Geometry Mock Test | Quantitative Aptitude | RRB NTPC

Q1. Find the equation of the circle passing through the origin and having intercepts of lengths 3 and 4 on the x and y axes respectively.

x^2 + y^2 - 3x - 4y = 0 x^2 + y^2 + 3x + 4y = 0 x^2 + y^2 - 4x - 3y = 0 x^2 + y^2 + 4x + 3y = 0

Q2. A polygon with five sides is called a:

Quadrilateral Hexagon Pentagon Octagon

Q3. Two circles are tangent externally. If the ratio of their radii is 2:3, what is the ratio of the distance between their centers to the sum of their radii?

1:1 2:3 3:2 5:5

Q4. If a figure is reflected, is it similar to the original figure?

Yes No Only if it's a reflection across the y-axis Cannot be determined

Q5. Which geometric shape is commonly used in cartography to represent administrative boundaries like states or countries?

Circles Triangles Polygons Ellipses

Q6. The grade of the geometric product of a vector and a bivector in 3D Euclidean space can be:

Only 1 Only 3 1 or 3 1, 2, or 3

Q7. The area of a circle is 100 pi sq cm. What is its circumference?

10 pi cm 20 pi cm 100 pi cm 200 pi cm

Q8. In triangle ABC, if angle A < angle B < angle C, then the sides opposite to these angles will satisfy:

a < b < c a > b > c b < a < c c < b < a

Q9. In Geometric Control Theory, which concept is used to study the set of states reachable by the system?

Transfer function Pole-zero plot Controllability distribution Stability margin

Q10. Which type of kernel is commonly used in SVMs to perform non-linear separation?

Linear Kernel Polynomial Kernel Radial Basis Function (RBF) Kernel Sigmoid Kernel

Q11. Which shape is formed by joining three points that are not in a straight line?

Square Circle Triangle Line Segment

Q12. What is the Jordan Curve Theorem related to?

The classification of surfaces. The property of being connected. The topological properties of simple closed curves in the plane. The concept of compactness.

Q13. What geometric concept is used to measure the angular separation between two celestial objects?

Parallax Light-year Angular Diameter Arcsecond

Q14. 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.

Q15. The sum of the interior angles of a polygon is 1080 degrees. How many sides does it have?

6 7 8 9

Q16. What is the geometric interpretation of a point at infinity in projective geometry?

A point that is infinitely far from the origin A point where parallel lines intersect A point that does not exist in Euclidean geometry A point on a line that is infinitely long

Q17. What is the role of the metric tensor in describing geometric structures in physics?

It defines the angles between vectors. It determines the lengths of vectors and the angles between them. It specifies the dimensionality of the space. It describes the rate of change of physical quantities.

Q18. A surveyor is measuring the height of a building. From a point on the ground 50 meters away from the base, the angle of elevation to the top of the building is 45 degrees. From another point 100 meters away, the angle of elevation is 30 degrees. What is the height of the building?

50 meters 57.7 meters 70.7 meters 86.6 meters

Q19. The geometric relationship between stress and strain in materials, often represented by Hooke's Law, describes a:

Non-linear relationship Linear relationship Exponential relationship Logarithmic relationship

Q20. A group with a solvable word problem is also known as:

A hyperbolic group A Tarski monster A solvable group A recursive group

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