assignment xi 2021

Search This Blog

Cbse mathematics.

Basic concepts, definitions and formulas of mathematics, mathematics assignments for 9th standard to 10+2 standard, maths study material for 8th, 9th, 10th, 11th, 12th classes, Mathematics lesson plan for classes 8th,10th and 12th standard, Interesting maths riddles and maths magic, Class-wise mathematics study material for students from 8th to 12. A complete resource centre of mathematics for students and teachers

Featured Posts

Mathematics lab manual class 10 | 20 lab activities, math assignment class xi ch - 2 | relations & functions, mathematics assignment chapter 2 class -11 relations and functions.

Extra questions of chapter 2 class 11  with answer and  hints to the difficult questions. Important and useful math. assignment for the students of class 11

ASSIGNMENT ON RELATIONS & FUNCTIONS

i)  Find x and y if  (x + 3, 5) = (6, 2x + y)        

Ans (x = 3, y = - 1)

ii) If ordered pair (x, -1) and (5, y) belongs to the set {(a, b): b = 2a - 3}, find the value of x and y

[Ans a = 2, b = 1]

(iv) If a  ∈  {-1, 2, 3, 4, 5}, b  ∈  {0, 3, 6}, write the set of all ordered pairs (a, b) such that a + b = 5 Solution -1 + 6 = 5  ⇒  (-1, 6)  ∈  (a, b) 2 + 3 = 5  ⇒  (2, 3)  ∈  (a, b) 5 + 0 = 5  ⇒  (5, 0)  ∈  (a, b) ⇒  R = {(-1, 6), (2, 3), (5, 0)}

i)  If A = {1, 3, 5, 6} and B = {2, 4}, find A  ×  B and B  ×  A

ii) If A = {1, 2, 3}, B = {3, 4} and C ={1, 3, 5}, find 

(a) A × (B ∩ C)     

(b)  (A  ×  B) ∩ (A  ×  C)

iii) If A = {1, 3, 5} , B = {x, y} then represent A  ×  B and B  ×  A in arrow diagrams

Find the domain and range of the relation R defined by   R = {(x,  x 3  ) : x is a prime number less than 10}              

(i) n(A) = 3, n(B) = 4, then find  n(A  ×  A  ×  B)  

Ans: 36 

Ans : {(1, 4), (4, 4)} 

[Ans:    2 2 ✕ 2   =  2 4  =16 ]

 R = {(x, y) : |x - y|  is odd}. Write R in roster form.

Ans:  R = {(1, 4), (1, 6),  (2, 9), (3, 4), (3, 6), (5, 4), (5, 6)

Express the following functions as set of ordered pair and determine their ranges

(i)   f : A ➝  R, f(x) = x 2  + 1,  where A = {-1, 0, 2, 4}   

Ans(i): Range = {1, 2, 5, 17}       

  Ans(ii) : Range = {2, 4, 6, 8, 10, 12, 14}

Let f : R - {2}  ➝   R be defined by 

 and g : R  ➝  R be  defined by g(x) = x + 2.  Find whether f = g or not.

Solution:     

Also g(x) = x + 2   ⇒  f(x) = g(x)

But  Domain of f(x) = R - {2}  and the domain of g(x) = R  and two functions 

are equal only if their domains are equal.

Hence f(x) ≠ g(x)

Find the domain for which the functions f(x) =  2x 2  - 1  and g(x) = 1 - 3x are equal

Solution:  

Here f(x) = g(x)

2x 2   - 1 = 1 - 3x   ⇒   2x 2  + 3x – 2 = 0  

⇒  x = -2, 1/2

⇒  f(x) and g(x) are equal on the set  {-2, 1 / 2 }

 If f, g, h are three functions defined from R to R as follows

(i) f(x) =  x 2       (ii)  f(x) = sinx    (iii) f(x) =  x 2  + 1

Find the range of each function

(i)   For all values of x,  f(x) takes only   +ve value. Also if x = 0, then f(x) = 0 . So Range  of  f(x)  =  [0, ∞)

(ii) Since  -1 ≤ sinx ≤ 1 for all values of x. So Range of f(x) = [-1,1]

(iii) Since   x 2  is ≥ 0  ⇒  x 2  + 1 ≥ 1   ⇒  Range of f(x) = [1, ∞)

