Gagan Pratap Advance Maths Complete Class Notes Exclusive [better]

Explanation: $67 \div 7$ leaves remainder 4. We need $4^99 \div 7$. Cyclicity of remainders for 4 powers by 7: $4^1=4$, $4^2=16 \to 2$, $4^3=8 \to 1$, $4^4=4$. Cycle: 4, 2, 1. Length 3. $99 = 3 \times 33$. Remainder is the 3rd term in the cycle, which is 1.

Detailed explanation of remainders, factors, and Cartesian planes. 2. The "Smart Approach" to Problem Solving gagan pratap advance maths complete class notes exclusive

Slopes, Area of triangles, and Point reflections. How to Study from These Notes Effectively Explanation: $67 \div 7$ leaves remainder 4

Gagan Pratap's Advance Maths Complete Class Notes is a comprehensive study material designed for students preparing for competitive exams, particularly those related to mathematics and quantitative aptitude. The notes are crafted by Gagan Pratap, a well-known educator and expert in the field of mathematics. Cycle: 4, 2, 1