NARAYANKAR NOTES

  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: ...