Solution:

Given, the equations of two regression lines are:

xy=6 and x+2y=10

Let us find the correlation coefficient between x and y.

Step 1: Find the mean of x and y

Let xi and yi be the values of x and y respectively.

n = 2 (since we have two pairs of values)

x1 = 1, y1 = 6

x2 = 2, y2 = 3

Mean of x = (x1 + x2)/n = (1+2)/2 = 1.5

Mean of y = (y1 + y2)/n = (6+3)/2 = 4.5

Step 2: Find the standard deviation of x and y

Using the formula,

σx = √[Σ(xi - x̄)²/n]

σy = √[Σ(yi - ȳ)²/n]

We get,

σx = √[(1-1.5)² + (2-1.5)²]/2 = 0.5

σy = √[(6-4.5)² + (3-4.5)²]/2 = 1.5/√2

Step 3: Find the correlation coefficient

Using the formula,

r = Σ[(xi - x̄)/σx][(yi - ȳ)/σy]/n

We get,

r = [(1-1.5)/0.5][(6-4.5)/(1.5/√2)] + [(2-1.5)/0.5][(3-4.5)/(1.5/√2)]/2

r = [-1/√2 + 3/√2]/2

r = 1/√2

Hence, the value of correlation between x and y is option (d) 1/√2.

Explanation:

Regression lines are lines that represent the relationship between two variables x and y. Correlation measures the strength and direction of the linear relationship between two variables. The correlation coefficient ranges from -1 to 1. If the correlation coefficient is positive, it indicates a positive linear relationship between the variables, and if it is negative, it indicates a negative linear relationship between the variables. A correlation coefficient of 0 indicates no linear relationship between the variables.

To find the correlation coefficient between x and y, we first find the mean of x and y, and then we find the standard deviation of x and y. Using these values, we can calculate the correlation coefficient using the formula r = Σ[(xi - x̄)/σx][(yi - ȳ)/σy]/n.

B