Agra 2023 Wwwmoviespapaliving Hindi 720p Hdri Fixed 〈ULTIMATE – Honest Review〉

A hypothetical case study or creative proposal


  • 720p vs. HDRI/3D:
  • Immersive storytelling:

  • Before diving into the technicalities of file formats, it is important to understand the film itself. Agra is a Hindi-language drama directed by Kanu Behl. It premiered at the prestigious Cannes Film Festival (Directors' Fortnight) and the 2023 Melbourne International Film Festival.

    The 2023 film , directed by Kanu Behl, is a bold erotic psychological drama that explores the claustrophobic reality of a middle-class Indian family. After a successful premiere at the Cannes Film Festival, where it received a five-minute standing ovation, the movie is now officially available for streaming. Agra (2023) Official Streaming & Details

    Official Platform: You can watch Agra on Amazon Prime Video India.

    Audio: The film is available in its original Hindi language with Dolby 5.1 audio.

    Storyline: The plot follows Guru (Mohit Agarwal), a call center employee living in a cramped house with his dysfunctional family. The film uses his intense sexual frustration and search for personal space as a lens to critique patriarchy and societal repression. Cast: Starring Mohit Agarwal, Priyanka Bose, and Rahul Roy.

    Runtime: Approximately 2 hours and 12 minutes (132 minutes). Why It's Making Waves

    Critics have praised the film for its "unflinching honesty" and raw performances. It won the Best Indie Film award at the 2023 Indian Film Festival of Melbourne and the Special Jury Prize at the Jio MAMI Mumbai Film Festival. Agra (2023) - IMDb

    Please note: The text "wwwmoviespapaliving" indicates the source of the file (an unauthorized piracy website), and "hdri fixed" refers to the technical file quality. I strongly advise using legal streaming platforms to watch movies to ensure safety from malware and to support the filmmakers.

    If you’re interested, I can instead write a thoughtful essay on one of these related topics:

    Directed by , the 2023 film is a raw, psychological drama that strips away the cinematic gloss often associated with Indian small-town life to reveal a suffocating reality of sexual repression and fractured masculinity. The Times of India

    Set in the titular city—not among the grand monuments like the Taj Mahal, but in its cramped, decaying residential lanes—the story follows

    (Mohit Agarwal), a young call center employee trapped in a dysfunctional, two-story home. The house itself is a physical manifestation of psychological trauma: Guru and his mother live on the ground floor, while his father resides upstairs with a mistress. Themes of Space and Repression

    The central conflict revolves around Guru’s desperate quest for a room on the terrace, which he believes will allow him to marry his colleague

    and finally achieve a sense of privacy and "manhood". The film explores several critical themes: agra 2023 wwwmoviespapaliving hindi 720p hdri fixed

    The film Agra (2023) is a provocative Hindi-language erotic psychological drama directed by Kanu Behl. Known for his gritty storytelling in Titli, Behl’s latest work explores the suffocating reality of sexual repression and the desperate need for personal space in modern India. Movie Overview and Synopsis

    The story centers on Guru (played by debutant Mohit Agarwal), a young call center employee living in a dilapidated, two-story house in Agra. The household is a pressure cooker of tension: Guru shares the ground floor with his mother, while his father lives on the upper floor with a mistress. Guru's life is defined by:

    Sexual Repression: Struggling with intense frustration, he retreats into vivid fantasies and dating apps.

    A Quest for Space: He becomes obsessed with claiming a room on the terrace to escape his cramped environment and live with his imagined (and later real) partners.

    Mental Deterioration: The constant friction with his family and his unmet desires push him toward a state of feverish insanity and self-harm. Cast and Crew

    The film features a powerful ensemble cast that has received widespread critical acclaim:

    Mohit Agarwal as Guru (Winner of Best Actor at the New York Indian Film Festival 2024).

