Analytical Geometry (2D and 3D) NDA PYQ Topic Wise

Explore: All NDA topics · NDA Mathematics PYQs · NDA hub · Syllabus & pattern · NDA 2026

Answer first

Analytical Geometry (2D and 3D) PYQs (previous year questions) for NDA: Analytical Geometry (2D and 3D) (Mathematics) had 299 questions across the 42 official NDA papers we tagged (2016–2026), and appeared in 21 of them. Asked in 11 of 11 years. The concepts asked in the most papers: Straight Lines, Circles, Ellipse.

Year-wise question count

Asked in 11 of 11 years.

Most-asked concepts

Sorted by the number of papers a concept appeared in.

How to practise Analytical Geometry (2D and 3D) PYQs

1. Start with the concepts at the top of the table. They have come back the most.
2. Solve one year’s Analytical Geometry (2D and 3D) questions from the official PDF against the clock, then check the answer listed below.
3. Log every miss as a concept gap, a calculation slip or a misread. Each needs a different fix.
4. Once a concept is clean in two papers, move to the next. Then sit a full paper from the year pages.

Questions by year

Each line gives the question number and paper, type, concept, our one-line summary and the official answer, with a link to the official PDF.

NDA2026

• Q.51 (NDA (I) Mathematics) · MCQ · Straight Lines: Angle between a line through the origin and a given line PDF
• Q.52 (NDA (I) Mathematics) · MCQ · Straight Lines: Angle of a line with the positive y-axis PDF
• Q.53 (NDA (I) Mathematics) · MCQ · 3D Geometry: Parallel and perpendicular checks for segments of four points PDF
• Q.54 (NDA (I) Mathematics) · MCQ · 3D Geometry: Value of PQ² + 2QS² - 2PR² for given points PDF
• Q.55 (NDA (I) Mathematics) · MCQ · Lines and Planes: Line through a point perpendicular to a plane PDF
• Q.56 (NDA (I) Mathematics) · MCQ · Lines and Planes: Direction ratios of a line parallel to the plane PDF
• Q.57 (NDA (I) Mathematics) · MCQ · Straight Lines: Position of three points whose coordinates are in AP PDF
• Q.58 (NDA (I) Mathematics) · MCQ · Straight Lines: Direction of line XZ when b = c and p, q, r are not in AP PDF
• Q.59 (NDA (I) Mathematics) · MCQ · Circles: Values of k for four concyclic points PDF
• Q.60 (NDA (I) Mathematics) · MCQ · Circles: Diameter of the circle through three given points PDF
• Q.61 (NDA (I) Mathematics) · MCQ · Conic Sections: Value of p when ellipse and hyperbola foci coincide PDF
• Q.62 (NDA (I) Mathematics) · MCQ · Conic Sections: Difference of eccentricities of the hyperbola and ellipse PDF
• Q.63 (NDA (I) Mathematics) · MCQ · Sphere: Radius of a concentric sphere passing through the origin PDF
• Q.64 (NDA (I) Mathematics) · MCQ · Sphere: Value of k when the sphere's radius is 8 PDF
• Q.51 (NDA (II) Mathematics) · MCQ · Circles: Centre of a circle touching y = x and y = -x at unit distance PDF
• Q.52 (NDA (II) Mathematics) · MCQ · Straight Lines: Distance of the intercept midpoint from the origin PDF
• Q.53 (NDA (II) Mathematics) · MCQ · Conic Sections: Focal distance PF of a point on an ellipse PDF
• Q.54 (NDA (II) Mathematics) · MCQ · Straight Lines: Line equidistant from two parallel lines PDF
• Q.55 (NDA (II) Mathematics) · MCQ · Straight Lines: Reflection of a light ray at the x-axis PDF
• Q.56 (NDA (II) Mathematics) · MCQ · Straight Lines: Line with given sum and product of intercepts PDF
• Q.57 (NDA (II) Mathematics) · MCQ · Straight Lines: Line whose intercept segment is divided 1:2 by a point PDF
• Q.58 (NDA (II) Mathematics) · MCQ · Straight Lines: Equation of diagonal AC of a square PDF
• Q.59 (NDA (II) Mathematics) · MCQ · Locus: Locus of vertex C given a cot A + cot B condition PDF
• Q.60 (NDA (II) Mathematics) · MCQ · Conic Sections: Eccentricity of the parabola 4x² + y = 0 PDF
• Q.61 (NDA (II) Mathematics) · MCQ · 3D Geometry: Sum of squares of medians of a triangle in space PDF
• Q.62 (NDA (II) Mathematics) · MCQ · Direction Cosines: Extreme values of direction-cosine sums when α + β = 90° PDF
• Q.63 (NDA (II) Mathematics) · MCQ · 3D Geometry: Area of a triangle with vertices in space PDF
• Q.64 (NDA (II) Mathematics) · MCQ · Planes: Plane through P perpendicular to OP PDF
• Q.65 (NDA (II) Mathematics) · MCQ · Planes: Value of D from the image of a point in a plane PDF

