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CLAT  >  SLAT Mock Test - 5 (New Pattern)

# SLAT Mock Test - 5 (New Pattern)

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## 60 Questions MCQ Test Mock Tests Series for Law Entrance Exams | SLAT Mock Test - 5 (New Pattern)

SLAT Mock Test - 5 (New Pattern) for CLAT 2023 is part of Mock Tests Series for Law Entrance Exams preparation. The SLAT Mock Test - 5 (New Pattern) questions and answers have been prepared according to the CLAT exam syllabus.The SLAT Mock Test - 5 (New Pattern) MCQs are made for CLAT 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for SLAT Mock Test - 5 (New Pattern) below.
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SLAT Mock Test - 5 (New Pattern) - Question 1

### Directions: Complete the following series.5824, 5242, ?, 4247, 3823

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 1 Each term in the series is obtained by subtracting the number formed by the first three digits of the preceding term from the preceding term.

5824 - 582 = 5242

5242 - 524 = 4718

4718 - 471 = 4247

4247 - 424 = 3823

SLAT Mock Test - 5 (New Pattern) - Question 2

### Directions: Find the missing term in the following series.?, 97, 167, 257, 367, 497, 647

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 2 The pattern is the addition of 50, 70, 90, 110, 130, 150.... to the series 47, 97, 167, 257, 367, 497, 647.

Therefore, the missing number is 47.

SLAT Mock Test - 5 (New Pattern) - Question 3

### Find the odd one out.

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 3 65 → 43 + 1,

344 → 73 + 1

730 → 93 + 1

SLAT Mock Test - 5 (New Pattern) - Question 4

Preeti has a son named Arun. Ram is Preeti's brother. Neeta has a daughter named Reema. Neeta is Ram's sister. How is Arun related to Reema?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 4 Arun is the cousin of Reema.

SLAT Mock Test - 5 (New Pattern) - Question 5

Directions: From the given five groups of letters, four of them are similar to each other in some manner, while one is different and this is to be choosen from the four alternative answers.

KP, MN, HR, GT, EV

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 5 All are opposite pairs except option 3.
SLAT Mock Test - 5 (New Pattern) - Question 6

Directions: Given question has a pair of CAPITALISED words followed by four pairs of words. Choose the pair of words which best expresses the relationship similar to that expressed in the capitalized pair.

BACHELOR : SPINSTER

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 6 Spinster is the feminine gender of bachelor; vixen is the feminine gender of fox.
SLAT Mock Test - 5 (New Pattern) - Question 7

Directions: In the following question, select the related word from the given alternatives.

Brick : Mason : : Colour : ?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 7 Brick is used by a mason and colour is used by a painter.
SLAT Mock Test - 5 (New Pattern) - Question 8

Gita is Amit's sister. Anjum is Amit's mother. Gaurav is Anjum's father. Puja is Gaurav's mother. How is Gita related to Gaurav?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 8

Thus, Gita is the granddaughter of Gaurav.

SLAT Mock Test - 5 (New Pattern) - Question 9

If the day on 4th April, 1988 was a Monday, then what was the day on 3rd November, 1987?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 9 1988 April 4th to 1987 November 3rd, we have 27 + 31 + 31 + 29 + 31 + 4 = 153 Days = 21 weeks + 6 odd days.

Six days before(because later date is given and former date is asked) a Monday comes a Tuesday.

SLAT Mock Test - 5 (New Pattern) - Question 10

If the second Sunday in October 2002 fell on the 13th of the month, then the first Sunday in November 2003 would fall on which date?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 10 Given: 13th October, 2002 was Sunday.

So, 13th October, 2003 was Monday.

12th October, 2003 was Sunday.

So, 19th October, 26th October and 2nd November were Sundays.

Hence, the first Sunday in November 2003 fell on 2nd.

SLAT Mock Test - 5 (New Pattern) - Question 11

If AROMA is coded as 24, GRAND as 22, then BREAD will be coded as

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 11 The numbers are assigned according to the English alphabet.

A = 1; B = 2; C = 3 ... Z = 26

AROMA = 1 + 18 + 15 + 13 + 1 = 48

(48/2) = 24; code assigned is 24.

GRAND = 7 + 18 + 1 + 14 + 4 = 44

(44/2) = 22; code assigned is 22.

BREAD = 2 + 18 + 5 + 1 + 4 = 30

(30/2) = 15; code will be 15.

SLAT Mock Test - 5 (New Pattern) - Question 12

In a certain code, RAIN is written as 8$%6 and MORE is written as 7#8@. How is REMAIN written in that code? Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 12 The coding of the words is done as given below. R = 8 A =$

I = %

N = 6

And,

M = 7

O = #

R = 8

E = @

So, the code for REMAIN will be 8@7$%6. SLAT Mock Test - 5 (New Pattern) - Question 13 Directions: The question consists of two statements, one labelled as Principle(s) and the other as Facts. You are to examine the Principle(s) and apply it/them to the given Facts carefully, and select the best option. Principle: Whoever makes any gesture, or any preparation intending or knowing it to be likely that such gesture or preparation will cause any person present to apprehend that he who makes that gesture or preparation is about to use criminal force to that person, is said to commit an assault. Facts: A shakes his fist at Z, intending or knowing it to be likely that he may thereby cause Z to believe that A is about to strike Z. Decide whether any criminal liability arises or not. Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 13 Yes, A has committed an assault because he makes the gesture at Z for striking him; and according to the principle, whosoever makes any gesture, or any preparation intending or knowing it to be likely that such gesture or preparation will cause any person present to apprehend that he who makes that gesture or preparation is about to use criminal force to that person, is said to commit an assault. SLAT Mock Test - 5 (New Pattern) - Question 14 Directions: The question consists of two statements, one labelled as Principle(s) and the other as Facts. You are to examine the Principle(s) and apply it/them to the given Facts carefully, and select the best option. Principle: Whoever makes any gesture, or any preparation intending or knowing it to be likely that such gesture or preparation will cause any person present to apprehend that he who makes that gesture or preparation is about to use criminal force to that person, is said to commit an assault. Facts: A shakes his fist at Z, intending or knowing it to be likely that he may thereby cause Z to believe that A is about to strike Z. Decide whether any criminal liability arises or not. Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 14 Yes, A has committed an assault because he makes the gesture at Z for striking him; and according to the principle, whosoever makes any gesture, or any preparation intending or knowing it to be likely that such gesture or preparation will cause any person present to apprehend that he who makes that gesture or preparation is about to use criminal force to that person, is said to commit an assault. SLAT Mock Test - 5 (New Pattern) - Question 15 Directions: The question consists of two statements, one labelled as Principle(s) and the other as Facts. You are to examine the Principle(s) and apply it/them to the given Facts carefully, and select the best option. Principle: Where anything which is an offence is made up of parts, any of which parts is itself an offence, the offender shall not be punished with the punishment of more than one of such his offences, unless it is so expressly provided. Facts: While A is beating Z, Y interferes, and A intentionally strikes Y. The blow given to Y is not the part of the act as A is voluntarily causing hurt to Z. Would beating Y be counted as a voluntary offence or not? Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 15 A is liable to one punishment for voluntarily causing hurt to Z, and to another for the blow given to Y. Beating Y cannot be treated as the voluntary offence because in the beginning, A did not have intention to beat Y and according to the given principle, where anything, which is an offence, is made up of parts, any of which parts is itself an offence, the offender shall not be punished with the punishment of more than one of such his offences, unless it is so expressly provided. SLAT Mock Test - 5 (New Pattern) - Question 16 Directions: The question consists of two statements, one labelled as Principle(s) and the other as Facts. You are to examine the Principle(s) and apply it/them to the given Facts carefully, and select the best option. Principle: Theft is robbery if, in order to the committing of the theft, or in committing the theft, or in carrying away or attempting to carry away property obtained by the theft, the offender, for that end, voluntarily causes or attempts to cause to any person, death or hurt or wrongful restraint, or fear of instant death or of instant hurt, or of instant wrongful restraint. Facts: A was a servant in B's house. One day, he decided to steal B's home theatre. While stealing, B's 7-year-old daughter C saw him. A, alarmed by this, threatened to kill C if she told this to anyone. Is B liable for robbery? Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 16 On a strict application of the principle to the given facts, it is clear that B caused fear of instant death in C while stealing home theatre, which amounts to robbery. SLAT Mock Test - 5 (New Pattern) - Question 17 Directions: The question consists of two statements, one labelled as Principle(s) and the other as Facts. You are to examine the principle and apply it to the given facts carefully and select the best option. Principle: A contract can be voided if consent was not freely given. Facts: Rahul wants to become a member of City Forest Club, but the Club Manager informs him that he must pay Rs. 50 Lakh in order to become a member. Rahul pays but later claims the amount back and contends that his consent was not freely given. Decide. Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 17 The Manager did not force him to pay the money. His consent was free, so he cannot recover now. He was simply told that in order to obtain the membership, he must pay. Once the membership is given, he cannot go back and claim that his consent was not free. SLAT Mock Test - 5 (New Pattern) - Question 18 Directions: The following question consists of two statements, one labelled as Assertion (A) and the other as Reason (R). You are to examine these two statements carefully and select the correct answer accordingly. Assertion (A): No person shall be condemned unheard. Reason (R): A person accused of an offence should not be compelled to be a witness against himself. Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 18 A is true. As per one of the principles of natural justice, audi alteram partem, no one shall be condemned unheard. The accused must be given a fair chance to put his part in front of the court to make the hearing fair. R is true. As per article 20(3), R embodies a principle of protection against compulsion of self-incrimination. But (R) is not a correct explanation of (A). SLAT Mock Test - 5 (New Pattern) - Question 19 Directions: The question consists of two statements, one labelled as Principle(s) and the other as Facts. You are to examine the Principle(s) and apply it/them to the given Facts carefully, and select the best option. Principle: All persons shall be competent to testify unless the court considers that they are prevented from understanding the questions put to them, or from giving rational answer to those questions, by tender years, extreme old age, disease, whether of body and mind, or any other cause of the same kind. Facts: A man of 80 years is hard of hearing but has a reliable memory with regard to the events of which he has visualised. Decide. Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 19 A man of 80 years who is hard of hearing but has a reliable memory with regard to the events of which he has to provide his testimony will not be prevented from testifying, as he can read the questions put to him and answer accordingly. All persons shall be competent to testify unless the court considers that they are prevented from understanding the questions put to them, or from giving rational answer to those questions, by tender years, extreme old age, disease, whether of body and mind, or any other cause of the same kind. SLAT Mock Test - 5 (New Pattern) - Question 20 Directions: The question consists of two statements, one labelled as Principle(s) and the other as Facts. You are to examine the Principle(s) and apply it/them to the given Facts carefully, and select the best option. Principle: Titles and positions in government are given on the basis of personal talent and the transfer of such titles by means of an agreement to other person is void and against public policy. Facts: A appeared for the exam of Indian Judicial Services. He cleared the exam after various rounds and then recruited on the position of Judge. A's friend M also appeared for the exam but couldn't clear it. Both of them enter into an agreement that A will transfer his position to M in return for a monthly consideration of Rs. 20,000. Decide. Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 20 Strictly following the principle, the transfer of titles or positions is against the public policy of the government. No one can transfer the position which he or she has earned after hard work. The transfer is against the policy of the GOI and hence void. SLAT Mock Test - 5 (New Pattern) - Question 21 Directions: The question consists of two statements, one labelled as Principle(s) and the other as Facts. You are to examine the Principle(s) and apply it/them to the given Facts carefully, and select the best option. Principle: If it appears from the nature of the case that it was the intention of the parties to a contract that any promise contained in it should be performed by the promisor himself, such promise must be performed by the promisor. In other cases, the promisor or his representative may employ a competent person to perform it. Facts: A promises to pay B a sum of money. A may perform this promise, either by personally paying the money to B or by causing it to be paid to B by another. What if A dies in this case before the due date of payment? Decide. Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 21 If A dies before the time appointed for payment, his representatives must perform the promise or employ some proper person to do so. If it appears from the nature of the case that it was the intention of the parties i.e. either A or B to the contract of paying money, then it should be performed by the promisor himself i.e. A in this case. In other cases, A or his representatives may employ a competent person to perform it. SLAT Mock Test - 5 (New Pattern) - Question 22 Directions: The question consists of one or more than one principle and some facts. You are to examine the principle(s) and apply it/them to the given facts, and select the best option. Principle: Marriage of minors under the Hindu Marriage Act, 1955, once performed is valid. Facts: Shivani filed a petition claiming maintenance from Mahesh, her husband. Mahesh rejected the demand saying that they were minors at the time of marriage and thus, the marriage is void. Shivani was 8 years and Mahesh 10 years of age at the time of their marriage. Can Shivani claim maintenance? Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 22 The marriage once performed is valid. Therefore, Mahesh here in this case cannot take the excuse of marriage being void.He has to pay for the maintenance. The principle makes it very clear that the marriage performed during the minority is also valid; therefore, all other legal consequences of marriage are being followed in this case. SLAT Mock Test - 5 (New Pattern) - Question 23 Directions: This question consists of one or more principles followed by certain facts. You are to examine the principle(s) and apply it/them to the given facts carefully and select the best option accordingly. Principles: 1. The Directive Principles of State Policy are guidelines considered irrefutable in the governance of the country, though unenforceable by any court. 2. Parliament's Equal Remuneration Act, 1976 makes equal pay for equal work compulsory. Facts: Naina, an actress, has always been very outspoken about not receiving as much remuneration as her male colleagues. She files a suit in the court, seeking constitutional remedy for equal pay for equal work as her right. Decide Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 23 Equal pay is an accompaniment of Right to Equality and has been included in an Equal Remuneration Act, 1976, enacted by the Parliament which gives it a shape of an enforceable law in the court. SLAT Mock Test - 5 (New Pattern) - Question 24 Directions: This question consists of one or more principles followed by certain facts. You are to examine the principle(s) and apply it/them to the given facts carefully and select the best option accordingly. Principle: No person shall be prosecuted and punished for the same offence more than once. This rule is known as double jeopardy. Facts: Nisha was a government employee. Embezzlement of funds was reported in her department. After the investigation, it came out that Nisha was responsible for this. So, she was handed over to the police for further criminal proceedings. She was convicted by the court and was given a punishment of 2 years of imprisonment. After this, a departmental inquiry was ordered to probe into the acts of Nisha by a government department. Nisha challenged this inquiry on the ground of above given principle. Decide Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 24 A departmental inquiry does not mean prosecution. It is a disciplinary action initiated by the employer. Rule of double jeopardy is only applicable in the case of criminal prosecution. SLAT Mock Test - 5 (New Pattern) - Question 25 Directions: There are four nurses - Anita, Beena, Chaiya, Dimple working at a private nursing home, which is open from Monday to Friday. Each nurse works according to the following rules: On Mondays, only Anita or Beena works. On Tuesdays, Beena works alone or with one of the other nurses, but not Anita. On Wednesdays, Chaiya works alone or with one of the other nurses. On Thursdays, two nurses work together, but Beena is not one of them. On Fridays, three nurses work together. Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 25 So, we can see from the table that Beena must work on Tuesday. SLAT Mock Test - 5 (New Pattern) - Question 26 What will come in place of the question mark (?) in the following equation? Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 26 ? = 15(⅖) SLAT Mock Test - 5 (New Pattern) - Question 27 A series is given with one term missing. Select the correct alternative from the given ones that will complete the series. CX, EV, GT, IR, ? Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 27 The pattern is as follows First letter: C (+2 letters) = E E (+2 letters) = G G (+2 letters) = I I (+2 letters) = K Second letter: X (-2 letters) = V V (-2 letters) = T T (-2 letters) = R R (-2 letters) = P Thus, missing term = KP SLAT Mock Test - 5 (New Pattern) - Question 28 The ratio of the present ages of Seema and Mohan is 2 : 5 and of Farah and Seema is 6 : 2. After 5 years, the ratio of the ages of Seema and Farah will be 3 : 7. What is the present age of Mohan? Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 28 Let the ages of Seema, Mohan and Farah be 2x, 5x and 6x, respectively. According to the question, 7(2x + 5) = 3(6x + 5) 14x + 35 = 18x + 15 18x – 14x = 35 - 15 4x = 20 x = 5 Age of Mohan = 5x = 5$\times\$ 5 = 25 years