Solution: 

Find the domain of the function f(x) defined by  

f(x) is defined for all x satisfying

4 - x ≥ 0 and x 2  - 1 > 0

x  ∈  (- ∞, -1) U (1, ∞),   But   x ≤ 4

Therefore : D f   = (- ∞, -1) U (1, 4]

By using quadratic formula we get 

Now x is defined (real) if 1 - 4y 2  ≥ 0 and y ≠ 0

⇒   4y 2  - 1  ≤ 0     ⇒   (2y + 1)(2y - 1)  ≤ 0

Critical points are  y = -1/2 and  1/2

(2y + 1)(2y - 1)  ≤ 0   and  y ≠ 0  ⇒  y   ∈  [ -1/2, 1/2] - {0}

⇒ R f  = [ -1/2, 1/2] - {0}   

Solution Hint: 

For range find x in terms of y we get

Solution (iii)

f (x) is defined for all real numbers except at x = 3

Therefore D f  = R - 3

 But x = 3  ∉  D f    ⇒   y = 3 + 3 = 6  ∉  R f     ⇒  R f  = R - {6}

Find the domain and range of the following functions

i) f(x) = |x - 1|        Ans : [D = R]  R = [0, ∞)

Ans: Domain = R - {2},   Range = R - {-1}

Ans: Domain = [-4, 4], Range = [0, 4]

Ans: Domain = (-3, 3) Range = [1, ∞)

Solution (vi)

⇒  9y 2  - x 2 y 2  = 9

⇒ x 2 y 2  = 9y 2  - 9

  x is defined if  (y + 1)(y - 1) ≥ 0 and  y ≠ 0

x is defined if  y ≤  -1,   y ≥ 1 and  y ≠ 0

⇒   y ∈ (-∞, -1] ⋃ [1, ∞) ⇒ R f   = (-∞, -1] ⋃ [1, ∞)

Ans: D f   = (-∞, -3] ⋃ (-1, 3]

Draw the graph of the following write its range

Find the domain of the following function

Solution: Let |x| = y 

 Critical points are  y = 5, y = 3

y = |x| = 5  and  y = |x| = 3  ⇒  x = 土 5,  x =  土 3

Question 20 : (DAV SP 2023)

Find the inverse relation R -1  in each of the following

(i) R = {(1,2), (1,3), (2, 3), (3, 2), (5, 6)          

Ans {(2,1), (3,1), (3,2), (2,3), (6,5)}

(ii) R = {(x, y) : x, y  ∈  N, x + 2y = 8 

Ans {(3, 2), (2, 4), (1,6)

Solution If  x = 2, y = 3  ⇒  2 + 2  ×  3 = 8  ⇒  (2, 3)  ∈  R

If  x = 4, y = 2  ⇒  4 + 2  ×  2 = 8  ⇒  (4, 2)  ∈  R

If  x = 6, y = 1  ⇒  6 + 2  ×  1 = 8  ⇒  (6, 1)  ∈  R

R = {(2, 3), (4, 2), (6, 1)}   ⇒  {(3, 2), (2, 4), (1, 6)}

Let f : R ➝ R be a function given by f(x) =  x 2  + 1. Find     f  -1 {10, 37}   

If f(x) = y then  x = f  -1 (y)

f  -1 (10) = x  ⇒  f(x) = 10  ⇒  x 2  + 1 = 10 

⇒  x 2  = 9   ⇒  x =  土  3

 f  -1 (37) = x  ⇒  f(x) = 37  ⇒  x 2  + 1 = 37 

⇒  x 2  = 36   ⇒  x =  土  6

 f  -1 {10, 37} = {-3, 3, - 6, 6}

 Let A = {-2, -1, 0, 1, 2} and f : A  ➝  Z be a function defined by  f(x) = x 2  - 2x - 3. Find

(i) Range of f i.e. f(A)          (ii) Pre - image of 6, - 3 and 5

(i)  f(A) = {f(-2), f(-1), f(0), f(1), f(2) } = {5, 0, - 3, - 4, - 3} = {- 4,- 3, 0, 5}

(ii) Let Pre - image of 6 = x  ⇒    f  -1 (6) = x  ⇒  f(x) = 6

⇒   x 2  - 2x - 3 = 6   ⇒     x 2  - 2x - 9= 0 

There is no real value of x which satisfies this equation. 

