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GRE Geometry: Circles — practice questions

Explore 22 free Geometry: Circles questions in GRE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Geometry: Circles questions and exercises with answers

Showing questions 1–22 of 22.

Which of the following is an impossible event when a fair die is thrown once?Read the answer and worked solution →A die is thrown once. What is the probability of getting a number greater than 4?Read the answer and worked solution →Events $A$ and $B$ are mutually exclusive with $P(A) = 0.4$ and $P(B) = 0.3$. Find $P(A \cup B)$.Read the answer and worked solution →Which of the following is NOT a measure of central tendency?Read the answer and worked solution →The mean of $n$ observations $x_1, x_2, \ldots, x_n$ is:Read the answer and worked solution →Range of a data set is defined as:Read the answer and worked solution →Batsman A scored 30, 91, 0, 64, 42, 80, 30, 5, 117, 71. What is the range of his scores?Read the answer and worked solution →A die is rolled. What is the probability of getting a number GREATER THAN 6?Read the answer and worked solution →As per your syllabus, what is the formula for the AREA of a TRIANGLE with base b and corresponding height h?Read the answer and worked solution →As per your syllabus, an equilateral triangle with side a has its height equal to which expression?Read the answer and worked solution →As per your syllabus, what is the area of an EQUILATERAL triangle with side a?Read the answer and worked solution →As per your syllabus, what is the formula for the AREA of a TRIANGLE with base b and corresponding height h?Read the answer and worked solution →Which of the following is an impossible event when a fair die is thrown once?Read the answer and worked solution →A die is thrown once. What is the probability of getting a number greater than 4?Read the answer and worked solution →Which of the following is NOT a measure of central tendency?Read the answer and worked solution →The mean of $n$ observations $x_1, x_2, \ldots, x_n$ is:Read the answer and worked solution →Range of a data set is defined as:Read the answer and worked solution →Batsman A scored 30, 91, 0, 64, 42, 80, 30, 5, 117, 71. What is the range of his scores?Read the answer and worked solution →Events $A$ and $B$ are mutually exclusive with $P(A) = 0.4$ and $P(B) = 0.3$. Find $P(A \cup B)$.Read the answer and worked solution →As per your syllabus, an equilateral triangle with side a has its height equal to which expression?Read the answer and worked solution →As per your syllabus, what is the area of an EQUILATERAL triangle with side a?Read the answer and worked solution →A die is rolled. What is the probability of getting a number GREATER THAN 6?Read the answer and worked solution →

Worked practice questions

Which of the following is an impossible event when a fair die is thrown once?

  1. Getting a number less than 7
  2. Getting an even number
  3. Getting a prime number
  4. Getting the number 8
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Correct answer: D. Getting the number 8

A die has faces numbered 1 to 6 only, so 8 cannot occur. **Therefore the event is impossible and its probability is 0.**

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A die is thrown once. What is the probability of getting a number greater than 4?

  1. $\frac{1}{6}$
  2. $\frac{1}{3}$
  3. $\frac{1}{2}$
  4. $\frac{2}{3}$
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Correct answer: B. $\frac{1}{3}$

The possible outcomes are $1,2,3,4,5,6$. Numbers greater than 4 are 5 and 6, so there are 2 favourable outcomes out of 6 total outcomes. **Thus $P=\frac{2}{6}=\frac{1}{3}$.**

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Events $A$ and $B$ are mutually exclusive with $P(A) = 0.4$ and $P(B) = 0.3$. Find $P(A \cup B)$.

  1. $0.12$
  2. $0.70$
  3. $1.00$
  4. $0.58$
Show answer and solution

Correct answer: B. $0.70$

Mutually exclusive events cannot occur together, so $P(A \cap B) = 0$. The general addition rule simplifies: $P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.4 + 0.3 - 0 = 0.7$. Option A ($0.12$) is the product $P(A) \cdot P(B)$, which is the joint probability for *independent* events, not mutually exclusive ones. **The distinction matters:** mutually exclusive means $P(A \cap B) = 0$ independent means $P(A \cap B) = P(A) \cdot P(B)$. These two assumptions cannot both hold unless one event has zero probability.

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More Mathematics topics

MathematicsStatistics and ProbabilityArithmetic ProgressionSets and RelationsQuadratic EquationsReal Numbers and PolynomialsUnit 1A1: Relations, Functions and GraphsUnit 6B: Definite Integration & Riemann Sums