SLAT Mock Test - 5 (New Pattern) - Question 29

Directions: In the question below, a statement is given, followed by several conclusions. You have to assume everything in the statement to be true and then decide which of the conclusions logically follow(s) the information given in the statement.

Statement:

Business is the best option for making money; still people prefer to go for service.

Conclusions:

(I) People do not like money.

(II) Business carries a risk factor as well.

(III) Jobs are available.

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 29 Conclusion (I) does not follow since the likes and dislikes of people cannot be commented on from the question statement.

Conclusion (II) does not follow as the passage gives no indication on the risks involved in business.

Conclusion (III) follows because unless jobs were available, opting for them would be absurd.

SLAT Mock Test - 5 (New Pattern) - Question 30

Raj walked 30 metres towards north. Then, he turned to his right and walked 20 metres. He then turned to his right again and walked 30 metres. Finally, he turned to his left and walked 20 metres.

At what distance was he from the starting point?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 30

Raj walked 30 metres towards north from the starting point. He turned to his right towards east and walked 20 metres. Then, he turned to his right again towards south and walked 30 metres. He finally turned to his left towards east and walked 20 metres. He is now to the east of his starting point.

Total distance between starting point and end point = 20 + 20 = 40 metres

SLAT Mock Test - 5 (New Pattern) - Question 31

Directions: There are four nurses - Anita, Beena, Chaiya, Dimple working at a private nursing home, which is open from Monday to Friday. Each nurse works according to the following rules:

On Mondays, only Anita or Beena works.

On Tuesdays, Beena works alone or with one of the other nurses, but not Anita.

On Wednesdays, Chaiya works alone or with one of the other nurses.

On Thursdays, two nurses work together, but Beena is not one of them.

On Fridays, three nurses work together.

If only Beena and Dimple are working on a certain day, which day must it be?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 31

If only Beena and Dimple are working on a certain day, it must be Tuesday, as Beena is certainly working on Tuesday.

SLAT Mock Test - 5 (New Pattern) - Question 32

The ratio of boys to girls in a class is 4 : 3. 30% of girls are good in Mathematics, whereas 60% of boys are poor in Mathematics. What % of boys are good in Mathematics out of the total students?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 32 Let the number of boys = 4x

Number of girls = 3x

Number of girls good in Mathematics = 30% of 3x = 0.9x

Number of boys good in Mathematics = 40% of 4x = 1.6x

Total number of students = 7x

% of boys who are good in Mathematics out of all the students = (1.6x/7x) x 100 = 22.86%

SLAT Mock Test - 5 (New Pattern) - Question 33

Mohan and Suresh can do a piece of work in 12 days and 18 days, respectively. If Mohan works for 2 days and Suresh works for 3 days, then what fraction of the work is left?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 33 Mohan's two day's work = 2/12 = ⅙

Suresh's three day's work = 3/18 = ⅙

Total work done =

Work left =

SLAT Mock Test - 5 (New Pattern) - Question 34

Directions: In making decisions about important questions, it is desirable to be able to distinguish between strong arguments and weak arguments. Strong arguments are those which are both important and directly related to the question. Weak arguments are those which are of minor importance, and they are directly related to the question or may be related to a trivial aspect of the question.

The question below is followed by two arguments numbered I and II. You have to decide which of the given arguments is/are strong argument(s).

Question: Should the public sector undertakings be allowed to adopt hire-and-fire policy?

Arguments:

I. Yes, this will help the public sector undertakings to get rid of non-performing employees and will also help to reward the performing employees.

II. No, the management may not be able to implement the policy in an unbiased manner and the employees will suffer due to the high-handedness of the management.

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 34 Argument I is strong because it will enhance efficiency of public sector undertakings. Argument II is strong as this policy is susceptible to corruption and high-handedness. Because both the arguments, though strong, are contrasting to each other, only one of them can be picked at a time.
SLAT Mock Test - 5 (New Pattern) - Question 35

Directions: In the following question, a statement is followed by assumptions. An assumption is something supposed or taken for granted. Consider the statement and the following assumptions, and choose the correct option.

Statement: PM Modi appeals to Kashmir's ''misguided youths'' to shun violence.

Assumptions:

I. The young ones of Kashmir would follow the appeal.

II. In case they don't shun violence, it could have negative consequences.

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 35 When the statement is in the form of an appeal, then the following standard assumptions may be taken as default

1. There is a necessity.

3. It will be beneficial for the people to whom the advice is given if they follow it.

4. It can have negative consequences if they don't.

Given assumptions indicate points 2 and 4, respectively. So, option 4 is the correct answer.

SLAT Mock Test - 5 (New Pattern) - Question 36

A man on a platform notices that a train going in one direction takes 10 seconds to pass him and a train of the same length going in the other direction takes 15 seconds to pass him. What is the time taken by the two trains to pass one another, if the length of both the trains is 200 m?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 36 Speed of train 1 = 200/10 = 20 m/s

Speed of train 2 = 200/15 = 13.33 m/s

The trains travel in opposite directions.

