HSC Commerce (English Medium) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Solve the following system of inequalities graphically.
2x – y ≥ 1, x – 2y ≤ – 1

If f(x) = 3x + 5, `"g"(x)` = 6x − 1, then find `("f" + "g") (x)`

If f(x) = 3x + 5, g(x) = 6x − 1, then find (f - g) (2).

If f(x) = 3x + 5, g(x) = 6x − 1, then find (fg) (3)

If f(x) = 3x + 5, g(x) = 6x – 1, then find `("f"/"g")`(x) and its domain.

If f(x) = 2x² + 3, g(x) = 5x − 2, then find fog.

If f(x) = 2x² + 3, g(x) = 5x − 2, then find gof.

If f(x) = 2x² + 3, g(x) = 5x – 2, then find fof.

Compute arithmetic mean and S.D. and C.V.
(Given `sqrt(296)` = 17.20)

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.