So Pre - image of  6 = Φ

Let Pre - image of - 3 = x  ⇒    f  -1 (-3) = x  ⇒  f(x) = - 3

⇒   x 2  - 2x - 3 = - 3   ⇒     x 2  - 2x = 0  ⇒   x = {0, 2}

Let Pre - image of 5 = x  ⇒    f  -1 (5) = x  ⇒  f(x) = 5

⇒   x 2  -2x - 3 = 5   ⇒    x 2  - 2x - 8 = 0  ⇒   x = {-2, 4}

(i) f(x) = 3x 4  - 5x 2  + 9, find  f(x - 1)          

Ans [3x 4  - 12x 3  + 13x 2   - 2x + 7]

 [Ans x = -1, 2/3]

Thanks for your visit

Please comment below

Post a Comment

Breaking news, popular post on this blog, lesson plan maths class 10 | for mathematics teacher.

Lesson Plan Maths Class XII | For Maths Teacher

Lesson Plan Maths Class X (Ch-5) | Arithmetic Progression

• Assignment 10 15
• Assignment 11 12
• Assignment 12 14
• Assignment 8 8
• Assignment 9 5
• Lesson plan 10 15
• Lesson Plan 12 13
• Lesson Plan 8 10
• Maths 10 20
• Maths 11 21
• Maths 12 17

SUBSCRIBE FOR NEW POSTS

Get new posts by email:.

MTH 419--Introduction to Abstract Algebra--Homework Assignments

Note: problems in brackets [ ] are to be done, but not turned in.

• Exam I: Monday, Oct 4 completed
• Exam II: Monday, Nov 1 completed
• Exam III: Monday, Nov 29 completed
• Final Exam: Monday, December 13, 11:45AM - 2:45 PM in Math 150
• Contemporary Abstract Algebra, 9th edition, by Joseph Gallian

Assignment XIII--Week of November 29:

• Quiz D1 Wed recitation: No Quiz in recitation this week, due in Gradescope
• Format for quizzes: one definition/statement, one problem/proof
• Quiz D2 Fri recitation: No Quiz in recitation this week, due in Gradescope
• Turn in Problem Set 12 (from the text book), due  Monday 12/06/2021, in Gradescope by 11:59 PM
• Chapter 10: [5], 6, 7, [8], 9, [14], 16, 19, [35]
• Note: some problems ask if there is a homomorphism from G onto H, rather than from G to H. This means that the homomorphism is supposed to be onto .
• homework should be typed, preferably in LaTeX.
• Note: problems listed for an assignment are  to be uploaded to Gradescope by the due date

Assignment XIV--Week of December 6:

• Quiz D1 Wed recitation: Quiz XI  in recitation this week, due in Gradescope
• Covers: Chapter 9, through Example 17; Chapter 10
• Quiz D2 Fri recitation: Quiz XI in recitation this week, due in Gradescope
• Covers: Chapter 9, through Example 17; Chapter 10, beginning of Chapter 11 (depending on where we get on Wednesday)
• Turn in Problem Set 13 (from the text book), due  ->Saturday<- 12/11/2021, in Gradescope by 11:59 PM
• Chapter 10: 40 - 42, 49, 58
• Chapter 11: 2, [6], 12, 21

Final Exam--Monday, December 13

• When 11:45 - 2:45 PM in Math 150
• Covers : 
• Chapters 0 (through page 7 and related homework)
• Chapters 1 - 11
• Chapter 8: skip Examples 4 & 5, skip Theorem 8.3 to end of chapter 8
• Chapter 9: only through Example 16)
• Chapter 11: up to, but not including Lemma 1
• Format: 2 or 3 statements of theorems/definitions; 6 to 12 problems/proofs
• proofs from the book or lecture, or pieces of proofs, may well be on the exam
• homework problems may well be on the exam
• properties left as exercises in class may well be on the exam
• Seating will be assigned
• Exam will be handed out in class
• Must be written in dark ink--black or blue; cross out anything you do not want graded
• Instructor will upload the exams to Gradescope
• Calculators: Only non-programmable, non-graphing, non-alphanumeric are allowed on exams
• Notes: None

Coming Attractions (tentative list of upcoming assignments): May be changed

Assignment i--week of august 30:.