Therefore, relative speed = 20 + 13.33 = 33.33 m/s

Now, time taken by the trains to cross each other =

SLAT Mock Test - 5 (New Pattern) - Question 37

Directions: Read the following passage and answer the question given after it.

Some statements are routinely issued by the government of the day and they become news. They become news not necessarily because they are newsworthy, but because they are headlined by the newspapers. Let us examine some of these statements. No one will be allowed to take law into his own hands; the corrupt will be dealt with firmly; indiscipline will not be tolerated whether it is in a campus or in a political outfit; India will not compromise on its principles and so on and so forth. These have been spoken on innumerable occasions and have been heard on umpteen occasions and will continue to be spoken and heard. They have become so routinely stale that they have ceased to convey any meaning to anyone. These statements are necessary evils of non-governance or ill-governance. Yet they make news and we have the mortification of having to encounter them every morning in bold prints. What do they actually mean when they say that they will not allow anyone to take law into his own hands? Law, in its various forms, is not only taken into hands, but is also wantonly disregarded. This is not only tolerated, but is often given respectability too. If it were not so, we would not have been seeing the mushrooming of people with dubious character on the ascendancy right in our midst. Today, words speak, actions do not.

Q. According to the passage, why is the author mortified by what he encounters every morning in bold prints?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 37 The gap between what is said by the politicians and what they do makes the statements in the newspaper a daily anguish for the author.
SLAT Mock Test - 5 (New Pattern) - Question 38

Directions: Read the following passage and answer the question given after it.

Some statements are routinely issued by the government of the day and they become news. They become news not necessarily because they are newsworthy, but because they are headlined by the newspapers. Let us examine some of these statements. No one will be allowed to take law into his own hands; the corrupt will be dealt with firmly; indiscipline will not be tolerated whether it is in a campus or in a political outfit; India will not compromise on its principles and so on and so forth. These have been spoken on innumerable occasions and have been heard on umpteen occasions and will continue to be spoken and heard. They have become so routinely stale that they have ceased to convey any meaning to anyone. These statements are necessary evils of non-governance or ill-governance. Yet they make news and we have the mortification of having to encounter them every morning in bold prints. What do they actually mean when they say that they will not allow anyone to take law into his own hands? Law, in its various forms, is not only taken into hands, but is also wantonly disregarded. This is not only tolerated, but is often given respectability too. If it were not so, we would not have been seeing the mushrooming of people with dubious character on the ascendancy right in our midst. Today, words speak, actions do not.

Q. The primary aim of the writer, in this passage, is to

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 38 This can be inferred from the lines, 'Some statements are routinely issued by the government of the day and they become news. They become news not necessarily because they are newsworthy, but because they are headlined by the newspapers.'
SLAT Mock Test - 5 (New Pattern) - Question 39

Directions: Read the following passage and answer the question given after it.

Some statements are routinely issued by the government of the day and they become news. They become news not necessarily because they are newsworthy, but because they are headlined by the newspapers. Let us examine some of these statements. No one will be allowed to take law into his own hands; the corrupt will be dealt with firmly; indiscipline will not be tolerated whether it is in a campus or in a political outfit; India will not compromise on its principles and so on and so forth. These have been spoken on innumerable occasions and have been heard on umpteen occasions and will continue to be spoken and heard. They have become so routinely stale that they have ceased to convey any meaning to anyone. These statements are necessary evils of non-governance or ill-governance. Yet they make news and we have the mortification of having to encounter them every morning in bold prints. What do they actually mean when they say that they will not allow anyone to take law into his own hands? Law, in its various forms, is not only taken into hands, but is also wantonly disregarded. This is not only tolerated, but is often given respectability too. If it were not so, we would not have been seeing the mushrooming of people with dubious character on the ascendancy right in our midst. Today, words speak, actions do not.

Q. Why does the author say - 'These statements are necessary evils of non-governance or ill-governance.'?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 39 The politicians routinely use these statements to hide their failure in executing their duties to the public. It is mentioned, 'These have been spoken on innumerable occasions and have been heard on umpteen occasions and will continue to be spoken and heard.'
SLAT Mock Test - 5 (New Pattern) - Question 40

Directions: Read the following passage and answer the question given after it.

Some statements are routinely issued by the government of the day and they become news. They become news not necessarily because they are newsworthy, but because they are headlined by the newspapers. Let us examine some of these statements. No one will be allowed to take law into his own hands; the corrupt will be dealt with firmly; indiscipline will not be tolerated whether it is in a campus or in a political outfit; India will not compromise on its principles and so on and so forth. These have been spoken on innumerable occasions and have been heard on umpteen occasions and will continue to be spoken and heard. They have become so routinely stale that they have ceased to convey any meaning to anyone. These statements are necessary evils of non-governance or ill-governance. Yet they make news and we have the mortification of having to encounter them every morning in bold prints. What do they actually mean when they say that they will not allow anyone to take law into his own hands? Law, in its various forms, is not only taken into hands, but is also wantonly disregarded. This is not only tolerated, but is often given respectability too. If it were not so, we would not have been seeing the mushrooming of people with dubious character on the ascendancy right in our midst. Today, words speak, actions do not.

Q. The author feels the statement 'No one will be allowed to take the law into his own hands' is an empty statement devoid of any real meaning because

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 40 It is mentioned, 'What do they actually mean when they say that they will not allow anyone to take law into his own hands? ... people with dubious character on the ascendancy right in our midst.' Option 3 is correct.
SLAT Mock Test - 5 (New Pattern) - Question 41

Directions: Read the following passage and answer the question given after it.

India's national flower, the lotus, is known by various names such as the Indian Lotus, Sacred Lotus, Bean of India or simply the lotus. In India, it is associated with several Hindu mythological deities such as Brahma, Saraswati and Lakshmi and is used for many religious purposes. Botanically speaking, it is an aquatic flowering plant which flowers for one or more years. It is often mistaken for a water lily which has a completely different structure. The water lily is majorly white in colour with slight hues of other colours too.

Another interesting fact about this splendid flower is that the common Egyptian ''white'' lotus is actually a water lily. The white lotus opens when the sun sets, while the blue water lily opens in the morning. The white lotus is a plant growing in wetland areas with water of two meters in depth which blooms in the night. The lotus flower symbolises awakening to the spiritual reality in Hinduism.

One thing which is worth noting about the lotus flower is that it is unstained even though it grows in the mud, which has become a metaphor for many Indians who battle many hardships and adverse circumstances to attain success and prosperity.

Q. Which of these is the correct habitat of the white lotus?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 41 It is mentioned, 'The white lotus is a plant growing in wetland areas with water of two metres in depth...' Option (2) is correct.
SLAT Mock Test - 5 (New Pattern) - Question 42

Directions: Read the following passage and answer the question given after it.

India's national flower, the lotus, is known by various names such as the Indian Lotus, Sacred Lotus, Bean of India or simply the lotus. In India, it is associated with several Hindu mythological deities such as Brahma, Saraswati and Lakshmi and is used for many religious purposes. Botanically speaking, it is an aquatic flowering plant which flowers for one or more years. It is often mistaken for a water lily which has a completely different structure. The water lily is majorly white in colour with slight hues of other colours too.

Another interesting fact about this splendid flower is that the common Egyptian ''white'' lotus is actually a water lily. The white lotus opens when the sun sets, while the blue water lily opens in the morning. The white lotus is a plant growing in wetland areas with water of two metres in depth which blooms in the night. The lotus flower symbolises awakening to the spiritual reality in Hinduism.

One thing which is worth noting about the lotus flower is that it is unstained even though it grows in the mud, which has become a metaphor for many Indians who battle many hardships and adverse circumstances to attain success and prosperity.

Q. According to the passage, how is the lotus different from a water lily?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 42 It is mentioned, 'It is often mistaken for a water lily which has a completely different structure.' Option (3) is correct.
SLAT Mock Test - 5 (New Pattern) - Question 43

Directions: Read the following passage and answer the question given after it.

India's national flower, the lotus, is known by various names such as the Indian Lotus, Sacred Lotus, Bean of India or simply the lotus. In India, it is associated with several Hindu mythological deities such as Brahma, Saraswati and Lakshmi and is used for many religious purposes. Botanically speaking, it is an aquatic flowering plant which flowers for one or more years. It is often mistaken for a water lily which has a completely different structure. The water lily is majorly white in colour with slight hues of other colours too.

Another interesting fact about this splendid flower is that the common Egyptian ''white'' lotus is actually a water lily. The white lotus opens when the sun sets, while the blue water lily opens in the morning. The white lotus is a plant growing in wetland areas with water of two metres in depth which blooms in the night. The lotus flower symbolises awakening to the spiritual reality in Hinduism.

One thing which is worth noting about the lotus flower is that it is unstained even though it grows in the mud, which has become a metaphor for many Indians who battle many hardships and adverse circumstances to attain success and prosperity.

Q. According to the passage, when does the white lotus open?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 43 It is stated in the passage, "The white lotus opens when the sun sets, while the blue water lily opens in the morning." Thus, option (2) is correct.
SLAT Mock Test - 5 (New Pattern) - Question 44

Directions: Read the following passage and answer the question given after it.

India's national flower, the lotus, is known by various names such as the Indian Lotus, Sacred Lotus, Bean of India or simply the lotus. In India, it is associated with several Hindu mythological deities such as Brahma, Saraswati and Lakshmi and is used for many religious purposes. Botanically speaking, it is an aquatic flowering plant which flowers for one or more years. It is often mistaken for a water lily which has a completely different structure. The water lily is majorly white in colour with slight hues of other colours too.

Another interesting fact about this splendid flower is that the common Egyptian ''white'' lotus is actually a water lily. The white lotus opens when the sun sets, while the blue water lily opens in the morning. The white lotus is a plant growing in wetland areas with water of two metres in depth which blooms in the night. The lotus flower symbolises awakening to the spiritual reality in Hinduism.

One thing which is worth noting about the lotus flower is that it is unstained even though it grows in the mud, which has become a metaphor for many Indians who battle many hardships and adverse circumstances to attain success and prosperity.

Q. Which of these words means 'colour or shade' as used in the passage?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 44 The word 'hue' refers to colour or shade, in the passage - 'The water lily is majorly white in colour with slight hues of other colours too.'
SLAT Mock Test - 5 (New Pattern) - Question 45

Directions: Read the following passage and answer the question given after it.

An earthquake is a tremor of high intensity in the earth's surface caused by the action of the end-genetic forces of the earth. It causes immense damage to life and property of the region if its intensity is measured as being above 7 on the Richter scale. Studies have shown that over 80% of our country's area comes under the moderate and high seismic zones.

