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ExamTest.live has 167+ Linear Equations questions with detailed explanations, covering easy, medium, and hard difficulty levels.

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Linear Equations Questions

Q: Which exams ask Linear Equations questions?

Linear Equations questions appear in Quantitative Aptitude, Mathematics, Mathematics and Science, Algebra, General Intelligence & Reasoning and other competitive exams.

Practice 167 Linear Equations questions with detailed answers and explanations. Free MCQs, PYQs, and mock test questions for NEET, JEE, GATE, SSC and more.

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167

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152

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Practice by Exam:Quantitative Aptitude(138)Mathematics(19)Mathematics and Science(2)Algebra(2)General Intelligence & Reasoning(2)General Intelligence and Reasoning(2)Numerical Ability(2)

About Linear Equations — practice questions, PYQs & concepts

Linear Equations is a frequently-tested topic on Quantitative Aptitude, Mathematics, Mathematics and Science. ExamTest.live currently lists 167 Linear Equations questions spanning previous-year papers from 2018 to 2026, each with worked solutions and a step-by-step explanation. Use the filters on this page to focus on a specific exam, difficulty level or year — every answer key is free, no sign-up required.

Linear Equations weight in competitive exams

Across our Linear Equations question bank, the largest sources are Quantitative Aptitude (138), Mathematics (19), Mathematics and Science (2), Algebra (2) and General Intelligence & Reasoning (2). Click any exam chip above to drill down to that exam-specific question set.

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All Linear Equations Questions(1–100 of 167)

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Q1mediummcqQuantitative AptitudeCompetitive Exam2026

0% accuracy

Rishi and Sarita have ₹4,760. If \frac{9}{16} of Rishi's amount is equal to \frac{3}{4} of Sarita's amount, how much does Sarita have?

Q2mediummcqQuantitative AptitudeCompetitive Exam2026

7% accuracy

The sum of two numbers is 450. If the greater number is decreased by 4% and the smaller number is increased by 20%, then the numbers obtained are equal. The smaller number is:

Q3mediummcqMathematicsMathematics Mock Test - 12026

8% accuracy

The system of equations k x + y + z = 1, x + k y + z = k, and x + y + k z = k^{2} has no solution if k equals:

Q4mediummcqQuantitative AptitudeCompetitive Exam2026

0% accuracy

The ratio of the ages of A and B is 3 : 2 . Ten years hence, the sum of their ages will be 80 . What are their respective present ages (in years)?

Q5mediummcqQuantitative AptitudeCompetitive Exam Practice2026

33% accuracy

The ratio of the sums of money Arun and Ahaan had is 9 : 5 . If Arun gives ₹ 12 from his share to Ahaan, then the ratio will change to 4 : 3 . How much money did Arun have initially?

Q6mediummcqQuantitative AptitudeSSC CGL2026

33% accuracy

The value of x for which the expressions 5x+17 and 17x-5 become equal is __________.

Q7mediummcqQuantitative AptitudeSSC Selection Post 2018 Higher Secondary Level2026

0% accuracy

A, B से ती न गुना अधि क का र्य कुशल है। यदि B कि सी का म को पूरा करने में 45 दि न का समय लेता है, तब समा न का म को पूरा करने में A कि तने दि न लेगा ?

Q8mediummcqQuantitative AptitudeSSC Selection Post 2018 Higher Secondary Level2026

0% accuracy

4 वर्ष पहले, पि ता की आयु उसके पुत्र की आयु की 8 गुना थी । वर्तमा न में, पि ता की आयु पुत्र की आयु की 4 गुना है। पुत्र की आयु ज्ञा त की जि ये

Q9mediummcqMathematicsMathematics Mock Test - 52026

50% accuracy

If the lines given by 3 x + 2 k y = 2 and 2 x + 5 y + 1 = 0 are parallel, then the value of k is:

Q10mediummcqQuantitative AptitudeCompetitive Exam2026

0% accuracy

Two students appeared for an examination. One student who scored 20 marks more than the other, his score was 60% of the sum of their marks. What was his score?

