Doubtify – JEE Ki Taiyaari, Simple Bhasha Mein

  🔢 Matrices & Determinants | JEE Maths | Doubtify JEE 📌 Question: The number of all 3 × 3 matrices A , with entries from the set {-1, 0, 1} , such that the sum of the diagonal elements of AAᵀ is 3 , is: 🖼️ Question Image:

🌀 Centroid of a Circular Plate with a Hole | System of Particles | JEE Physics | Doubtify JEE ❓ Question: A circular hole of radius (a/2) is cut out of a circular disc of radius ‘a’ , as shown in the figure. What will be the position of the centroid of the remaining circular portion with respect to point ‘O’ ? 🖼️ Question Image: 🧠 Solution Image: ✍️ Detailed Explanation: To solve this problem, we apply the concept of mass moment (or area moment) . When a portion is cut out from a symmetric object, we use the principle of superposition — treat the hole as a negative mass or negative area. Let’s break it down: 🧮 Step 1: Assume mass per unit area = σ Area of full disc = πa² Area of hole = π(a/2)² = (πa²)/4 Remaining area = πa² – (πa²)/4 = (3πa²)/4 🧮 Step 2: Find centroid of each part Full disc’s centroid = At origin (O) Hole’s centroid is at a distance of a/2 from O along the radius. 🧮 Step 3: Apply formula for center of mass (COM): Let x be the position of the c...

  📈 Velocity-Time Graph Problem | Motion in One Dimension | Physics | Doubtify JEE 💡 Question: The velocity (v) and time (t) graph of a body in a straight-line motion is shown in the figure. Point S is at 4.333 sec. The total distance covered by the body in 6 seconds is? 🖼️ Question Image: 🧠 Solution Image:

  🔥 Balance Redox Reaction Using Oxidation Number Method | JEE Chemistry | Doubtify ⚛️ Question : Balance the following equation by the oxidation number method: K₂Cr₂O₇ + HCl → KCl + CrCl₃ + H₂O + Cl₂

  📈 Acceleration as a Function of Distance – Motion in One Dimension | JEE Physics | Doubtify JEE 🧮 Question: The distance x covered by a particle in one-dimensional motion varies with time t as: x² = at² + 2bt + c . If the acceleration of the particle depends on x as x⁻ⁿ , where n is an integer, what is the value of n ? 🖼️ Question Image: ✅ Detailed Concept & Solution: This is a JEE-level conceptual problem involving the relation between distance, velocity, and acceleration — with a twist of functional dependence. We are given: x² = at² + 2bt + c — (1) To find acceleration and its dependency on x , let’s differentiate both sides of equation (1): Differentiate w.r.t. time t : 2x(dx/dt) = 2at + 2b ⇒ v = dx/dt = (at + b)/x — (2) Now differentiate velocity v w.r.t time to find acceleration: a = dv/dt = d/dt[(at + b)/x] Use quotient rule: a = [a·x - (at + b)(dx/dt)] / x² Plug dx/dt = (at + b)/x from (2): a = [a·x - (at + b)·((at + b)/x)] / x² ⇒ ...

  🧲 The Sum of Two Forces P and Q is R | Angle Between 2P and Q | JEE Physics Doubt Solved

  🚴 Velocity-Displacement Graph of a Bicycle | Find the Acceleration-Displacement Graph | Motion in 1D – Doubtify JEE 📌 Question : The velocity-displacement graph describing the motion of a bicycle is shown in the figure. What will the corresponding acceleration-displacement graph look like? 🎯 Concept Tested: This question tests your graphical understanding of motion — a frequently asked and often misunderstood area in JEE Mains and Advanced . It focuses on converting one type of graph (v-s) into another (a-s) using calculus concepts. 🔍 How to Approach: If you're given a velocity-displacement (v-s) graph , and you need to find the acceleration-displacement (a-s) graph , you must apply: a = v ⋅ d v d s a = v \cdot \frac{dv}{ds} This is derived from the chain rule: a = d v d t = d v d s ⋅ d s d t = v ⋅ d v d s a = \frac{dv}{dt} = \frac{dv}{ds} \cdot \frac{ds}{dt} = v \cdot \frac{dv}{ds} Depending on the slope of the v-s graph: If velocity increases with displaceme...

