Smart study corner

  <h2> Mensuration – Surface Area and Volume</h2> <h3>1. Introduction</h3> <p>Mensuration is the branch of mathematics that deals with the measurement of <b>length, area, and volume</b> of different shapes and solids.</p> <h3>2. 2D Shapes and Formulas</h3> <ol>   <li><b> Square :</b><br>     Area = a²<br>     Perimeter = 4a   </li>   <li><b> Rectangle :</b><br>     Area = l × b<br>     Perimeter = 2(l+b)   </li>   <li><b> Triangle :</b><br>     Area = ½ × base × height<br>     Using Heron’s Formula :<br>     √[s(s-a)(s-b)(s-c)], s = (a+b+c)/2   </li>   <li><b> Circle :</b><br>     Area = πr²<br>     Circumf...

 Circle – Definition, Formulas, and Applications 1. Definition A circle is the set of all points in a plane that are at a fixed distance (radius) from a fixed point (center). --- 2. Important Terms Center (O): The fixed point. Radius (r): Distance from center to any point on the circle. Diameter (d): Twice the radius.  Circumference (C): The perimeter of the circle. Chord: A line joining two points on the circle. Arc: A part of the circumference. Sector: A region bounded by two radii and an arc. --- 3. Formulas 1. Circumference: C = 2\pi r A = \pi r^2 L = \frac{\theta}{360^\circ} \times 2\pi r A_{\text{sector}} = \frac{\theta}{360^\circ} \times \pi r^2 --- 4. Applications In wheels, coins, clocks. For calculating distances in circular tracks. In geometry problems and engineering designs. --- 5. Example Problem Q: A circle has radius . Find its circumference and area. Solution: C = 2\pi r = 2 \times 3.14 \times 7 = 43.96 \text{ cm} A = \pi r^2 = 3.14 \times 7^2 = 153.86 \text{ ...

  <h2>1. What is a Circle?</h2> <p>A <strong>circle</strong> is the set of all points in a plane that are at a fixed distance (called the <strong>radius</strong>) from a fixed point (the <strong>centre</strong>).</p> <ul>   <li><strong>Centre</strong> = (h, k)</li>   <li><strong>Radius</strong> = r</li>   <li><strong>Diameter</strong> = d = 2r</li> </ul> <h2>2. Important Formulas</h2> <ul>   <li><strong>Circumference</strong>: C = 2 &pi; r</li>   <li><strong>Area</strong>: A = &pi; r²</li>   <li><strong>Length of an arc</strong> (angle θ in degrees): arc = (θ / 360) × 2 &pi; r</li>   <li><strong>Sector area</strong> (angle θ in degrees): sector = (θ / 360) × &pi...

 Top Tips to Prepare for MHT-CET Effectively MHT-CET (Maharashtra Common Entrance Test) is an important state-level exam for students aiming for engineering, pharmacy, or agriculture courses in Maharashtra. A good score can secure admission in top colleges, so preparation must be strategic. 1. Know the Syllabus Thoroughly The CET syllabus is based on the Maharashtra State Board curriculum. Class 11 syllabus: 20% weightage Class 12 syllabus: 80% weightage Focus more on Class 12 topics but do not skip Class 11 concepts. 2. Strengthen Concepts, Not Just Formulas In CET, many questions are application-based. Understand the logic behind formulas so you can solve tricky problems. 3. Practice Time Management The CET exam is 180 minutes for 150 questions. Practice mock tests to improve speed and accuracy. 4. Solve Previous Year Papers Past papers give you an idea about question trends, difficulty level, and important topics. 5. Use Short Notes for Revision Create small notes for formulas, ...

 Important Study Tips for NEET Preparation NEET is one of the most competitive and prestigious exams in India. To crack it, you need proper planning, consistent effort, and the right mindset. Here are some important tips that can boost your preparation: 1. Understand the Complete Syllabus NEET’s syllabus is based on NCERT, especially Physics, Chemistry, and Biology from classes 11 and 12. Read every chapter carefully. 2. Make a Daily Routine Keep your morning hours for difficult subjects and revise at night. 3. Practice MCQs The more MCQs you practice, the more confident you will be in the exam. 4. Solve Previous Year Papers Solving old papers helps you understand the exam pattern, types of questions, and time management. 5. Prepare Revision Notes Short notes make last-minute revision quick and effective. 6. Take Care of Your Health Maintain proper sleep and a healthy diet during preparation.   Author: Sarthak Prakash Patil

  📘 Basic Trigonometric Ratios: sin θ, cos θ, tan θ, cot θ, sec θ, cosec θ sin 0° = 0, cos 0° = 1, tan 0° = 0 sin 30° = 1/2, cos 30° = √3/2, tan 30° = 1/√3 sin 45° = 1/√2, cos 45° = 1/√2, tan 45° = 1 sin 60° = √3/2, cos 60° = 1/2, tan 60° = √3 sin 90° = 1, cos 90° = 0, tan 90° = ∞ --- 📘 Trigonometric Identities: 1. sin²θ + cos²θ = 1   2. 1 + tan²θ = sec²θ   3. 1 + cot²θ = cosec²θ --- 📘 Other Formulas: tan θ = sin θ / cos θ   cot θ = cos θ / sin θ   sec θ = 1 / cos θ   cosec θ = 1 / sin θ --- 📘 Complementary Angles: sin(90° - θ) = cos θ   cos(90° - θ) = sin θ   tan(90° - θ) = cot θ   cot(90° - θ) = tan θ   sec(90° - θ) = cosec θ   cosec(90° - θ) = sec θ --- 📘 Formulas in Triangle: Area = (1/2) × a × b × sin C   Law of Sines: a/sin A = b/sin B = c/sin C   Law of Cosines: c² = a² + b² – 2ab cos C --- 📌 Posted by: Sarthak Prakash Patil