Q11mediummcqQuantitative AptitudeSSC Selection Post 2018 Higher Secondary Level2026

0% accuracy

1,500 रुपये की धनरा शि को A और B के बी च वि भा जि त कि या जा ता है। A को प्रा प्त हुआ 4/5 भा ग, B के 2/5 भा ग के बरा बर है, तो B के द्वा रा प्रा प्त धनरा शि क्या थी ?

Q12mediummcqQuantitative AptitudeSSC CGL2026

0% accuracy

A bag contains a total of 180 coins in the denominations of ₹5 and ₹1. Find the number of ₹5 coins in the bag, if the total value of the coins is ₹500.

Q13mediummcqQuantitative AptitudeStaff Selection Commission2026

100% accuracy

The value of x for which the expressions 7 x + 13 and 13 x - 7 become equal is ______.

Q14mediummcqQuantitative AptitudeCompetitive Exam2026

0% accuracy

When 44 is subtracted from a number; it reduces to its 60%. Three-fifth of that number is:

Q15mediummcqQuantitative AptitudeCompetitive Exam2026

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For what value of p does the system of equations 18 x + 36 y + 45 = 0 and p x - 54 y + 67 = 0 have no solution?

Q16mediummcqQuantitative AptitudeSSC CGL2026

0% accuracy

The ratio of present ages of Ratnabali and Shaukat is 8 : 5 . After 22 years the ratio of their ages will be 10 : 9 . At present, what is Ratnabali's age?

Q17mediummcqQuantitative AptitudeCompetitive Exam Practice2026

0% accuracy

A farmer covered a total distance of 70 km in 10 hours . He travelled part of the distance on foot at a speed of 5 km/h and the remaining distance by bicycle at a speed of 10 km/h . Find the distance travelled on foot.

Q18mediummcqQuantitative AptitudeIndian Competitive Exam Prep2026

0% accuracy

Given the simultaneous linear equations 2 x - 3 y = - 12 and \frac{x}{y} = \frac{3}{4}, what are the values of x and y ?

Q19mediummcqQuantitative AptitudeSSC CGL2026

100% accuracy

If 23 x + 23 y = 184, then what is the average of x and y ?

Q20mediummcqAlgebraSSC CGL2026

0% accuracy

If (4x-5)=(3x-1), then the numerical value of (x+4) 2 is

Q21mediummcqQuantitative AptitudeCompetitive Exam2026

0% accuracy

A company is manufacturing three different products - Glass, Plate and Bowl. The number of Plates is double the number of Glasses. The number of Glasses manufactured is twice the number of Bowls. What is the difference between the number of Plates and the number of Bowls if the total units manufactured by the company is 2380 ?

Q22mediummcqQuantitative AptitudeSSC CGL2026

0% accuracy

If (8 - 10 x) - (13 x - 2) = - 9, then the value of x is:

Q23mediummcqQuantitative AptitudeSSC CGL2026

100% accuracy

If 51.97-(81.18-x)-59.39=5.268, then value of x will be

Q24mediummcqQuantitative AptitudeSSC CGL2026

100% accuracy

If 31% of an electricity bill is deducted, Rs 1794 is still to be paid. How much was the original bill amount?

Q25mediummcqQuantitative AptitudeSSC CGL2026

0% accuracy

Two cars travel from city A to city B at a speed of 60 and 108 km/hr respectively. If one car takes 2 hours lesser time than the other car for the journey, then the distance between City A and City B?

Q26mediummcqQuantitative AptitudeSSC CGL2026

0% accuracy

Two cars travel from city A to city B at a speed of 42 km/hr and 60 km/hr respectively. If one car takes 2 hours lesser time than the other car for the journey, then the distance between City A and City B is:

Q27mediummcqQuantitative AptitudePrepp2026

0% accuracy

57% of Ranita's weekly income is equal to 76% of Bhaskar's weekly income. If Ranita's weekly income is decreased by ₹400 while Bhaskar's weekly income remains unchanged, the ratio of the weekly incomes of Ranita and Bhaskar becomes 6 : 5 respectively. What is the weekly income of Bhaskar (in ₹)?

