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  How to Revise Effectively for JEE Main 2026 (Science-Backed Strategy) Revising for JEE Main is not about reading the same notes again and again. If that worked, every sincere student would already be confident. The real problem is this: most students revise passively, but JEE tests active recall, speed, and accuracy under pressure. This post explains a scientifically correct revision system that actually improves scores, not just comfort. 1. What Revision Really Means for JEE Main Revision is not: Re-reading NCERT again and again Highlighting formulas without application Watching the same lectures repeatedly Revision is: Recalling concepts without looking Identifying conceptual gaps Training your brain to think under time pressure JEE does not ask, “Have you seen this?” It asks, “Can you apply this in 90 seconds?” 2. The 3-La...

  Score: 0 Attempted: 0 Chemical Bonding – Interactive PYQ Quiz Topic: Molecular Geometry & VSEPR | JEE Main PYQs Q1. [16 March 2021 | Shift-1] Assertion: H–O–H bond angle in water is 104.5°. Reason: Lone pair–lone pair repulsion is maximum. A is false but R is true Both true but R not explanation A true, R false Both true and R correct explanation Check Answer Lone pair–lone pair repulsion compresses bond angle below 109.5°. Q2. [JEE Main 2024] Correct increasing order of bond angles: BF₃ < PF₃ < ClF₃ PF₃ < BF₃ < ClF₃ ClF₃ < PF₃ < BF₃ BF₃ = PF₃ < ClF₃ Check Answer ClF₃ (T-shape) < PF₃ (pyramidal) < BF₃ (120°). Q3. [11 April 2023 | Shift-1] Match geometries correctly: A-III, B-II, C-I, D-IV A-III, B-I, C-II, D-IV A-III, B-IV, C-I, D-II A-III, B-IV, C-II, D-I Check Answer H₂O⁺ → pyramidal, acetylide → linear, NH₃ → pyramidal, ClO₂⁻ → bent. Q4. [27 Jan 2022 | Shi...

    Circular Motion – Complete Formula & Concept Revision Circular motion refers to motion of a particle along a circular path. Although speed may remain constant, velocity always changes due to continuous change in direction. 1. Angular Quantities Angular displacement: $\theta$ (radians) Angular velocity: $\omega = \dfrac{d\theta}{dt}$ Angular acceleration: $\alpha = \dfrac{d\omega}{dt}$ Relation with linear quantities: $v = r\omega$ $a_t = r\alpha$ $a_c = r\omega^2 = \dfrac{v^2}{r}$ 2. Time Period & Frequency Time period: $T = \dfrac{2\pi}{\omega}$ Frequency: $f = \dfrac{1}{T}$ $\omega = 2\pi f$ 3. Centripetal Acceleration $a_c = \dfrac{v^2}{r} = r\omega^2$ Always directed toward centre Changes direction of velocity, not magnitude Trap: Zero centripetal acceleration means no circular motion. 4. Non-Uniform Circular Motion Acceleration has two components: Centripetal: $a_c = \dfrac{v^2}{r}$ Tangential: $a_t = \dfr...

    Work, Energy and Power – Complete JEE Revision This chapter connects force and motion through energy. JEE loves testing signs, reference frames, variable forces, and conservation traps . 1. Work (a) Work by Constant Force $W = \vec{F}\cdot\vec{s} = Fs\cos\theta$ Work depends on the component of force along displacement . $\theta=0^\circ$ → Maximum work $\theta=90^\circ$ → Zero work (centripetal force) $\theta=180^\circ$ → Negative work (b) Variable Force $W = \int \vec{F}\cdot d\vec{r}$ Work equals area under F–x graph . 2. Special Forces & Work Gravity: Conservative → path independent Friction: Non-conservative → path dependent Normal force: Usually zero work Centripetal force: Always zero work 3. Kinetic Energy (KE) $K = \frac{1}{2}mv^2$ Work–Energy Theorem Net work done = Change in kinetic energy $W_{\text{net}} = \Delta K$ Applies even when forces are complicated. 4. Potential Energy (PE) (a) Gr...

