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

If f(x) = 3x² − 5x + 7 find f(x − 1).

The mean and S.D. of 200 items are found to be 60 and 20 respectively. At the time of calculation, two items were wrongly taken as 3 and 67 instead of 13 and 17. Find the correct mean and variance.

The mean and S.D. of a group of 48 observations are 40 and 8 respectively. If two more observations 60 and 65 are added to the set, find the mean and S.D. of 50 items.

The mean height of 200 students is 65 inches. The mean heights of boys and girls are 70 inches and 62 inches respectively and the standard deviations are 8 and 10 respectively. Find the number of boys and combined S.D.

From the following data available for 5 pairs of observations of two variables x and y, obtain the combined S.D. for all 10 observations. 
where, `sum_("i" = 1)^"n" "x"_"i"` = 30, `sum_("i" = 1)^"n" "y"_"i"` = 40, `sum_("i" = 1)^"n" "x"_"i"^2` = 225, `sum_("i" = 1)^"n" "y"_"i"^2` = 340

For a distribution, mean = 100, mode = 80 and S.D. = 20. Find Pearsonian coefficient of skewness Sk_p.

For a distribution, mean = 60, median = 75 and variance = 900. Find Pearsonian coefficient of skewness Sk_p.

For a frequency distribution, the mean is 200, the coefficient of variation is 8% and Karl Pearsonian’s coefficient of skewness is 0.3. Find the mode and median of the distribution.

Calculate Karl Pearsonian’s coefficient of skewness Sk_p from the following data:

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

A student passes an examination if he/she secures a minimum in each of the 7 subjects. Find the number of ways a student can fail.

Five balls are to be placed in three boxes, where each box can contain up to five balls. Find the number of ways if no box is to remain empty.

A hall has 12 lamps and every lamp can be switched on independently. Find the number of ways of illuminating the hall.

How many quadratic equations can be formed using numbers from 0, 2, 4, 5 as coefficient if a coefficient can be repeated in an equation.

A question paper has 6 questions. How many ways does a student have if he wants to solve at least one question?

Three groups of children contain respectively 3 girls and 1 boy, 2 girls and 2 boys and 1 girl and 3 boys. One child is selected at random from each group. What is the chance that three selected consists of 1 girl and 2 boys?

A, B, and C are mutually exclusive and exhaustive events associated with the random experiment. Find P(A), given that P(B) = `3/2` P(A) and P(C) = `1/2` P(B).

Two-third of the students in a class are boys and rest are girls. It is known that the probability of girl getting first class is 0.25 and that of boy getting is 0.28. Find the probability that a student chosen at random will get first class.

Show that 1 + i¹⁰ + i²⁰ + i³⁰ is a real number.

Find the value of i⁴⁹ + i⁶⁸ + i⁸⁹ + i¹¹⁰