• No classes: Monday, Sept 6 (Labor Day)
• Quiz D1 recitation: Quiz I in recitation, due in Gradescope
• Covers: Division algorithm
• Quiz D2 recitation: Quiz I in recitation, due in Gradescope
• Covers: Division algorithm, Bezout's Lemma (GCD is a linear combination), Euclid's Lemma
• Turn in Problem Set 1: (from the text book), due Tuesday, 09/07/2021, in Gradescope by 11:59 PM
• Chapter 0: 4 - 9, 11- 13, 18 - 21, 30

Assignment II--Week of September 6:

• NO LECTURE ON WEDNESDAY, Sept 8
• Lecture is recorded: UBlearns>Zoom -> cloud recordings sign in with sso. Two recordings from 09/05/21. Start with the older recording.
• Quiz D1 Wed recitation: Quiz II in recitation, due in Gradescope
• Covers: Bezout's Lemma (GCD is a linear combination), Euclid's Lemma, Modular arithmetic
• Quiz D2 Fri recitation: Quiz II in recitation, due in Gradescope
• Covers: Modular arithmetic, symmetries of a square
• Turn in Problem Set 2: (from the text book), due Monday, 09/13/2021, in Gradescope by 11:59 PM
• Chapter 1: [1], 2, 5, [6], 8, 10, 13, 15, 18 Problems in parentheses are to be done but not turned in

Assignment III--Week of September 13:

• Quiz D1 Wed recitation: Quiz III in recitation, due in Gradescope
• Covers: symmetries of square, groups
• Quiz D2 Fri recitation: Quiz III in recitation, due in Gradescope
• Covers: Groups, including U(n)
• Turn in Problem Set 3: (from the text book), due Monday, 09/20/2021, in Gradescope by 11:59 PM
• Chapter 2: 4 - 6, 9 - 12, 17, 22, 25, 26, [31], 32, 37
• Note: Table 2.1 contains a typo. The inverse in C* should have a^2 + b^2 in the denominator for both terms.

Assignment IV--Week of September 20:

• NO LECTURE ON WEDNESDAY, Sept 22
• Lecture is recorded: UBlearns>Zoom -> cloud recordings sign in with sso.
• Quiz D1 Wed recitation: Quiz IV in recitation, due in Gradescope
• Covers: Groups, including U(n), subgroup tests
• Quiz D2 Fri recitation: Quiz IV in recitation, due in Gradescope
• Covers: subgroup tests, cyclic groups
• Turn in Problem Set 4: (from the text book), due Monday, 09/27/2021, in Gradescope by 11:59 PM
• Chapter 3: [1 - 5], 13, 17, 19, 23, 31, [34], 44, 47, 70, 71, 73
• Chapter 4: 2, 3, [4], 5, 7

Assignment V--Week of September 27:

• NO LECTURE ON WEDNESDAY, Sept 29
• Quiz D1 Wed recitation: Quiz V in recitation, due in Gradescope
• Covers: order of elements, cyclic groups
• Quiz D2 Fri recitation: No quiz this week
• Turn in Problem Set 5: (from the text book), due -->Wednesday<-- 10/06/2021, in Gradescope by 11:59 PM
• Chapter 4: [8], 9, [12], 14, [23], 24, 31, 35, 50, 60, 77

Assignment VI--Week of October 4:

• Quiz D1 Wed recitation: No quiz in recitation this week, due in Gradescope
• Quiz D2 Fri recitation: Quiz V in recitation, due in Gradescope
• Covers: Cyclic subgroups, generators
• Turn in Problem Set 6: (from the text book), due Monday 10/11/2021, in Gradescope by 11:59 PM
• Chapter 4: 13, 29, 53, 68, [Try 85]
• Chapter 4: 35, 70

Assignment VII--Week of October 11:

• Quiz D1 Wed recitation: Quiz VI in recitation this week, due in Gradescope
• Covers: Cyclic subgroups, generators, subgroup lattice
• Quiz D2 Fri recitation: Quiz VI in recitation, due in Gradescope
• Covers: subgroup lattice, beginning of permutations
• Turn in Problem Set 7: (from the text book), due ->>Tuesday<<- 10/19/2021, in Gradescope by 11:59 PM
• Chapter 5: 1 - 3, [4 - 8], 9, 13, [15], 16, 17, [19], 23, [26], 28, 29, [32]