  ⚗️ Balance the Equation: Mg + HNO₃ ⟶ Mg(NO₃)₂ + N₂O + H₂O ❓ Question: Balance the following chemical equation: Mg + HNO₃ ⟶ Mg(NO₃)₂ + N₂O + H₂O This question appears simple at first glance, but it actually requires deep understanding of redox reactions and balancing complex equations . 🎯 Key Concepts Tested: Oxidation and reduction processes Balancing redox equations using ion-electron method or oxidation number method Conservation of mass and conservation of charge Identifying oxidizing and reducing agents Understanding product formation in acidic medium (presence of HNO₃) 🧠 Step-by-Step Solution Strategy: Step 1: Identify oxidation states Let’s determine oxidation states of all elements in reactants and products: Mg (0) → Mg²⁺ in Mg(NO₃)₂ → Oxidation (Mg is losing electrons) N in HNO₃: +5 N in N₂O: +1 → Reduction (N is gaining electrons) Step 2: Write unbalanced half-reactions Oxidation (Mg): Mg → Mg²⁺ + 2e⁻ Reduction (N): 2...

🔥 Combustion Analysis – Percentage of Oxygen in an Organic Compound | JEE Chemistry | Doubtify JEE

  ⏱️ Acceleration-Time Graph – Find Time When Initial Velocity is Regained | JEE Physics | Doubtify JEE ❓ Question: The acceleration-time graph of a particle is as shown. At what time does the particle acquire its initial velocity again?

🔄 Circular Motion | Physics | Doubtify JEE

🧪 Question: The ratio of mass percent of C and H of an organic compound (CxHyOz) is 6:1. If one molecule of the above compound contains half as much oxygen as required to burn one molecule of compound CxHy completely to CO₂ and H₂O, then what is the empirical formula of the compound? 📌 Why This Question is Important: This question combines two highly testable concepts in JEE Chemistry – combustion analysis and empirical formula derivation . You’re not only working with mass percent ratio , but also applying oxygen balancing logic in a combustion reaction. Such questions are frequently seen in organic chemistry chapters , particularly under Basic Principles of Organic Chemistry and Stoichiometry . Mastering this helps you crack more complex analysis-based questions in JEE Mains and even Advanced . 💡 Concept Used: To find the empirical formula , we first convert the mass percent ratio of C and H into moles , assuming 100 g of substance. Then we apply a stoichiometric appr...

🎯 Question: A balloon was moving upwards with a uniform velocity of 10 m/s. An object of finite mass is dropped from the balloon when it was at a height of 75 m from the ground level. The height of the balloon from the ground, when the object strikes the ground, was around: (Take g = 10 m/s²)

     📌 Question: Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at the 4th second after its fall to the next droplet is 34.3 m . At what rate are the droplets coming from the tap? (Take g = 9.8 m/s²) 🖼️ Question Image:

🧮 Question: 100 grams of propane is completely reacted with 1000 grams of oxygen. The mole fraction of carbon dioxide in the resulting mixture is X × 10⁻². The value of x is: 🖼️ Question Image:

     🧲 Solutions  | Chemistry  |  Doubtify JEE 🧮 Question: The density of the NaOH solution is 1.2 g/cm³. What is the molality of the solution? 🖼️ Question Image: ⚗️ Concept Overview: This is a fundamental problem from the Solutions chapter of Physical Chemistry. It tests your understanding of molality , density , and the method of converting between different concentration units. In many JEE Main and Advanced problems, students get confused between molality (mol/kg) and molarity (mol/L) . This problem helps to eliminate that confusion and improve conceptual clarity. 🧠 Step-by-Step Explanation: Let’s assume we are working with 1000 cm³ = 1 L of NaOH solution. Density = 1.2 g/cm³ So, total mass of 1 L solution = 1.2   g/cm³ × 1000   cm³ = 1200   g 1.2 \, \text{g/cm³} \times 1000 \, \text{cm³} = 1200 \, \text{g} Let’s say the solution is x% NaOH by mass (you may be given the percentage or molarity in the full version of the question – for no...