NDA2025

• Q.51 (NDA (I) Mathematics) · MCQ · Straight Lines: Condition for two lines with parameters m, n to be perpendicular PDF
• Q.52 (NDA (I) Mathematics) · MCQ · Straight Lines: p+q when (p,1), (1,q), (0,0) form an equilateral triangle PDF
• Q.53 (NDA (I) Mathematics) · MCQ · Straight Lines: Incentre of a triangle with given vertices PDF
• Q.54 (NDA (I) Mathematics) · MCQ · Straight Lines: Point at distance √2 on perpendicular bisector of a segment PDF
• Q.55 (NDA (I) Mathematics) · MCQ · Straight Lines: Equation of base BC of an equilateral triangle from altitude PDF
• Q.56 (NDA (I) Mathematics) · MCQ · Circles: Circle equation from diameter length and two diameters PDF
• Q.57 (NDA (I) Mathematics) · MCQ · Circles: Vertex of a square inscribed in a given circle PDF
• Q.58 (NDA (I) Mathematics) · MCQ · Parabola: Point of contact of a 45° tangent to y^2=4x PDF
• Q.59 (NDA (I) Mathematics) · MCQ · Hyperbola: Distance between foci of a hyperbola PDF
• Q.60 (NDA (I) Mathematics) · MCQ · Ellipse: Eccentricity of ellipse with parametric point (3sinα, 5cosα) PDF
• Q.61 (NDA (I) Mathematics) · MCQ · Direction Cosines: cos(α+β)cos(α-β) for direction angles of a line PDF
• Q.62 (NDA (I) Mathematics) · MCQ · 3D Geometry: Area of a rectangle from three vertices in space PDF
• Q.63 (NDA (I) Mathematics) · MCQ · 3D Geometry: k when a triangle in space is right-angled at B PDF
• Q.64 (NDA (I) Mathematics) · MCQ · Direction Cosines: cos2θ for angle of a 3D line with the y-axis PDF
• Q.65 (NDA (I) Mathematics) · MCQ · Planes: Plane through (1,1,1) perpendicular to a line with given direction ratios PDF
• Q.51 (NDA (II) Mathematics) · MCQ · Planes: Direction ratios of the line of intersection of two planes PDF
• Q.52 (NDA (II) Mathematics) · MCQ · Planes: Plane containing a line of intersection and parallel to a given line PDF
• Q.53 (NDA (II) Mathematics) · MCQ · Sphere: Radius of smallest sphere through three unit points on axes PDF
• Q.54 (NDA (II) Mathematics) · MCQ · Sphere: Plane on which the centre of that sphere lies PDF
• Q.55 (NDA (II) Mathematics) · MCQ · 3D Geometry: Fourth vertex of a parallelogram in space PDF
• Q.56 (NDA (II) Mathematics) · MCQ · Direction Cosines: cos^2 of angle BCD of a parallelogram in space PDF
• Q.57 (NDA (II) Mathematics) · MCQ · Straight Lines: Family of lines 4y=mx-m+2 for varying m PDF
• Q.58 (NDA (II) Mathematics) · MCQ · Locus: Constant k in the locus equidistant from two points PDF
• Q.59 (NDA (II) Mathematics) · MCQ · Parabola: Statements on opening, axis and latus rectum of x^2+3y=0 PDF
• Q.60 (NDA (II) Mathematics) · MCQ · Straight Lines: Sum of intercepts of a given line on the axes PDF
• Q.61 (NDA (II) Mathematics) · MCQ · Straight Lines: Normal (perpendicular) form of √3x+2y=7 PDF
• Q.62 (NDA (II) Mathematics) · MCQ · Straight Lines: Area of a square from its diagonal vertices PDF
• Q.63 (NDA (II) Mathematics) · MCQ · Straight Lines: Sine of acute angle between two given lines PDF
• Q.64 (NDA (II) Mathematics) · MCQ · Circles: Distance between points where a circle touches both axes PDF
• Q.65 (NDA (II) Mathematics) · MCQ · Hyperbola: Distance between foci of x^2-4y^2=1 PDF

NDA2024

• Q.51 (NDA (I) Mathematics) · MCQ · Circles: a^2+b^2+c^2 from centre and radius of a circle PDF
• Q.52 (NDA (I) Mathematics) · MCQ · Sphere: u+v+w for a sphere with given diameter endpoints PDF
• Q.53 (NDA (I) Mathematics) · MCQ · Straight Lines: Number of points represented by x=5 on the xy-plane PDF
• Q.54 (NDA (I) Mathematics) · MCQ · Direction Cosines: Expression in direction cosines of a plane's normal PDF
• Q.55 (NDA (I) Mathematics) · MCQ · Lines and Planes: Point where a given line meets a plane PDF
• Q.56 (NDA (I) Mathematics) · MCQ · Lines and Planes: Distance from origin to plane through three unit points PDF
• Q.57 (NDA (I) Mathematics) · MCQ · Direction Cosines: l^2+m^2-n^2 for direction cosines satisfying two relations PDF
• Q.58 (NDA (I) Mathematics) · MCQ · Locus: Locus of midpoint of intercept of a line through a fixed point PDF
• Q.59 (NDA (I) Mathematics) · MCQ · Straight Lines: Line through a point perpendicular to xcosθ+ysinθ=9 PDF
• Q.60 (NDA (I) Mathematics) · MCQ · Straight Lines: Points on a line at distance 2 from a given point PDF
• Q.61 (NDA (I) Mathematics) · MCQ · Straight Lines: Area of a square with two sides on parallel lines PDF
• Q.62 (NDA (I) Mathematics) · MCQ · Centroid: Centroid of a triangle from a vertex and two side midpoints PDF
• Q.63 (NDA (I) Mathematics) · MCQ · Straight Lines: cotθ for an isosceles triangle with sides on given lines PDF
• Q.64 (NDA (I) Mathematics) · MCQ · Parabola: Statements on a point of y^2=8x with focal distance 8 PDF
• Q.65 (NDA (I) Mathematics) · MCQ · Ellipse: Eccentricity of ellipse when foci subtend 90° at minor axis end PDF
• Q.56 (NDA (II) Mathematics) · MCQ · Straight Lines: Type of quadrilateral from the lines of its diagonals PDF
• Q.57 (NDA (II) Mathematics) · MCQ · Ellipse: PQ+PR for a point on an ellipse and its foci PDF
• Q.58 (NDA (II) Mathematics) · MCQ · Coordinates: x+y for the fourth vertex of a parallelogram PDF
• Q.59 (NDA (II) Mathematics) · MCQ · Circles: Endpoints of a diameter of a circle in product form PDF
• Q.60 (NDA (II) Mathematics) · MCQ · Parabola: Angle PAQ for two points on a parabola and its vertex PDF
• Q.61 (NDA (II) Mathematics) · MCQ · Circles: Angle BAC for a triangle inscribed in x^2+y^2=100 PDF
• Q.62 (NDA (II) Mathematics) · MCQ · Circles: Coordinates of vertex A of the inscribed triangle PDF
• Q.63 (NDA (II) Mathematics) · MCQ · Coordinates: Fourth vertex D of an isosceles trapezium PDF
• Q.64 (NDA (II) Mathematics) · MCQ · Straight Lines: Intersection of the diagonals of the trapezium PDF
• Q.65 (NDA (II) Mathematics) · MCQ · Sphere: Diameter of a sphere from its general equation PDF
• Q.66 (NDA (II) Mathematics) · MCQ · Sphere: Plane on which the centre of the sphere lies PDF
• Q.67 (NDA (II) Mathematics) · MCQ · Lines and Planes: Direction ratios of the line of intersection of two planes PDF
• Q.68 (NDA (II) Mathematics) · MCQ · Direction Cosines: Expression in the direction cosines of that line PDF
• Q.69 (NDA (II) Mathematics) · MCQ · Lines and Planes: Direction ratios of a line given in symmetric plane form PDF
• Q.70 (NDA (II) Mathematics) · MCQ · Lines and Planes: Point of intersection of a line and a plane PDF