In the past, a number of devastating earthquakes have occurred. Earthquakes measuring more than 7 on Richter scale in the sea bed may produce high sea waves called tsunamis. Such tsunamis were caused due to the earthquake near Sumatra coast on 26th December, 2004, which led to a loss of more than 5 lakh people in Indonesia, Sri Lanka and India. In India, heavy damage to life and property was caused in Andaman-Nicobar islands and Tamil Nadu coast. Severity of the tsunamis was a little minimised along the coasts having wider continental shelves and luxuriant growth of mangrove forests. Since Andaman area lies in the high seismic zone, the recurrence of tsunamis cannot be ruled out if there is a high-intensity earthquake. The need is early warning system, planting of mangroves and building of protection walls.

Q. What does the word 'luxuriant' mean in the context of the passage?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 45 The context of the passage suggests that severity of the tsunamis was a little minimised along the coasts having wider continental shelves and abundant growth of mangrove forests. Thus, option 1 is the correct answer. The other options do not fit in the context.
SLAT Mock Test - 5 (New Pattern) - Question 46

Directions: Read the following passage and answer the question given after it.

An earthquake is a tremor of high intensity in the earth's surface caused by the action of the end-genetic forces of the earth. It causes immense damage to life and property of the region if its intensity is measured as being above 7 on the Richter scale. Studies have shown that over 80% of our country's area comes under the moderate and high seismic zones.

In the past, a number of devastating earthquakes have occurred. Earthquakes measuring more than 7 on Richter scale in the sea bed may produce high sea waves called tsunamis. Such tsunamis were caused due to the earthquake near Sumatra coast on 26th December, 2004, which led to a loss of more than 5 lakh people in Indonesia, Sri Lanka and India. In India, heavy damage to life and property was caused in Andaman-Nicobar islands and Tamil Nadu coast. Severity of the tsunamis was a little minimised along the coasts having wider continental shelves and luxuriant growth of mangrove forests. Since Andaman area lies in the high seismic zone, the recurrence of tsunamis cannot be ruled out if there is a high-intensity earthquake. The need is early warning system, planting of mangroves and building of protection walls.

Q. According to the passage, tsunamis may be triggered by

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 46 It is mentioned, 'Earthquakes measuring more than 7 on Richter scale in the sea bed may produce high sea waves called tsunamis.' Option 3 is correct.
SLAT Mock Test - 5 (New Pattern) - Question 47

Directions: Read the following passage and answer the question given after it.

An earthquake is a tremor of high intensity in the earth's surface caused by the action of the end-genetic forces of the earth. It causes immense damage to life and property of the region if its intensity is measured as being above 7 on the Richter scale. Studies have shown that over 80% of our country's area comes under the moderate and high seismic zones.

In the past, a number of devastating earthquakes have occurred. Earthquakes measuring more than 7 on Richter scale in the sea bed may produce high sea waves called tsunamis. Such tsunamis were caused due to the earthquake near Sumatra coast on 26th December, 2004, which led to a loss of more than 5 lakh people in Indonesia, Sri Lanka and India. In India, heavy damage to life and property was caused in Andaman-Nicobar islands and Tamil Nadu coast. Severity of the tsunamis was a little minimised along the coasts having wider continental shelves and luxuriant growth of mangrove forests. Since Andaman area lies in the high seismic zone, the recurrence of tsunamis cannot be ruled out if there is a high-intensity earthquake. The need is early warning system, planting of mangroves and building of protection walls.

Q. Which area(s) suffered relatively less despite the destructive tsunami in 2004?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 47 It is mentioned, 'Severity of the tsunamis was a little minimised along the coasts having wider continental shelves and luxuriant growth of mangrove forests.' Option 2 is correct.
SLAT Mock Test - 5 (New Pattern) - Question 48

Directions: Read the following passage and answer the question given after it.

An earthquake is a tremor of high intensity in the earth's surface caused by the action of the end-genetic forces of the earth. It causes immense damage to life and property of the region if its intensity is measured as being above 7 on the Richter scale. Studies have shown that over 80% of our country's area comes under the moderate and high seismic zones.

In the past, a number of devastating earthquakes have occurred. Earthquakes measuring more than 7 on Richter scale in the sea bed may produce high sea waves called tsunamis. Such tsunamis were caused due to the earthquake near Sumatra coast on 26th December, 2004, which led to a loss of more than 5 lakh people in Indonesia, Sri Lanka and India. In India, heavy damage to life and property was caused in Andaman-Nicobar islands and Tamil Nadu coast. Severity of the tsunamis was a little minimised along the coasts having wider continental shelves and luxuriant growth of mangrove forests. Since Andaman area lies in the high seismic zone, the recurrence of tsunamis cannot be ruled out if there is a high-intensity earthquake. The need is early warning system, planting of mangroves and building of protection walls.

Q. The statement 'over 80% of our country's area comes under the moderate and high seismic zones' implies that

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 48 'Over 80%' is a large figure that means a large part of our country is in the earthquake-prone zone.
SLAT Mock Test - 5 (New Pattern) - Question 49

Who is the author of the book titled ''Why I am a Hindu''?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 49 ''Why I am a Hindu'' is written by Shashi Tharoor. He is a Congress MP and author of fourteen books, and has won numerous literary awards, including a Commonwealth Writers' Prize.
SLAT Mock Test - 5 (New Pattern) - Question 50

The General Assembly of United Nations meets

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 50 The United Nations General Assembly is one of the six principal organs of the United Nations, the only one in which all member nations have equal representation, and the main deliberative, policy-making, and representative organ of the UN. The General Assembly of United Nations meets once a year.
SLAT Mock Test - 5 (New Pattern) - Question 51

Who is known as the father of Indian cinema?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 51 Dhundiraj Govind Phalke who is popularly known as Dadasaheb Phalke laid the founding stone of the Indian cinema. Phalke is also referred as the father of Indian cinema. Dadasaheb Phalke was a producer-director-screenwriter in the Indian film industry.

He began his career as a small town photographer in Godhra, but had to leave business after the death of his first wife and child in an outbreak of the bubonic plague.

The Dadasaheb Phalke Award, for lifetime contribution to cinema, was instituted in his honour by the Government of India in 1969. The award is one of the most prestigious awards in Indian cinema and is the highest official recognition for film personalities in the country.

SLAT Mock Test - 5 (New Pattern) - Question 52

Which bank, in 2021, launched Video Life Certificate (VLC) facility for pensioners?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 52 The State Bank of India (SBI), in 2021, launched Video Life Certificate (VLC) facility for pensioners. This facility was launched with an aim to offer seamless life certificate submission experience for millions of pensioners (other than family pensioners).

As per SBI, with the help of VLC facility, pensioners can schedule a video call with SBI staff at their convenience and complete the process of life certificate submission without having to visit the bank branch.

SLAT Mock Test - 5 (New Pattern) - Question 53

Who won the 2021 Booker Prize?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 53 South African playwright and novelist, Damon Galgut won the 2021 Booker Prize for The Promise, his third shortlisted novel which chronicles a family in his homeland from the late apartheid era through to Jacob Zuma's presidency. Spanning several decades, the book shows the family's growing disintegration as the country emerges into democracy.
SLAT Mock Test - 5 (New Pattern) - Question 54

Name the Lok Sabha Speaker who was awarded the Padma Bhushan in 2021.

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 54 Former Lok Sabha Speaker Sumitra Mahajan was awarded the Padma Bhushan by President Ram Nath Kovind at Rashtrapati Bhawan in 2021.

Veteran politician Mahajan was the Speaker of Lok Sabha from 2014 to 2019. She belongs to Bharatiya Janata Party and represented the Indore constituency of Madhya Pradesh from 1989 to 2019.

SLAT Mock Test - 5 (New Pattern) - Question 55

_____ in 2021 became India's seventh woman billionaire and the wealthiest self-made billionaire.

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 55 In 2021, Nykaa founder Falguni Nayar became India's seventh woman billionaire and the wealthiest self-made billionaire.

Nykaa, India's first unicorn start-up headed by a woman, was founded by Falguni Nayar in 2012. The e-commerce platform sells beauty and personal care products via its mobile app and website.

SLAT Mock Test - 5 (New Pattern) - Question 56

Global Day of Parents is observed annually on June

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 56 Global Day of Parents is a United Nations (UN) observance that is celebrated on June 1 each year to honour parents and their commitment to children worldwide.

On September 17, 2012, the UN publicly declared that the Global Day of Parents would be held annually on June 1.

This observance recognises parents as vital in providing protection and positive development for their children.

SLAT Mock Test - 5 (New Pattern) - Question 57

In 2021, in which country was the world's largest fuel cell plant inaugurated?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 57 The Ministry of Trade, Industry and Energy of South Korea held that the 'Shinincheon Bitdream Fuel Cell Power Plant' at the Shinincheon Bitstream headquarters of Korea Southern Power in Seo-gu, Incheon had been completed and inaugurated in 2021.

The power plant, operated by South Korea's independent power production company, POSCO Energy and Doosan Fuel Cell, is the world's largest fuel cell plant currently (as in 2021) in operation.

SLAT Mock Test - 5 (New Pattern) - Question 58

Who became the first Indian male cricketer to sign up for the Big Bash League in 2021?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 58 In 2021, Unmukt Chand became the first Indian male cricketer to sign up for the Big Bash League. The 28-year-old (as in 2021), who led India to the Under-19 World Cup title in 2012, represented India A, apart from featuring in teams like Delhi Daredevils, Mumbai Indians, and Rajasthan Royals in the IPL. He announced his retirement from Indian cricket in August 2021 stating that he would explore 'better opportunities from around the world'.
SLAT Mock Test - 5 (New Pattern) - Question 59

Which word was chosen as the 'Word of the Year' by the Oxford English Dictionary (OED) in 2021?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 59 'Vax' was chosen as the 'Word of the Year' by the Oxford English Dictionary (OED) in 2021.

'Vax' is derived from the Latin word 'Vacca', which means 'cow'. Vax is used as a short form for vaccines and means 'a substance put into a person's body to prevent them from getting a disease'.

Due to the Covid-19 pandemic, words related to vaccines saw a surge in 2021, including terms like double-vaxxed, unvaxxed and anti-vaxxer.

SLAT Mock Test - 5 (New Pattern) - Question 60

Which country in 2021 approved the world's first pill to treat cases of symptomatic COVID-19?

Detailed Solution for SLAT Mock Test - 5 (New Pattern) - Question 60 Britain's health regulators in 2021 approved the world's first pill to treat cases of symptomatic COVID-19. Medicines and Healthcare Products Regulatory Agency (MHRA) said, the antiviral molnupiravir has been found to be safe and effective at reducing the risk of hospitalisation and death in people with mild to moderate COVID-19, who are at increased risk of developing the disease.

