Mock Test

Exam: SSC CGL Subject: Quantitative Aptitude Topic: Geometry

Total Questions: 20

Q1. The diagonal of a rhombus is 12 cm and 30 cm. What is the perimeter of the rhombus?

34 cm 36 cm 68 cm 72 cm
Q2. The study of non-Euclidean geometries raised philosophical questions about:

The absolute truth of Euclidean geometry The nature of perception The possibility of multiple realities All of the above
Q3. The classification of geometric transformations and the Erlangen Program were significant contributions by which mathematician?

David Hilbert Henri Poincaré Felix Klein Sophus Lie
Q4. What geometric shape is a Toblerone chocolate bar typically?

Cube Cylinder Prism Pyramid
Q5. The Rod-and-Frame illusion demonstrates how the surrounding geometric frame can influence our perception of the orientation of an object, affecting:

Brightness Hue Verticality Saturation
Q6. The indifference curves for a Giffen good are characterized by being:

Convex to the origin. Concave to the origin. L-shaped. Straight lines.
Q7. The 'chaos game' is a method for generating fractals. Which of the following is a key characteristic of this method?

It uses deterministic rules for generating points. It relies on the random selection of vertices and copying transformations. It always converges to a single point. It involves complex algebraic equations.
Q8. A dome's structural integrity, particularly in ancient Roman architecture, was often a consequence of its form approximating a hemisphere. What geometric property of a hemisphere ensures that compressive forces are efficiently distributed?

Its planar symmetry Its lack of edges Its inherent resistance to tensile stress Its ability to generate a constant radius of curvature
Q9. Which geometric term describes the point where two lines meet?

Line segment Ray Vertex Angle
Q10. What geometrical shape describes the outline of a shadow cast by a celestial body?

Circle Ellipse Cone Square
Q11. What is the genus of a torus?

0 1 2 3
Q12. What is the value of $\cos 0^\circ$?

$0$ $1$ $\frac{1}{2}$ $\frac{\sqrt{3}}{2}$
Q13. To construct a tangent to a circle from an external point, you first find the midpoint of the line segment joining the external point to the center of the circle. What is the next step?

Draw a chord through the external point. Draw a circle with the midpoint as the center and radius equal to half the distance. Draw a perpendicular from the external point to the circle. Draw a secant line from the external point.
Q14. What is the value of $\sin^2 \theta + \cos^2 \theta$?

$0$ $1$ $2$ $\sin \theta \cos \theta$
Q15. The development of analytic geometry by Descartes and Fermat allowed for the translation of geometric problems into algebraic ones, which had philosophical implications for:

The separation of mind and matter The unity of knowledge and the power of abstract reasoning The limitations of mathematical representation The subjective nature of spatial perception
Q16. During the Islamic Golden Age, mathematicians preserved and expanded upon Greek geometric knowledge. Al-Khwarizmi's work laid foundations for algebra. Which geometric problem was central to his algebraic solutions?

Squaring the circle Doubling the cube Solving quadratic equations Finding the area of a triangle
Q17. The bond angle in NH3 is approximately 107 degrees because the lone pair on nitrogen exerts greater repulsion than bonding pairs, causing a compression of the H-N-H angles. This is a direct application of:

Hybridization Theory Molecular Orbital Theory VSEPR Theory Coulomb's Law
Q18. The sum of the exterior angles of any convex polygon is:

180 degrees 360 degrees 540 degrees It depends on the number of sides
Q19. Which molecule has a tetrahedral geometry?

NH₃ H₂O CH₄ CO₂
Q20. A circle passes through the points (0, 0), (a, 0), and (0, b). What is the equation of the circle?

x^2 + y^2 - ax - by = 0 x^2 + y^2 + ax + by = 0 x^2 + y^2 - ax + by = 0 x^2 + y^2 + ax - by = 0

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