NDA2023

• Q.55 (NDA (I) Mathematics) · MCQ · Straight Lines: Diagonal through the origin of a quadrilateral formed by four lines (official answer: C) PDF
• Q.56 (NDA (I) Mathematics) · MCQ · Straight Lines: Equation of the other diagonal of the quadrilateral (official answer: D) PDF
• Q.57 (NDA (I) Mathematics) · MCQ · Ellipse: Sum of focal distances of a point on x^2 + 4y^2 = 1 (official answer: B) PDF
• Q.58 (NDA (I) Mathematics) · MCQ · Ellipse: Which points lie on a latus rectum of the ellipse (official answer: D) PDF
• Q.61 (NDA (I) Mathematics) · MCQ · Sphere: Sum u + v + w for a sphere with given diameter ends (official answer: A) PDF
• Q.62 (NDA (I) Mathematics) · MCQ · Sphere: Value of PA^2 + PB^2 for a point P on the sphere (official answer: B) PDF
• Q.63 (NDA (I) Mathematics) · MCQ · Direction Ratios: Find k for two lines inclined at a given angle (official answer: A) PDF
• Q.64 (NDA (I) Mathematics) · MCQ · Direction Ratios: Direction ratios of a line perpendicular to both lines (official answer: D) PDF
• Q.52 (NDA (II) Mathematics) · MCQ · Parabola: Length of latus rectum of that parabola (official answer: B) PDF
• Q.81 (NDA (II) Mathematics) · MCQ · Parabola: Directrix of y^2 = 4bx with b negative root of a quadratic (official answer: B) PDF
• Q.82 (NDA (II) Mathematics) · MCQ · Points and Coordinates: Nature of four given points (official answer: D) PDF
• Q.83 (NDA (II) Mathematics) · MCQ · Pair of Straight Lines: Point lying on a pair of lines under a given condition (official answer: B) PDF
• Q.84 (NDA (II) Mathematics) · MCQ · Circles: Midpoint of a chord of x^2 + y^2 = 25 (official answer: B) PDF
• Q.85 (NDA (II) Mathematics) · MCQ · Conic Sections: Values of k giving ellipse, hyperbola or circle (official answer: C) PDF
• Q.86 (NDA (II) Mathematics) · MCQ · Hyperbola: Statements on foci and eccentricity of a hyperbola in θ (official answer: C) PDF
• Q.87 (NDA (II) Mathematics) · MCQ · Circles: Statements about a circle touching the axes (official answer: B) PDF
• Q.88 (NDA (II) Mathematics) · MCQ · Straight Lines: Values of k making a line parallel to x + y = 17 (official answer: B) PDF
• Q.89 (NDA (II) Mathematics) · MCQ · Section Formula: Ratio in which x + y = 4 divides segment PQ (official answer: B) PDF
• Q.90 (NDA (II) Mathematics) · MCQ · Straight Lines: Sum of intercepts of a line in normal form (official answer: C) PDF
• Q.96 (NDA (II) Mathematics) · MCQ · 3D Lines: Points on a line at distance 2 from a given point (official answer: D) PDF
• Q.97 (NDA (II) Mathematics) · MCQ · Planes: Plane parallel to a given line (official answer: D) PDF
• Q.98 (NDA (II) Mathematics) · MCQ · 3D Lines: Angle between two lines given in symmetric form (official answer: D) PDF
• Q.99 (NDA (II) Mathematics) · MCQ · Sphere: Sphere concentric with a given sphere through the origin (official answer: D) PDF
• Q.100 (NDA (II) Mathematics) · MCQ · Section Formula: Sum of coordinates of a point on line AB with given z (official answer: A) PDF