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text:
# Converting Images from Grayscale to Color

### Contents

Brett‘s Pick this week is gray2rgb, by Jeny Rajan.

### Win One of Several MATLAB Hats! Read On!!

This week’s blog is image processing-centric, but it includes a challenge for MATLAB geeks everywhere. Jeny, of course, is
due some swag–it’s on the way, Jeny! But I’ll also send MATLAB hats to four readers who can rise to the challenges I posed
below. (Who says the MATLAB Central Contest Team gets to have all the fun? :) ) If you’re interested, read on…

### Grayscale to RGB

Typically, when I’m analyzing color images, I find that I can do my analyses in “gray space” rather than in color space. That
is, I can usually get all of the information I need from one or more individual color planes, or from a grayscale representation
of the color image. Converting to grayscale generally simplifies–and often speeds up–the processing of these color images.

Creating a grayscale image as a linear combination of multiple colorplanes is a common task, and one that the Image Processing Toolbox facilitates with the function rgb2gray.

Recently, while browsing the File Exchange, I came across Jeny’s file, which allows one to convert images “the other way.”
That is, you can provide a grayscale image along with a color image whose pallete you want to copy, and gray2rgb will create a color version of your grayscale image, matching (to some extent) the color of the second input image. I was
intrigued, so I played with the file. Here is a sample that shows what this function can do:

figure
subplot(2,2,1)
imshow('liftingbody.png');
subplot(2,2,2)
imshow('gantrycrane.png');
colorIm = gray2rgb('liftingbody.png','gantrycrane.png');
subplot(2,2,3.5)
imshow(colorIm)

It’s clear that many people have found gray2rgb to be useful; the file has been on the File Exchange for many years, and is getting close to 100 downloads per month. Plus,
there are several “thank you’s” and good reviews. Nonetheless, I’d like to note that this calculation took a very long time –on the order of two-and-a-half minutes ! Jeny discussed a couple of approaches to making this faster. One could subsample the color image (at the potential cost
of quality), or one could use “jittered sampling.” Unfortunately, no examples are provided that show how one would implement
these time-saving approaches.

### A Multi-Part Challenge

Digging into the underlying code, we see that Jeny’s function converts both input images to yCbCr. (The grayscale image is first expanded to 3D, with replicated information in the red, green, and blue colorplanes.) Then,
the output image is generated by processing the converted images pixel by pixel (!) , using a nested for loop. That works, but it can be slow indeed. I can think of several ways to improve the performance
of this code, and I’m betting that some of our readers can as well.

I’ll send a MATLAB cap to the first person who can exactly duplicate the results of colorIm generated above by vectorizing Jeny’s implementation of gray2rgb!

It also occurs to me that there are other approaches to the same problem. For example, using a function that I have previously shared on the File Exchange, I generated this color image:

Creating this image, using my function on my computer, took 0.02 seconds.

Swag to the first person who can find, from among my File Exchange submissions, a function that generates the image above
using a one-line command. (Note that there’s also an Image Processing Toolbox function that facilitates the same calculation,
though you’ll have to use it “cleverly.”)

Next, I’ll send swag to anyone who can come up with an alternate solution that differs substantively from Jeny’s approach,
and from the one I used. The only other rule besides “differs substantively” is that it has to run quickly –say 1 second or faster, using the same input images.

Now the question arises: why would one want to do this? Does anyone have a practical use case for converting grayscale images
to rgb by matching the colors of a second image? If anyone can provide an intriguing use case for modifying images in this
way, I’d love to hear it. Swag for the first compelling rationale. (For our purposes here, reasons like “it looks cool” or “it creates an interesting special effect” don’t count!)

format: plain


text:
(love seeing assumptions that are pretty clearly just meant to make annoying terms go away)

when you have a $$\frac{1}{n^2g^{j+2}}\left \{\int |L^Z*L^Z(u;g)|\,du\right\}\left \{\int |t|^j|\varphi_L(t)|^2|\varphi_Z(t/g)|^{-2}\,dt\right \}$$ problem that you need to get rid of, just add a little $$\left \{\int |L^Z*L^Z(u;g)|\,du\right\}\left \{\int |t|^j|\varphi_L(t)|^2|\varphi_Z(t/g)|^{-2}\,dt\right \} = o(n^2g^{j+2})$$ to your assumptions!

is latex/mathjax support a standard mastodon feature or just a mathstodon.xyz feature? are people on other mastodons seeing the raw tex?

mastodon has the following bad characteristics: it is new to me and therefore feels unfamiliar.

The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!


text:
# nLab Matthew Ando

Selected writrings

## Selected writrings

On elliptic genera, the Witten genus and the string orientation of tmf:

Specifically on twisted K-theory and twisted tmf:

category: people

Last revised on November 19, 2020 at 14:45:40. See the history of this page for a list of all contributions to it.


text:
# Matrix Condition Numbers

Higham, Nicholas J. (1983) Matrix Condition Numbers. Masters thesis, The University of Manchester.

## Abstract

Several properties of matrix norms and condition numbers are described. The sharpness of the norm bounds in the standard perturbation results for $Ax = b$ is investigated. For perturbations in $A$ the bounds are sharp and quite likely to be realistic. For perturbations in $b$ the usual bound is not sharp and can be unduly pessimistic; a more suitable measure of the conditioning than cond(A) is suggested. Some important concepts relating to the problem of condition estimation are discussed, careful consideration being given to the reliability and computational cost of condition estimators. The LINPACK condition estimation algorithm is described, its weaknesses, including two counter-examples, pointed out, and some observations given. Let $A$ be an $n\times n$ tridiagonal matrix. We show that it is possible to compute $\| A^{-1} \|_{\infty}$, and hence $\mathrm{cond}_{\infty}(A)$, in $O(n)$ operations. Several algorithms which perform this task are given. All but one of the algorithms apply to irreducible tridiagonal matrices: those having no zero elements on the subdiagonal and superdiagonal. It is shown how these algorithms may be employed in the computation of $\| A^{-1} \|_{\infty}$ when $A$ is reducible. If $A$ is, in addition, positive definite then it is possible to compute $\| A^{-1} \|_{\infty}$ as the $\ell_{\infty}$ norm of the solution to a linear system involving $A$'s comparison matrix, $M(A)$, which is also positive definite and tridiagonal. Utilising a relation between the $\mathrm{LDL^T}$ factors of $A$ and $M(A)$ we show how the LINPACK routine SPTSL, which solves $Ax = b$ for positive definite tridiagonal matrices $A$, can be modified so that it also computes $\mathrm{cond}_{\infty}(A)$, the increase in computational cost being 00 approximately 60 percent

Item Type: Thesis (Masters) MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theoryMSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis Nick Higham 06 Sep 2016 20 Oct 2017 14:13 http://eprints.maths.manchester.ac.uk/id/eprint/2499


text:
# Odd rep cap behavior?

Noticed a bit of strange behavior around the rep cap yesterday. I had an answer to a hot network question that got a bunch of upvotes, so I hit the cap [+200], then some more upvotes [still +200], then someone retracted their upvote [+190] (no idea if this was one of the votes from before or after I hit the cap, but that might be related to the cause of the bug), then some further upvotes [still +190].

Is the rep cap intended to be on net change, or on positive contribution? I guess it might make sense to have down-votes lower the cap, but a retracted upvote seems like it shouldn't.

I'm not too fussed about the 10 rep, but it would be a bit unfortunate if this disqualified the day from counting toward things like Epic (not that I'm ever likely to be Epic, but it's the principle!).

• I thought that case was suppose to get sorted these days. That display may be cached and slow to update. You can check it at physics.stackexchange.com/reputation . Scroll to the bottom. – dmckee Jul 4 '14 at 18:56
• @dmckee Ah, makes sense. Thanks for the link. – Kyle Oman Jul 4 '14 at 19:04
• @Kyle - ''... retracted the upvote ...'' ! How? Don't votes get locked after sometime ? (Or is it some punishment that the site has only inflicted on me?) – 299792458 Jul 6 '14 at 4:49
• @New_new_newbie Don't think so, just click upvote again... – Kyle Oman Jul 6 '14 at 14:51
• @New_new_newbie you have five minutes to retract a vote, or if the post is edited then you can freely change any vote you cast on it prior to the latest edit. Votes cast more than five minutes ago where the post has not been edited since the vote are indeed locked in. – David Z Jul 6 '14 at 22:22
• @DavidZ - Thanks for the info :) – 299792458 Jul 7 '14 at 5:44

## 1 Answer

dmckee♦ is correct, this seems to be due to a slow cache. Changes shown at physics.stackexchange.com/reputation show +200.

2 122790 (10) 2 122790 (10) 2 122790 (10) 2 122790 (10) 2 122790 (10) 2 122790 (10) 2 122790 (10) 2 122790 (10) 2 122790 (10) 2 122790 (10) 2 122790 (10) 2 122790 (10) 2 122790 (10) 2 122790 (10) 2 122790 (10) 2 122790 (10) 2 122790 (10) 2 122790 (10) 2 122790 (10) 2 122790 [10] 2 122790 [0] 2 122790 [0] 2 122790 [0] 2 122790 [0] 2 74691 [0] 2 122790 [0] 16 1659 [0] 2 122790 [0] 2 122790 [0] 2 122790 [0] -- 2014-07-03 rep +200 = 3384


text:
# How do you use the binomial series to expand (5 + x)^4?

Apr 17, 2018

${\left(5 + x\right)}^{4} = 625 + 500 x + 150 {x}^{2} + 20 {x}^{3} + {x}^{4}$

#### Explanation:

The binomial series expansion for (a+bx)^n,ninZZ;n>0 is given by:
(a+bx)^n=sum_(r=0)^n((n!)/(r!(n-1)!)a^(n-r)(bx)^r)

So, we have:
(5+x)^4=(4!)/(0!*4!)5^4+(4!)/(1!*3!)(5)^3x+(4!)/(2!*2!)(5)^2x^2+(4!)/(4!*1!)(5)x^3+(4!)/(4!*0!)x^4

${\left(5 + x\right)}^{4} = {5}^{4} + 4 {\left(5\right)}^{3} x + 6 {\left(5\right)}^{2} {x}^{2} + 4 \left(5\right) {x}^{3} + {x}^{4}$

${\left(5 + x\right)}^{4} = 625 + 500 x + 150 {x}^{2} + 20 {x}^{3} + {x}^{4}$


text:
# Subgroups of $GL(k,q)$ for bounded $k$

This question on subgroups of $GL(2,q)$ asked by Jan, and especially wonderful answers to it given by Geoff Robinson, Ralph, and Will Sawin showing that "almost no finite groups" inject in $GL(2,q)$ made me wonder (completely recreationally, I have to admit) whether there exists $N$ such that every finite group, or "most finite groups" inject in $GL(N,q)$.