Q28mediummcqQuantitative AptitudePrepp2026

0% accuracy

The sum of two numbers x and y (where x > y) is equal to four times their difference. Find the value of \frac{5 x y}{3 ( x ^{2} - y ^{2} )} .

Q29mediummcqMathematicsCompetitive Exam Mock2026

0% accuracy

In an enclosure, there are crows as well as cows. If there are 30 heads and 100 legs, what is the ratio of the cows to crows?

Q30mediummcqQuantitative AptitudeCompetitive Exam2026

0% accuracy

There are 100 questions in a question paper, each carrying 2 marks. But there is a negative marking. 1 mark is deducted for each question answered incorrectly. A student answering all the questions got 80 marks. The number of questions correctly answered by him is

Q31mediummcqQuantitative AptitudeStaff Selection Commission2026

0% accuracy

If 3 x + 2 y = 7 and 4 x - y = 24, then find the value of x - y .

Q32mediummcqQuantitative AptitudeCompetitive Exam Practice Paper2026

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A group of 1280 individuals, consisting of teachers and students, is attending a conference. For every 15 students, there is one teacher. How many teachers are in the group?

Q33hardmcqQuantitative AptitudeCompetitive Exam2026

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What is the solution to the following system of linear equations? 3 x - 9 y + 4 z = 5 2 x + 7 y + z = 12 3 x - z = 0

Q34mediummcqQuantitative AptitudeCompetitive Exam2026

0% accuracy

The average weight of X and Y is 40kg. The average weight of Y and R is 62kg and the average weight of X and R is 56kg. The weight of X is:

Q35mediummcqQuantitative AptitudeStaff Selection Commission2026

0% accuracy

Two students appeared for an examination. One of them secured 24 marks more than the other and his marks were 65% of the sum of their marks. The marks obtained by them are ______.

Q36mediummcqQuantitative AptitudeSSC CGL2026

0% accuracy

Determine the value of ' r' for which the equation 13 x + 5 = r x + 18 has no solution.

Q37mediummcqMathematicsMathematics Mock Test - 42026

0% accuracy

The system of equations 7 x + 9 y = 15 and 14 x + 18 y = 30 has:

Q38mediummcqNumerical AbilityUP Police Assistant Operator Exam2026

A train can travel 75% faster than a car. Both start from point A at the same time and reach point B, 70 km away from A, at the same time. On the way, however, the train lost about 18 minutes while stopping at the stations. The speed of the car is:

Q39mediummcqQuantitative AptitudePractice Test2026

In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. A student attempted all 200 questions and scored 500 marks. What is the number of questions he answered correctly?

Q40mediummcqQuantitative AptitudePractice Test2026

The average weight of 30 students in a class is 60kg. If the weight of the class teacher is included, the average increases by 0.5kg. The weight (in kg) of the teacher is:

Q41mediummcqQuantitative AptitudePractice Test2026

If x+2 2x ​ + 2x+4 1 ​ - 2x 2 +4x 12-x ​ =a+ x b ​, where a and b are integers, then the value of ab=_____.

Q42mediummcqGeneral Intelligence and ReasoningCompetitive Exam2026

A few students went on a trip and the total amount planned to be spent was ₹ 96 . However, 4 students did not turn up and as a result the remaining students had to contribute ₹ 4 extra. The number of students who attended the trip was:

Q43easymcqQuantitative AptitudeSSC CGL2026

If 70 is subtracted from 70% of a number, the remainder is 70. What is the number?

Q44easymcqMathematicsUPTET 2021 Memory Based Paper 12026

A number exceeds 20% of itself by 60. The number is:

Q45easymcqMathematics and ScienceUPTET Paper 2 (Maths & Science)2026

The graphs of the lines x + 2 y - 3 = 0 and 2 x + 4 y + 11 = 0 are

Q46mediummcqQuantitative AptitudeCompetitive Exam2026

A sum of Rs. 12,500 is distributed among A, B, C and D such that A gets Rs. 800 more than what B gets, C gets twice of what B gets and D gets Rs. 900 more than what A gets. The ratio in which D, C, B and A receive the sums is:

Q47mediummcqQuantitative AptitudeCompetitive Exam2026

There are 1550 boys and girls in a school. The number of girls exceeds the number of boys by 500. What is the percentage (to the nearest integer) of girls in the school?