NDA2022

• Q.81 (NDA (I) Mathematics) · MCQ · Straight Lines: Value of pq when three parametric points are collinear (official answer: C) PDF
• Q.82 (NDA (I) Mathematics) · MCQ · Straight Lines: Line through (1, -2) with equal intercepts (official answer: C) PDF
• Q.83 (NDA (I) Mathematics) · MCQ · Circles: Circle touching both axes and the line y = 2 (official answer: C) PDF
• Q.84 (NDA (I) Mathematics) · MCQ · Parabola: Parabola with focus (3, 0) and a given directrix (official answer: D) PDF
• Q.85 (NDA (I) Mathematics) · MCQ · Ellipse: Distance between foci of x^2 + 2y^2 = 1 (official answer: B) PDF
• Q.87 (NDA (I) Mathematics) · MCQ · Straight Lines: Sum of intercepts of a line through the intersection of two lines (official answer: A) PDF
• Q.88 (NDA (I) Mathematics) · MCQ · Straight Lines: Condition for two lines ax+by+c=0 and bx+ay+c=0 to be parallel (official answer: C) PDF
• Q.89 (NDA (I) Mathematics) · MCQ · Locus: Locus of midpoint of the intercept of x + y = p (official answer: A) PDF
• Q.90 (NDA (I) Mathematics) · MCQ · Locus: Locus of points equidistant from two given points (official answer: C) PDF
• Q.91 (NDA (I) Mathematics) · MCQ · Plane and Sphere: Value of k from a plane and sphere through its axis intercepts (official answer: B) PDF
• Q.92 (NDA (I) Mathematics) · MCQ · Plane and Sphere: Perpendicular distance from sphere centre to a plane (official answer: B) PDF
• Q.93 (NDA (I) Mathematics) · MCQ · 3D Lines: Line through origin and the centre of a sphere (official answer: D) PDF
• Q.94 (NDA (I) Mathematics) · MCQ · Plane and Sphere: Direction ratios of the normal to a plane (official answer: A) PDF
• Q.95 (NDA (I) Mathematics) · MCQ · Plane and Sphere: Sum of intercepts of a plane on the axes (official answer: B) PDF
• Q.56 (NDA (II) Mathematics) · MCQ · Straight Lines: Statements on a line through origin at 75 degrees (official answer: C) PDF
• Q.57 (NDA (II) Mathematics) · MCQ · Straight Lines: Line whose intercept segment has a given midpoint (official answer: B) PDF
• Q.58 (NDA (II) Mathematics) · MCQ · Straight Lines: Line through (8, 0) parallel to a side of an equilateral triangle (official answer: B) PDF
• Q.59 (NDA (II) Mathematics) · MCQ · Circles: Line containing the centre of a circle with given intercepts (official answer: A) PDF
• Q.60 (NDA (II) Mathematics) · MCQ · Ellipse: Eccentricity of an ellipse through two given points (official answer: A) PDF
• Q.61 (NDA (II) Mathematics) · MCQ · Parabola: Side of an equilateral triangle inscribed in a parabola (official answer: C) PDF
• Q.62 (NDA (II) Mathematics) · MCQ · 3D Coordinates: Whether four points in space form a rectangle (official answer: B) PDF
• Q.63 (NDA (II) Mathematics) · MCQ · Plane and Sphere: Statements about a given sphere's tangency and centre (official answer: B) PDF
• Q.64 (NDA (II) Mathematics) · MCQ · Plane and Sphere: Direction cosines of normal to a plane from intercepts (official answer: C) PDF
• Q.65 (NDA (II) Mathematics) · MCQ · Direction Cosines: Direction ratios of the y-axis and lines perpendicular to z-axis (official answer: C) PDF

NDA2021

• Q.56 (NDA (I) Mathematics) · MCQ · Circles: Radius of a circle from its general equation (official answer: D) PDF
• Q.57 (NDA (I) Mathematics) · MCQ · Section Formula: Fourth vertex of a parallelogram from three vertices (official answer: A) PDF
• Q.58 (NDA (I) Mathematics) · MCQ · Straight Lines: Condition for two lines to be perpendicular (official answer: C) PDF
• Q.59 (NDA (I) Mathematics) · MCQ · Straight Lines: Fixed point of Ax+2By+C=0 when A, B, C in AP (official answer: D) PDF
• Q.60 (NDA (I) Mathematics) · MCQ · Straight Lines: Line about which a point is reflected to a given image (official answer: B) PDF
• Q.61 (NDA (I) Mathematics) · MCQ · Straight Lines: Collinearity and quadrant of three parametric points (official answer: A) PDF
• Q.62 (NDA (I) Mathematics) · MCQ · Straight Lines: Acute angle between two given lines (official answer: B) PDF
• Q.63 (NDA (I) Mathematics) · MCQ · Straight Lines: Equation of diagonal BD of a square centred at origin (official answer: A) PDF
• Q.64 (NDA (I) Mathematics) · MCQ · Conic Sections: Eccentricity of hyperbola from parametric point (official answer: D) PDF
• Q.65 (NDA (I) Mathematics) · MCQ · Conic Sections: Eccentricity values for circle, parabola, ellipse (official answer: D) PDF
• Q.66 (NDA (I) Mathematics) · MCQ · Direction Cosines and Ratios: Angle between two lines with given direction ratios (official answer: B) PDF
• Q.67 (NDA (I) Mathematics) · MCQ · Direction Cosines and Ratios: Sum of squares of direction cosines of a line (official answer: B) PDF
• Q.68 (NDA (I) Mathematics) · MCQ · Direction Cosines and Ratios: Projection of a segment on the y-axis (official answer: C) PDF
• Q.69 (NDA (I) Mathematics) · MCQ · 3D Lines: Values of k for which three points are collinear (official answer: A) PDF
• Q.70 (NDA (I) Mathematics) · MCQ · 3D Planes: Foot of perpendicular from origin to x+y+z=3 (official answer: C) PDF
• Q.51 (NDA (II) Mathematics) · MCQ · Circles: Centre of a circle through three points (official answer: D) PDF
• Q.52 (NDA (II) Mathematics) · MCQ · Circles: Range of the radius of a circle through three points (official answer: D) PDF
• Q.53 (NDA (II) Mathematics) · MCQ · Coordinate Geometry Basics: Third vertex and area of an equilateral triangle (official answer: C) PDF
• Q.54 (NDA (II) Mathematics) · MCQ · Coordinate Geometry Basics: Difference of coordinates of the third vertex (official answer: D) PDF
• Q.55 (NDA (II) Mathematics) · MCQ · Straight Lines: Equation of diagonal BD of a parallelogram (official answer: C) PDF
• Q.56 (NDA (II) Mathematics) · MCQ · Coordinate Geometry Basics: Area of a parallelogram from vertices (official answer: C) PDF
• Q.57 (NDA (II) Mathematics) · MCQ · Straight Lines: Altitude from B to AC given side equations (official answer: D) PDF
• Q.58 (NDA (II) Mathematics) · MCQ · Straight Lines: Circumcentre of triangle formed by three lines (official answer: A) PDF
• Q.59 (NDA (II) Mathematics) · MCQ · Parabola: Number of parabolas with given latus rectum ends (official answer: B) PDF
• Q.60 (NDA (II) Mathematics) · MCQ · Parabola: Statements on origin and focus of such parabolas (official answer: C) PDF
• Q.61 (NDA (II) Mathematics) · MCQ · 3D Planes: Locus of points with z = 7 (official answer: D) PDF
• Q.62 (NDA (II) Mathematics) · MCQ · Direction Cosines and Ratios: Statements on direction ratios and cosines (official answer: C) PDF
• Q.63 (NDA (II) Mathematics) · MCQ · Section Formula: Ratio in which xy-plane divides a segment (official answer: C) PDF
• Q.64 (NDA (II) Mathematics) · MCQ · Sphere: Number of spheres of radius r touching the axes (official answer: C) PDF
• Q.65 (NDA (II) Mathematics) · MCQ · Direction Cosines and Ratios: cos 2a + cos 2b for angles in a cuboid (official answer: B) PDF

