HSC Commerce: Marketing and Salesmanship १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Represent the following statement by the Venn diagram.

If n is a prime number and n ≠ 2, then it is odd.

Express the truth of the following statement by the Venn diagram.

All men are mortal.

Express the truth of the following statement by the Venn diagram.

Some persons are not politician.

Express the truth of the following statement by the Venn diagram.

No child is an adult.

Find `("d"^2"y")/"dx"^2`, if y = `sqrt"x"`

Find `("d"^2"y")/"dx"^2`, if y = `"x"^5`

Find `("d"^2"y")/"dx"^2`, if y = `"x"^-7`

Find `("d"^2"y")/"dx"^2`, if y = `"e"^"x"`

Find `("d"^2"y")/"dx"^2`, if y = `"e"^"log x"`

Find `("d"^2"y")/"dx"^2`, if y = `"e"^((2"x" + 1))`.

Find `("d"^2"y")/"dx"^2`, if y = log (x).

Find `("d"^2"y")/"dx"^2`, if y = 2at, x = at²

Find `("d"^2"y")/"dx"^2`, if y = `"x"^2 * "e"^"x"`

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

If ax² + 2hxy + by² = 0, then show that `("d"^2"y")/"dx"^2` = 0

For bivariate data. `bar x = 53`, `bar y = 28`, b_yx = −1.2, b_xy = −0.3. Find the correlation coefficient between x and y.

For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find estimate of Y for X = 50.

For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find estimate of X for Y = 25.

From the data of 7 pairs of observations on X and Y, following results are obtained.

∑(x_i - 70) = - 35,  ∑(y_i - 60) = - 7,

∑(x_i - 70)² = 2989,    ∑(y_i - 60)² = 476, 

∑(x_i - 70)(y_i - 60) = 1064

[Given: `sqrt0.7884` = 0.8879]

Obtain

1. The line of regression of Y on X.
2. The line regression of X on Y.
3. The correlation coefficient between X and Y.

You are given the following information about advertising expenditure and sales.

Correlation coefficient between X and Y is 0.8

1. Obtain the two regression equations.
2. What is the likely sales when the advertising budget is ₹ 15 lakh?
3. What should be the advertising budget if the company wants to attain sales target of ₹ 120 lakh?