Doubtify – JEE Ki Taiyaari, Simple Bhasha Mein

❓ Question The percentage increase in magnetic field B B  when the space within a current-carrying solenoid is filled with magnesium , given that the magnetic susceptibility of magnesium is χ Mg = 1.2 × 10 − 5 , is equal to ? 🖼️ Question Image ✍️ Short Solution This is a direct concept-based JEE question . No lengthy derivation — just one clean relation between magnetic field and susceptibility. 🔹 Step 1 — Magnetic field inside a solenoid (key idea 🔥)** For a long solenoid: In air (or vacuum) : B 0 = μ 0 n I When filled with a magnetic material : B = μ 0 ( 1 + χ ) n I Here: χ \chi  = magnetic susceptibility of the material n n  = turns per unit length I I  = current 📌 The geometry and current remain the same — only permeability changes. 🔹 Step 2 — Change in magnetic field Increase in magnetic field: Δ B = B − B 0 = μ 0 n I χ So, Δ B B 0 = χ 👉 This is the golden result. 🔹 Step 3 — Percentage increase formula % ...

  ❓ Concept 🎬 Reflexive, Transitive but NOT Symmetric — Easy JEE Trick in 60 Sec Relations ke chapter mein yeh 3 words sabse zyada confusion create karte hain: Reflexive , Transitive , Symmetric . Good news? 👉 Inko samajhne ke liye formula nahi , sirf arrow-logic chahiye 🔥 🖼️ Concept Image ✍️ Short Explanation JEE mein relations ko ordered pairs se zyada, arrows on elements ke jaise socho. Jaise hi arrows clear hue, ✔ property identify ✔ options reject ✔ counting easy 🔹 Step 1 — Reflexive Relation Rule (NON-NEGOTIABLE ⚠️)** Agar set: A = { 1 , 2 , 3 } Toh reflexive hone ke liye: ( 1 , 1 ) ,   ( 2 , 2 ) ,   ( 3 , 3 ) MUST be present . 📌 Inme se ek bhi missing hua → relation reflexive hi nahi rahega. Self-loops = compulsory. 🔹 Step 2 — Transitive Relation Rule (CHAIN EFFECT 🔥)** Rule: ( a , b ) ∈ R  and  ( b , c ) ∈ R ⇒ ( a , c ) ∈ R (a,b)\in R \ \text{and}\ (b,c)\in R \Rightarrow (a,c)\in R Arrow language: Agar a → b...

❓ Question Uniform magnetic fields of different strengths B 1 B_1 B 1 ​ and B 2 B_2 B 2 ​ , both normal to the plane of the paper , exist as shown in the figure. A charged particle of mass m m m and charge q q q , at the interface at an instant, moves into region 2 with velocity v v v and returns to the interface . It then continues to move into region 1 and finally reaches the interface again. What is the displacement of the particle along the interface during this complete motion? 🖼️ Question Image ✍️ Short Solution This is a pure concept-based JEE magnetism problem . No equations of motion — only circular motion + geometry . 🔹 Step 1 — Motion of a charged particle in uniform magnetic field When a charged particle with velocity v v v enters a region with a uniform magnetic field B B B (perpendicular to the velocity): The particle moves in a circular path Radius of circular motion: r = m v q B So in the two regions: r 1 = m v q B 1 , r 2 = m v q B 2...

❓ Concept 🎬 Discontinuity Trick for Greatest Integer Function | JEE in 60 Sec GIF (floor function) dikha? Samajh jao — continuity ka game start ho gaya hai 🔥 Is concept ko pakad liya, toh GIF ke 90% questions automatic clear . 🖼️ Concept Image ✍️ Short Explanation Students ki sabse badi galti: ❌ “GIF non-integers par toot-ta hai” Reality: 👉 GIF non-integers par continuous hota hai 👉 Sirf integers par jump aata hai Bas inside expression ko dhyaan se dekho — answer wahin se niklega. 🔹 Step 1 — GIF Breaks Only at Integers (CORE RULE 💯)** Greatest Integer Function [ x ] [x] : Continuous at every NON-integer Discontinuous ONLY at INTEGERS 📌 Important correction: Function ka argument integer hona chahiye, na ki x x  khud. 👉 So first rule: Find where the INSIDE expression becomes an integer. 🔹 Step 2 — Break the Function into Parts Typical JEE form: f ( x ) = [ something 1 ] − [ something 2 ] f(x)=[\text{something}_1]-[\text{something}_...