  Three Dimensional Geometry – Quiz 2 Topic: Equation of Line in 3D (Worked examples converted into interactive quiz) Key Formulae Vector form: r = a + λb Cartesian form: (x − x₁)/l = (y − y₁)/m = (z − z₁)/n Distance between two points: √[(x₂−x₁)²+(y₂−y₁)²+(z₂−z₁)²] Q1. The direction ratios of the line passing through (1,2,3) and (3,6,7) are: (2,2,2) (1,2,2) (2,4,4) (3,6,7) Check Solution: Direction ratios = (3−1,6−2,7−3) = (2,4,4) Q2. Which of the following is the Cartesian equation of a line passing through (2,−1,3) with direction ratios (1,2,−1)? (x−2)/2 = (y+1)/1 = (z−3)/(−1) (x−2)/1 = (y+1)/2 = (z−3)/(−1) (x+2)/1 = (y−1)/2 = (z+3)/(−1) (x−2)/1 = (y−1)/2 = (z+3) Check Solution: Use (x−x₁)/l = (y−y₁)/m = (z−z₁)/n Q3. Find the distance between points A(1,2,3) and B(4,6,6). Check Solution: Distance = √[(3)²+(4)²+(3)²] = √34 ≈ 5.83 Q4. The vector equation of a line passing through the origin and p...

  Three Dimensional Geometry – Interactive Quiz 1 Topic: Direction Cosines & Direction Ratios (Worked examples converted into quiz format) Key Formulae Direction cosines: l = cosα, m = cosβ, n = cosγ Condition: l² + m² + n² = 1 If direction ratios are (a, b, c): l = a/√(a²+b²+c²), m = b/√(a²+b²+c²), n = c/√(a²+b²+c²) Q1. If the direction ratios of a line are (2, −2, 1), the direction cosine along x-axis is: 2/3 2/√9 2/√6 √6/2 Check Solution: √(2²+(-2)²+1²)=√9=3 l = 2/3 Q2. If a line makes equal angles with all three coordinate axes, find its direction cosine (nearest 3 decimals). Check Solution: l = m = n 3l² = 1 ⇒ l = 1/√3 ≈ 0.577 Q3. The direction ratios of a line perpendicular to the plane x + 2y − 2z + 5 = 0 are: (1, −2, 2) (2, 1, −2) (1, 2, −2) (−1, 2, 2) Check Solution: Normal to plane = coefficients of x,y,z = (1,2,−2) Q4. If the direction cosines of a line are (l, m, n) and l = m, find ...

  Methods of Differentiation – Complete JEE Revision Differentiation is about choosing the correct method , not brute force. JEE questions are designed to punish wrong method selection. This chapter systematically covers all differentiation methods used in JEE Mains & Advanced. 1. Basic Concept \[ \frac{dy}{dx} = \lim_{h\to0}\frac{f(x+h)-f(x)}{h} \] Differentiation measures the rate of change of one quantity with respect to another. 2. Standard Derivatives (Must Memorise) \(\frac{d}{dx}(x^n)=nx^{n-1}\) \(\frac{d}{dx}(e^x)=e^x\) \(\frac{d}{dx}(a^x)=a^x\ln a\) \(\frac{d}{dx}(\ln x)=\frac{1}{x}\) \(\frac{d}{dx}(\sin x)=\cos x\) \(\frac{d}{dx}(\cos x)=-\sin x\) \(\frac{d}{dx}(\tan x)=\sec^2 x\) \(\frac{d}{dx}(\cot x)=-\csc^2 x\) \(\frac{d}{dx}(\sec x)=\sec x\tan x\) \(\frac{d}{dx}(\csc x)=-\csc x\cot x\) 3. Method 1 – Differentiation from First Principle Used mainly in conceptual or proof-based questions. Example: Differentiate \(f(...