    Priyanka Bose as Priti, a woman Guru meets who shares a deep, raw connection with him. Rahul Roy as Daddy Ji, Guru's father. Vibha Chhibber as Mummy Ji. Ruhani Sharma as Mala. Streaming and OTT Availability Agra:Riveting and Ruthless story of our Indian daily life

    The 2023 film Agra, directed by Kanu Behl, is an intense Hindi-language erotic psychological drama that explores the crushing reality of patriarchy and sexual repression in modern India. The film gained significant international attention after its world premiere at the 2023 Cannes Film Festival in the Directors' Fortnight section, where it received a five-minute standing ovation. Film Synopsis and Themes

    The story follows Guru (played by debutant Mohit Agarwal), a young call center employee living in a deeply dysfunctional and overcrowded household in Agra. The home's layout reflects the family's fractured dynamics: Guru lives on the ground floor with his mother, while his father lives on the upper floor with his mistress.

    Sexual Repression: Guru suffers from extreme sexual frustration, leading him into a downward spiral of delusions, dating app obsessions, and self-harm.

    Contested Space: A central conflict involves Guru's desperate desire to build a room on the terrace for himself and an imagined partner, a space also coveted by other family members for their own economic and personal survival.

    Societal Critique: The film serves as a brutal critique of Indian patriarchal norms and the lack of physical and emotional privacy in middle-class urban life. Cast and Crew

    The film features a mix of newcomers and veteran actors who have been praised for their raw, uninhibited performances: Agra (2023) - IMDb A hypothetical case study or creative proposal

    The search term "agra 2023 wwwmoviespapaliving hindi 720p hdri fixed" refers to the Indian Hindi-language film Agra, which premiered at the Cannes Film Festival in 2023. While the query contains terms commonly associated with illegal file-sharing and piracy sites (like "wwwmoviespapaliving" and "720p hdri fixed"), this article focuses on the legitimate cinematic details of the film. Movie Overview: Agra (2023)

    Directed and co-written by Kanu Behl (known for Titli), Agra is an erotic psychological drama that explores the suffocating reality of patriarchy and sexual repression in contemporary India. Director: Kanu Behl Writers: Kanu Behl and Atika Chohan Premiere: 24 May 2023 at the Cannes Directors' Fortnight Theatrical Release (India): 14 November 2025 Running Time: 132 minutes IMDb Rating: 5.6/10 to 6.1/10 (varies by source) Plot Summary

    The film follows Guru (played by debutant Mohit Agarwal), a sexually frustrated young man working at a call centre who still lives with his parents in a cramped, two-story house in Agra. The household is dysfunctional: Guru and his mother live on the ground floor, while his father lives on the upper floor with a mistress.

    Desperate for his own physical and emotional space, Guru becomes obsessed with building a room on the terrace so he can marry his colleague, Mala. As his family and societal pressures block his path, Guru spirals into a feverish state of fantasies, dating apps, and self-harm. His journey eventually leads him to Priti (Priyanka Bose), an older, polio-afflicted internet café owner, resulting in a complex and raw exploration of intimacy and desire. Main Cast & Crew

    The film features an ensemble cast praised for their "top-notch" and raw performances: Mohit Agarwal as Guru Priyanka Bose as Priti Ruhani Sharma as Mala Rahul Roy as Daddy Ji Vibha Chhibber as Mummy Ji Aanchal Goswami as Chhavi (Guru's cousin) Critical Reception

    Agra received a five-minute standing ovation at its Cannes premiere. Critics have described it as a "brave and daring" film that uses raw imagery to confront uncomfortable issues like generational frustration and the lack of privacy in middle-class Indian homes. Legal & Safety Note

    The keywords in your query often lead to piracy websites that host unauthorized copies of films. These sites can be hazardous, frequently containing malware, invasive ads, and phishing scams. To support the filmmakers and ensure a safe viewing experience, it is highly recommended to watch Agra through official theatrical screenings or authorized streaming platforms once available.