❓ Concept 🎬 Subsets with No Consecutive Numbers — JEE in 60 Sec Set ke subsets banana hai… lekin ek strict rule — 👉 koi do numbers consecutive nahi hone chahiye! JEE mein yeh pattern baar-baar repeat hota hai, aur iska answer hamesha Fibonacci logic se aata hai 🔥 🖼️ Concept Image ✍️ Short Explanation Is concept ka core idea bahut simple hai: 👉 har number ke paas sirf 2 choices hoti hain — include ya exclude. Bas ek restriction add ho jaata hai: include karte hi next number block ho jaata hai . 🔹 Step 1 — Problem Type Given set: { 1 , 2 , 3 , … , n } Allowed: Any subset But NO two consecutive elements Examples: { 1 , 3 , 5 } \{1,3,5\}  ✔ allowed { 1 , 2 , 4 } \{1,2,4\}  ❌ not allowed (1 & 2 consecutive) 🔹 Step 2 — Define a Counting Function Let: f ( n ) = number of valid subsets of  { 1 , 2 , … , n } 📌 Ab poora question f(n) nikaalne ka hai. 🔹 Step 3 — Key Idea (MOST IMPORTANT 🔥)** Element ...

❓ Question A lens having refractive index 1.6 1.6 1.6 has a focal length of 12 cm when it is placed in air . Find the focal length of the same lens when it is placed in water , given that the refractive index of water is 1.28 . 🖼️ Question Image ✍️ Short Solution This is a pure concept-based JEE optics question . 👉 The shape of the lens does NOT change , 👉 Only the surrounding medium changes , 👉 So we compare focal lengths using the lens maker idea in different media . 🔹 Step 1 — Key lens concept (VERY IMPORTANT 🔥)** For a thin lens: 1 f ∝ ( μ lens μ medium − 1 ) Where: μ lens \mu_{\text{lens}} ​ = refractive index of lens material μ medium \mu_{\text{medium}}  = refractive index of surrounding medium 📌 Since radius of curvature is same , we compare focal lengths by ratio only . 🔹 Step 2 — Write ratio formula Let: f a f_a ​ = focal length in air f w f_w ​ = focal length in water Then: f w f a = ( μ lens μ air − 1 ) ( μ lens μ water ...

❓ Concept 🎬 Hyperbola – Focus & Latus Rectum Concept in 59 Sec Hyperbola dikhe, focus dikhe, aur latus rectum right angle subtend kar raha ho? 👉 Samajh jao — geometry ka gold mine mil chuka hai 🔥 Yahan formula kam , logic zyada kaam karta hai. 🖼️ Concept Image ✍️ Short Explanation Is type ke questions JEE mein isliye favourite hain kyunki: ✔ Algebra aur geometry perfectly combine hote hain ✔ Ek right-angle condition poora problem lock kar deta hai Agar steps clear hain, toh answer clean aur fast nikalta hai. 🔹 Step 1 — Standard Hyperbola Basics (FOUNDATION 💯)** Standard form: x 2 a 2 − y 2 b 2 = 1 Is hyperbola ke liye: c 2 = a 2 + b 2 c^2=a^2+b^2 Foci = ( ± c , 0 ) 📌 Agar focus diya ho , toh c directly mil jaata hai — aur yahin se poora question start hota hai. 🔹 Step 2 — Latus Rectum of Hyperbola Hyperbola ka latus rectum : Har focus se guzarta hai Transverse axis ke perpendicular hota hai Equation: x = ± c x=\pm c Endpoints: ( ±...

  ❓ Question The number of singular matrices of order 2 , whose elements are taken from the set { 2 ,   3 ,   6 ,   9 } , is equal to ? 🖼️ Question Image ✍️ Short Solution A 2×2 matrix is singular if and only if its determinant is zero . So the entire question reduces to counting how many choices make the determinant zero . 🔹 Step 1 — Write the general 2×2 matrix Let the matrix be: A = ( a b c d ) where a , b , c , d ∈ { 2 , 3 , 6 , 9 } . 🔹 Step 2 — Condition for singular matrix A matrix is singular iff: ∣ A ∣ = a d − b c = 0 So we need: a d = b c 👉 This is the ONLY condition to check. 🔹 Step 3 — Key observation (MOST IMPORTANT 🔥)** The set: { 2 , 3 , 6 , 9 } has a multiplicative structure : 2 × 3 = 6 , 3 × 3 = 9 , 2 × 6 = 12   ( not allowed ) , 3 × 6 = 18   ( not allowed ) So equality a d = b c ad = bc a d = b c happens only when the ratios match : a b = c d 👉 That means: Either rows are proportional Or columns are proporti...