Mathematics · Quantitative Aptitude

Geometry and Coordinate Geometry

84 Questions

Geometry questions test your knowledge of triangle properties, congruence, similarity, and quadrilaterals. They form a significant portion of the mathematics section in competitive exams. Practicing these builds spatial reasoning and theorem application skills.

triangle similaritycongruence rulesquadrilateral propertiesright angle properties

Geometry and Coordinate Geometry Questions

Multiple choice maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

In the trapezium PQRS, PQ is  parallel to RS and the diagonals intersect at O. If $OP.SR= m(OR . PQ)$, then the value of m is :

  1. $\dfrac{1}{4}$
  2. $\dfrac{1}{3}$
  3. $1$
  4. $\dfrac{1}{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In Trapezium PQRS, $\Delta OPQ$ is similar to $\Delta OSR$ by AA similarity.
$\therefore \dfrac{OP}{OR}=\dfrac{OS}{OQ}=\dfrac{PQ}{SR}$
$\therefore OP.SR=OR.PQ$
Hence, $m=1$

Multiple choice

A rectangular garden has a length of 20 meters and a width of 15 meters. If a path of uniform width x meters is constructed around the garden, what is the area of the path?

  1. 350 + 100x square meters

  2. 400 + 100x square meters

  3. 450 + 100x square meters

  4. 500 + 100x square meters
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The area of the path can be calculated by subtracting the area of the garden from the area of the larger rectangle formed by the garden and the path. The area of the garden is 20 * 15 = 300 square meters. The length of the larger rectangle is 20 + 2x meters, and the width is 15 + 2x meters. Therefore, the area of the larger rectangle is (20 + 2x) * (15 + 2x) = 400 + 100x + 4x^2. Subtracting the area of the garden, we get the area of the path: 400 + 100x + 4x^2 - 300 = 400 + 100x square meters.

Multiple choice

The ancient Indian concept of 'Shulba Sutras' is significant in which field of modern technology?

  1. Architecture

  2. Astronomy

  3. Medicine

  4. Metallurgy
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The 'Shulba Sutras' contain geometric rules and formulas that were essential for constructing altars and temples in ancient India. These concepts are now used in architecture for designing buildings and structures with precise dimensions and alignments.

Multiple choice

What is the equation of an ellipsoid?

  1. $x^2/a^2 + y^2/b^2 + z^2/c^2 = 1$
  2. $x^2 + y^2 + z^2 = a^2$
  3. $x^2/a^2 + y^2/b^2 - z^2/c^2 = 1$
  4. $x^2 + y^2 - z^2 = a^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The equation of an ellipsoid is $x^2/a^2 + y^2/b^2 + z^2/c^2 = 1$, where $a$, $b$, and $c$ are the lengths of the semi-major axis, semi-minor axis, and semi-vertical axis, respectively.

Multiple choice

The Sulba Sutras are a collection of ancient Indian texts that deal with:

  1. Geometry

  2. Arithmetic

  3. Algebra

  4. Trigonometry
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Sulba Sutras are a collection of ancient Indian texts that deal with geometry, particularly the construction of altars and other religious structures.

Multiple choice

What is the angle between two great circles?

  1. The angle between the two planes that contain the great circles

  2. The angle between the two lines that intersect the great circles at right angles

  3. The angle between the two lines that are tangent to the great circles at the same point

  4. The angle between the two lines that are parallel to the great circles at the same point
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The angle between two great circles is the angle between the two planes that contain the great circles.

Multiple choice

What is the angle between two small circles?

  1. The angle between the two planes that contain the small circles

  2. The angle between the two lines that intersect the small circles at right angles

  3. The angle between the two lines that are tangent to the small circles at the same point

  4. The angle between the two lines that are parallel to the small circles at the same point
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The angle between two small circles is the angle between the two planes that contain the small circles.

Multiple choice

What is the role of geometry in our understanding of the physical world?

  1. Geometry provides us with a way to measure and describe the physical world.

  2. Geometry provides us with a way to understand the structure of the physical world.

  3. Geometry provides us with a way to predict the behavior of objects in the physical world.

  4. All of the above.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Geometry provides us with a way to measure and describe the physical world, understand its structure, and predict the behavior of objects in it.

Multiple choice

What is the center of mass of a triangle?

  1. The center of the triangle

  2. The midpoint of a side of the triangle

  3. The intersection of the medians of the triangle

  4. The vertex of the triangle
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The center of mass of a triangle is the intersection of the medians of the triangle. This is because the mass of the triangle is evenly distributed throughout its area.