    If you are looking for where to watch it legally, I can check for its current availability on major streaming services. Agra (2023) - Full cast & crew - IMDb

    The text you provided appears to be a specific file name or search string typically used on third-party file-sharing or torrent websites. It refers to the 2023 film

    , directed by Kanu Behl, which premiered at the Cannes Film Festival.

    If you are looking for information about the movie itself or where to watch it legally:

    Synopsis: Agra is a psychological drama that explores sexual repression and the claustrophobia of a crowded household in small-town India. It follows a young man named Guru who dreams of having his own room and finding love while navigating family tensions.

    Official Availability: The film has been showcased at various international festivals (like Cannes). For home viewing, it is best to check major regional streaming platforms like MUBI, Netflix, or Amazon Prime Video, as they often host acclaimed Indian independent cinema after their festival runs.

    Safety Note: Be cautious with websites like the one mentioned in your query ("moviespapaliving"). These are often unauthorized sites that may host malicious software, intrusive ads, or low-quality rips. It is always safer to use official streaming services to ensure high-quality video and protect your device. 720p vs

    Agra is an Indian Hindi-language erotic psychological drama that explores the visceral realities of sexual repression, claustrophobia, and the lack of physical and emotional space in middle-class India. 1. Production Overview Director: Kanu Behl, known for his gritty debut Titli. Writers: Kanu Behl and Atika Chohan. Release History:

    World Premiere: May 24, 2023, at the Cannes Film Festival (Directors' Fortnight section). Theatrical Release (India): November 14, 2025. Streaming Debut: April 17, 2026, on Amazon Prime Video. 2. Synopsis

    The film follows Guru (Mohit Agarwal), a young call centre employee living in a cramped, dysfunctional household in Agra. He shares a room with his mother on the ground floor, while his father lives on the upper floor with a mistress. Guru’s desperate quest for his own room on the terrace—and his obsession with a colleague named Mala—spirals into a "sexual odyssey" that borders on madness, blurring the lines between reality and pathetic fantasy. 3. Key Themes & Analysis Agra (2023) - IMDb

    Draft Text:

    "Get ready to experience the cinematic brilliance of 'Agra' in 2023, now available on www.moviespapaliving.hindi! This highly anticipated movie is now streaming in high-quality 720p HDRi fixed, ensuring a visually stunning experience for viewers.

    The movie 'Agra' has been making waves in the industry, and fans have been eagerly waiting for its release. With its engaging storyline and impressive performances, 'Agra' promises to be a blockbuster hit.

    On www.moviespapaliving.hindi, you can enjoy 'Agra' 2023 in Hindi, with crystal-clear picture quality and immersive sound. The HDRi fixed version ensures that every frame is rich in detail and vibrant colors.

    So, what are you waiting for? Head over to www.moviespapaliving.hindi and indulge in the cinematic magic of 'Agra' 2023, exclusively in 720p HDRi fixed!"

    In the cramped, two-story maze of an Agra household, , a socially awkward call center employee, lives a life defined by physical and psychological suffocation. He shares the ground floor with his mother, while his father resides upstairs with a mistress—a family arrangement never openly discussed but constantly felt.

    Guru’s existence is a "fever dream" of unfulfilled desires and digital fantasies. He is obsessed with a work colleague named

    , whom he hopes to marry just so he can justify building his own private room on the terrace. However, his mother has her own plans for that space, intending it for a dental clinic for his cousin,

    As his family actively jeopardizes his quest for space, Guru spirals into a desperate sexual odyssey. His reality begins to fracture until he encounters

    , an older, polio-stricken widow who runs an internet cafe. In her, Guru finds a raw, transactional intimacy that finally pulls him out of his mental loop, though the resulting chaos exposes the deep-seated repressions and toxic patriarchy of his world. Ultimately, the story of

    (2023) is a bleak, unflinching look at how the lack of physical space in a crowded world can corrode the human mind and family structures alike.

