Doubtify – JEE Ki Taiyaari, Simple Bhasha Mein

  ❓ Concept 🎬 GP → AP Concept in 59 Sec Kabhi question bole: 👉 “Numbers GP mein hain, par kuch subtract/add karne ke baad AP ban gaye” Yeh coincidence nahi hota — yeh pure logic + standard form ka game hai 🔥 🖼️ Concept Image ✍️ Short Explanation Is type ke questions mein students ki sabse badi galti hoti hai: ❌ numbers ko direct manipulate karna JEE ka smart approach hai: 👉 GP ko standard form mein likho 👉 AP ki difference condition lagao 👉 a aur r cleanly nikal jaate hain 🔹 Step 1 — Write GP in Standard Form (CONTROL STEP 🔥)** Agar x 1 ,   x 2 ,   x 3 ,   x 4 x_1,\ x_2,\ x_3,\ x_4 GP mein hain, toh hamesha likho: x 1 = a , x 2 = a r , x 3 = a r 2 , x 4 = a r 3 x_1=a,\quad x_2=ar,\quad x_3=ar^2,\quad x_4=ar^3 📌 Bas yahin se poora question control mein aa jaata hai. 🔹 Step 2 — Apply the Given Operation Question mein jo operation diya ho (usually subtraction/addition), apply karo: ( x 1 − k 1 ) ,   ( x 2 − k 2 ) ,   ...

  ❓ Question Let x 1 , x 2 , x 3 , x 4 x_1, x_2, x_3, x_4 ​ be in a geometric progression . If 2, 7, 9, 5 are subtracted respectively from x 1 ,   x 2 ,   x 3 ,   x 4 , then the resulting numbers form an arithmetic progression . Find the value of 1 24 ( x 1 x 2 x 3 x 4 ) . 🖼️ Question Image ✍️ Short Solution We’ll express the GP in standard form, apply the AP equal-difference condition , solve for the first term & common ratio, then compute the product — and finally divide by 24. 🔹 Step 1 — Assume the GP Let x 1 = a , x 2 = a r , x 3 = a r 2 , x 4 = a r 3 x_1=a,\quad x_2=ar,\quad x_3=ar^2,\quad x_4=ar^3 🔹 Step 2 — Form the AP after subtraction Given that a − 2 , a r − 7 , a r 2 − 9 , a r 3 − 5 a-2,\quad ar-7,\quad ar^2-9,\quad ar^3-5 are in AP , so: ( a r − 7 ) − ( a − 2 ) = ( a r 2 − 9 ) − ( a r − 7 ) (ar-7)-(a-2) = (ar^2-9)-(ar-7) and ( a r 2 − 9 ) − ( a r − 7 ) = ( a r 3 − 5 ) − ( a r 2 − 9 ) (ar^2-9)-(ar-7) = (ar^3-5)-(ar^2-9) 🔹 Ste...