Q. In a circle, if an angle subtended by an arc at the center is 80 degrees, what is the angle subtended by the same arc at any point on the remaining part of the circle? (2023)
A.
40 degrees
B.
80 degrees
C.
60 degrees
D.
20 degrees
Solution
The angle subtended at the circumference is half the angle subtended at the center. Therefore, it is 80/2 = 40 degrees.
Q. In a circle, if an angle subtended by an arc at the center is 80 degrees, what is the angle subtended by the same arc at any point on the circumference?
A.
20 degrees
B.
40 degrees
C.
80 degrees
D.
160 degrees
Solution
The angle subtended at the circumference is half the angle subtended at the center. Therefore, the angle at the circumference is 80/2 = 40 degrees.
Q. In a circle, if the angle subtended by an arc at the center is 60 degrees, what is the angle subtended at any point on the remaining part of the circle?
A.
30 degrees
B.
60 degrees
C.
90 degrees
D.
120 degrees
Solution
The angle subtended at the circumference is half of that at the center, so it is 30 degrees.
Q. In a parallelogram, which of the following properties is NOT true?
A.
Opposite angles are equal.
B.
Adjacent angles are supplementary.
C.
All sides are equal.
D.
Diagonals bisect each other.
Solution
In a parallelogram, while opposite angles are equal and diagonals bisect each other, all sides being equal is a property of a rhombus, not all parallelograms.
Q. In a quadrilateral ABCD, if angle A is 90 degrees and angle B is 45 degrees, what can be inferred about the other angles? (2023)
A.
Angle C is 45 degrees and angle D is 90 degrees.
B.
Angle C is 90 degrees and angle D is 45 degrees.
C.
Angle C is 135 degrees and angle D is 135 degrees.
D.
Angle C is 180 degrees and angle D is 0 degrees.
Solution
In a quadrilateral, the sum of the angles is 360 degrees. Given angle A (90) and angle B (45), angle C + angle D = 360 - (90 + 45) = 225 degrees. The only option that fits is angle C = 135 degrees and angle D = 135 degrees.
Correct Answer:
C
— Angle C is 135 degrees and angle D is 135 degrees.
Geometry & Mensuration are crucial topics in mathematics that play a significant role in various school and competitive exams. Mastering these concepts not only enhances your problem-solving skills but also boosts your confidence during exams. Practicing MCQs and objective questions helps you familiarize yourself with the exam pattern, making it easier to tackle important questions effectively.
What You Will Practise Here
Understanding basic geometric shapes and their properties
Calculating area and perimeter of various figures
Exploring volume and surface area of 3D shapes
Applying the Pythagorean theorem in problem-solving
Utilizing important formulas for quick calculations
Interpreting diagrams and visual representations
Solving real-life problems using mensuration concepts
Exam Relevance
Geometry & Mensuration are integral parts of the mathematics syllabus for CBSE, State Boards, NEET, and JEE. These topics frequently appear in the form of objective questions and MCQs, often focusing on the application of formulas and theorems. Students can expect questions that require both theoretical understanding and practical application, making it essential to practice regularly to excel in these exams.
Common Mistakes Students Make
Confusing the formulas for area and perimeter
Overlooking units of measurement in calculations
Misinterpreting diagrams, leading to incorrect answers
Neglecting to apply the Pythagorean theorem correctly
Failing to check for the conditions of geometric properties
FAQs
Question: What are the key formulas I should remember for Geometry & Mensuration? Answer: Important formulas include area and perimeter for 2D shapes, volume and surface area for 3D shapes, and the Pythagorean theorem for right-angled triangles.
Question: How can I improve my speed in solving Geometry & Mensuration MCQs? Answer: Regular practice of MCQs and timed quizzes can help improve your speed and accuracy in solving these types of questions.
Start solving practice MCQs today to strengthen your understanding of Geometry & Mensuration. With consistent effort, you can master these topics and achieve your desired scores in exams!
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