NDA2020

• Q.51 (NDA (I & II) Mathematics) · MCQ · Circles: Centre of a circle given in diameter form (official answer: C) PDF
• Q.52 (NDA (I & II) Mathematics) · MCQ · Straight Lines: Other diagonal of a square from one diagonal (official answer: C) PDF
• Q.53 (NDA (I & II) Mathematics) · MCQ · Ellipse: Sum of focal distances on 25x² + 16y² = 400 (official answer: B) PDF
• Q.54 (NDA (I & II) Mathematics) · MCQ · Straight Lines: k from the circumcentre of a triangle of lines (official answer: C) PDF
• Q.55 (NDA (I & II) Mathematics) · MCQ · Parabola: Length of a chord of y² = x through the vertex (official answer: B) PDF
• Q.56 (NDA (I & II) Mathematics) · MCQ · Collinearity: Condition for three points to be collinear (official answer: C) PDF
• Q.57 (NDA (I & II) Mathematics) · MCQ · Distance Formula: Length of BC from midpoints of AB and AC (official answer: B) PDF
• Q.58 (NDA (I & II) Mathematics) · MCQ · Straight Lines: k from the foot of a perpendicular (official answer: C) PDF
• Q.59 (NDA (I & II) Mathematics) · MCQ · Straight Lines: Obtuse angle between lines with given slopes (official answer: B) PDF
• Q.60 (NDA (I & II) Mathematics) · MCQ · Straight Lines: Area of a square from two parallel sides (official answer: C) PDF
• Q.61 (NDA (I & II) Mathematics) · MCQ · Sphere: Diameter of a sphere touching a given plane (official answer: D) PDF
• Q.62 (NDA (I & II) Mathematics) · MCQ · 3D Lines: Distance from a point to the x-axis line (official answer: B) PDF
• Q.63 (NDA (I & II) Mathematics) · MCQ · Direction Cosines: Sum of squares of direction cosines (official answer: D) PDF
• Q.64 (NDA (I & II) Mathematics) · MCQ · 3D Coordinate Geometry: Number of octants made by coordinate planes (official answer: C) PDF
• Q.65 (NDA (I & II) Mathematics) · MCQ · Planes: Plane parallel to xy-plane with z-intercept 5 (official answer: B) PDF