Q48mediummcqQuantitative AptitudeSSC CGL2026

The sum of two numbers is 19, while the difference between the two numbers is 3. Find the smaller number out of these two numbers.

Q49mediummcqMathematicsJEE Main2026

The number of values of k, for which the system of equations (k + 1) x + 8 y = 4 k k x + (k + 3) y = 3 k - 1 has no solution, is:

Q50easymcqQuantitative AptitudeCompetitive Exam2026

The cost of a mango is 8 each, while a guava costs 6 each. A woman spends a total of 52 on these fruits. How many mangoes and guavas did she buy?

Q51mediummcqQuantitative AptitudeCompetitive Exam2026

If 70% of a number is 56, what is the value of the number after increasing it by 25% ?

Q52mediummcqQuantitative AptitudePractice Test2026

In three containers - yellow, white and black, 120 marbles are placed. There are twice as many marbles in the white and yellow containers combined as there are in the black container. Also, there are twice as many marbles in the black container as there are in the yellow container. How many marbles are there in the white container?

Q53mediummcqQuantitative AptitudeCompetitive Exam2026

In triangle PQR, the length of side QR is less than twice the length of side PQ by 3 cm . The length of side PR exceeds the length of side PQ by 14 cm . If the perimeter is 55 cm, find the length of the smallest side of the triangle PQR .

Q54mediummcqQuantitative AptitudeCompetitive Exams2026

A teacher travelled a distance of 22km in 7 hours. He travelled partly on foot at the speed of 2km/h and partly on bicycle at the rate of 4km/h. The distance travelled on foot is:

Q55hardmcqQuantitative AptitudePractice Paper2026

There were two candidates in an election. 10% of voters did not cast their votes. 60 votes were found invalid. The winning candidate got 47% of the total votes and won by 308 votes. Find the number of voters enrolled.

Q56mediummcqGeneral Intelligence & ReasoningUP Police Constable Re-Exam2026

A few students went on a trip and the total amount planned to be spent was ₹ 96 . However, 4 students did not turn up and as a result the remaining students had to contribute ₹ 4 extra. The number of students who attended the trip was:

Q57mediummcqQuantitative AptitudeCompetitive Exam2026

Mr Gogia invested an amount of ₹13,900 divided into two different schemes A and B at the simple interest rate of 14%p.a. and 11%p.a., respectively. If the total amount of simple interest earned in 2 years is ₹3,508, what was the amount invested in scheme B?

Q58mediummcqQuantitative AptitudePractice Paper2026

If half of a number is equal to two-thirds of 60, find the number.

Q59mediummcqNumerical AbilityUP Police Assistant Operator Exam2026

The total amount of 49 is distributed among A, B, and C. A receives 5 more than B and B receives 4 more than C. What is the ratio of their shares?

Q60mediummcqQuantitative AptitudeSSC Competitive Exams2026

The average cost of a pencil is ₹8 and the average cost of an eraser is ₹4. The cost of 8 erasers, 4 pencils and 12 sharpeners are ₹148. The average cost of a sharpener is ₹ ______.

Q61mediummcqQuantitative AptitudeCompetitive Exam Paper2026

The average monthly income of A and B is Rs. 1400, that of B and C is Rs. 1560 and of A and C is Rs. 1440 . The monthly income of C is:

Q62mediummcqQuantitative AptitudePractice Test2026

At present, Ritika’s age is 3 times the age of Vipul. After 7 years, Ritika will be 2 times as old as Vipul. What is the present age of Ritika (in years)?

Q63mediummcqQuantitative AptitudeCompetitive Exam2026

With a uniform speed, a car covers a distance in 16 hours. Had the speed been increased by 20km/h, the same distance would have been covered in 12 hours. The total distance covered by the car is:

Q64mediummcqQuantitative AptitudePractice Test2026

Find the value of x : 0.2 x + 0.04 = 0.5 x - 0.11

Q65hardmcqQuantitative AptitudePractice Test2026

Out of the total income, a family saves 15% and the rest of the amount is spent on three types of expenditure - health, education and food in the ratio of 1:2:2. The income is Rs. 300 less than thrice the expenditure incurred on education. What is the difference between the savings and the expenditure incurred on health?

