HSC Commerce (Marathi Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Obtain the trend values for the following data using 5 yearly moving averages:

Following table shows the amount of sugar production (in lakh tonnes) for the years 1931 to 1941:

Complete the following activity to fit a trend line by method of least squares:

If x² + 6xy + y² = 10, then show that `("d"^2y)/("d"x^2) = 80/(3x + y)^3`

For 50 students of a class, the regression equation of marks in statistics (X) on the marks in accountancy (Y) is 3y − 5x + 180 = 0.  The variance of marks in statistics is `(9/16)^"th"` of the variance of marks in accountancy. Find the correlation coefficient between marks in two subjects.

Solve the following problem :

Consider the problem of assigning five operators to five machines. The assignment costs are given in following table.

Operator A cannot be assigned to machine 3 and operator C cannot be assigned to machine 4. Find the optimal assignment schedule.

Choose the correct alternative:

If for a bivariate data, b_YX = – 1.2 and b_XY = – 0.3, then r = ______

Choose the correct alternative:

If the regression equation X on Y is 3x + 2y = 26, then b_xy equal to 

Choose the correct alternative:

If b_yx < 0 and b_xy < 0, then r is ______

Choose the correct alternative:

|b_yx + b_xy| ≥ ______

Choose the correct alternative:

Find the value of the covariance between X and Y, if the regression coefficient of Y on X is 3.75 and σ_x = 2, σ_y = 8

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b_xy and b_yx are ______

Choose the correct alternative:

If r = 0.5, σ_x = 3, `σ_"y"^2` = 16, then b_yx = ______

Choose the correct alternative:

If r = 0.5, σ_x = 3, σ_y² = 16, then b_xy = ______

Choose the correct alternative:

Both the regression coefficients cannot exceed 1

State whether the following statement is True or False:

If b_yx = 1.5 and b_xy = `1/3` then r = `1/2`, the given data is consistent

State whether the following statement is True or False: 

If b_xy < 0 and b_yx < 0 then ‘r’ is > 0

State whether the following statement is True or False:

The following data is not consistent: b_yx + b_xy =1.3 and r = 0.75

State whether the following statement is True or False: 

If u = x – a and v = y – b then b_xy = b_uv 

State whether the following statement is True or False:

Corr(x, x) = 0

State whether the following statement is True or False:

Cov(x, x) = Variance of x