    Continuity & Differentiability – Complete JEE Main 2026 Revision This chapter connects limits → graphs → calculus . Most JEE errors happen due to confusing continuity with differentiability . 1. Continuity A function $f(x)$ is continuous at $x=a$ if and only if: $\displaystyle \lim_{x\to a^-}f(x)=\lim_{x\to a^+}f(x)=f(a) $ All three conditions must hold simultaneously. Types of Discontinuity (JEE Favourite) Type Description Removable LHL = RHL but ≠ f(a) Jump LHL ≠ RHL Infinite Limit → ±∞ Oscillatory No definite approach value 📌 Polynomials, exponential, trigonometric functions are continuous everywhere. 2. Differentiability A function is differentiable at $x=a$ if: $\displaystyle \lim_{h\to0}\frac{f(a+h)-f(a)}{h} $ exists. ✔ Differentiability ⇒ Continuity ❌ Continuity ⇏ Differentiability Non-Differentiable Points (Very Important) Sharp corners (e.g. $|x|$ at $0$) Cusps Vertical tangents Disc...

  Limits – Complete JEE Main 2026 Revision A limit describes the value a function approaches as the variable gets close to a point. It does not require the function to be defined at that point. 1. Definition of Limit $\displaystyle \lim_{x \to a} f(x) = L$ This means $f(x)$ can be made arbitrarily close to $L$ by taking $x$ sufficiently close to $a$. 2. Left & Right Hand Limits $\displaystyle \lim_{x \to a^-} f(x)$ (Left Hand Limit) $\displaystyle \lim_{x \to a^+} f(x)$ (Right Hand Limit) Limit exists iff: $\displaystyle \lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x)$ JEE Main frequently tests piecewise functions using this. 3. Direct Substitution Rule If $f(x)$ is continuous at $x=a$: $\displaystyle \lim_{x \to a} f(x) = f(a)$ Fails when substitution gives indeterminate form. 4. Standard Limits (Core JEE Main) Trigonometric $\displaystyle \lim_{x \to 0} \frac{\sin x}{x} = 1$ $\displaystyle \lim_{x \to 0} \frac{\tan x}{x}...

Home  ›  JEE Mains  ›  GOC Revision   General Organic Chemistry (GOC) – Conceptual Foundation General Organic Chemistry explains why molecules behave the way they do . Every reaction mechanism, acidity order, and stability trend originates here. Mastering GOC means predicting reactions instead of memorizing them. 1. Reactive Intermediates (a) Carbocation (C⁺) Carbon atom with positive charge and 6 electrons Hybridization: sp² , planar structure Acts as an electrophile Stability Order: 3° > 2° > 1° > CH₃⁺ Reason: +I effect and hyperconjugation stabilize positive charge. (b) Carbanion (C⁻) Carbon atom with negative charge and lone pair Hybridization: usually sp³ Acts as a nucleophile Stability Order: CH₃⁻ > 1° > 2° > 3° Reason: Electron donating alkyl groups destabilize negative charge. (c) Free Radical (•) Carbon with one unpaired electron Neutral species Hybridizat...

Home  ›  JEE Mains  ›  Coordination compound Revision   Coordination Compounds – High Return Revision Notes Coordination chemistry is a scoring chapter if patterns are recognized instead of memorized. This revision focuses on structure–property logic , standard formulas, and repeated JEE & Board traps . 1. Basic Terminology (Must-Know) Coordination entity: Central metal atom/ion + surrounding ligands Ligand: Electron pair donor (Lewis base) Coordination number (CN): Number of donor atoms bonded to metal Oxidation state: Charge on metal assuming ligands are neutral/ionic Complex ion vs neutral complex: Based on overall charge 2. Ligands – Classification & Key Exceptions Type Examples Exam Notes Monodentate NH₃, Cl⁻, CN⁻ CN⁻ is strong field ligand Bidentate ...

Home  ›  JEE Mains  ›  Chemical Bonding Revision   Chemical Bonding – Complete JEE Mains Revision Chemical bonding explains how atoms combine to form molecules and solids. JEE frequently tests exceptions, trends, geometry, and stability arguments . 1. Why Do Atoms Form Bonds? Atoms form bonds to achieve lower potential energy and higher stability. Noble gases → already stable Others → bond to achieve octet / duplet JEE Trap: Octet rule has many exceptions – it is NOT a universal law. 2. Types of Chemical Bonds (a) Ionic (Electrovalent) Bond Complete transfer of electrons High lattice energy High melting point Lattice Energy: $$ U \propto \frac{z^+z^-}{r} $$ Repeated Question: Smaller ions + higher charge → stronger ionic bond (b) Covalent Bond Electron sharing Directional Low melting point (generally) (c) Coordinate (Dative) Bond Both electrons contributed by one atom. ...