Q66mediummcqMathematicsMathematics Mock Test - 82026

The real value of k for which the system of equations 2 k x - 2 y + 3 z = 0, x + k y + 2 z = 0, 2 x + k z = 0, has a non-trivial solution is:

Q67mediummcqQuantitative AptitudeCompetitive Exam2026

How many solutions will a pair of linear equations have, if the equations are 7 x + 4 y - 16 = 0 and 14 x + 6 y - 32 = 0 ?

Q68mediummcqQuantitative AptitudeCompetitive Exam2026

The sum of two numbers is 80 and their difference is 8 . What is the ratio of the two numbers?

Q69mediummcqQuantitative AptitudeUP Police Constable Re-Exam2026

The batting average for 30 innings of a cricket player is 40 runs . His highest score exceeds his lowest score by 100 runs . If these two innings are not included, the average of the remaining 28 innings is 38 runs . Then the lowest score of the player is:

Q70mediummcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026

The average monthly salary of A, B, C and D is ₹ 27, 200 . A gets ₹ 800 more than B, B gets ₹ 600 more than C, and C gets ₹ 400 more than D. Find the monthly salary of A (in ₹).

Q71mediummcqQuantitative AptitudeCompetitive Exam2026

In a college election between two rivals, a candidate got 30% of the total votes polled. He was defeated by his rival by 200 votes. The total number of votes polled was:

Q72mediummcqQuantitative AptitudeCompetitive Exam2026

If the average of 46, x, 30, 36, 59, 82, 68, and 94 is 56.5, then what is the value of x ?

Q73mediummcqGeneral Intelligence & ReasoningCompetitive Exam2026

Read the question and statements provided and then decide whether the information provided in the statements is sufficient to answer the question. Find the unique values of x, y and z, if: Statements: I. 2 x + 3 y + z = 16 II. x = y

Q74easymcqMathematicsAIEEE2026

Consider the system of linear equations: x_{1} + 2 x_{2} + x_{3} = 3 2 x_{1} + 3 x_{2} + x_{3} = 3 3 x_{1} + 5 x_{2} + 2 x_{3} = 1 The system has:

Q75easymcqQuantitative AptitudeCompetitive Exam2026

Determine the value of x if 30% of 4200 + 35% of 2400 = x % of 4200 .

Q76mediummcqQuantitative AptitudeCompetitive Exam2026

After 60 years, Hardik's age will be seven times the age he was 6 years ago. What is his present age?

Q77mediummcqQuantitative AptitudePractice Paper2026

The average per day income of A, B and C is Rs. 45 . If the average per day income of A and B is Rs. 40 and that of B and C is Rs. 43, then the per day income of B is:

Q78mediummcqQuantitative AptitudeCompetitive Exam2026

If 2x+3y=0 and 3x-4y=34, then x-y=____.

Q79mediummcqQuantitative AptitudePractice Test2026

Find the value of K from the given equation: 13450 + 12846 - 1230 - K = 23670 + 987

Q80mediummcqQuantitative AptitudeSSC CGL2026

If 5 A = 13 B = 7 C, find the value of A : B : C .

Q81mediummcqQuantitative AptitudePractice Test2026

The present ages of Prajwal and Lavanya are in the ratio 5 : 6 respectively. After 3 years, the ratio of Prajwal's age to Lavanya's age will be 6 : 7 . What is Prajwal's present age?

Q82mediummcqQuantitative AptitudeSSC CGL2026

To travel 708 km, an Express train takes 6 hours more than Rajdhani train. If however, the speed of the Express train is doubled, it takes 3 hours less than Rajdhani train. What is the speed of Rajdhani train?

