Doubtify – JEE Ki Taiyaari, Simple Bhasha Mein

  ❓ Concept 🎬 Statistics Correction Trick in 59 Sec Kabhi data entry mein galti ho jaaye — ek value galat feed ho jaaye — toh mean bhi wrong nikalta hai aur standard deviation bhi ! Good news? 👉 Dono ko correct karna ek simple logical trick se possible hai. 🖼️ Concept Image ✍️ Short Explanation Statistics mein ek hi observation wrong ho toh poora dataset ke: ✔ Σx ✔ Σx² dono par effect padta hai — aur isi se mean & standard deviation change hote hain. 🔹 Step 1 — Why Correction Is Needed Agar one observation wrong hai : 👉 Wrong mean nikalta hai 👉 Wrong σ (standard deviation) nikalta hai Isliye pehle mean correct karte hain , phir σ ko recompute karte hain . 🔹 Step 2 — Correction in Mean (Fastest Formula 💡) Correct mean: Correct Mean = Wrong Mean + Correct Value − Wrong Value n Yahaan n = number of observations n = \text{number of observations} 📌 Matlab sirf difference / n add–subtract hota hai. Full recom...

  ❓ Concept Parameter-Based Quadratic Tricks (α, β) in 59 Sec Whenever you see a quadratic with p, k, λ in coefficients, panic mat karo . 👉 Parameter-based quadratics follow a fixed golden framework — once you apply it step-by-step, answers come automatically. 1️⃣ Quadratic with Parameter General form: a x 2 + b x + c = 0 ax^2 + bx + c = 0 Here, a ,   b ,   c depend on a parameter  p a,\ b,\ c \quad \text{depend on a parameter } p Roots are: α ,   β \alpha,\ \beta 👉 Goal in JEE questions: Find range of p such that roots satisfy a given condition. 2️⃣ Real Roots Condition (ALWAYS STEP 1) For real roots: D = b 2 − 4 a c ≥ 0 D = b^2 - 4ac \ge 0 📌 This step is non-negotiable . Most students forget it and lose marks. 👉 Solve: b 2 − 4 a c ≥ 0 ⇒ range of  p b^2 - 4ac \ge 0 \Rightarrow \text{range of } p 3️⃣ Sign of Roots (α, β) Use standard relations: α + β = − b a , α β = c a \alpha + \beta = -\frac{b}{a}, \quad \...