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

Use the method of least squares to fit a trend line to the data in Problem 1 above. Also, obtain the trend value for the year 1975.

The following table gives the production of steel (in millions of tonnes) for years 1976 to 1986.

Fit a trend line to the above data by the graphical method.

Choose the correct alternative :

Which of the following can’t be a component of a time series?

Moving averages are useful in identifying ______. 

An overall upward or downward pattern in an annual time series would be contained in which component of the times series?

Choose the correct alternative :

The following trend line equation was developed for annual sales from 1984 to 1990 with 1984 as base or zero year. Y = 500 + 60X (in 1000 Rs). The estimated sales for 1984 (in 1000 Rs) is:

Which component of time series refers to erratic time series movements that follow no recognizable or regular pattern?

Fill in the blank :

_______ component of time series is indicated by a smooth line.

_______ component of time series is indicated by periodic variation year after year.

_______ component of time series is indicated by a long wave spanning two or more years.

Fill in the blank :

_______ component of time series is indicated by up and down movements without any pattern.

State whether the following is True or False :

The secular trend component of time series represents irregular variations.

State whether the following is True or False :

Seasonal variation can be observed over several years.

Cyclical variation can occur several times in a year.

Irregular variation is not a random component of time series.

Solve the following LPP by graphical method:

Maximize z = 11x + 8y, subject to x ≤ 4, y ≤ 6, x + y ≤ 6, x ≥ 0, y ≥ 0

Solve the following L.P.P. by graphical method :

Maximize : Z = 7x + 11y subject to 3x + 5y ≤ 26, 5x + 3y ≤ 30, x ≥ 0, y ≥ 0.

Solve the following L.P.P. by graphical method:

Maximize: Z = 10x + 25y
subject to 0 ≤ x ≤ 3,
0 ≤ y ≤ 3,
x + y ≤ 5.
Also find the maximum value of z.

Solve the following L.P.P. by graphical method :

Maximize: Z = 3x + 5y subject to x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0 also find maximum value of Z.

Solve the following L.P.P. by graphical method :

Minimize : Z = 7x + y subject to 5x + y ≥ 5, x + y ≥ 3, x ≥ 0, y ≥ 0.