answer:
Solution (a)
Solution (a)
Consider the following statements regarding President election:
Select the answer:
Solution (a)
The members who are nominated to either House of Parliament or the Legislative Assemblies of State including NCT of Delhi and UT of Puducherry are not eligible to be included in the Electoral College.
The Election Commission, in consultation with the Central Government, appoints the Secretary General of Lok Sabha and Rajya Sabha, by rotation, as the Returning Officer. Accordingly, the Secretary General, Rajya Sabha was appointed as the Returning Officer for the recent election to the Office of the President.
Solution (a)
The members who are nominated to either House of Parliament or the Legislative Assemblies of State including NCT of Delhi and UT of Puducherry are not eligible to be included in the Electoral College.
The Election Commission, in consultation with the Central Government, appoints the Secretary General of Lok Sabha and Rajya Sabha, by rotation, as the Returning Officer. Accordingly, the Secretary General, Rajya Sabha was appointed as the Returning Officer for the recent election to the Office of the President.
Which of the following provisions is related to 69th Constitution amendment act?
Solution (b)
The 69th amendment to the Constitution of India inserted Article 239AA, which declared the Union Territory of Delhi to be administered by a L-G who works on aid and advice of the elected legislative assembly.
Solution (b)
The 69th amendment to the Constitution of India inserted Article 239AA, which declared the Union Territory of Delhi to be administered by a L-G who works on aid and advice of the elected legislative assembly.
Which of the following constitutional amendment was made for the reservation of seats for the admission of citizens belonging to schedule caste and schedule tribes and other backward classes in the educational institution?
Solution (b)
Solution (b)
Consider the following statements about the Ordinance-making power of the President:
Which of the statements given above is/are correct?
Solution (b)
Statement 1 | Statement 2 |
Incorrect | Correct |
Cooper’s case judgment states that satisfaction of the president for promulgation of the ordinance on whether the situation is unforeseen, urgent and clause of recess time period, wherein the whole of the president’s satisfaction and situation present is questionable in the court of law. | Ordinances cannot be issued for amending Constitution of India. But it can be issued for Amending bills pending in the Parliament. |
Note:
PRESIDENT ORDINANCE MAKING POWER:
Solution (b)
Statement 1 | Statement 2 |
Incorrect | Correct |
Cooper’s case judgment states that satisfaction of the president for promulgation of the ordinance on whether the situation is unforeseen, urgent and clause of recess time period, wherein the whole of the president’s satisfaction and situation present is questionable in the court of law. | Ordinances cannot be issued for amending Constitution of India. But it can be issued for Amending bills pending in the Parliament. |
Note:
PRESIDENT ORDINANCE MAKING POWER:
Consider the following statements about Red Sand Boa:
How many of the given statements are correct?
Solution (b)
Solution (b)
Consider the following statements about the Bharat Stage (BS) norms:
How many of the above statements are correct?
Solution (b)
Note:
Solution (b)
Note:
Consider the following statements:
How many of the given statements are correct?
Solution (b)
Solution (b)
Consider the following statements about the National Pension System (NPS):
How many of the above statements are correct?
Solution (c)
Solution (c)
Consider the following statements regarding the deemed to be university:
Choose the correct code:
Solution (a)
Solution (a)
In the context of Indian polity, consider the following statements:
Choose the correct code:
Solution (a)
Note: The Constitution does not use the term “special session”.The term sometimes refers to sessions the government has convened for specific occasions like commemorating parliamentary or national milestones. However, Article 352 (Proclamation of Emergency) of the Constitution does refer to a “special sitting of the House”.
Solution (a)
Note: The Constitution does not use the term “special session”.The term sometimes refers to sessions the government has convened for specific occasions like commemorating parliamentary or national milestones. However, Article 352 (Proclamation of Emergency) of the Constitution does refer to a “special sitting of the House”.
Consider the following statements regarding Walking leaves:
Choose the correct code:
Solution (c)
Solution (c)
Which of the following are the reasons for the declining population of penguins?
How many of the above statements are correct?
Solution (b)
The reasons for the declining population of penguins:
Solution (b)
The reasons for the declining population of penguins:
Consider the following statements regarding the DIKSHA Platform:
How many of the given statements are correct?
Solution (c)
Solution (c)
Consider the following statements regarding Aarogya Maitri Cube:
How many of the above statements are correct?
Solution (c)
Solution (c)
A worker reaches his factory 5 minutes late if his speed from his house to the factory is 5 km/hr. If he walks at a speed of 6 km/hr, he reaches the factory 5 minutes early. What is
the distance of the factory from his house?
Solution (c)
Explanation: Let the distance between his house and factory be ‘x’ km.
x/5 – x/6 = 10/60 ( The time difference between the two different speeds)
X = 5 km
Solution (c)
Explanation: Let the distance between his house and factory be ‘x’ km.
x/5 – x/6 = 10/60 ( The time difference between the two different speeds)
X = 5 km
A car starts running at the speed of 50 km per hour. The speed of car increases by 2 km at the end of every one hour. What will be the distance covered at the end of ten hours from the start of the journey?