Probably no such $N$ exists, but the ideas I had when thinking about the $N=2$ case use the specifics of the $2\times2$-situation way too much. Is it true, for instance that, along the lines of Ralph's and Will's answer, an abelian $p$-subgroup of $GL(N,q)$ may only have a bounder number of cyclic factors?

-

If $p$ is prime, the least dimension for a faithful representation of $(\mathbf{Z}/p)^d$ over any field of characteristic $\neq p$ is $d$. The argument is very easy, as you can assume the field algebraically closed and diagonalize.

It follows that if $G$ is a group containing isomorphic copies of $(\mathbf{Z}/p)^d$ for two distinct primes $p$ (e.g. $(\mathbf{Z}/6)^d$) then its smaller faithful representation over some field is of dimension $d$.

Note: for $(\mathbf{Z}/6)^d$, on the other hand there is a faithful representation in dimension two over a commutative ring (the product of finite fields $F_{2^d}\times F_{3^d}$), and looking at representations in arbitrary commutative rings seems more natural for obvious stability reasons. On the other hand, if $S$ is finite, simple non-abelian and has a faithful rep. in dimension $d$ over a commutative ring, then it has one over a finite field.

-
OK, I guess I just have to accept this one, because it's extremely beautiful in its simplicity, and makes me most embarrassed for not thinking of it! – Vladimir Dotsenko Mar 20 '12 at 17:31

For a (finite) group $G$, let $R(G)$ be the smallest dimension of any faithful (possibly projective) representation of $G$ over any field. There are many results in the literature giving lower bounds for $R(G)$ for the various classes of finite simple groups.

For example, for $n \ge 9$, we have $R(A_n) = n-2$. So, for $n \ge 9$ and $n > N+2$, $A_n$ is not a subgroup of ${\rm GL}(n,K)$ for any field $K$. I can look up references if you like.

Similarly, for all sufficiently large $d$, if $G$ is an irreducible quasi-simple classical group of dimension $d$ then, $R(G) = d$. So, for example, for large enough $d$, ${\rm GL}(d,2)$ is not a subgroup of ${\rm GL}(d-1,K)$ for any field $K$.

I believe there are also bounds as functions of $d$ on things the derived length of solvable groups with faithful representations of degree $d$ so, for any fixed $d$, there exist solvable (and probably also nilpotent) groups that do not embed into ${\rm GL}(d,K)$ for any $K$.

-
That's very nice! For some reason I never fully realised there is a uniform bound in terms of a field, though I must have experienced some evidence of that. – Vladimir Dotsenko Mar 20 '12 at 17:30

Yes, the idea that works for ${\rm GL}(2,q)$ with Abelian subgroups works with higher derived lengths for other ${\rm GL}(N, q).$ If $p$ is a prime which does not divide $q$ then the Sylow $p$-subgroups of ${\rm GL}(n,q)$ are monomial (up to equivalence) over some extension field. An easy indction argument (no pun intended) show that a monomial $p$ goup with a faithful representation of degree $p^{k}$ or less has derived length at most $k+1.$ Hence the Sylow $p$-subgroups of ${\rm GL}(N,q)$ have derived length at most $1 +\log_{p}(N)$ for all such $p.$ If $q$ is a power of $p,$ the bound on the derived length of a Sylow $p$-subgroup of ${\rm GL}(N,q)$ is similar. The nilpotence class of the upper unitriangular group is at most $N-1$, so the derived length is at most $\log_{2}(N),$ because for any nilpotent group $U,$ we have $U^{(k)} \leq L_{2^{k}}(U),$ where $U^{(k)}$ is the $k$-the term of the derived series and $L_{m}(U)$ is the $m$-th term of the lower central series. Hence in particular, no $p$-group of derived length $2 + \log_2(N)$ or more is a subgroup of any ${\rm GL}(N,q)$.

-
Oh yes, that's very close to what I was thinking about. Now I will wonder forever why I thought there was a problem. Thanks! – Vladimir Dotsenko Mar 20 '12 at 17:28


text:
#### Half yearly model question paper - Economics

11th Standard

Reg.No. :
•
•
•
•
•
•

Economics

Do not write anything on question paper.

Time : 02:30:00 Hrs
Total Marks : 90

Part A

20 x 1 = 20
1. Which of the following is a micro economics statement?

(a)

The real domestic output increased by 2.5 percent last year

(b)

Unemployment was 9.8 percent of the labour force last year

(c)

The price of wheat determines its demand

(d)

The general price level increased by 4 percent last year

2. Capital goods also called as_____good

(a)

Consumer

(b)

Producer's

(c)

Free goods

(d)

None of these

3. Gossen's first law is known as

(a)

Law of Equi-Marginal Utility

(b)

Law of Diminishing Marginal Utility

(c)

Law of Demand

(d)

Law of Diminishing returns

4. The foundation for various other economic law is ____

(a)

Law of diminishing marginal utility

(b)

Law of equi-marginal utility

(c)

Consumer surplus

(d)

None of these

5. Formula for calculating AP is

(a)

$\frac { \Delta TP }{ N }$

(b)

$\frac { \Delta TP }{ \Delta N }$

(c)

$\frac { TP }{ MP }$

(d)

$\frac { TP }{ N }$

6. Production means overall increase in the creation of _____________

(a)

Exchange

(b)

Distribution

(c)

Utility

(d)

Demand

7. Money cost is also known as _____ cost.

(a)

explicit

(b)

implicit

(c)

social

(d)

real

8. A shop keeper sold 20 bags with the price of Rs. 100 each. The total revenue of the seller is Rs.

(a)

200

(b)

20

(c)

2000

(d)

1500

9. In which of the following is not a type of market structure price will be very high?

(a)

Perfect competition

(b)

Monopoly

(c)

Duopoly

(d)

Oligopoly

10. Rent is the reward for the use of _________.

(a)

Capital

(b)

Labour

(c)

Land

(d)

Organization

11. Higher the risks, the greater are the ________.

(a)

Loss

(b)

Subsidy

(c)

profit

(d)

None of these

12. The position of Indian Economy among the other strongest economies in the world is ______

(a)

Fourth

(b)

Sixth

(c)

Fifth

(d)

Tenth

13. The power for governance of lndia was transferred from the East India Company (EIC) to the British crown in ___________.

(a)

1758

(b)

1858

(c)

1958

(d)

1658

14. Annual plans formed in the year __ .

(a)

1989 - 1991

(b)

1990 - 1992

(c)

2000 - 2001

(d)

1981 - 1983

15. Expansion of FDI____

(a)

Foreign Private Investment

(b)

Foreign Portfolio

(c)

Foreign Direct Investment

(d)

Forex Private Investment

16. The Raja Chelliah Committee on Trade Policy Reforms suggested the peak rate on import duties at____.

(a)

25%

(b)

50%

(c)

60%

(d)

100%

17. How do you term people employed in excess over and above the requirements?

(a)

Unemployment

(b)

Underemployment or Disguised Unemployment

(c)

Full employment

(d)

Self employment

18. What is the other name for concealed unemployment?

(a)

Open

(b)

Disguised

(c)

Seasonal

(d)

Rural

19. The main source of irrigation in Tamil Nadu is ------------

(a)

river

(b)

tank

(c)

well

(d)

canals

20. Which Union Territory has the highest sex ratio?

(a)

Chandigarh

(b)

Pondicherry

(c)

(d)

Andaman Nicobar

21. Part B

Answer any Seven in which question no. 30 is compulsory.

7 x 2 = 14
22. Distinguish goods from services

23. Write the formula of consumers surplus?

24. What is ISO- cost line?

25. Give the definition for 'Real cost'.

26. Distinguish between real and money wages.

27. What are the objectives of Tenth five year plan?

28. State the reasons for implementing LPG.

29. What was called as PURA by former President Abdul Kalam

30. Mention any four food crops which are favourable to Tamil Nadu

31. What is price discrimination?

32. Part C

Answer any Seven in which question no. 40 is compulsory.

7 x 3 = 21
33. Explain the theory of "Consumer's surplus"

34. Explain briefly characteristics of Demand?

35. Write a short note on Marginal Revenue.

36. Explain 'Monopsony'

37. Write the V.K.R.V. Rao's contribution on multiplier concept.

38. How are the energy sources classified? Explain.

39. Write any three objectives of Industrial Policy 1991.

40. Explain the Planning Commission's National Human Development Reports 2011 and 2016.

41. List out the objectives of MUDRA Bank

42. Explain GSDP in Tamil Nadu

43. Part D

7 x 5 = 35
1. Explain various divisions of Economics.

2. Explain the law of Equi - marginal utility

1. Changes in Tastes and fashions the demand for some goods and services is very suscrptible to change in tastes and fashions?

2. Elucidate the Laws of Returns to scale. lliustrate.

1. If total cost = 10+ Q3, find out AC, AVC, TFC, AFC when Q = 5.

2. Explain the meaning of Fixed and Variable factors and costs.

1. Illustrate price and output determination under Monopoly.

2. Elucidate the Loanable Funds Theory of Interest.

1. What are the assumptions of the Marginal Productivity 'Theory of Distribution?

2. Write the importance of mineral resources in India.

1. Explain the objectives of nationalization of commercial banks.

2. Describe the salient features of EXIM policy (2015 - 2020)

1. Discuss the problems of Rural Economy.

2. Explain the various sources of energy in Tamil Nadu.


text:
Multiple solutions for polyharmonic equations with potential vanishing at infinity
• Kisoeb Park,
• Jae-Myoung Kim,
• Jongrak Lee
Kisoeb Park
Incheon National University
Author Profile
Jae-Myoung Kim
Andong National University
Author Profile
Jongrak Lee
Jeju National University
Author Profile

## Abstract

We are concerned with the following polyharmonic equation: \begin{equation*} \Delta_p^L u+V(x)|u|^{p-2}u = K(x)f(x,u) and u>0 in \Bbb R^N, \end{equation*} where $1< p<\infty$, $N>Lp$, $L=1,2,\cdots$ and the potential functions $V, K:\Bbb R^{N}\to(0,\infty)$ are continuous. We study the existence and multiplicity of nontrivial positive weak solutions for the problem above via mountain pass theorem and fountain theorem.


text:
# Separate boxplots for multiple violin plot

I am using the following function from seurat package to generate multiple violon plots and I am interested in adding box plots to them but it doesn't work when I have plotted different data at once. Is there a way to solve it ?

