Take timed practice tests on Coordinate Geometry Mixed Practice for JEE Main and JEE Advanced with session-wise drills, score review, and explanation-led revision.
Six 20-question timed sessions plus one 60-question module test. Each question is original and calibrated from the uploaded material pattern without copying PDF wording.
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1. The distance between points (−1, 3) and (2, −1) is:
Explanation: d = √((2−(−1))² + (−1−3)²) = √(9+16) = √25 = 5.
2. The equation 2x² + 2y² − 8x + 4y + 1 = 0 represents:
Explanation: When x² and y² have equal positive coefficients and no xy term, the conic is a circle. Dividing by 2: x² + y² − 4x + 2y + 1/2 = 0, a circle.
3. The line y = mx + c is tangent to y² = 4ax if:
Explanation: Condition for y = mx + c to be tangent to y² = 4ax: c = a/m. This is the standard tangency condition.
4. A point moves such that it is equidistant from (3,4) and (1,2). Its locus is:
Explanation: Midpoint of (3,4) and (1,2): (2, 3). Slope of joining line: (4−2)/(3−1) = 1. Perpendicular bisector slope: −1. Equation: y − 3 = −1(x − 2) → y − 3 = −x + 2 → x + y = 5.
5. The combined equation of pair of lines through origin and perpendicular to the pair 3x²−7xy+2y²=0 is:
Explanation: If slopes of given pair are m₁, m₂, perpendicular slopes are −1/m₁, −1/m₂. The combined equation of perpendicular lines is obtained by swapping coefficients of x² and y² in the original equation: 3x²−7xy+2y²=0 becomes 2x²+7xy+3y²=0.
6. The angle subtended by a chord at the centre is double the angle subtended at any point on the major arc. This is:
Explanation: Inscribed angle theorem: central angle = 2 × inscribed angle subtending the same arc. This is a fundamental circle theorem used in many JEE geometry problems.