Assignment VIII--Week of October 18:

• Quiz D1 Wed recitation: Quiz VII in recitation this week, due in Gradescope
• Covers: Permutations, S_n, A_n
• order of permutations, even/odd permutations, writing a permutation as as a product of disjoint cylces
• writing a permutation as a product of transpositions
• Quiz D2 Fri recitation: Quiz VII in recitation, due in Gradescope
• Permutations, S_n, A_n
• isomorphisms and isomorphic groups
• Turn in Problem Set 8: (from the text book), due Monday 10/25/2021, in Gradescope by 11:59 PM
• Chapter 5: 35, 36, 53, 57, 61, 65
• Chapter 6: [1], [4, 5], 6, 7, 12, [22], 36, 39, 41

Assignment IX--Week of October 25:

• Quiz D1 Wed recitation: Quiz VIII in recitation this week, due in Gradescope
• properties of isomorphisms
• Quiz D2 Fri recitation: no quiz this week
• Turn in Problem Set 8: (from the text book), due -->Tuesday<-- 11/02/2021, in Gradescope by 11:59 PM
• Chapter 6: 51, 53, [try 67]
• Chapter 6: 2, 9, 14, 17 -19, 26, 60

Assignment X--Week of November 1:

• Quiz D1 Wed recitation: no quiz this week
• Quiz D2 Fri recitation: Quiz VIII in recitation this week, due in Gradescope
• Covers: automorphisms
• including Inn(G), Aut(G), Aut(Z), Aut(Z_n)
• Turn in Problem Set 9: (from the text book), due  Monday 11/08/2021, in Gradescope by 11:59 PM
• Chapter 7: 1, [2], 3 - 8, 12, 13, [15, 16], 17 - 19, 22, 26
• Problem 8 has a misprint. Should be: HK = {hk |  h in H, k in K}.

Assignment XI--Week of November 8:

• Quiz D1 Wed recitation: Quiz IX in recitation this week, due in Gradescope
• Covers: automorphisms and cosets
• Quiz D2 Fri recitation: Quiz IX in recitation this week, due in Gradescope
• Covers: cosets
• including normalizer-stabilizer theorem
• Turn in Problem Set 10 (from the text book), due  ->Tuesday<- 11/16/2021, in Gradescope by 11:59 PM
• Chapter 7: 30, 33 , [45], 53, [58], 59
• Chapter 8: 1, 5 - 7, 14, 16, 27. Note: 11, 34 have been deleted from the assignment.

Assignment XII--Week of November 15:

• Quiz D1 Wed recitation: Quiz X in recitation this week, due in Gradescope
• Covers: cosets, direct product of groups
• including orbit-stabilizer theorem
• Quiz D2 Fri recitation: Quiz X in recitation this week, due in Gradescope
• Covers: direct product of groups, normal subgroups
• Turn in Problem Set 11 (from the text book), due  Monday 11/22/2021, in Gradescope by 11:59 PM
• Chapter 9: 2, 5, 6, 9, [10 - 12], 17, [18, 19], 22, 37, [43], 51, 59, 61, 67, [71]

Exam I--Monday, October 4

• When 11:30 - 12:20 PM in Math 150
• Covers :  Chapters 0 (through page 7 and related homework), 1 - 4 (through Theorem 4.1 only)
• 1 or 2 statements/definitions; 3 or 4 problems/proofs

Exam II--Monday, November 1

• Covers :  Chapters 4 - 6 (up to, but not including Automorphisms on  page 128)
• be sure to review center, centralizer, order of a group

Exam III--Monday, November 29

• Covers :  Chapters 6 - 9 (Chapter 8: skip Examples 4 & 5, skip Theorem 8.3 to end of chapter 8; Chapter 9: only through Example 16)

Bubba Wallace's future with 23XI Racing receives a big update in 2024

B ubba Wallace has been with 23XI Racing since Denny Hamlin and Michael Jordan formed the organization for the 2021 NASCAR season. Since then, Wallace has won two races at Talladega Superspeedway in 2021 and Kansas Speedway in 2022. With the 23XI Racing driver in a contract year, will he return to the team in 2025?

