Geometry Mock Test | Quantitative Aptitude | RRB NTPC

Q1. The development of 'differential geometry' in the 19th century, spearheaded by Gauss and Riemann, allowed for the rigorous study of:

The properties of abstract algebraic structures The local and global properties of curved surfaces and spaces The geometrical properties of points and lines The combinatorial properties of shapes

Q2. In modeling the spread of innovations or ideas, the 'epidemic threshold' concept, borrowed from epidemiology, relates to the critical density of connections in a social network above which an innovation will spread widely. This is a property of the network's geometric structure, specifically its:

Average path length Diameter Degree distribution and clustering coefficient Number of cliques

Q3. Which of the following statements is true for all three types of geometry (Euclidean, Spherical, Hyperbolic)?

The sum of angles in a triangle is always 180 degrees. Through a point not on a line, there is exactly one parallel line. The shortest distance between two points is a straight line (or geodesic). Parallel lines never meet.

Q4. Lines that never intersect are called:

Intersecting lines Perpendicular lines Parallel lines Coincident lines

Q5. Which of the following is a closed geometric shape with straight sides?

Circle Ellipse Polygon Parabola

Q6. The parametric equations of a curve are x = 2cos(t) and y = 3sin(t). What is the Cartesian equation of this curve?

x^2/4 + y^2/9 = 1 x^2/9 + y^2/4 = 1 x^2 + y^2 = 1 9x^2 + 4y^2 = 36

Q7. A square is rotated by 45 degrees about its center. What is the area of the overlapping region between the original square and the rotated square?

Half the area of the square Three-quarters the area of the square One-quarter the area of the square Two-thirds the area of the square

Q8. The Frobenius theorem is important for determining when a distribution is:

Controllable Observable Integrable to a foliation Stable

Q9. What is the area of a trapezoid with parallel sides of length 8 cm and 12 cm, and a height of 5 cm?

40 sq cm 50 sq cm 100 sq cm 120 sq cm

Q10. What is the surface area of a sphere with radius 'r'?

4*pi*r^2 2*pi*r^2 4/3*pi*r^3 pi*r^2

Q11. What is the primary role of a 'control cage' in certain geometric modeling systems?

To define the material properties of a surface To influence the shape of a deformable surface or object To specify the rendering order of objects To store the vertex normals

Q12. What is the next shape in the pattern: Circle, Square, Circle, Square, ...?

Circle Square Triangle Rectangle

Q13. A ship is sailing on a Mercator projection map. The shortest distance between two points on the Earth's surface (a great circle route) is represented as a straight line on the map if and only if the route is:

Along the equator Along a meridian Along the equator or a meridian Any straight line on the map

Q14. What is the probability that a random chord of a circle is longer than the side of an inscribed square?

1/2 1/3 1/4 2/3

Q15. When analyzing the geometric relationship between points, what does a 'k-nearest neighbors' (k-NN) approach focus on?

The global distribution of all points. The characteristics of the k closest data points to a given point. The average distance of all points from the centroid. The variance of the dataset.

Q16. How many lines of symmetry does an equilateral triangle have?

0 1 2 3

Q17. In hyperbolic geometry, how many lines parallel to a given line can be drawn through a point not on the line?

Zero One Two Infinitely many

Q18. The Ricci tensor in general relativity is related to which aspect of spacetime?

Conformal symmetry Volume distortion Tidal forces Rotation

Q19. What geometric shape is the apparent path of the Sun across the sky during a day?

Circle Ellipse Arc Spiral

Q20. The study of shapes, sizes, positions of figures, and properties of space is known as:

Algebra Arithmetic Geometry Calculus

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