1. Find the value of √2 up to two decimal places using square root. Answer: √2 ≈ 1.41 2. Write two irrational numbers whose sum and product are rational. Answer: Let the two irrational numbers be √2 and −√2 Sum = √2 − √2 = 0 (rational) Product = √2 × (−√2) = −2 (rational) 3. Write all integers between −5 and 5 with the help of number line. Answer: Integers: −4, −3, −2, −1, 0, 1, 2, 3, 4 4. Show that a⁰ = 1 using aᵐ ÷ aⁿ = aᵐ⁻ⁿ (taking m = n). Answer: aᵐ ÷ aᵐ = aᵐ⁻ᵐ = a⁰ But aᵐ ÷ aᵐ = 1 ∴ a⁰ = 1 5. Show that a⁻ⁿ = 1/aⁿ using aᵐ ÷ aⁿ = aᵐ⁻ⁿ (taking m = 0). Answer: a⁰ ÷ aⁿ = a⁰⁻ⁿ = a⁻ⁿ But a⁰ = 1 ∴ 1 ÷ aⁿ = a⁻ⁿ ∴ a⁻ⁿ = 1/aⁿ 6. Find LCM and HCF using prime factorisation (i) 321, 396 321 = 3 × 107 396 = 2² × 3² × 11 HCF = 3 LCM = 2² × 3² × 11 × 107 = 42372 (ii) 455, 42 455 = 5 × 7 × 13 42 = 2 × 3 × 7 HCF = 7 LCM = 2 × 3 × 5 × 7 × 13 = 2730 (iii) 408, 170 408 = 2³ × 3 × 17 170 = 2 × 5 × 17 HCF = 2 × 17 = 34 LCM = 2³ × 3 × 5 × 17 = 204...
Chapter 1: The Ever Evolving World of Science. A. Recalling Ideas I. Select the correct option: 1. Science often begins with: (a) Difficult theories (b) Simple questions and playful ideas ✅ (c) Making elaborate notes (d) Sitting idle 2. Exploration in science is how we approach the unknown with: (a) Curiosity, questions and an open mind ✅ (b) Confusion and closed mind (c) Discussion (d) Confusion and discussion 3. What connects different branches of science like physics, chemistry and biology? (a) History (b) Observation and experimentation ✅ (c) Ancient traditions (d) Games and puzzles 4. Science is a journey of: (a) Memorising (b) Learning (c) Discovery ✅ (d) Revising 5. What is the purpose of a sundial? (a) To measure weight (b) To study motion (c) To tell time using shadows ✅ (d) To generate electricity 6. Which of the following is not a feature of science learning? (a) Curiosity (b) Exploration (c) Passive listening ✅ (d) Hands-on activiti...