For example, this works:

library(Seurat)
VlnPlot(object = pbmc_small, features.plot = 'PC1') +
geom_boxplot()

But this will simply lead into an empty box on top of my plots:

VlnPlot(object = pbmc_small, features.plot = c('PC1', 'PC2')) +
geom_boxplot()

This happens because the violin plots are combined using cowplot::plot_grid before being returned by VlnPlot. You can prevent the plots from being combined by setting combine=FALSE, then modify each one by adding a boxplot, then combine the modified plots using Seurat::CombinePlots.

However, the combine argument is currently broken in VlnPlot. I have pushed a fix but it's not on the public branch yet. VlnPlot is just a wrapper around ExIPlot (expression by identity plot) in Seurat v3 so right now this will work:

library(Seurat)
library(ggplot2)

plots <- ExIPlot(object = pbmc_small,
features = c('PC1', 'PC2'),
pt.size = 1,
combine = FALSE)

for(i in 1:length(plots)) {
plots[[i]] <- plots[[i]] + geom_boxplot() + theme(legend.position = 'none')
}
CombinePlots(plots)

Note this answer is for Seurat v3

The vioplot package comes built in with boxplots. You can download it from CRAN or there are more features (including formula input and separate colours) in the development version on GitHub: https://github.com/TomKellyGenetics/vioplot

devtools::install_github(“TomKellyGenetics/vioplot”)
library(“vioplot”)
vioplot(pbmc_small@dr@pca[,1]~pbmc_small@meta.data$ident)  To plot several PCs: library(“RColorBrewer”) colours <- brewer.pal(length(unique(pbmc_small@meta.data$$ident)), “Set3”) par(mfrow = c(1, 2)) vioplot(pbmc_small@dr@pca[,1]~pbmc_small@meta.data$$ident, main = “PC1”, xlab = “Identity”, col = colours) vioplot(pbmc_small@dr@pca[,2]~pbmc_small@meta.data$ident , main = “PC2”, xlab = “Identity”, col = colours)
par(mfrow = c(1, 1))

• You can add points to these with jitter: plot(pbmc_small@dr@pca[,1]~jitter(pbmc_small@meta.data\$ident, 0.5), add = TRUE) Dec 29 '18 at 3:59
• This version is now support on CRAN Jan 28 '19 at 1:29


text:
# Overview

This is Rubber.

Rubber is a building system for LaTeX documents. It is based on a routine that runs just as many compilations as necessary and runs companion programs like BibTeX and Makeindex when needed. The module system provides a great flexibility that virtually allows support for any package with no user intervention, as well as pre- and post-processing of the document. A good number of standard packages are supported, including graphics/graphicx with automatic conversion between various graphics formats and Metapost compilation. The associated tool "rubber-info" extracts information, such as dependency relations or post-compilation diagnostics.

• Installation

Compiling and running Rubber just requires Python version 2.2 or newer. For compilation, you will need the Python Distutils, which are usually included in developpement packages (in Debian, this is the python-dev package). Of course it won't be of much use without a working LaTeX environment (Rubber is known to work on teTeX and VTeX on various flavours of Unix including Darwin and Cygwin, any feedback is welcome about other systems).

To compile and install Rubber, just follow the usual procedure:

./configure make make install

The options for configuration can be shown using ./configure --help.

• Usage

As civility requires, saying rubber --help' and rubber-info --help' provides a short description of the command line's syntax. The included manual pages (available in English and French) and Texinfo documentation contain more precise usage information.

• Author

Rubber is written and maintained by Emmanuel Beffara <emmanuel@beffara.org>.

Thanks to all those who provided testing, comments and suggestions, and re-thanks to those who wrote patches and bugfixes.

Any kind of feedback is appreciated, in order to make this program as useful, robust and powerful as possible...


text:
# Number of ordered pairs of n-length binary strings with edit distance n-1

An edit operation is a single character insert, delete or substitution. The edit distance between two strings is the minimum number of edit operations needed to transform one string into the other one.

How many ordered pairs of binary strings of length $$n$$ are there with edit distance exactly $$n-1$$?

For $$n = 1,\dots, 10$$ the exact numbers are $$2, 8, 26, 54, 92, 138, 192, 254, 324, 402, 488, 582$$ which is not in the OEIS. For $$n=3$$ the full list of pairs is:

000 011
000 101
000 110
001 010
001 100
001 111
010 001
010 100
010 101
010 111
011 000
011 101
011 110
100 001
100 010
100 111
101 000
101 010
101 011
101 110
110 000
110 011
110 101
111 001
111 010
111 100

For comparison, the number of ordered pairs of binary strings of length $$n$$ which have edit distance exactly $$n$$ is $$2n$$.

$$\begin{array} 2 & & 8 & & 26 & & 54 & & 92 & & 138 & & 192 & & 254 & & 324 & & 402\\ & 6 & & 18 & & 28 & & 38 & & 46 & & 54 & & 62 & & 70 & & 78 & \\ & & 12 & & 10 & & 10 & & 8 & & 8 & & 8 & & 8 & & 8 & & \\ & & & -2 & & 0 & & -2 & & 0 & & 0 & & 0 & & 0 & & & \\ & & & & 2 & & -2 & & 2 & & 0 & & 0 & & 0 & & & & \\ & & & & & -4 & & 4 & & -2 & & 0 & & 0 & & & & & \\ & & & & & & 8 & & -6 & & 2 & & 0 & & & & & & \\ & & & & & & & -14 & & 8 & & -2 & & & & & & & \\ & & & & & & & & 22 & & -10 & & & & & & & & \\ & & & & & & & & & -32 & & & & & & & & & \end{array}$$
That seems to indicate that except for the first three terms the sequence is given by a quadratic polynomial. Trying again without the first three terms yields the polynomial $$2\left(2n^2+13n+12\right)$$. Since you seem to have code for producing initial terms, maybe you can produce a few more to check this. In view of the result for Average number of strings with edit distance exactly 2, it seems plausible that the result would be a polynomial. If you need a proof, some of the ideas I applied in the answer to that question may prove helpful.
• @fomin: Yes; somehow I thought that the third row of differences being zero implies degree $3$, but you're right, it's quadratic, obviously. – joriki Mar 4 '20 at 9:56


text:
# Baby-sitting bash script using DVD drive

This is the script I wrote to make an automated POC baby-sitter in 5 lines.

I first found this on a GIF or meme site and thought of making a POC script that does the same.

#How Linux users babysit
while :
do
eject
eject -t
done

I don't know aything about bash. So, I want improvements.

You can find the origin and the script at https://linuxandstuff.wordpress.com/2015/11/21/messing-with-the-dvd-drive-in-command-line/

• Add some delay to that. – Ave Jun 19 '16 at 13:14

## 1 Answer

These days a -T (toggle) argument exists. That allows us to make this a lot neater:

watch -n0 eject -T

You can alter the delay between rocks by changing the -n0 argument.

watch is used to run any designated command at regular intervals.

http://www.linfo.org/watch.html


text:
## Stream: new members

### Topic: What does it mean to "use Choice"?

#### Ken Lee (Jun 18 2020 at 16:48):

In maths, we are often given a surjection $\pi : \alpha \to \beta$ and $f : \alpha \to \gamma$ which preserves preimages of elements in $\beta$ and want to lift $f$ to a map $g : \beta \to \gamma$. I've written what I believe is a faithful representation of the "mathematical argument" in Lean :

universes u v w
theorem quotient_exists_lift {α : Sort u} {β : Sort v} {γ : Sort w}
{π : α → β} {f : α → γ} (hπ : function.surjective π)
(hf : ∀ x y : α, π x = π y → f x = f y) :
∃ g : β → γ, g ∘ π = f := ⟨
λ b : β, f $classical.some (hπ b), funext$ λ a : α,
hf (classical.some (hπ (π a))) a \$ classical.some_spec (hπ (π a))
⟩

My questions are :

1. I have used classical.some in the proof, so does this count as having "used choice" as we say it in maths?
2. The second part of the constructor corresponds in the "mathematical argument" to checking the function is well-defined and "independent of choice of representative". Does this mean I have "not used choice" or is this just a coincidence in the language?
3. I understand that using classical.choice or any of its corollaries means I have to mark my theorems noncomputable. Is the reverse true and how is this related to when we have "used choice" in maths? In particular, since Lean did not complain that the above theorem is noncomputable, does it mean I have "not used choice"?

#### Johan Commelin (Jun 18 2020 at 16:50):

definition and theorem are treated differently here, I think.

#### Bhavik Mehta (Jun 18 2020 at 16:50):

1. Yes. You can do #print axioms quotient_exists_lift to see

#### Johan Commelin (Jun 18 2020 at 16:50):

If you #print axioms quotient_exists_lift -- nvm Bryan Bhavik's faster

#### Bryan Gin-ge Chen (Jun 18 2020 at 16:52):

So fast that I got @Bhavik Mehta to post in my stead!

#### Bhavik Mehta (Jun 18 2020 at 16:52):

1. The second part of the constructor corresponds to showing that you've got an actual lift of f, rather than just any function beta -> gamma

#### Johan Commelin (Jun 18 2020 at 16:53):

Oops, sorry Bhavik...

No worries!

#### Ken Lee (Jun 18 2020 at 16:57):

Bhavik Mehta said:

1. Yes. You can do #print axioms quotient_exists_lift to see

I know that I have used classical.choice. What I meant to ask was whether this is exactly what we mean by "using choice" in maths. Sorry I should've worded this better.

#### Reid Barton (Jun 18 2020 at 16:58):

It depends on your exact foundational setup and interpretation of Prop, quantifiers etc.

#### Reid Barton (Jun 18 2020 at 17:06):

If you replace the existential quantifier in hπ and the conclusion by trunc, then you can prove this without axioms. But in classical foundations you can't distinguish between existential quantification and trunc.

#### Reid Barton (Jun 18 2020 at 17:07):

("without axioms" = maybe still using stuff like funext)

Last updated: May 15 2021 at 02:11 UTC


text:
# For which sites are all constant presheaves separated?

I'm intererested in open surjective geometric morphisms induced by fibrations of sites $S\to T$ a la Moerdijk, but as a warm-up, let's consider the case $S \to \ast$. In the case that $S$ is a poset $P$ as naturally turns up in set theory, then every constant presheaf is separated. My naive extrapolation is that this is at least partly due to the fact $P$ has no initial object, so we don't have any alteration there when applying the functor $(-)^+$ to the constant presheaf.

But is this enough in general? Do we need a condition like asking that the topos $Sh(S)$ is localic?

And then I'd like to know the relative case: given a fibration of sites $S\to T$, when are presheaves on $S$ that are given by pullback along the fibration of sheaves on $T$ separated?