Home  ›  Mathematics  ›  Matrices Revision Matrices – Complete Revision Series (JEE Level) Matrices provide a powerful algebraic language to represent systems of equations, transformations, and logical structure. In JEE, this chapter blends precision with speed. 1. Matrix Definition \[ A = [a_{ij}]_{m \times n} \] A matrix is a rectangular array of elements arranged in rows and columns. 2. Types of Matrices Row Matrix: \(1 \times n\) Column Matrix: \(m \times 1\) Square Matrix: \(n \times n\) Zero Matrix Diagonal Matrix Scalar Matrix Identity Matrix \(I_n\) Symmetric Matrix: \(A^T = A\) Skew-Symmetric Matrix: \(A^T = -A\) Important: Diagonal elements of a skew-symmetric matrix are always zero. 3. Matrix Operations Addition \[ A+B = [a_{ij}+b_{ij}] \] Scalar Multiplication \[ kA = [ka_{ij}] \] 4. Matrix Multiplication If \(A_{m\times n}\) and \(B_{n\times p}\), then \[ (AB)_{ij} = ...

Home  ›  Mathematics  ›  Determinants Revision Determinants – Complete Revision Series (JEE Level) Determinants form the backbone of solving linear equations, understanding area, geometry, and matrix algebra. This chapter is formula-rich but logic-driven — once patterns are clear, questions become mechanical. 1. Determinant of Order 2 For a matrix \[ A=\begin{vmatrix} a & b\\ c & d \end{vmatrix} \] \[ |A| = ad - bc \] Important Results: \(|A| = 0\) ⇒ rows/columns are linearly dependent Interchanging rows changes sign of determinant Multiplying a row by \(k\) multiplies determinant by \(k\) 2. Determinant of Order 3 \[ \begin{vmatrix} a & b & c\\ d & e & f\\ g & h & i \end{vmatrix} = a(ei-fh)-b(di-fg)+c(dh-eg) \] Student Pain Point: Sign mistakes occur due to improper expansion. Always expand along a row/column with maximum zeros. 3. Minors & Cofactors M...

Home  ›  Mathematics  ›  JEE Mathematics Revision 2026   JEE Mathematics Complete Revision & PYQ Hub (2026) This is a central revision hub for JEE Mathematics , covering Algebra, Coordinate Geometry, Calculus, Trigonometry, and Vectors with topic-wise PYQs and concept explanations. 🔹 Foundations of Algebra Sets Basic Definitions & Operations Relations & Functions Domain, Range & Types Quadratic Equations Roots, Nature & Graphs 📐 Coordinate Geometry Straight Lines JEE Main 2026 Revision Circle Complete Concepts & PYQs Parabola Standard JEE Problems Ellipse Concepts & PYQs Hyperbola Exam-Focused Revision Conic Sections (Combined) PYQ Series 📊 Algebra Quadratic Equations Roots, Graphs & PYQs Sequence & Series AP, GP & Special Series Permutation & Combination Counting Techniques Binomial Theore...

Home  ›  Mathematics  ›  probability Revision Probability — JEE Mains 2026 Revision capsule  A compact, high-yield probability capsule — every formula, every trap, P&C connections, solved examples and a fast recall ladder. MathJax renders all equations. 🔁 Revision Series 🔗 Permutation & Combination 🔗 Binomial Axioms \(0\le P(A)\le1,\; P(S)=1,\; P(A^c)=1-P(A)\) Add/Mul Rules \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\) \(P(A\cap B)=P(A)P(B|A)\) Bayes & Total \(P(A)=\sum_i P(B_i)P(A|B_i)\) \(P(B_k|A)=\dfrac{P(B_k)P(A|B_k)}{\sum_i P(B_i)P(A|B_i)}\) Exam-Killer (memorize): “At least one” → use complement: \(1-P(\text{none})\). Without replacement → events dependent. Use combinations, not product of probabilities. Bayes = prior × likelihood ...