HSC Commerce: Marketing and Salesmanship 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Draw a cumulative frequency curve more than type for the following data and hence locate Q₁ and Q₃. Also, find the number of workers with daily wages
(i) Between ₹ 170 and ₹ 260
(ii) less than ₹ 260

Draw ogive of both the types for the following frequency distribution and hence find median.

For a distribution, Q₁ = 25, Q₂ = 35 and Q₃ = 50. Find Bowley’s coefficient of skewness Sk_b.

For a distribution Q₃ – Q₂ = 40, Q₂ – Q₁ = 60. Find Bowley’s coefficient of skewness Sk_b.

For a distribution, Bowley’s coefficient of skewness is 0.6. The sum of upper and lower quartiles is 100 and median is 38. Find the upper and lower quartiles.

Calculate Bowley’s coefficient of skewness Sk_b from the following data:

Find Sk_b for the following set of observations:
18, 27, 10, 25, 31, 13, 28.

Following table shows how the samples of Mathematics and Economics scores of 25 students are distributed:

Find the value of χ² statistic.

Compute χ² statistic from the following data:

Attitude of 250 employees towards a proposed policy of the company is as observed in the following table. Calculate the χ² statistic.

In a certain sample of 1000 families, 450 families are consumers of tea. Out of 600 Hindu families, 286 families consume tea. Calculate the χ² statistic.

A sample of boys and girls were asked to choose their favourite sport, with the following results. Find the value of the χ² statistic.

A box contains 25 tickets numbered 1 to 25. Two tickets are drawn at random. What is the probability that the product on the numbers is even?

Two throws are made, the first with 3 dice and the second with 2 dice. The faces of each die are marked with the number 1 to 6. What is the probability that the total in first throw is not less than 15 and at the same time the total in the second throw is not less than 8?

A number of two digits is formed using the digits 1, 2, 3, ….., 9. What is the probability that the number so chosen is even and less than 60?

A bag contains 8 red balls and 5 white balls. Two successive draws of 3 balls are made without replacement. Find the probability that the first drawing will give 3 white balls and second drawing will give 3 red balls.

Find the values of x and y which satisfy the following equations (x, y ∈ R): (x + 2y) + (2x – 3y i + 4i = 5

Find the values of x and y which satisfy the following equations (x, y ∈ R):

`(x + 1)/(1 + "i") + (y - 1)/(1 - "i")` = i

Solve the following quadratic equation: 

8x² + 2x + 1 = 0

Solve the following quadratic equation:

`2x^2 - sqrt(3)  x + 1` = 0