According to The Athletic's Jordan Bianchi, "all indications" point to Wallace returning to the No. 23 car for 23XI Racing in 2025. Wallace and Tyler Reddick have been quick for the 23XI Racing, but the former has seen less success. Wallace only sits 13th in the point standings and hasn't shown race-winning speed as much as Reddick.

However, the 30-year-old driver is a perfect fit and has found a home at 23XI Racing moving forward. Wallace is a playoff-caliber driver who should be among the final 16 competitors yearly. The expectations are the same for Wallace in 2024, and based on a recent report, those will stay in place for the 2025 season and beyond.

This article originally appeared on Motorsports Wire: Bubba Wallace's future with 23XI Racing receives a big update in 2024

France's new ambassador to the U.S. puts his flair on party diplomacy

WASHINGTON — On his first day as France’s ambassador to the United States, Laurent Bili faced a terrifying decision: Which of the two receptions that he’d been invited to was he going to attend?

For the self-described introvert, it was a bit of a nightmare.

Bili, 62, had a total of three visitors in three years at his last posting in China, and one of them was his wife, Sabine. 

He arrived in Beijing four months before the country went into lockdown, rendering China's capital city a ghost town. A visit to France during the pandemic required a three-week quarantine upon his return and meals served by tray table that were left at his door. 

Bili spent the first few weeks of the pandemic prospecting personal protective equipment, helping embassy staff find masks and other medical gear at the best prices, on behalf of the government in Paris.

Prep for the polls: See who is running for president and compare where they stand on key issues in our Voter Guide

The career diplomat has since traded isolation and PPE for cocktail parties and passed hors d'oeuvres. Yet, he's still a little overwhelmed by the carousing that takes place in Washington, nearly three months into the job.

“I get the impression that my eyes are a bit deeper,” Bili said in an interview, pointing to his slightly sunken under eyes as he made light of the exhaustive pace.

The first in his family to graduate from high school, he did not envision himself working in a field that required him to learn foreign languages. The soft-spoken diplomat from Brittany, in western France, said he was inspired to join the foreign service in his youth after a meeting a group of Finnish diplomats while he was hitchhiking in Peru.

He discovered through the experience that diplomacy was a real line of work that would also allow him to travel. He eventually became ambassador to Turkey, Brazil and, later, China.

France’s recent ambassadors to the U.S. have been known for their party diplomacy – a brand of soft power that Bili said is a striking contrast to his experience in Beijing. There, he said, diplomacy is a very sober affair. Here, lawmakers, journalists, administration officials and foreign envoys routinely mingle and exchange ideas at cultural events. 

Although he is more eager to provide insight on how to avoid a conflict with China than he is to rub elbows with a packed room full of guests, Bili has sought to leave his own mark on the position by hosting parties with a purpose.

He held his first function – a reception at the ambassador’s residence honoring International Women’s Day – four days into his tenure in Washington. The next evening, he hosted Mark Milley, chairman of the Joint Chiefs of Staff, at an event toasting the First Amendment.

Diplomats sometimes have different styles, Bili said. "I’m … maybe a more introverted guy."

Bili thought he would remain in China, which was just beginning to reopen, until he received the call that would land him in Washington. 

The assignment was not one Bili had been seeking. He expected his posting in China to last for at least another six months and was not searching for a new job. “In fact, I was not dreaming to come here,” Bili said.

The posting in Washington has always been considered a plum but important ambassadorship. However, the scope of the role has expanded in the past two years.

 A  diplomatic spat in 2021 , prompted by President Joe Biden convincing Australia to renege on a lucrative submarine deal with France, led French President Emmanuel Macron to recall the ambassador – Bili's predecessor – for the first time in history. Five months later, war broke out in Europe with Russian leader Vladimir Putin's invasion of Ukraine. 

‘Tough moment for relations’

Bili arrives at a period of rapprochement between the U.S. and France, following Macron's state visit to Washington. 

In December, the French president became the first world leader to be feted by Biden since the U.S leader came into office. The lavish White House event helped to repair the frayed relationship between the historically close countries.

“That was a tough moment for relations,” Bili said of the estrangement.

