NARAYANKAR NOTES

  Multiplication Revision (4th Standard) Show / Hide Answers Level 1: Easy (2-digit × 1-digit) 1. 23 × 2 = ___ 2. 45 × 3 = ___ 3. 67 × 4 = ___ 4. 81 × 5 = ___ 5. 29 × 6 = ___ Level 2: Easy-Medium (2-digit × 2-digit) 6. 12 × 11 = ___ 7. 24 × 13 = ___ 8. 35 × 14 = ___ 9. 46 × 12 = ___ 10. 58 × 15 = ___ Level 3: Medium (3-digit × 1-digit) 11. 123 × 2 = ___ 12. 245 × 3 = ___ 13. 367 × 4 = ___ 14. 489 × 5 = ___ 15. 512 × 6 = ___ Level 4: Medium-Hard (3-digit × 2-digit) 16. 123 × 12 = ___ 17. 234 × 13 = ___ 18. 345 × 14 = ___ 19. 456 × 15 = ___ 20. 567 × 16 = ___ Level 5: Hard (4-digit × 1-digit) 21. 1234 × 2 = ___ 22. 2345 × 3 = ___ 23. 3456 × 4 = ___ 24. 4567 × 5 = ___ 25. 5678 × 6 = ___ Level 6: Very Hard (4-digit × 2-digit) 26. 1234 × 12 = ___ 27. 2345 × 13 = ___ 28. 3456 × 14 = ___ 29. 4567 × 15 = ___ 30. 5678 × 16 = ___ Answers 1. 46 2. 135 3. 268 4. 405 5. 174 6. 132 7. 312 8. 490 9. 552 10. 870 11. 246 12. 7...

  Multiplication and Division Revision Sheet Multiplication & Division Revision Sheet Multiplication (गुणा) Explanation (समझाव) Multiplication means repeated addition. गुणा का मतलब होता है बार-बार जोड़ना। 3 × 4 = 3 + 3 + 3 + 3 = 12 Practice Sums 3 × 7 = ___ 8 × 2 = ___ 9 × 5 = ___ 11 × 3 = ___ 6 × 6 = ___ Division (भाग) Explanation (समझाव) Division means equal sharing. भाग का मतलब होता है बराबर बांटना। 10 ÷ 2 = 5 Practice Sums 18 ÷ 3 = ___ 16 ÷ 4 = ___ 25 ÷ 5 = ___ 30 ÷ 6 = ___ 21 ÷ 7 = ___ Show / Hide Answers Answers 3 × 7 = 21 8 × 2 = 16 9 × 5 = 45 11 × 3 = 33 6 × 6 = 36 18 ÷ 3 = 6 16 ÷ 4 = 4 25 ÷ 5 = 5 30 ÷ 6 = 5 21 ÷ 7 = 3 Decimal Multiplication for Kids Decimal Multiplication for Kids Decimal Multiplication Decimal Number Multiplication 🔹 What is a Decimal Number? A decimal number is a number that has a dot (.) in it. Example: 2.5, 0.3, 4.75 Decimal number ...

  Multiplication for 4th Standard Multiplication for 4th Standard What is Multiplication? Multiplication means adding the same number again and again . Example: 3 × 4 = 3 + 3 + 3 + 3 = 12 Multiplication Terms Multiplicand → Number being multiplied (3) Multiplier → How many times (4) Product → Answer (12) Easy Trick Multiplication is repeated addition . 5 × 2 = 5 + 5 = 10 Table of 4 4 × 1 = 4 4 × 2 = 8 4 × 3 = 12 4 × 4 = 16 4 × 5 = 20 Simple Sums 6 × 2 = ___ 7 × 3 = ___ 5 × 5 = ___ 9 × 2 = ___ Word Problems A box has 4 pencils. There are 5 boxes. Total pencils = ___ ...

