Geometry Mock Test | Quantitative Aptitude | SSC CGL

Q1. The division of a musical phrase into sections can be seen as a form of:

Symmetry Asymmetry Fractal division Random distribution

Q2. The rhythmic complexity of a musical piece can be analyzed using concepts from information theory and fractal geometry. If a composer uses nested rhythmic patterns with varying subdivision factors, the overall rhythmic structure might exhibit fractal dimensions. If a primary beat is divided into 3 equal parts, and each of those parts is divided into 2 equal parts, what is the effective subdivision factor of the smallest unit within the primary beat?

1/3 1/2 1/6 1/5

Q3. Consider the refraction of light at the interface between two media with refractive indices n1 and n2. If a light ray strikes the interface at an angle of incidence θ1, and refracts at an angle θ2, Snell's law states n1 sin(θ1) = n2 sin(θ2). What geometric quantity does sin(θ1)/sin(θ2) represent?

The tangent of the angle of deviation The secant of the critical angle The ratio of the speeds of light in the two media The cosine of the angle of reflection

Q4. Euclid's seminal work, 'Elements,' organized geometric knowledge based on:

Empirical observation and experimentation Logical deduction from axioms and postulates Practical applications in architecture Historical development of geometric ideas

Q5. In a simple polygon, what is the minimum number of diagonals required to triangulate it?

n-1 n-2 n n+1

Q6. If the medians of a triangle are in the ratio 1:2:3, then the triangle is:

Equilateral Isosceles Right-angled Obtuse-angled

Q7. The theorem that relates the moment of inertia of a body about an axis through its centroid to the moment of inertia about a parallel axis is:

Pythagorean Theorem Parallel Axis Theorem Perpendicular Axis Theorem Euler's Theorem

Q8. What is the perimeter of a square whose area is 36 sq cm?

12 cm 18 cm 24 cm 36 cm

Q9. To construct an angle of 120 degrees, you can combine two angles of:

45 and 75 degrees 30 and 90 degrees 60 and 60 degrees 90 and 30 degrees

Q10. If a triangle has sides of length 7 cm, 24 cm, and 25 cm, is it a right-angled triangle?

Yes No Cannot be determined Only if it's isosceles

Q11. The area of a circle is 154 sq cm. Find its circumference.

44 cm 22 cm 88 cm 154 cm

Q12. The design of amphitheaters, with their tiered seating arranged in a semi-circular or elliptical form, is a practical application of:

Concentric circles Hyperbolas Ellipses and circular segments Spiral curves

Q13. The concept of the incircle and circumcircle of a triangle was extensively studied by:

Pythagoras Euclid Archimedes Thales

Q14. The integrability condition for the Frenet-Serret formulas involves the relationship between:

Curvature and Torsion Tangent and Normal vectors Principal curvatures Gaussian and Mean curvatures

Q15. What is the radius of the circle given by the equation x^2 + y^2 - 6x + 8y - 11 = 0?

4 5 6 7

Q16. In a right-angled triangle ABC, with the right angle at B, if AB = 8 and BC = 15, what is the length of AC?

17 18 19 20

Q17. When fitting tiles to a floor or wall, understanding the area and how shapes tessellate is crucial to minimize waste. This involves the geometric concept of:

Mensuration Tessellations Symmetry Proportions

Q18. Each interior angle of a regular polygon is 108 degrees. How many sides does the polygon have?

5 6 7 8

Q19. The volume of a cuboid is 720 cubic cm. If its length is 12 cm and width is 6 cm, find its height.

10 cm 8 cm 12 cm 6 cm

Q20. In macroeconomic equilibrium, the intersection of the aggregate demand (AD) and aggregate supply (AS) curves represents:

The inflation rate and unemployment rate. The equilibrium price level and the equilibrium real GDP. The optimal level of government spending. The rate of economic growth.

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