“It's difficult to be in a real trust relationship if you are not playing openly with your allies,” he said, before adding, “We have to look forward now, and the French side is doing that.”

Tough moment: France recalls ambassadors to US, Australia over submarine deal

For both countries, a lot is at stake on the world stage. Bili understands this.

For his part, he has been seeking to build influence with lawmakers on Capitol Hill.  

An aspect of French policy he said he hopes to impress upon them is that Europe has collectively provided more aid to Ukraine since the beginning of the war than they realize. Europe also has been working to improve its military capabilities and defense spending.

“It's really I think it's important for people on the Hill to realize that we are doing a lot, we are ready to do more, and that we are in the same boat and it's important that we stick together,” Bili said.

Macron traveled to China to discuss the Ukraine war in early April, weeks after Bili was already in the United States. Beijing has sought to portray itself as a neutral party that can mediate an end to the conflict, despite being a close ally of Moscow. 

U.S. relations with China are currently at a low point, following the downing of a Chinese spy balloon off the coast of South Carolina in February and the threat that China could provide lethal weapons to Russia. Secretary of State Antony Blinken canceled a trip to Beijing that has yet to be rescheduled.

The visit by Macron, one of the United States' top allies, was very important, Bili said, because in the past three years, there was no direct contact between Macron and Chinese President Xi Jinping.

“When you just have these phone calls,” he said, “you start to realize that, that doesn't work.”

At a time of estrangement between Biden and Xi, Macron and the Chinese leader had a nine-hour tête-à-tête.

The time spent with Xi gave Macron an opportunity to “deconstruct the Russian narrative” about NATO’s responsibility for the war in Ukraine, the French diplomat said.

An unannounced meeting between Biden’s national security adviser, Jake Sullivan, and his Chinese counterpart, Wang Yi, in Vienna this month was seen as a sign that a Biden call or a Blinken visit could be on the way now, too.

“I think also that the momentum is changing again,” Bili said. “I'm quite confident that we will see a restart of discussions.”

Bili spoke with Xi personally only once when in Beijing. But Bili said his impression was that Xi is a leader who is willing to pay a certain price to achieve his goals in terms of China’s image and its relations with its neighbors.

“The last three years have been obviously a wake-up call for many countries, and also the fact that they obviously support Russia politically, after the aggression of Ukraine, has had a very dramatic effect on the perception … of most of European countries,” he said.

Since his arrival in Washington in March, Bili said, he has met with Biden once, when he received his diplomatic credentials. “It was a very friendly and warm welcome,” he said.

The ceremony was one of the most amazing the diplomat said he’s ever seen in his career. 

“It's really well organized and gives a real sense of the grandeur of the moment. But at the same time, it has to be quite short,” he said, noting there are 12 ambassadors. "... But it was a very nice and warm moment.”

Bili’s term in the U.S. is undetermined, but typically diplomatic assignments last three to four years. He said has become quite comfortable in Washington and hopes to remain here until 2028. His wife, who is a judge in France, took a sabbatical to join him.

In spite of the cynicism that many Americans feel about their politicians, Bili said, in Washington there is an openness to discussion and expressing nuances that was surprising after his stint in Beijing.

As for the functions at the ambassador’s residence, which doubles as a reception space, Bili said he will continue to open up his home. He's not giving up on the big parties for which his country's embassy has become known.

“As long as the guests want to come,” he said with a smile, “I would be very pleased to receive them.”

Text: A A A Print Sci-tech

Shenzhou xviii crew conducts 1st spacewalk.

Shenzhou XVIII mission commander Senior Colonel Ye Guangfu carries out tasks outside the Tiangong space station on Tuesday in this photo of a screen at the Beijing Aerospace Control Center. (XU BU/FOR CHINA DAILY)

The Shenzhou XVIII astronauts conducted their first spacewalk outside the Tiangong space station on Tuesday, completing several assignments, according to the China Manned Space Agency.

Mission commander Senior Colonel Ye Guangfu and crew member Lieutenant Colonel Li Guangsu returned to the Wentian science module at 6:58 pm after floating outside the colossal orbital station for nearly eight-and-a-half hours, the agency said in a news release. The third crew member, Lieutenant Colonel Li Cong, stayed inside Tiangong to provide support, it said.

