JEE Mathematics Questions & Solutions

Matrices and Determinants

• Q1. If A = [[1, 2], [3, 4]], find A² - 5A + 6I.
• Q2. Solve for x: |2 3; 1 x| = 5.
• Q3. Prove that det(AB) = det(A) × det(B).

Straight Lines and Pair of Straight Lines

• Q1. Find the equation of the line passing through (1, 2) and perpendicular to 3x + 4y = 7.
• Q2. Determine the point of intersection of 2x - 3y + 4 = 0 and x + y - 2 = 0.
• Q3. Show that ax² + 2hxy + by² = 0 represents two straight lines.

Circles, Parabola, Ellipse, Hyperbola

• Q1. Find the equation of a circle with center (2, 3) and radius 5.
• Q2. Find the equation of the parabola with vertex at origin and focus at (0, 3).
• Q3. Determine the eccentricity of the ellipse x²/9 + y²/4 = 1.
• Q4. Find the asymptotes of the hyperbola x²/16 - y²/9 = 1.