-
See e.g. here cheng.staff.shef.ac.uk/pssl88/pssl88-duncan.pdf for the definition of a fibration of sites, if you can't get the Elephant or Moerdijk's original paper. –  David Roberts Jun 19 '13 at 11:55
Not sure about separated right now, but for actual sheaves, you need something like this here ncatlab.org/nlab/show/locally+connected+site –  Urs Schreiber Jun 19 '13 at 23:37
Hmm, it might be that I need the weaker condition noted under definition 1, that all covering families are inhabited. I saw this in the Elephant in relevant sections, but I didn't notice whether it gave me what I wanted. (This condition is in particular violated when we have the empty covering family of initial objects.) –  David Roberts Jun 19 '13 at 23:49

OK, I've found the answer in the Elephant. Given the map of sites $p\colon S\to \ast$, we get a functor of toposes $Set = Pre(\ast) \to Pre(S)$ by precomposition with $p$, which lands in separated presheaves precisely when $p$ preserves covers. Since $\ast$ has only the cover $id\colon \ast \to \ast$, then we see that constant presheaves are separated if and only if all covering families are inhabited.
More generally, for the case of a fibration of sites, we need $S\to T$ to preserve covering families, which is equivalent to asking that $S\to T$ induces a geometric morphism which is an open surjection.


text:
# Properties

 Label 1386.2.k.f Level $1386$ Weight $2$ Character orbit 1386.k Analytic conductor $11.067$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1386.k (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$11.0672657201$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{-3})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 462) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## $q$-expansion

Coefficients of the $$q$$-expansion are expressed in terms of a primitive root of unity $$\zeta_{6}$$. We also show the integral $$q$$-expansion of the trace form.

 $$f(q)$$ $$=$$ $$q -\zeta_{6} q^{2} + ( -1 + \zeta_{6} ) q^{4} + ( 3 - 2 \zeta_{6} ) q^{7} + q^{8} +O(q^{10})$$ $$q -\zeta_{6} q^{2} + ( -1 + \zeta_{6} ) q^{4} + ( 3 - 2 \zeta_{6} ) q^{7} + q^{8} + ( -1 + \zeta_{6} ) q^{11} + 4 q^{13} + ( -2 - \zeta_{6} ) q^{14} -\zeta_{6} q^{16} + ( -1 + \zeta_{6} ) q^{17} + 3 \zeta_{6} q^{19} + q^{22} -\zeta_{6} q^{23} + ( 5 - 5 \zeta_{6} ) q^{25} -4 \zeta_{6} q^{26} + ( -1 + 3 \zeta_{6} ) q^{28} + q^{29} + ( -6 + 6 \zeta_{6} ) q^{31} + ( -1 + \zeta_{6} ) q^{32} + q^{34} + 3 \zeta_{6} q^{37} + ( 3 - 3 \zeta_{6} ) q^{38} + 6 q^{41} + q^{43} -\zeta_{6} q^{44} + ( -1 + \zeta_{6} ) q^{46} -\zeta_{6} q^{47} + ( 5 - 8 \zeta_{6} ) q^{49} -5 q^{50} + ( -4 + 4 \zeta_{6} ) q^{52} + ( 3 - 2 \zeta_{6} ) q^{56} -\zeta_{6} q^{58} + ( 7 - 7 \zeta_{6} ) q^{59} -6 \zeta_{6} q^{61} + 6 q^{62} + q^{64} + ( 4 - 4 \zeta_{6} ) q^{67} -\zeta_{6} q^{68} + 15 q^{71} + ( -12 + 12 \zeta_{6} ) q^{73} + ( 3 - 3 \zeta_{6} ) q^{74} -3 q^{76} + ( -1 + 3 \zeta_{6} ) q^{77} -6 \zeta_{6} q^{82} + 16 q^{83} -\zeta_{6} q^{86} + ( -1 + \zeta_{6} ) q^{88} -8 \zeta_{6} q^{89} + ( 12 - 8 \zeta_{6} ) q^{91} + q^{92} + ( -1 + \zeta_{6} ) q^{94} + 7 q^{97} + ( -8 + 3 \zeta_{6} ) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{2} - q^{4} + 4q^{7} + 2q^{8} + O(q^{10})$$ $$2q - q^{2} - q^{4} + 4q^{7} + 2q^{8} - q^{11} + 8q^{13} - 5q^{14} - q^{16} - q^{17} + 3q^{19} + 2q^{22} - q^{23} + 5q^{25} - 4q^{26} + q^{28} + 2q^{29} - 6q^{31} - q^{32} + 2q^{34} + 3q^{37} + 3q^{38} + 12q^{41} + 2q^{43} - q^{44} - q^{46} - q^{47} + 2q^{49} - 10q^{50} - 4q^{52} + 4q^{56} - q^{58} + 7q^{59} - 6q^{61} + 12q^{62} + 2q^{64} + 4q^{67} - q^{68} + 30q^{71} - 12q^{73} + 3q^{74} - 6q^{76} + q^{77} - 6q^{82} + 32q^{83} - q^{86} - q^{88} - 8q^{89} + 16q^{91} + 2q^{92} - q^{94} + 14q^{97} - 13q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$$.

 $$n$$ $$155$$ $$199$$ $$1135$$ $$\chi(n)$$ $$1$$ $$-\zeta_{6}$$ $$1$$

## Embeddings

For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.

For more information on an embedded modular form you can click on its label.

Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
793.1
 0.5 − 0.866025i 0.5 + 0.866025i
−0.500000 + 0.866025i 0 −0.500000 0.866025i 0 0 2.00000 + 1.73205i 1.00000 0 0
991.1 −0.500000 0.866025i 0 −0.500000 + 0.866025i 0 0 2.00000 1.73205i 1.00000 0 0
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.c even 3 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1386.2.k.f 2
3.b odd 2 1 462.2.i.d 2
7.c even 3 1 inner 1386.2.k.f 2
7.c even 3 1 9702.2.a.bv 1
7.d odd 6 1 9702.2.a.bq 1
21.g even 6 1 3234.2.a.j 1
21.h odd 6 1 462.2.i.d 2
21.h odd 6 1 3234.2.a.c 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
462.2.i.d 2 3.b odd 2 1
462.2.i.d 2 21.h odd 6 1
1386.2.k.f 2 1.a even 1 1 trivial
1386.2.k.f 2 7.c even 3 1 inner
3234.2.a.c 1 21.h odd 6 1
3234.2.a.j 1 21.g even 6 1
9702.2.a.bq 1 7.d odd 6 1
9702.2.a.bv 1 7.c even 3 1

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(1386, [\chi])$$:

 $$T_{5}$$ $$T_{13} - 4$$ $$T_{17}^{2} + T_{17} + 1$$ $$T_{23}^{2} + T_{23} + 1$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + T + T^{2}$$
$3$ $$T^{2}$$
$5$ $$T^{2}$$
$7$ $$7 - 4 T + T^{2}$$
$11$ $$1 + T + T^{2}$$
$13$ $$( -4 + T )^{2}$$
$17$ $$1 + T + T^{2}$$
$19$ $$9 - 3 T + T^{2}$$
$23$ $$1 + T + T^{2}$$
$29$ $$( -1 + T )^{2}$$
$31$ $$36 + 6 T + T^{2}$$
$37$ $$9 - 3 T + T^{2}$$
$41$ $$( -6 + T )^{2}$$
$43$ $$( -1 + T )^{2}$$
$47$ $$1 + T + T^{2}$$
$53$ $$T^{2}$$
$59$ $$49 - 7 T + T^{2}$$
$61$ $$36 + 6 T + T^{2}$$
$67$ $$16 - 4 T + T^{2}$$
$71$ $$( -15 + T )^{2}$$
$73$ $$144 + 12 T + T^{2}$$
$79$ $$T^{2}$$
$83$ $$( -16 + T )^{2}$$
$89$ $$64 + 8 T + T^{2}$$
$97$ $$( -7 + T )^{2}$$


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# Monthly Archives: July 2020

## Epidemic Models 1, Part 7

David A. Tanzer, July 27, 2020

# The SEIR model

Last time, we started a tour of extensions to the SIR model. Now we conclude the tour and this series by describing an extension SEIR, which gives accurate description of the facts on the ground for pandemics like covid. It stands for stands for Susceptible, Exposed, Infectious, Recovered.

In SEIR, the infection process from SIR gets … Read more

## Epidemic Models 1, Part 6

David A. Tanzer, July 27, 2020

# A diversity of compartmental models

Last time, we finished our pilot study of the SIR model. By taking variations on this theme, we are now in a position to grasp the structure of a diverse range of compartmental models. So we begin a small tour. Having absorbed the general ideas through SIR, these other models will be low-hanging fruits to comprehend.

## Epidemic Models 1, Part 5

David A. Tanzer, July 26, 2020

# The SIR model (cont’d)

Last time, we introduced the SIR model, and looked at the formula for one of its reactions, recovery. Here we complete the effort, by looking into the more complex reaction, infection.

SIR-network

## The infection reaction

Recall that the recovery reaction has the formula:

$$\mathrm{Infected} \xrightarrow{\mathit{recovery}} \mathrm{Recovered}$$

The infection reaction has more arrows connecting it to the compartments than the … Read more

## Epidemic Models 1, Part 4

David A. Tanzer, July 18, 2020

# The SIR model

Last time, we introduced the general idea of reactions. Now we turn to the SIR reaction network, which is a fundamental model:

SIR-network

Footnote: such diagrams are called ‘Petri nets’, after Carl Petri, who invented them in 1939, at age 13, to describe chemical reactions. They are now more widely applied.

Here we see that the three compartments are represented … Read more

## Epidemic Models 1, Part 3

David A. Tanzer, July 18, 2020

# General idea of reactions

Last time we surveyed some compartmental models in epidemiology. Now it’s time to look deeper, as the compartments are only part of a model.

The models also contain reactions, which connect the compartments and cause them to change over time; they are processes which ‘stir’ and transform the contents of the compartments. A reaction proceeds in small steps. In … Read more

## Epidemic Models 1, Part 2

David A. Tanzer, July 10, 2020

# A menu of compartmental models

Last time, we talked about the idea of compartmental models, where the population is divided into compartments like Susceptible and Infected. If these are the only compartments, the model is called SI. But SI is very simplistic, and cannot express things like recovery, immunity or death.

Richer models are obtained by introducing more compartments.

## Epidemic Models 1, Part 1

David A. Tanzer, July 10, 2020

# A first look at compartmental models

The grim curves that we see in the papers show things like the number of daily infections, and the number of daily deaths. Epidemic models aim to predict these curves. The models depend both on natural parameters such as infectiousness and the duration of the infectious period, as well as on social parameters like the degree of distancing. … Read more

## Welcome to the Signal Beat!

On the menu bar above, see the tab called ROADMAP! That contains an full explanation of what this site is about, along with an organized index of links to the articles here. It will be continually updated as new articles are added. So, see you at the roadmap!… Read more