JEE Main 2020

Sequences and Series

The Greatest Positive Integer k for Which 49ᵏ + 1 Is a Factor of the Sum 49¹²⁵ + 49¹²⁴ + ⋯ + 49² + 49 + 1 Is
ByShiwam October 8, 2026September 16, 2026

Find the greatest positive integer k such that 49^k+1 divides 1+49+49²+…+49¹²⁵, by writing the sum as a GP and factoring it as a difference of squares.

Read More The Greatest Positive Integer k for Which 49ᵏ + 1 Is a Factor of the Sum 49¹²⁵ + 49¹²⁴ + ⋯ + 49² + 49 + 1 Is
Vectors and 3D Geometry

If a and b Are Unit Vectors, Then the Greatest Value of √3|a+b| + |a−b| Is
ByShiwam October 2, 2026September 16, 2026

Find the greatest value of √3|a+b|+|a−b| where a and b are unit vectors, by writing both magnitudes in terms of the half-angle between them.

Read More If a and b Are Unit Vectors, Then the Greatest Value of √3|a+b| + |a−b| Is