List of top Mathematics Questions on Relations and Geometry asked in JEE Main

In an equilateral triangle PQR, let the vertex P be at (3, 5) and the side QR be along the line x + y = 4. If the orthocentre of the triangle PQR is ($\alpha, \beta$), then 9($\alpha + \beta$) is equal to:

Let \( X = {R} \times {R} \). Define a relation \( R \) on \( X \) as: \[ (a_1, b_1) \, R \, (a_2, b_2) \iff b_1 = b_2. \] Statement-I: \( R \) is an equivalence relation. Statement-II: For some \( (a, b) \in X \), the set \( S = \{(x, y) \in X : (x, y) R (a, b)\ \) represents a line parallel to \( y = x \).}