Solution (c)
Total distance covered by the car in 10 hours = 50 + 52 + 54 + 56 + 58 + 60 + 62 + 64 + 66 + 68
The sum of ten terms in arithmetic progression whose first number is 50 and last number is 68 is = 10/2 * (50 + 68) =590 km
Therefore, the required result will be 590 km.
Solution (c)
Total distance covered by the car in 10 hours = 50 + 52 + 54 + 56 + 58 + 60 + 62 + 64 + 66 + 68
The sum of ten terms in arithmetic progression whose first number is 50 and last number is 68 is = 10/2 * (50 + 68) =590 km
Therefore, the required result will be 590 km.
9 boys and 12 girls perform a task in 15 days. The same task is performed by 39 boys and 72 girls in 3 days. Then what will be the time taken by 20 boys and 5 girls in performing the same task?
Solution (d)
Let 1 boy’s 1 day’s work = x (i.e. efficiency of 1 boy = ‘x’ units/day) and
1 girl’s 1 day’s work = y (i.e. efficiency of 1 girl = ‘y’ units/day).
Then, 9x + 12y = 1/15 ………………І
(9 boys’ & 12 girls’ 1 day’s work)
39x + 72y = 1/3 ………….…ІІ
(39 boys’ & 72 girls’ 1 day’s work).
Multiplying equation І by 6 and then subtracting equation ІІ from it, we get,
x = 1/225.
Putting the value of x in either equation І or equation ІІ will yield
y = 1/450.
So, 20 boys’ and 5 girls’ 1 day’s work
= 20/225 + 5/450
= 1/10.
Since 1/10 part is performed in 1 day.
So, 1 part is performed in 1/(1/10) day,i.e. 10 days.
Solution (d)
Let 1 boy’s 1 day’s work = x (i.e. efficiency of 1 boy = ‘x’ units/day) and
1 girl’s 1 day’s work = y (i.e. efficiency of 1 girl = ‘y’ units/day).
Then, 9x + 12y = 1/15 ………………І
(9 boys’ & 12 girls’ 1 day’s work)
39x + 72y = 1/3 ………….…ІІ
(39 boys’ & 72 girls’ 1 day’s work).
Multiplying equation І by 6 and then subtracting equation ІІ from it, we get,
x = 1/225.
Putting the value of x in either equation І or equation ІІ will yield
y = 1/450.
So, 20 boys’ and 5 girls’ 1 day’s work
= 20/225 + 5/450
= 1/10.
Since 1/10 part is performed in 1 day.
So, 1 part is performed in 1/(1/10) day,i.e. 10 days.
In an examination 70% of the candidate passed in English, 80% passed in Mathematics, 10% failed in both subjects. If 144 candidates passed in both, the total number of candidates was:
Solution (c)
Failed candidates in English = (100 – 70) = 30%
Failed candidates in Mathematics = (100 – 80) = 20%
Candidates who fail in both subject = 10% Candidates who only fail in English = 30 – 10 = 20%
Candidates who only fail in Mathematics = 20 – 10 = 10%
Percentage of passed students in both subject
= 100 – (Candidates who only fail in English + Candidates who only fail in Mathematics + Candidates who fail in both subject)
= 100 – (20 + 10 + 10)
= 60%
According to the question,
60% of students = 144
Total students:
= (144/60) × 100
= 240
Solution (c)
Failed candidates in English = (100 – 70) = 30%
Failed candidates in Mathematics = (100 – 80) = 20%
Candidates who fail in both subject = 10% Candidates who only fail in English = 30 – 10 = 20%
Candidates who only fail in Mathematics = 20 – 10 = 10%
Percentage of passed students in both subject
= 100 – (Candidates who only fail in English + Candidates who only fail in Mathematics + Candidates who fail in both subject)
= 100 – (20 + 10 + 10)
= 60%
According to the question,
60% of students = 144
Total students:
= (144/60) × 100
= 240
One Amoeba splits into ten Amoeba to form the next generation, but due to the prevailing ecological conditions, only 50% survive. If the number of surviving amoebas in the 6th generation is 3125, what must have been their number in the first generation?
Solution (b)
Let there be ‘x’ Amoeba in the first generation, i.e. n1 = x.
So, n2 = 10x, but only 50% survive,
So, n2, survived = 10x/2 = 5x.
n3 = 10(5x), but only 50% survive,
So, n3, survived = 10(5x)/2 = 25x = 52x.
Similarly, n6,survived = 56-1 x = 55x
Now, it’s given that: 55x = 3125
⇒ 3125x = 3125
∴ x = 1.
Solution (b)
Let there be ‘x’ Amoeba in the first generation, i.e. n1 = x.
So, n2 = 10x, but only 50% survive,
So, n2, survived = 10x/2 = 5x.
n3 = 10(5x), but only 50% survive,
So, n3, survived = 10(5x)/2 = 25x = 52x.
Similarly, n6,survived = 56-1 x = 55x
Now, it’s given that: 55x = 3125
⇒ 3125x = 3125
∴ x = 1.
All the Best
IASbaba