NDA2019

• Q.51 (NDA (I) Mathematics) · MCQ · Straight Lines: Perpendicular distance formulas for lines (official answer: D) PDF
• Q.52 (NDA (I) Mathematics) · MCQ · Circles: Circle on a chord of x² + y² = a² as diameter (official answer: B) PDF
• Q.53 (NDA (I) Mathematics) · MCQ · Ellipse: Sum of focal distances of a point on an ellipse (official answer: B) PDF
• Q.54 (NDA (I) Mathematics) · MCQ · Conic Sections: Identify the conic 2x² - 3y² - 6 = 0 (official answer: D) PDF
• Q.55 (NDA (I) Mathematics) · MCQ · Parabola: Intersection points of y² = 4ax and x² = 4ay (official answer: A) PDF
• Q.56 (NDA (I) Mathematics) · MCQ · Straight Lines: Find c when rectangle vertices lie on y = 2x + c (official answer: D) PDF
• Q.57 (NDA (I) Mathematics) · MCQ · Straight Lines: Value of b for three concurrent lines (official answer: C) PDF
• Q.58 (NDA (I) Mathematics) · MCQ · Straight Lines: Line perpendicular to y = x through (3, 2) (official answer: B) PDF
• Q.59 (NDA (I) Mathematics) · MCQ · Straight Lines: Type of triangle formed by three lines (official answer: A) PDF
• Q.60 (NDA (I) Mathematics) · MCQ · Circles: y-intercept cut by a given circle (official answer: A) PDF
• Q.61 (NDA (I) Mathematics) · MCQ · 3D Coordinate Geometry: Centroid of a triangle in space (official answer: B) PDF
• Q.62 (NDA (I) Mathematics) · MCQ · Sphere: Radius of a given sphere (official answer: C) PDF
• Q.63 (NDA (I) Mathematics) · MCQ · Planes: Plane through intersection of two planes and a point (official answer: A) PDF
• Q.64 (NDA (I) Mathematics) · MCQ · Planes: Distance between two parallel planes (official answer: A) PDF
• Q.65 (NDA (I) Mathematics) · MCQ · Direction Cosines: Direction cosines of the z-axis (official answer: D) PDF
• Q.51 (NDA (II) Mathematics) · MCQ · Straight Lines: When ax + by + c = 0 represents a line (official answer: D) PDF
• Q.52 (NDA (II) Mathematics) · MCQ · Straight Lines: Angle between two lines in normal-type form (official answer: D) PDF
• Q.53 (NDA (II) Mathematics) · MCQ · Distance Formula: Distance between two points in trigonometric form (official answer: A) PDF
• Q.54 (NDA (II) Mathematics) · MCQ · Triangles: Third vertex of an equilateral triangle (official answer: C) PDF
• Q.55 (NDA (II) Mathematics) · MCQ · Ellipse: Eccentricity from angle at a focus to minor axis ends (official answer: B) PDF
• Q.56 (NDA (II) Mathematics) · MCQ · Direction Cosines: Direction cosines of a line through a parametric point (official answer: A) PDF
• Q.57 (NDA (II) Mathematics) · MCQ · 3D Lines: Point lying on a given 3D line (official answer: B) PDF
• Q.58 (NDA (II) Mathematics) · MCQ · Lines and Planes: k for which a line lies on a plane (official answer: D) PDF
• Q.59 (NDA (II) Mathematics) · MCQ · 3D Lines: Angle between two possible positions of a line (official answer: B) PDF
• Q.60 (NDA (II) Mathematics) · MCQ · Collinearity: x and y for three collinear points in space (official answer: A) PDF

NDA2018

• Q.51 (NDA (I) Mathematics) · MCQ · Section Formula: Distance between internal and external division points (official answer: A) PDF
• Q.52 (NDA (I) Mathematics) · MCQ · Straight Lines: Angle between two lines in m and n (official answer: B) PDF
• Q.53 (NDA (I) Mathematics) · MCQ · Straight Lines: Line with given intercept and inclination 30° (official answer: D) PDF
• Q.54 (NDA (I) Mathematics) · MCQ · Straight Lines: Line through intersection parallel to a given line (official answer: C) PDF
• Q.55 (NDA (I) Mathematics) · MCQ · Straight Lines: Statements on perpendicular length from origin (official answer: C) PDF
• Q.56 (NDA (I) Mathematics) · MCQ · Ellipse: Ellipse with given vertices and foci (official answer: A) PDF
• Q.57 (NDA (I) Mathematics) · MCQ · Straight Lines: Line through (2,3) with y-intercept twice x-intercept (official answer: B) PDF
• Q.58 (NDA (I) Mathematics) · MCQ · 3D Lines: Foot of perpendicular from A on BC (official answer: C) PDF
• Q.59 (NDA (I) Mathematics) · MCQ · 3D Planes: Plane through three points (official answer: A) PDF
• Q.60 (NDA (I) Mathematics) · MCQ · Sphere: Locus of centroid for sphere through origin (official answer: C) PDF
• Q.61 (NDA (I) Mathematics) · MCQ · 3D Geometry Basics: Angle PRQ in a triangle in space (official answer: D) PDF
• Q.62 (NDA (I) Mathematics) · MCQ · Straight Lines: Perpendiculars from a line to two lines (official answer: C) PDF
• Q.63 (NDA (I) Mathematics) · MCQ · Straight Lines: Line whose intercept is divided by (2,3) in a ratio (official answer: D) PDF
• Q.64 (NDA (I) Mathematics) · MCQ · Straight Lines: Distance between two parallel lines (official answer: B) PDF
• Q.65 (NDA (I) Mathematics) · MCQ · Sphere: Equation of sphere with given centre and radius (official answer: A) PDF
• Q.51 (NDA (II) Mathematics) · MCQ · Circles: Circle with given diameter endpoints (official answer: D) PDF
• Q.52 (NDA (II) Mathematics) · MCQ · Conic Sections: Curve represented by a second-degree equation (official answer: A) PDF
• Q.53 (NDA (II) Mathematics) · MCQ · Straight Lines: Angle between two general lines (official answer: C) PDF
• Q.54 (NDA (II) Mathematics) · MCQ · Straight Lines: Statements on distance between parallel lines (official answer: D) PDF
• Q.55 (NDA (II) Mathematics) · MCQ · Straight Lines: Line through intersection parallel to a given line (official answer: A) PDF
• Q.56 (NDA (II) Mathematics) · MCQ · 3D Planes: Distance of a point from a plane (official answer: A) PDF
• Q.57 (NDA (II) Mathematics) · MCQ · 3D Geometry Basics: Values of m and n for a parallelogram in space (official answer: C) PDF
• Q.58 (NDA (II) Mathematics) · MCQ · 3D Lines: Equation of a line in space (official answer: D) PDF
• Q.59 (NDA (II) Mathematics) · MCQ · 3D Planes: Statements on angle and distance between planes (official answer: C) PDF
• Q.60 (NDA (II) Mathematics) · MCQ · Coordinate Geometry Basics: Statement pair on angle subtended at origin and cosine rule (official answer: D) PDF
• Q.61 (NDA (II) Mathematics) · MCQ · Coordinate Geometry Basics: Area of a triangle with given vertices (official answer: D) PDF
• Q.62 (NDA (II) Mathematics) · MCQ · Circles: Where the normal at the y-axis contact point meets the circle (official answer: B) PDF

