GR 12 GENERAL MATHEMATICS M3
10 To find the number of ways of arranging 10 people in a circular table, we use
A. $(10-1)!$
B. $10!/(10-1)!$
C. $10!$
D. $1/2(10-1)!$
11 The regression line of $Y$ on $x$ is given as $Y=a+bX$. What does the '$b$' represent?
A. $Y$-intercept
B. Slope of the line
C. Dependent variable
D. Independent variable
Answer (2)
For question 10, the number of ways to arrange 10 people in a circular table is given by ( 10 − 1 )! , so the answer is A. For question 11, the coefficient 'b' in the regression line Y = a + b X represents the slope of the line, making the answer B.
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Question 10: The number of ways to arrange 10 people in a circular table is ( 10 − 1 )! . The answer is A .
Question 11: In the regression line Y = a + b X , 'b' represents the slope of the line. The answer is B .
Explanation
Problem Overview The problem consists of two independent multiple-choice questions. We will address each question separately.
Question 10 Solution For question 10, we need to determine the formula for arranging 10 people around a circular table. The number of ways to arrange n distinct objects in a circle is ( n − 1 )! . In this case, n = 10 , so the number of ways is ( 10 − 1 )! = 9 ! . Therefore, the correct answer is A.
Question 11 Solution For question 11, we are given the regression line equation Y = a + b X . We need to identify what 'b' represents. In this equation, 'a' represents the Y-intercept, and 'b' represents the slope of the line. Therefore, the correct answer is B.
Final Answer The answer to question 10 is A, and the answer to question 11 is B.
Examples
Circular permutations are useful in scenarios like seating arrangements for meetings or planning social events where the order matters but the starting point is irrelevant. Regression lines are used in statistical analysis to model the relationship between two variables, such as predicting sales based on advertising expenditure. Understanding these concepts helps in making informed decisions in various real-world situations.