  Division for 4th Standard Division for 4th Standard What is Division? Division means sharing equally or grouping . Example: If you have 12 chocolates and 4 friends : 12 ÷ 4 = 3 Each friend gets 3 chocolates . Division Terms Dividend → Number we divide (12) Divisor → Number we divide by (4) Quotient → Answer (3) Easy Trick Division is the reverse of multiplication . Example: 15 ÷ 3 = ? Think: 3 × ? = 15 → Answer = 5 Simple Sums 10 ÷ 2 = ___ 18 ÷ 3 = ___ 20 ÷ 4 = ___ 16 ÷ 2 = ___ Word Problems 24 apples are shared among 6 children. Each child gets ___ apples. 15 candies are divided into 5 boxes. Each box has ___ candies. ...

  MCQ Questions (Logic & Switching Circuits) The negation of p→q is: a) ¬p→q b) p∧¬q c) ¬p∧q d) p∨q The statement p↔q is equivalent to: a) (p→q)∨(q→p) b) (p→q)∧(q→p) c) p∨q d) p∧q The dual of p∨(q∧r) is: a) p∧(q∨r) b) p∨(q∨r) c) p∧(q∧r) d) p∨q∨r A statement which is always true is called: a) Contradiction b) Tautology c) Contingency d) Negation In switching circuits, series connection represents: a) OR b) AND c) NOT d) XOR Parallel switches represent: a) AND b) OR c) NOT d) NAND The negation of p∨q is: a) ¬p∨¬q b) ¬p∧¬q c) p∧q d) p∨¬q Complementary switches are denoted by: a) S₁, S₂ b) S, S′ c) p, q d) A, B The statement ¬(¬p) is equal to: a) p b) ¬p c) p∨p d) p∧p The truth value of p∧q is true when: a) Both false b) One true c) Both true d) None The symbolic form of implication is: a) ∧ b) ∨ c) → d) ¬ A statement which is always false is: a) Tautology b) Contradiction c) Contingency d) Implication

  📘 Math: Squares, Cubes & Identities 🔷 TOPIC: SQUARE (n²) A square means multiplying a number by itself. Example: 2 × 2 = 4 So, square of 2 is 4. Number Square 1 1 2 4 3 9 4 16 5 25 6 36 7 49 8 64 9 81 10 100 11 121 12 144 13 169 14 196 15 225 16 256 17 289 18 324 19 361 20 400 🔶 TOPIC: CUBE (n³) A cube means multiplying a number three times. Example: 2 × 2 × 2 = 8 So, cube of 2 is 8. Number Cube 1 1 2 8 3 27 4 64 5 125 6 216 7 343 8 512 9 729 10 1000 11 1331 12 1728 13 2197 14 2744 15 3375 16 4096 17 4913 18 5832 19 6859 20 8000 📐 TOPIC: IDENTITIES Identities are formulas that always work and make math easy! 📘 Identities with Clear Diagrams 1. (a + b)² This is a big square of side (a + b) a² ab ab b² (a + b)² = a² + 2ab + b² 2. (a - b)² Start with big square and remove parts (a - b)² = a² - 2ab + b² 3. a² - b² Big...

  Physics Answer Key Chapter 14: Dual Nature of Radiation and Matter SECTION A Q1. Select and write the correct answer 1) The photoelectric effect supports: The photoelectric effect supports the particle nature of light. 2) The relation E = hν was proposed by: The relation E = hν was proposed by Max Planck. 3) Stopping potential depends on: Stopping potential depends on the frequency of incident light. 4) Threshold frequency is: Threshold frequency is the minimum frequency required for emission of photoelectrons. 5) Photoelectric current depends on: Photoelectric current depends on the intensity of incident light. 6) De Broglie wavelength is given by: De Broglie wavelength is given by the relation λ = h/mv. 7) Work function is: Work function is the minimum energy required to emit electrons from a metal surface. 8) If frequency increases, kinetic energy of electrons: If frequency increases, the kinetic energy of electrons increases. 9) Photoelectric...

