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most important definitions Class 11 Mathematics

 Here are the most important definitions from each chapter of Class 11 Mathematics (Punjab Textbook 2025 Syllabus) — specially selected to help in short questions, MCQs, and concept clarity . 🔢 Chapter 1: Complex Numbers Complex Number : A number of the form a + bi , where a and b are real numbers and i = √–1 . Imaginary Unit : The symbol i such that i² = –1 . Modulus : |z| = √(a² + b²) for z = a + bi. Conjugate : If z = a + bi, then its conjugate is a – bi. ✖️ Chapter 2: Matrices and Determinants Matrix : A rectangular array of numbers arranged in rows and columns. Order of a Matrix : Number of rows × number of columns. Determinant : A scalar value associated with a square matrix used in solving linear equations. Inverse of a Matrix : A⁻¹ such that AA⁻¹ = I. 🔁 Chapter 3: Quadratic Equations Quadratic Equation : An equation in the form ax² + bx + c = 0, where a ≠ 0. Discriminant : D = b² – 4ac, determines the nature of roots. Roots ...
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Class 11 Urdu (Punjab Board) ke 2026 ke liye high‑probability short question guesses

Yahan Class 11 Urdu (Punjab Board) ke 2026 ke liye high‑probability short question guesses   📘 Chapter 1: Uswa‑e‑Hasna (PBUH) اس وابستگی کے معنی کیا ہیں؟ حضرت محمد ﷺ کی کون سی خصوصیت بیان کی گئی؟ اس قصّے میں اخلاقی سبق کیا ہے؟ مصنف نے کس کیفیت کا ذکر کیا؟ مرکزی پیغام کیا ہے؟ راوی کا نقطۂ نظر کیا تھا؟ اسلامی تہذیب کی کون سی جھلک پیش کی؟ کون سا کردار مرکزی تھا؟ عنوان کا مفہوم کیا بنتا ہے؟ بیان انداز کیسی ہے؟ 📘 Chapter 2: Apni Madad Aap یہ عنوان ہمیں کیا سکھاتا ہے؟ مصنف نے خود انحصاری کی کون سی مثال دی؟ مرکزی خیال کیا ہے؟ کون سی حکمت عملی بیان کی گئی؟ نوجوانوں کو کیا ترغیب ملتی ہے؟ مصنف مواد کیسا استعمال کرتا ہے؟ اخلاقی پیغام کیا ہے؟ آپ اپنی زبان میں خلاصہ لکھیں۔ کون سی شخصیت کا ذکر ہے؟ تحریر کا انداز کیسا ہے؟ 📘 Chapter 3: Sir Syed ke Akhlaq o Khasail سر سید احمد خان کے بنیادی نظریات کیا ہیں؟ مصنف نے کس پہلو پر روشنی ڈالی؟ اخلاق اور عملی زندگی کا ربط کیا ہے؟ تاریخ سے کون سی مثال دی گئی؟ خیالات کا اظہ...
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10 important short questions per chapter for Class 11 English

 Here are 10 important short questions per chapter for Class 11 English Core (CBSE), based on the Hornbill and Snapshots textbooks  📝 Hornbill (Main Textbook) Chapter 1: The Portrait of a Lady (Prose) Who is the narrator? Describe the grandmother’s personality. How does the narrator feel about the grandmother’s way of life? What demonstrates the grandmother’s simplicity? Why does the grandmother refuse material gifts? What emotion does the narrator experience during their train journey? Why is the grandmother’s death painful for the narrator? What change does the narrator notice in himself after her death? What lesson does the grandmother teach about selflessness? Explain the title “The Portrait of a Lady.” Chapter 2: We’re Not Afraid to Die… if We Can All Be Together (Prose) What is the central conflict in the story? How is courage portrayed in the family? Describe the father’s leadership qualities. What decisions save the...
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10 short, high‑yield questions for each of the typical 14 chapters of Class 11 Biology (2025 syllabus)

 Here are 10 short, high‑yield questions for each of the typical 14 chapters of Class 11 Biology (2025 syllabus) Chapter 1: Diversity in the Living World Define taxonomy. What is binomial nomenclature? Who proposed the two‑kingdom system? What are the major five-kingdoms? Define species. What is biological classification? Explain hierarchy of classification. What is the naming system for organisms? Example of a unicellular eukaryote. Criteria to classify living organisms. Chapter 2: Structural Organisation in Plants Define tissue. What is parenchyma? Define collenchyma. What is sclerenchyma? Differentiate xylem and phloem. What is stomata? Define meristem. Role of epidermis in plants. Function of endodermis. What is secondary growth? Chapter 3: Structural Organisation in Animals Define tissue in animals. What is epithelial tissue? Define connective tissue. Function of muscular tissue. What is nerv...
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10 short questions from each of the 14 chapters of Class 11 Chemistry (2025 syllabus)

 Here are 10 short questions from each of the 14 chapters of Class 11 Chemistry (2025 syllabus) Chapter 1: Physical Chemistry – Some Basic Concepts Define mole. What is molar mass? Explain Avogadro’s number. What is empirical formula? Difference between empirical and molecular formula. Define percent composition. What is molality? What is molarity? Define mass percent. How to calculate molecular formula from composition? Chapter 2: Structure of Atom State Rutherford’s model. Define atomic number. What is mass number? Define isotopes. Define isobars. What is an energy level? What are orbitals? Define electronic configuration. Why is Bohr model limited? Define ionization energy. Chapter 3: Classification of Elements & Periodicity What is periodic table? Define periodicity. What is atomic radius? Define electronegativity. Trend of ionization energy in a group. Trend of metallic character acro...
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10 important short questions from each chapter of a typical Class 11 Physics

  Here are 10 important short questions from each chapter of a typical Class 11 Physics syllabus.  Chapter 1: Physical World & Measurement What is physics? Define physical quantity and its types. What is dimensional analysis? Explain system of units (SI units). Define accuracy and precision. What is significant figures? Difference between base and derived units. How do you check dimensional consistency of an equation? Why is dimensional analysis important? Give an example of a dimensionless constant. Chapter 2: Kinematics Define displacement and distance. Difference between speed and velocity. What is uniform acceleration? Define instantaneous velocity. Write equations of motion under constant acceleration. How to derive v² = u² + 2as? Define projectile motion. What is relative velocity? A particle moves in a circle at constant speed—describe its velocity. Graphically represent distance-time vs velocity-ti...
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10 important short questions from each of the 14 chapters of Class 11 Math (2025 Syllabus)

 Here are 10 important short questions from each of the 14 chapters of Class 11 Math (2025 Syllabus): Chapter 1: Sets What is a set? Define null and singleton set. What is a power set? Difference between subset and proper subset. Define universal set. What is the union of two sets? What is the intersection of two sets? Draw Venn diagram for A ∪ B. What is the complement of a set? If A = {1, 2}, B = {2, 3}, find A ∪ B. Chapter 2: Relations and Functions Define relation with example. What is a function? Define domain, co-domain, and range. What is one-one function? What is onto function? Define identity function. Define inverse of a function. What is constant function? If f(x) = x + 2, find f(3). Graph of linear function looks like? Chapter 3: Trigonometric Functions Define all 6 trigonometric ratios. Convert 60° to radian. Convert π/3 to degree. What is unit circle? Evaluate sin 45°, tan 30°. Wh...
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