NDA2017

• Q.51 (NDA (I) Mathematics) · MCQ · Coordinate Geometry Basics: Centroid from a vertex and two side midpoints (official answer: D) PDF
• Q.52 (NDA (I) Mathematics) · MCQ · Coordinate Geometry Basics: Incentre of a triangle with given vertices (official answer: D) PDF
• Q.53 (NDA (I) Mathematics) · MCQ · Coordinate Geometry Basics: Fourth vertex of a parallelogram (official answer: A) PDF
• Q.54 (NDA (I) Mathematics) · MCQ · Circles: Condition on r for two circles to meet at two points (official answer: A) PDF
• Q.55 (NDA (I) Mathematics) · MCQ · Circles: Circle through two points with centre on a line (official answer: B) PDF
• Q.56 (NDA (I) Mathematics) · MCQ · Section Formula: Ratio in which a point divides a segment (official answer: B) PDF
• Q.57 (NDA (I) Mathematics) · MCQ · Ellipse: Equation of ellipse with given focus and eccentricity (official answer: A) PDF
• Q.58 (NDA (I) Mathematics) · MCQ · Straight Lines: Line through a point parallel to a given line (official answer: A) PDF
• Q.59 (NDA (I) Mathematics) · MCQ · Straight Lines: Acute angle between two lines (official answer: A) PDF
• Q.60 (NDA (I) Mathematics) · MCQ · Coordinate Geometry Basics: Find x and y from the centroid of a triangle (official answer: A) PDF
• Q.61 (NDA (I) Mathematics) · MCQ · 3D Lines: Line with direction cosines (0,1,0) (official answer: B) PDF
• Q.62 (NDA (I) Mathematics) · MCQ · 3D Geometry Basics: Point equidistant from origin and three axis points (official answer: C) PDF
• Q.63 (NDA (I) Mathematics) · MCQ · 3D Geometry Basics: Nature of four given points in space (official answer: C) PDF
• Q.64 (NDA (I) Mathematics) · MCQ · 3D Lines: Point where a line meets the yz-plane (official answer: D) PDF
• Q.65 (NDA (I) Mathematics) · MCQ · 3D Lines: Condition for two lines to be perpendicular (official answer: C) PDF
• Q.41 (NDA (II) Mathematics) · MCQ · Coordinate Geometry Basics: Nature of three given points (official answer: D) PDF
• Q.42 (NDA (II) Mathematics) · MCQ · 3D Planes: Length of normal from origin to a plane (official answer: B) PDF
• Q.43 (NDA (II) Mathematics) · MCQ · Direction Cosines: Identities in direction angles of a vector (official answer: C) PDF
• Q.44 (NDA (II) Mathematics) · MCQ · Straight Lines: Compare angles between two pairs of lines (official answer: B) PDF
• Q.49 (NDA (II) Mathematics) · MCQ · Ellipse: Area enclosed by a path with constant focal-distance sum (official answer: B) PDF
• Q.50 (NDA (II) Mathematics) · MCQ · Straight Lines: Distance of a point from a line along a direction (official answer: D) PDF
• Q.52 (NDA (II) Mathematics) · MCQ · 3D Lines: Point where a line meets the XY-plane (official answer: A) PDF
• Q.53 (NDA (II) Mathematics) · MCQ · 3D Lines: Smaller x for given angle between two lines (official answer: B) PDF
• Q.54 (NDA (II) Mathematics) · MCQ · Ellipse: Position of a point relative to an ellipse (official answer: A) PDF
• Q.55 (NDA (II) Mathematics) · MCQ · Straight Lines: Line with given y-intercept and inclination 120° (official answer: A) PDF
• Q.56 (NDA (II) Mathematics) · MCQ · Straight Lines: Line through a point and intersection of two lines (official answer: B) PDF
• Q.57 (NDA (II) Mathematics) · MCQ · Ellipse: Ellipse with given eccentricity and latus rectum (official answer: B) PDF
• Q.58 (NDA (II) Mathematics) · MCQ · Circles: Circle through three given points (official answer: C) PDF
• Q.59 (NDA (II) Mathematics) · MCQ · Sphere: Locus of centre of sphere OABC through a fixed point (official answer: C) PDF
• Q.60 (NDA (II) Mathematics) · MCQ · 3D Planes: Plane through intersection of planes perpendicular to another (official answer: A) PDF