Q83mediummcqQuantitative AptitudePractice Test2026

Find the value of x from the given linear equation: 2.75 + 3.5 x = 9.25 + 1.5 x

Q84mediummcqQuantitative AptitudePractice Paper2026

A group of 6 chairs and 3 tables together has 54 legs. If each chair has 4 legs, how many legs does one table have ?

Q85mediummcqQuantitative AptitudeCompetitive Exam2026

Sudha decide to donate 12% of her monthly income to an orphanage. On the day of donation, she changed her decision and donate a sum of Rs. 3,600, which was equal to 60% of what she had decided earlier. What is her monthly income (in Rs.)?

Q86mediummcqQuantitative AptitudeCompetitive Exam2026

When 'p' is subtracted from each of 18, 15, 23 and 16, then the numbers so obtained in this order are in proportion. What is the value of (p-14)?

Q87mediummcqQuantitative AptitudeCompetitive Exam2026

\frac{9}{15} of \frac{7}{3} of a number is greater than \frac{7}{12} of \frac{3}{5} of the same number by 7 . Find twice the number.

Q88mediummcqQuantitative AptitudeCompetitive Exam2026

In a Panchayat election, three contestants - A, B, and C - are contesting. 75% of the total population of 8000 cast their votes. There were no invalid or NOTA votes in the election. A got the least votes, with only 300 votes. B got 66% of the total votes and won the election. How many votes did B get?

Q89mediummcqMathematicsAIEEE-CBSE-ENG-032026

If the system of linear equations x + 2 a y + a z = 0 x + 3 b y + b z = 0 x + 4 cy + cz = 0 has a non-zero solution, then a, b, c :

Q90mediummcqQuantitative AptitudeCompetitive Exam2026

The value of x for which the expressions 15-7x and 15x+7 become equal is ________.

Q91mediummcqMathematicsMathematics Mock Test - 32026

The system of equations x + 2 y + z = 0, x - z = k, x + y = 0 has infinitely many solutions. If adj (A) = 1 - 1 1 1 - 1 1 - 2 2 - 2, then the possible value of k is:

Q92mediummcqQuantitative AptitudeUP Police Constable Re-Exam2026

There are Senior officers and Secretaries in an office. If 15 Secretaries went on leave, then every Secretary has two Senior officers. After that 45 Senior officers went on leave and now every Senior officer has 5 Secretaries . Then find out how many Secretaries were there initially.

Q93mediummcqQuantitative AptitudeCompetitive Exam2026

Dinesh is travelling on his bike. He will reach point P at 6 p. m. if he travels at 20 km/h. He will reach point P at 2 p. m. if he travels at 30 km/h. At what speed must he travel to reach point P at 4 p. m.?

Q94mediummcqQuantitative AptitudeCompetitive Exam2026

The average of the ages of A and B is 25 years, that of B and C is 30 years and that of C and A is 32 years. The age of C (in years) is:

Q95mediummcqQuantitative AptitudeCompetitive Exam2026

If 7% of S.P. is equal to 8% of C.P. and if 9% of S.P. is Rs. 2 more than 10% of C.P, then find C.P. and S.P.:

Q96easymcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026

A certain distance is covered by a car at a uniform speed in 8 hours. If the speed is reduced by 6 km/h, it will take 1 hour more. What is the original speed of the car (in km/h)?

Q97mediummcqQuantitative AptitudeCompetitive Exam2026

The price of a television set and a washing machine are in the ratio of 8:7. If the cost of the television set is ₹4,800 more than the cost of the washing machine, then find the price of the washing machine.

Q98mediummcqQuantitative AptitudePractice Test2026

Find the value of m : m - \frac{2}{3} = \frac{5}{6} + \frac{1}{2}

Q99mediummcqMathematicsCompetitive Exam2026

The Venn diagram shows the number of people who bought ice-cream and drinks in a theatre. Ice-cream is sold for INR 3 and drinks are sold for INR 2. A total of INR 262 is spent. How many people bought both a drink and an ice-cream?

Q100mediummcqQuantitative AptitudeSSC CGL2026

If (x+10)% of 300 is 57.5% more than x% of 250, then 15% of x is what percentage less than 20% of (x+13)?

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