With cooperation and assistance from ground controllers and the space station's robotic arm, the team completed all its assigned tasks, including installing space debris shields and checking the condition of extravehicular equipment, the agency said.

This was the 16th spacewalk carried out by Chinese astronauts, and also marked the second spacewalk by Ye and the first by Li Guangsu.

The Shenzhou XVIII astronauts — the seventh group of inhabitants of the Chinese space station — were launched on April 25 by a Long March 2F carrier rocket from the Jiuquan Satellite Launch Center in northwestern China. They arrived at the Tiangong space station the next morning to take over from their Shenzhou XVII peers.

As a member of the country's second generation of astronauts, Ye was part of the Shenzhou XIII mission, which took place from October 2021 to April 2022, and made his first spacewalk during the six-month flight.

The Shenzhou XVIII is the first spaceflight for Li Cong and Li Guangsu, both of whom belong to China's third generation of astronauts. The three astronauts are scheduled to work onboard Tiangong until late October and then hand over the orbital outpost to the Shenzhou XIX crew.

As of Tuesday, Ye and his team have stayed in space for 33 days and fulfilled a host of tasks such as equipment maintenance, examinations and tests on spacewalk suits, emergency response exercises and medical aid drills.

They also engaged in an array of space science experiments and mounted the second set of material exposure experimental apparatus, the agency said.

Over the remaining period of their stay, the astronauts will carry out many scientific experiments and technological tests, and will conduct multiple spacewalks and payload deployment operations, it added.

Related news

Shenzhou XVII crew conducts 1st spacewalk

Shenzhou-15 taikonauts complete 4th spacewalk, setting China record

Longest intercity railway welcomes over 78,000 passenger trips on first operating day

4 killed in residential building collapse in E China

Satellite captures post-landslide view in Papua New Guinea

Breathtaking sunrise scenery in Hangzhou

'Chinese Bridge' contest for high school students held in Australia

Giant panda Ya Ji celebrates 10th birthday

Over 670 people died in massive Papua New Guinea landslide

Villagers enhance night training for upcoming Dragon Boat Festival in Guangdong

7th Digital China Summit kicks off in E China

Creative ceramic jewelry showcase unique Chinese aesthetics

Porcelain of Qing Dynasty in spotlight at Hong Kong auction

Xi inspects Rizhao in east China's Shandong Province

Most beautiful wetland in the Beijing-Tianjin-Hebei region

Solar power station drives green development in Shandong

Giant pandas enjoy themselves in Chengdu

Hong Kong-Zhuhai-Macao Bridge receives over 10 mln passenger trips

Archaeological findings of 2,200-year-ago tomb released

Singapore Airlines flight makes emergency landing in Bankok

Starry night at Shennongjia National Nature Reserve in C China

China launches Beijing-3C satellite constellation

Iran mourns tragic deaths of president and foreign minister

China's largest freshwater lake sees water level increasing

Heavy rainstorm hits south China's Guangxi

Lake Namtso welcomes tourism season in Xizang

Iranian president's helicopter makes hard landing

Farmers busy with rice seeding ahead of traditional Chinese solar term Xiaoman

Comicomment: 'How to suppress China's new energy industry?'

Concert celebrating 75th anniv. of China-Russia diplomatic relations staged in Beijing

Exploring biodiversity at horticultural exhibition 2024 in Chengdu

Chinese white dolphins spotted in Leizhou Bay

Xi holds restrictive meeting with Putin at Zhongnanhai

Xi, Putin attend opening ceremony of China-Russia Years of Culture

Marine ecological pasture complex gains development momentum in E China

Folk festival Siyueba celebrated in Guizhou

Magnificent scenery of Gangshika snow peak in Qinghai

Giant planet with density like cotton candy discovered

Most popular in 24h, more top news.

• National reunification 'will surely be accomplished'
• China's northernmost high-speed railway starts laying track
• China, Central Asian countries consider establishing earthquake scientific investigation mechanism
• Australian offshore energy storage project undertaken by Chinese company starts construction
• China Eastern Airlines receives sixth C919, as the jet marks 1st anniversary of commercial operation

Insights丨U.S. economist: China's better-organized economy sparks economic surge, sets global resilience example

Insights | Tunisian official: my daughter gives me a shopping list before trip to China