    Written Exam Format

    Brief Description

    Detailed Description

    Devices and software

    Problems and Solutions

    Exam Stages

    A hypothetical case study or creative proposal


  • 720p vs. HDRI/3D:
  • Immersive storytelling:

  • Before diving into the technicalities of file formats, it is important to understand the film itself. Agra is a Hindi-language drama directed by Kanu Behl. It premiered at the prestigious Cannes Film Festival (Directors' Fortnight) and the 2023 Melbourne International Film Festival.

    The 2023 film , directed by Kanu Behl, is a bold erotic psychological drama that explores the claustrophobic reality of a middle-class Indian family. After a successful premiere at the Cannes Film Festival, where it received a five-minute standing ovation, the movie is now officially available for streaming. Agra (2023) Official Streaming & Details

    Official Platform: You can watch Agra on Amazon Prime Video India.

    Audio: The film is available in its original Hindi language with Dolby 5.1 audio.

    Storyline: The plot follows Guru (Mohit Agarwal), a call center employee living in a cramped house with his dysfunctional family. The film uses his intense sexual frustration and search for personal space as a lens to critique patriarchy and societal repression. Cast: Starring Mohit Agarwal, Priyanka Bose, and Rahul Roy.

    Runtime: Approximately 2 hours and 12 minutes (132 minutes). Why It's Making Waves

    Critics have praised the film for its "unflinching honesty" and raw performances. It won the Best Indie Film award at the 2023 Indian Film Festival of Melbourne and the Special Jury Prize at the Jio MAMI Mumbai Film Festival. Agra (2023) - IMDb

    Please note: The text "wwwmoviespapaliving" indicates the source of the file (an unauthorized piracy website), and "hdri fixed" refers to the technical file quality. I strongly advise using legal streaming platforms to watch movies to ensure safety from malware and to support the filmmakers.

    If you’re interested, I can instead write a thoughtful essay on one of these related topics:

    Directed by , the 2023 film is a raw, psychological drama that strips away the cinematic gloss often associated with Indian small-town life to reveal a suffocating reality of sexual repression and fractured masculinity. The Times of India

    Set in the titular city—not among the grand monuments like the Taj Mahal, but in its cramped, decaying residential lanes—the story follows

    (Mohit Agarwal), a young call center employee trapped in a dysfunctional, two-story home. The house itself is a physical manifestation of psychological trauma: Guru and his mother live on the ground floor, while his father resides upstairs with a mistress. Themes of Space and Repression

    The central conflict revolves around Guru’s desperate quest for a room on the terrace, which he believes will allow him to marry his colleague

    and finally achieve a sense of privacy and "manhood". The film explores several critical themes:

    The film Agra (2023) is a provocative Hindi-language erotic psychological drama directed by Kanu Behl. Known for his gritty storytelling in Titli, Behl’s latest work explores the suffocating reality of sexual repression and the desperate need for personal space in modern India. Movie Overview and Synopsis

    The story centers on Guru (played by debutant Mohit Agarwal), a young call center employee living in a dilapidated, two-story house in Agra. The household is a pressure cooker of tension: Guru shares the ground floor with his mother, while his father lives on the upper floor with a mistress. Guru's life is defined by:

    Sexual Repression: Struggling with intense frustration, he retreats into vivid fantasies and dating apps.

    A Quest for Space: He becomes obsessed with claiming a room on the terrace to escape his cramped environment and live with his imagined (and later real) partners.

    Mental Deterioration: The constant friction with his family and his unmet desires push him toward a state of feverish insanity and self-harm. Cast and Crew

    The film features a powerful ensemble cast that has received widespread critical acclaim:

    Mohit Agarwal as Guru (Winner of Best Actor at the New York Indian Film Festival 2024).

