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JEE Mathematics: Set, Relation & Function (Doubt Questions) Lecture 04 (Home Work) – Question 11 In an examination of a certain class, at least 70% of the students failed in Physics, at least 72% failed in Chemistry, at least 80% failed in Mathematics and at least 85% failed in English. How many at least must … Read more

JEE Mathematics: Ratio, Proportion, k-method, Interval (Lecture 04) Topic 1: Ratio, Proportion and k-method A ratio is a comparison of two quantities of the same kind, expressed as $a:b$ or $\frac{a}{b}$. A proportion is an equation stating that two ratios are equal, i.e., $\frac{a}{b} = \frac{c}{d}$. k-method: If a series of ratios are equal, such … Read more

JEE Mathematics: Indices & Rationalization (Lecture 03) Topic 1: Rationalization of Surds & Simplification Rationalization is the process of eliminating surds (square roots, cube roots, etc.) from the denominator of a fraction. To rationalize a binomial denominator like $a + b\sqrt{x}$, multiply both the numerator and the denominator by its conjugate, $a – b\sqrt{x}$. Use … Read more

JEE Mathematics: Remainder & Factor Theorem (Lecture 02) Topic 1: Remainder Theorem If a polynomial $P(x)$ of degree $n \ge 1$ is divided by a linear polynomial $(x – a)$, then the remainder is $P(a)$. If $P(x)$ is divided by $(ax + b)$, the remainder is $P(-b/a)$. When dividing by a quadratic polynomial, the remainder … Read more

JEE MAIN MATHS – LECTURE 01: Identities & Number System Topic 1: Number System & Prime Numbers Number System: It comprises various types of numbers including natural numbers ($\mathbb{N}$), integers ($\mathbb{Z}$), and rational numbers ($\mathbb{Q}$). Rational Numbers ($\mathbb{Q}$): Any number that can be expressed as the fraction $p/q$, where $p$ and $q$ are integers and … Read more

JEE Mathematics Lecture Plan Lecture 07: Function & its Domain & Range Theory – 1: Definition & Identification of a Function A relation from set A to set B is called a function if every element of set A has exactly one unique image in set B. It means no input from the domain can … Read more

Lecture 06: Ordered Pair, Cartesian Product, Relation, Domain and Range Theory – 1: Ordered Pair & Cartesian Product An Ordered Pair consists of two elements written in a fixed order within parentheses, like $(a, b)$. The order is strictly maintained, meaning $(a, b) \neq (b, a)$ unless $a = b$. ક્રમયુક્ત જોડ (Ordered Pair) માં … Read more