NDA2016

• Q.7 (NDA (I) Mathematics) · MCQ · Straight Lines: Area of triangle OPQ when (3,5) is midpoint of intercepts PQ (official answer: D) PDF
• Q.8 (NDA (I) Mathematics) · MCQ · Circles: Radius b of circle centred (0,b) touching line y=x−2 (official answer: A) PDF
• Q.12 (NDA (I) Mathematics) · MCQ · Curve Intersection: Intersection points of x|x|−1 and a piecewise curve (official answer: C) PDF
• Q.27 (NDA (I) Mathematics) · MCQ · Straight Lines: Area of triangle formed by y=3x, y=6x and y=9 (official answer: A) PDF
• Q.28 (NDA (I) Mathematics) · MCQ · Straight Lines: Centroid of triangle formed by y=3x, y=6x and y=9 (official answer: B) PDF
• Q.32 (NDA (I) Mathematics) · MCQ · Curve Intersection: Intersection points of y=|x−1| and |x|=2 (official answer: C) PDF
• Q.40 (NDA (I) Mathematics) · MCQ · Circles: Distance between centres of two given circles (official answer: A) PDF
• Q.41 (NDA (I) Mathematics) · MCQ · Circles: Condition on r for two circles to intersect at two points (official answer: D) PDF
• Q.42 (NDA (I) Mathematics) · MCQ · Straight Lines: Line through intersection of two lines parallel to x-axis (official answer: D) PDF
• Q.43 (NDA (I) Mathematics) · MCQ · Straight Lines: Line through intersection of two lines parallel to y-axis (official answer: B) PDF
• Q.58 (NDA (I) Mathematics) · MCQ · Coordinate Geometry Basics: Value of AC² for a parallelogram with given vertices (official answer: C) PDF
• Q.59 (NDA (I) Mathematics) · MCQ · Coordinate Geometry Basics: Intersection point of diagonals of a parallelogram (official answer: A) PDF
• Q.60 (NDA (I) Mathematics) · MCQ · Coordinate Geometry Basics: Area of a parallelogram with given vertices (official answer: D) PDF
• Q.65 (NDA (I) Mathematics) · MCQ · 3D Planes: Direction ratios of the line of intersection of two planes (official answer: A) PDF
• Q.66 (NDA (I) Mathematics) · MCQ · 3D Planes: Plane through intersection of two planes and a given point (official answer: B) PDF
• Q.67 (NDA (I) Mathematics) · MCQ · Sphere: Radius of sphere centred at origin touching the plane P (official answer: C) PDF
• Q.72 (NDA (I) Mathematics) · MCQ · Circles: Line on which centre of circle through origin and two points lies (official answer: A) PDF
• Q.73 (NDA (I) Mathematics) · MCQ · Circles: Sum of squares of intercepts of the circle on the axes (official answer: B) PDF
• Q.88 (NDA (I) Mathematics) · MCQ · Section Formula: Find k from midpoint condition with a−2b=7 (official answer: A) PDF
• Q.115 (NDA (I) Mathematics) · MCQ · Straight Lines: Acute angle between two given lines (official answer: A) PDF
• Q.51 (NDA (II) Mathematics) · MCQ · Coordinate Geometry Basics: Third vertex of an equilateral triangle (official answer: C) PDF
• Q.52 (NDA (II) Mathematics) · MCQ · Straight Lines: Perpendicular bisector of a segment (official answer: A) PDF
• Q.53 (NDA (II) Mathematics) · MCQ · Circles: Radius of circle with centre at intersection of two lines (official answer: D) PDF
• Q.54 (NDA (II) Mathematics) · MCQ · Hyperbola: Hyperbola with given latus rectum and eccentricity (official answer: A) PDF
• Q.55 (NDA (II) Mathematics) · MCQ · Straight Lines: Condition for (a,a) to lie between lines |x+y|=2 (official answer: C) PDF
• Q.56 (NDA (II) Mathematics) · MCQ · Straight Lines: Line through intersection point perpendicular to a given line (official answer: D) PDF
• Q.57 (NDA (II) Mathematics) · MCQ · Straight Lines: Conditions for a point at unit distance from a line (official answer: B) PDF
• Q.58 (NDA (II) Mathematics) · MCQ · Ellipse: Length of chord cut by a line on an ellipse (official answer: A) PDF
• Q.59 (NDA (II) Mathematics) · MCQ · Straight Lines: Foot of perpendicular from a point to a line (official answer: D) PDF
• Q.60 (NDA (II) Mathematics) · MCQ · Hyperbola: Eccentricity of a rectangular hyperbola (official answer: A) PDF
• Q.61 (NDA (II) Mathematics) · MCQ · 3D Planes: Image of a point in a plane and related statements (official answer: D) PDF
• Q.62 (NDA (II) Mathematics) · MCQ · 3D Lines: Direction ratios and cosines of segment PQ (official answer: C) PDF
• Q.63 (NDA (II) Mathematics) · MCQ · 3D Planes: Direction ratios of line of intersection of two planes (official answer: C) PDF
• Q.64 (NDA (II) Mathematics) · MCQ · 3D Lines: Equation of a line through a point parallel to two planes (official answer: A) PDF
• Q.87 (NDA (II) Mathematics) · MCQ · Straight Lines: Shortest distance from that point to the line (official answer: C) PDF

Other Mathematics topics

• Algebra PYQs
• Matrices and Determinants PYQs
• Trigonometry PYQs
• Differential Calculus PYQs
• Integral Calculus and Differential Equations PYQs
• Vector Algebra PYQs
• Statistics and Probability PYQs

FAQ

How many Analytical Geometry (2D and 3D) questions come in NDA?

In the official papers we tagged: 29 in 2026 (2 papers), 30 in 2025 (2 papers), 30 in 2024 (2 papers), 24 in 2023 (2 papers), 24 in 2022 (2 papers), 30 in 2021 (2 papers), 15 in 2020 (1 paper), 25 in 2019 (2 papers), 27 in 2018 (2 papers), 30 in 2017 (2 papers) and 35 in 2016 (2 papers). That is 299 questions in all, about 12% of Mathematics.

Which Analytical Geometry (2D and 3D) topics repeat in NDA?

Asked in the most papers: Straight Lines, Circles, Ellipse. The concept table lists every one with its count.

Are these official NDA questions?

Yes. Every question is from an official NDA paper hosted on our year pages. The one-line summaries are ours; open the PDF linked beside each question for the full text.