    🧲 Motion in a Plane  |  Physics |  Doubtify JEE 💡 Question: A mosquito is moving with a velocity  v = 0.5 t² î + 3t ĵ + 9 k̂ m/s and accelerating in uniform conditions. What will be the direction of motion of the mosquito after 2 seconds? 🖼️ Question Image: 🔬 Concept Overview: This is a vector motion problem where you're given a time-dependent velocity vector in three dimensions. To find the direction of motion , we must compute the velocity vector at  t = 2 t  =  2 seconds and then determine its direction using unit vector analysis or angle calculation with respect to axes. This is a key concept from the chapter "Motion in a Plane" , often asked in JEE Mains or Advanced. 🧠 Step-by-Step Explanation: Given: v ⃗ ( t ) = 0.5 t 2 i ^ + 3 t j ^ + 9 k ^ \vec{v}(t) = 0.5t^2 \hat{i} + 3t \hat{j} + 9 \hat{k} At t = 2 t = 2  seconds: i-component: 0.5 × 2 2 = 2   m/s j-component: 3 × 2 = 6   m/s 3 \times 2 = 6 \, \text{m/s} ...

  🧲 Motion in a Straight Line  |  Physics |  Doubtify JEE 💡 Question: A car accelerates from rest at a constant rate α for some time, after which it decelerates at a constant rate β to come to rest. If the total time elapsed is t seconds, the total distance traveled is: 🖼️ Question Image: 🧠 Solution (Image): 🎥 Video Solution: 🔍 Why this Question is Important: This is a classic and conceptual question from Kinematics , frequently appearing in JEE Main exams. It tests your understanding of uniformly accelerated and retarded motion, and time-division-based distance calculation – a vital part of motion in a straight line. 📩 Have a Doubt? Drop us a mail at  doubtifyqueries@gmail.com  or DM us on  Instagram . Stay consistent. Watch – Pause – Solve – Repeat. Team Doubtify is with you till the finish line! 💪

  🧪Motion in a Straight Line  | Physics |  JEE Mains ❓ Question: A person goes to his office from his home daily at a fixed speed. But today he decided to reduce his speed by 20%, and as a result, he reaches his office 16 minutes late. What's the actual/original time he takes to reach his office daily? 🖼️ Question Image: 🧠 Solution (Image): 🎥 Video Solution: 🔍 Why this Question is Important: This is a frequently asked conceptual problem in  Kinematics  that tests your understanding of the relationship between speed, time, and distance. It’s a perfect example of how real-life reasoning can be applied to JEE Physics problems — and a favorite in  JEE Mains  question banks. 📩 Have a Doubt? Drop us a mail at  doubtifyqueries@gmail.com  or DM us on  Instagram . Stay consistent. Watch – Pause – Solve – Repeat. Team Doubtify is with you till the finish line! 💪

🧪 Redox Reactions | Chemistry |  JEE Mains 📌 Question: Balance the equation by ion-electron method in basic medium: Zn + NO 3 − → Zn 2 + + NH 4 +​ This is a classic redox equation where zinc is oxidized and nitrate is reduced. The balancing must be done using the ion-electron method under basic medium conditions . 🖼️ Question Image: 🧠 Solution (Image): 🎥 Video Solution: 🔍 Why this Question is Important: This question is frequently asked in JEE Mains and Advanced , especially in the chapter Redox Reactions . It tests key skills like: Identifying oxidation and reduction half-reactions Using the ion-electron method properly in basic medium Applying concepts of oxidation states, electrons, and balancing H₂O/OH⁻ ions Understanding this concept is crucial for solving more advanced redox problems in competitive exams. 📩 Have a Doubt? Drop us a mail at  doubtifyqueries@gmail.com  or DM us on  Instagram . Stay consistent. Watch – Pause – Solve – Repeat. ...

🧪 Kinematics – Motion in a Straight Line | Physics | JEE Mains 📌 Question: A stone is dropped from the top of a building.  When it crosses a point 5 m below the top , another stone starts to fall from a point 25 m below the top , and both stones reach the bottom of the building simultaneously . Find the height of the building . (Take g = 10 m/s²) 🖼️ Question Image: 🧠 Solution (Image): 🎥 Video Solution: 🔍 Why this Question is Important: This is a  classic conceptual question from Kinematics , commonly asked in  JEE Mains  and other engineering entrance exams. It checks your understanding of  relative motion ,  free fall , and  time equations of motion  – topics that are often mixed to form trick questions. 📩 Have a Doubt? Drop us a mail at  doubtifyqueries@gmail.com  or DM us on  Instagram . Stay consistent. Watch – Pause – Solve – Repeat. Team Doubtify is with you till the finish line! 💪