    Priyanka Bose as Priti, a woman Guru meets who shares a deep, raw connection with him. Rahul Roy as Daddy Ji, Guru's father. Vibha Chhibber as Mummy Ji. Ruhani Sharma as Mala. Streaming and OTT Availability Agra:Riveting and Ruthless story of our Indian daily life

    The 2023 film Agra, directed by Kanu Behl, is an intense Hindi-language erotic psychological drama that explores the crushing reality of patriarchy and sexual repression in modern India. The film gained significant international attention after its world premiere at the 2023 Cannes Film Festival in the Directors' Fortnight section, where it received a five-minute standing ovation. Film Synopsis and Themes

    The story follows Guru (played by debutant Mohit Agarwal), a young call center employee living in a deeply dysfunctional and overcrowded household in Agra. The home's layout reflects the family's fractured dynamics: Guru lives on the ground floor with his mother, while his father lives on the upper floor with his mistress.

    Sexual Repression: Guru suffers from extreme sexual frustration, leading him into a downward spiral of delusions, dating app obsessions, and self-harm.

    Contested Space: A central conflict involves Guru's desperate desire to build a room on the terrace for himself and an imagined partner, a space also coveted by other family members for their own economic and personal survival.

    Societal Critique: The film serves as a brutal critique of Indian patriarchal norms and the lack of physical and emotional privacy in middle-class urban life. Cast and Crew

    The film features a mix of newcomers and veteran actors who have been praised for their raw, uninhibited performances: Agra (2023) - IMDb

    The search term "agra 2023 wwwmoviespapaliving hindi 720p hdri fixed" refers to the Indian Hindi-language film Agra, which premiered at the Cannes Film Festival in 2023. While the query contains terms commonly associated with illegal file-sharing and piracy sites (like "wwwmoviespapaliving" and "720p hdri fixed"), this article focuses on the legitimate cinematic details of the film. Movie Overview: Agra (2023)

    Directed and co-written by Kanu Behl (known for Titli), Agra is an erotic psychological drama that explores the suffocating reality of patriarchy and sexual repression in contemporary India. Director: Kanu Behl Writers: Kanu Behl and Atika Chohan Premiere: 24 May 2023 at the Cannes Directors' Fortnight Theatrical Release (India): 14 November 2025 Running Time: 132 minutes IMDb Rating: 5.6/10 to 6.1/10 (varies by source) Plot Summary

    The film follows Guru (played by debutant Mohit Agarwal), a sexually frustrated young man working at a call centre who still lives with his parents in a cramped, two-story house in Agra. The household is dysfunctional: Guru and his mother live on the ground floor, while his father lives on the upper floor with a mistress.

    Desperate for his own physical and emotional space, Guru becomes obsessed with building a room on the terrace so he can marry his colleague, Mala. As his family and societal pressures block his path, Guru spirals into a feverish state of fantasies, dating apps, and self-harm. His journey eventually leads him to Priti (Priyanka Bose), an older, polio-afflicted internet café owner, resulting in a complex and raw exploration of intimacy and desire. Main Cast & Crew

    The film features an ensemble cast praised for their "top-notch" and raw performances: Mohit Agarwal as Guru Priyanka Bose as Priti Ruhani Sharma as Mala Rahul Roy as Daddy Ji Vibha Chhibber as Mummy Ji Aanchal Goswami as Chhavi (Guru's cousin) Critical Reception

    Agra received a five-minute standing ovation at its Cannes premiere. Critics have described it as a "brave and daring" film that uses raw imagery to confront uncomfortable issues like generational frustration and the lack of privacy in middle-class Indian homes. Legal & Safety Note

    The keywords in your query often lead to piracy websites that host unauthorized copies of films. These sites can be hazardous, frequently containing malware, invasive ads, and phishing scams. To support the filmmakers and ensure a safe viewing experience, it is highly recommended to watch Agra through official theatrical screenings or authorized streaming platforms once available.

    If you are looking for where to watch it legally, I can check for its current availability on major streaming services. Agra (2023) - Full cast & crew - IMDb

    The text you provided appears to be a specific file name or search string typically used on third-party file-sharing or torrent websites. It refers to the 2023 film

    , directed by Kanu Behl, which premiered at the Cannes Film Festival.