1. The Cell Wall (The Outer Layer) The cell wall is a rigid, protective layer found outside the plasma membrane in plants, fungi, and some protists. Composition: Algae: Contains cellulose, galactans, mannans, and calcium carbonate. Land Plants: Primarily hemicelluloses, pectin, lipids, and proteins. Strength: Cellulose microfibrils provide the primary structural rigidity. Special Depositions: Depending on the plant's needs, the wall may contain: Silica: Provides grit and strength (e.g., grass stems). Cutin & Wax: Prevents water loss (epidermal cells). Suberin: Acts as a waterproof seal (root endodermal cells). Lignin: Provides wood-like structural support. Function: It determines cell shape and acts as a shield against mechanical injury and infection. 

  Physics Test (50 Marks) Chapter:  Dual Nature of Radiation and Matter Time:  2 Hour Section A:  Q.1) Multiple Choice Questions  (10 marks) A photocell used in street lights works with: a) Infrared    b) Visible    c) UV    d) X-rays Cathode material suitable for photoelectric effect: a) Zinc    b) Aluminium    c) Nickel    d) Potassium Stopping potential depends on: a) Average wavelength b) Longest wavelength c) Shortest wavelength d) Intensity Longest de Broglie wavelength (same KE): a) Electron    b) Proton    c) Alpha    d) Hydrogen atom For equal power sources: a) Red < Blue photons b) Red = Blue c) Red > Blue d) None Equation E = pc is valid for: a) Electron    b) Photon    c) Both    d) None Increasing intensity increases: a) KE b) Stopping potential c) Number of electrons d) Work function Threshold frequenc...

  SECTION I : LANGUAGE STUDY (Q.1) Question: If he selects a three-to-one scale, the tip of the robot’s arm will move just one inch. (State whether the sentence is Simple, Compound or Complex.) Answer: Complex Sentence Question: Johnsy was preparing herself for her last journey. (Replace the underlined phrase with a clause.) Answer: Johnsy was preparing herself for the journey that would be her last. Question: Though Sue looked after her well, Johnsy showed no signs of improvement. (Rewrite as affirmative sentence.) Answer: Though Sue looked after her well, Johnsy failed to show signs of improvement. Question: One morning, Ramanujan’s mother made a startling announcement. (Change the voice.) Answer: One morning, a startling announcement was made by Ramanujan’s mother. Question: Tenali Raman is the greatest of all scholars. (Rewrite beginning with “No other…”) Answer: No other scholar is as...

  Test: Inheritance and Variation Time: 2 Hours Maximum Marks: 50 Section A – Multiple Choice Questions( 7 Marks) 1. Phenotypic ratio in incomplete dominance is: a) 3:1   b) 1:2:1   c) 2:1:1   d) 9:3:3:1 2. A cross with recessive parent is called: a) Back cross   b) Test cross   c) Dihybrid cross   d) Monohybrid cross 3. Chromosomal theory was proposed by: a) Mendel   b) Darwin   c) Sutton & Boveri   d) Watson & Crick 4. Turner’s syndrome has: a) XXY   b) XO   c) XXX   d) XY 5. Law of dominance explains: a) Mutation   b) Dominant expression   c) Crossing over   d) Linkage 6. Find the mis match pair :-  a). Down’s syndrome = 44 + XY     b).Turner’s syndrome = 44 + XO  c).Klinefelter syndrome = 44 + XXY   d). Normal female = 44 + XXX 7.Chromosomal theory of inheritance was proposed by ................  a).Sutton and Boveri.    ...

MHT-CET MCQ Practice - Oscillation Oscillation MCQ Practice Physics | MHT-CET Previous year questions with detailed solutions MHT-CET Q1. Two springs of constants k₁ and k₂ have equal maximum velocities, when executing simple harmonic motion. The ratio of their amplitudes (masses are equal) will be: (A) \(\frac{k_1}{k_2}\) (B) \(\frac{k_2}{k_1}\) (C) \(\left(\frac{k_1}{k_2}\right)^{1/2}\) (D) \(\left(\frac{k_2}{k_1}\right)^{1/2}\) Correct Answer (D) \(\left(\frac{k_2}{k_1}\right)^{1/2}\) Solution: The maximum velocity (\(v_{max}\)) in SHM is given by: \[v_{max} = A\omega\] Where \(\omega = \sqrt{\frac{k}{m}}\). Since the masses (\(m\)) and maximum velocities are equal for both springs: ...