HSC Commerce Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

The number of Hawkins-Simon conditions for the viability of an input-output analysis is ______.

The inventor of input-output analysis is ______.

The data are about an economy of two industries A and B. The values are in crores of rupees.

Find the output when the final demand changes to 300 for A and 600 for B.

If the equation ax² + 5xy – 6y² + 12x + 5y + c = 0 represents a pair of perpendicular straight lines, find a and c.

Show that the equation 12x² – 10xy + 2y² + 14x – 5y + 2 = 0 represents a pair of straight lines and also find the separate equations of the straight lines.

Show that the pair of straight lines 4x² + 12xy + 9y² – 6x – 9y + 2 = 0 represents two parallel straight lines and also find the separate equations of the straight lines.

Find the angle between the pair of straight lines 3x² – 5xy – 2y² + 17x + y + 10 = 0.

If m₁ and m₂ are the slopes of the pair of lines given by ax² + 2hxy + by² = 0, then the value of m₁ + m₂ is:

The angle between the pair of straight lines x² – 7xy + 4y² = 0 is:

If the lines 2x – 3y – 5 = 0 and 3x – 4y – 7 = 0 are the diameters of a circle, then its centre is:

Combined equation of co-ordinate axes is:

ax² + 4xy + 2y² = 0 represents a pair of parallel lines then ‘a’ is:

From the data given below:

Find

1. The two regression equations,
2. The coefficient of correlation between marks in Economics and Statistics,
3. The mostly likely marks in Statistics when the marks in Economics is 30.

The heights (in cm.) of a group of fathers and sons are given below:

Find the lines of regression and estimate the height of the son when the height of the father is 164 cm.

The following data give the height in inches (X) and the weight in lb. (Y) of a random sample of 10 students from a large group of students of age 17 years:

Estimate weight of the student of a height 69 inches.

Obtain the two regression lines from the following data N = 20, ∑X = 80, ∑Y = 40, ∑X² = 1680, ∑Y² = 320 and ∑XY = 480.

Given the following data, what will be the possible yield when the rainfall is 29.

Coefficient of correlation between rainfall and production is 0.8.

The following data relate to advertisement expenditure (in lakh of rupees) and their corresponding sales (in crores of rupees)

Estimate the sales corresponding to advertising expenditure of ₹ 30 lakh.

You are given the following data:

If the Correlation coefficient between X and Y is 0.66, then find

1. the two regression coefficients,
2. the most likely value of Y when X = 10.

Find the equation of the regression line of Y on X, if the observations (X_i, Y_i) are the following (1, 4) (2, 8) (3, 2) (4, 12) (5, 10) (6, 14) (7, 16) (8, 6) (9, 18).