    If you are looking for information about the movie itself or where to watch it legally:

    Synopsis: Agra is a psychological drama that explores sexual repression and the claustrophobia of a crowded household in small-town India. It follows a young man named Guru who dreams of having his own room and finding love while navigating family tensions.

    Official Availability: The film has been showcased at various international festivals (like Cannes). For home viewing, it is best to check major regional streaming platforms like MUBI, Netflix, or Amazon Prime Video, as they often host acclaimed Indian independent cinema after their festival runs.

    Safety Note: Be cautious with websites like the one mentioned in your query ("moviespapaliving"). These are often unauthorized sites that may host malicious software, intrusive ads, or low-quality rips. It is always safer to use official streaming services to ensure high-quality video and protect your device.

    Agra is an Indian Hindi-language erotic psychological drama that explores the visceral realities of sexual repression, claustrophobia, and the lack of physical and emotional space in middle-class India. 1. Production Overview Director: Kanu Behl, known for his gritty debut Titli. Writers: Kanu Behl and Atika Chohan. Release History:

    World Premiere: May 24, 2023, at the Cannes Film Festival (Directors' Fortnight section). Theatrical Release (India): November 14, 2025. Streaming Debut: April 17, 2026, on Amazon Prime Video. 2. Synopsis

    The film follows Guru (Mohit Agarwal), a young call centre employee living in a cramped, dysfunctional household in Agra. He shares a room with his mother on the ground floor, while his father lives on the upper floor with a mistress. Guru’s desperate quest for his own room on the terrace—and his obsession with a colleague named Mala—spirals into a "sexual odyssey" that borders on madness, blurring the lines between reality and pathetic fantasy. 3. Key Themes & Analysis Agra (2023) - IMDb

    Draft Text:

    "Get ready to experience the cinematic brilliance of 'Agra' in 2023, now available on www.moviespapaliving.hindi! This highly anticipated movie is now streaming in high-quality 720p HDRi fixed, ensuring a visually stunning experience for viewers.

    The movie 'Agra' has been making waves in the industry, and fans have been eagerly waiting for its release. With its engaging storyline and impressive performances, 'Agra' promises to be a blockbuster hit.

    On www.moviespapaliving.hindi, you can enjoy 'Agra' 2023 in Hindi, with crystal-clear picture quality and immersive sound. The HDRi fixed version ensures that every frame is rich in detail and vibrant colors.

    So, what are you waiting for? Head over to www.moviespapaliving.hindi and indulge in the cinematic magic of 'Agra' 2023, exclusively in 720p HDRi fixed!"

    In the cramped, two-story maze of an Agra household, , a socially awkward call center employee, lives a life defined by physical and psychological suffocation. He shares the ground floor with his mother, while his father resides upstairs with a mistress—a family arrangement never openly discussed but constantly felt.

    Guru’s existence is a "fever dream" of unfulfilled desires and digital fantasies. He is obsessed with a work colleague named

    , whom he hopes to marry just so he can justify building his own private room on the terrace. However, his mother has her own plans for that space, intending it for a dental clinic for his cousin,

    As his family actively jeopardizes his quest for space, Guru spirals into a desperate sexual odyssey. His reality begins to fracture until he encounters

    , an older, polio-stricken widow who runs an internet cafe. In her, Guru finds a raw, transactional intimacy that finally pulls him out of his mental loop, though the resulting chaos exposes the deep-seated repressions and toxic patriarchy of his world. Ultimately, the story of

    (2023) is a bleak, unflinching look at how the lack of physical space in a crowded world can corrode the human mind and family structures alike.

    Math Written Exam for the 4-year program

    Question 1. A globe is divided by 17 parallels and 24 meridians. How many regions is the surface of the globe divided into?

    A meridian is an arc connecting the North Pole to the South Pole. A parallel is a circle parallel to the equator (the equator itself is also considered a parallel).

    Question 2. Prove that in the product $(1 - x + x^2 - x^3 + \dots - x^{99} + x^{100})(1 + x + x^2 + \dots + x^{100})$, all terms with odd powers of $x$ cancel out after expanding and combining like terms.

    Question 3. The angle bisector of the base angle of an isosceles triangle forms a $75^\circ$ angle with the opposite side. Determine the angles of the triangle.

    Question 4. Factorise:
    a) $x^2y - x^2 - xy + x^3$;
    b) $28x^3 - 3x^2 + 3x - 1$;
    c) $24a^6 + 10a^3b + b^2$.

    Question 5. Around the edge of a circular rotating table, 30 teacups were placed at equal intervals. The March Hare and Dormouse sat at the table and started drinking tea from two cups (not necessarily adjacent). Once they finished their tea, the Hare rotated the table so that a full teacup was again placed in front of each of them. It is known that for the initial position of the Hare and the Dormouse, a rotating sequence exists such that finally all tea was consumed. Prove that for this initial position of the Hare and the Dormouse, the Hare can rotate the table so that his new cup is every other one from the previous one, they would still manage to drink all the tea (i.e., both cups would always be full).

    Question 6. On the median $BM$ of triangle $\Delta ABC$, a point $E$ is chosen such that $\angle CEM = \angle ABM$. Prove that segment $EC$ is equal to one of the sides of the triangle.

    Question 7. There are $N$ people standing in a row, each of whom is either a liar or a knight. Knights always tell the truth, and liars always lie. The first person said: "All of us are liars." The second person said: "At least half of us are liars." The third person said: "At least one-third of us are liars," and so on. The last person said: "At least $\dfrac{1}{N}$ of us are liars."
    For which values of $N$ is such a situation possible?

    Question 8. Alice and Bob are playing a game on a 7 × 7 board. They take turns placing numbers from 1 to 7 into the cells of the board so that no number repeats in any row or column. Alice goes first. The player who cannot make a move loses.

    Who can guarantee a win regardless of how their opponent plays?

    Math Written Exam for the 3-year program

    Question 1. Alice has a mobile phone, the battery of which lasts for 6 hours in talk mode or 210 hours in standby mode. When Alice got on the train, the phone was fully charged, and the phone's battery died when she got off the train. How long did Alice travel on the train, given that she was talking on the phone for exactly half of the trip?

    Question 2. Factorise:
    a) $x^2y - x^2 - xy + x^3$;
    b) $28x^3 - 3x^2 + 3x - 1$;
    c) $24a^6 + 10a^3b + b^2$.

    Question 3. On the coordinate plane $xOy$, plot all the points whose coordinates satisfy the equation $y - |y| = x - |x|$.

    Question 4. Each term in the sequence, starting from the second, is obtained by adding the sum of the digits of the previous number to the previous number itself. The first term of the sequence is 1. Will the number 123456 appear in the sequence?

    Question 5. In triangle $ABC$, the median $BM$ is drawn. The incircle of triangle $AMB$ touches side $AB$ at point $N$, while the incircle of triangle $BMC$ touches side $BC$ at point $K$. A point $P$ is chosen such that quadrilateral $MNPK$ forms a parallelogram. Prove that $P$ lies on the angle bisector of $\angle ABC$.

    Question 6. Find the total number of six-digit natural numbers which include both the sequence "123" and the sequence "31" (which may overlap) in their decimal representation.

    Question 7. There are $N$ people standing in a row, each of whom is either a liar or a knight. Knights always tell the truth, and liars always lie. The first person said: "All of us are liars." The second person said: "At least half of us are liars." The third person said: "At least one-third of us are liars," and so on. The last person said: "At least $\dfrac{1}{N}$ of us are liars."
    For which values of $N$ is such a situation possible?

    Question 8. Alice and Bob are playing a game on a 7 × 7 board. They take turns placing numbers from 1 to 7 into the cells of the board so that no number repeats in any row or column. Alice goes first. The player who cannot make a move loses.

    Who can guarantee a win regardless of how their opponent plays?